Universit`a degli Studi di Modena e Reggio Emilia

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This chapter introduces the basic principles of laser operation and the properties of the laser beam ...... D. Schuocker Chapman and Hall, first edition, 1996. [7] R.N Hall, G.E. Fenner, and J.D. Kingsley et al. Coherent ...... 55 - 42000 - 350. 1.756.

Universit` a degli Studi di Modena e Reggio Emilia

DISMI Dipartimento di Scienze e Metodi dell’Ingegneria

Corso di Dottorato in Ingegneria dell’Innovazione Industriale (XXII ciclo)

Analysis and simulation of laser micromachining and laser surface hardening processes

Tesi di Dottorato di Ricerca in Tecnologie e sistemi di lavorazione

Candidato: Ing. Gabriele Cuccolini

Relatore: Dott. Leonardo Orazi

CONTENTS

Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

7 11 13

1. Fundamental of laser theory . . . . . . . . . . . . . . . . . . . . 1.1 The nature of light and the electromagnetic waves . . . . 1.1.1 Atoms, molecules and energy levels . . . . . . . . . 1.1.2 Population inversion . . . . . . . . . . . . . . . . . 1.2 Laser pumping . . . . . . . . . . . . . . . . . . . . . . . . 1.2.1 Optical resonance and laser resonator . . . . . . . 1.3 Laser beam properties . . . . . . . . . . . . . . . . . . . . 1.3.1 Monochromaticity, Directionality and Focusability 1.3.2 Spatial energy distribution and resonator modes . 1.3.3 Gaussian Beam propagation . . . . . . . . . . . . . 1.3.4 Beam quality . . . . . . . . . . . . . . . . . . . . . 1.3.5 Temporal energy distribution . . . . . . . . . . . . 1.4 The laser spot size . . . . . . . . . . . . . . . . . . . . . . 1.4.1 Diffraction . . . . . . . . . . . . . . . . . . . . . . 1.4.2 Aberration . . . . . . . . . . . . . . . . . . . . . . 1.5 Beam delivery systems . . . . . . . . . . . . . . . . . . . . 1.5.1 Thermal lensing effect . . . . . . . . . . . . . . . . 1.5.2 Mirrors . . . . . . . . . . . . . . . . . . . . . . . . 1.5.3 Beam expander . . . . . . . . . . . . . . . . . . . . 1.5.4 Focus with fiber . . . . . . . . . . . . . . . . . . .

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2. Types of industrial laser . . . . . . . 2.1 Types of Industrial Lasers . . . 2.2 CO2 Laser . . . . . . . . . . . . 2.2.1 Slow Flow Lasers . . . . 2.2.2 Fast Axial Flow Lasers . 2.2.3 Transverse Flow Laser . 2.3 Nd:YAG Laser . . . . . . . . . 2.4 Diode Laser . . . . . . . . . . . 2.5 Yb:glass fiber laser . . . . . . .

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3. Laser hardening . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Laser surface hardening . . . . . . . . . . . . . . . . . . 3.2 Laser sources for laser hardening . . . . . . . . . . . . . 3.3 Metallurgy of laser hardening of low alloy steels . . . . . 3.4 Literature review: Laser Hardening models for low Alloy

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3.4.1 3.4.2 3.4.3 3.4.4

The intra-granular carbon diffusion into the pearlitic structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Inter-granular carbon diffusion between pearlitic and ferritic grains . . . . . . . . . . . . . . . . . . . . . . . . . . The martensite formation . . . . . . . . . . . . . . . . . . The tempering effect . . . . . . . . . . . . . . . . . . . . .

61 64 66 69

4. A model for laser hardening of hypo-eutectoid steels . . . . . . . . . . 77 4.1 The thermal model . . . . . . . . . . . . . . . . . . . . . . . . . . 80 4.2 LS Laser Simulator . . . . . . . . . . . . . . . . . . . . . . . . . . 84 4.3 The micro-structural approach . . . . . . . . . . . . . . . . . . . 92 4.3.1 Laser hardening simulation of AISI 1043 roller torque limiter 95 4.4 The fast austenitization approach . . . . . . . . . . . . . . . . . . 101 4.4.1 Distributed grain austenization . . . . . . . . . . . . . . . 103 4.4.2 Experimental Results and Discussion . . . . . . . . . . . . 105 4.5 The tempering model . . . . . . . . . . . . . . . . . . . . . . . . 113 4.5.1 Model validation . . . . . . . . . . . . . . . . . . . . . . . 116 4.5.2 Model refinement . . . . . . . . . . . . . . . . . . . . . . . 119 4.5.3 The transformation time and the activation energy evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 4.5.4 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . 121 4.6 Industrial cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 4.6.1 Laser hardening of large cylindrical martensitic stainless steel surface . . . . . . . . . . . . . . . . . . . . . . . . . 129 5. Laser micro machining . . . . . . . . . . . . . . . . . . . . 5.1 Laser micro machining . . . . . . . . . . . . . . . . . 5.2 Literature review: physical models . . . . . . . . . . 5.2.1 Interaction between laser radiation and target 5.2.2 Laser-plasma interaction . . . . . . . . . . . .

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6. A model for laser ablation of metals . 6.1 Physical model . . . . . . . . . . 6.2 Simulation and results . . . . . . 6.2.1 The influence of ηp and ρp 6.2.2 Experimental comparison

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7. APS - Automated Parameter Setup . . . . . . . . . . . . . . . . . . . 7.1 Laser ablation in industry . . . . . . . . . . . . . . . . . . . . . . 7.2 The Empirical Approach . . . . . . . . . . . . . . . . . . . . . . . 7.2.1 Experimental System . . . . . . . . . . . . . . . . . . . . 7.2.2 Manual Setup . . . . . . . . . . . . . . . . . . . . . . . . . 7.2.3 Automated Parameters Setup (APS) . . . . . . . . . . . . 7.3 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.4 Experimental tests on TiAl6V4 titanium alloy and an Inconel 718 superalloy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.4.1 TiAl6V4 Titanium Alloy . . . . . . . . . . . . . . . . . . .

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Appendix A. Appendix . . . . . . . . . . . . A.1 The Analysis of Variance A.2 Example of project . . . . Conclusion . . . . . . . . . . . Acknowledgment . . . . . . . .

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Nomenclature A A0 A1 Ac3 Aρ B c C Ci Ciγ∗ Ciα∗ Cv Cp dx dy dz d0 dr dl ds ds,g D Dv D0 DOF Dα Dγ e0 e1 E Ez0 Ep En f fa f10 fm fi fǫ fα fc fiα Fin Fout Fst Fabs g h

absorptivity absorbtance of the metal at absolute zero rate of change of absorptance with temperature austenitization temperature [K] absorptance of the metal surface magnetic field [N/(Am)] speed of light [m/s] carbon content solute concentration at the interface solute concentrations at the interface in the γ phase solute concentrations at the interface in the α phase solute concentration specific heat [J/kgK] infinitesimal length in x direction [m] infinitesimal length in y direction [m] infinitesimal length in z direction [m] beam waist radius [m] laser beam diameter out from the resonator [m] laser beam diameter incident on the focal lens [m] laser beam spot diameter [m] diffraction limited spot size [m] thermal diffusivity [m2 /s] solute diffusivity [m2 /s] diffusion constant [m2 /s] depth of focus [m] diffusion coefficient of carbon in the ferrite [m2 /s] diffusion coefficient of carbon in the austenite [m2 /s] atom energy in the ground state [J] atom energy in the first excited state [J] electric field [V /m] maximum amplitude of the electric field [V /m] photon energy [J] ionization energy of the excited states [J] photon frequency [Hz] or focal length [m] austenite fraction photon frequency [Hz] martensite volume fraction pearlite volume fraction ǫ-Carbide phase fractions ferrite phase fractions cementite phase fractions volume fraction of phase α photon flux in [1/m2 ] photon flux out [1/m2 ] photons emitted by stimulated emission photons absorbed by the medium average grain size Planck constant [Js]

Ha H Hm Hf HVM H0 H∞ Hυ Hv k Hvjk I IH I0 IL IP IW b IP b Ij→i,th Ip→a Ip→a,th Ip→a,min Ip→a,max Im→a Im→a,th k kb ke kB lp l L m M M2 M RR ncr N Ni N0 N1 p0 pb Ppk PH q Qpulse Q Qp→a Qm→a

activation enthalpy of the microstructural transformation [J/kg] hardness martensite hardness ferrite hardness martensite Vickers hardness hardness after quenching hardness in the annealed state hardness of an intermediate state between the as-quenched state and the annealed state hardness variation in correspondence of the tk instant hardness of a generic phase j at the instant tk intensity [W/m2 ] ionization potential of hydrogen [J] intensity of the laser source at the waist position [W/m2 ] intensity of the incident laser radiation [W/m2 ] self-emission of the plasma [W/m2 ] intensity balance of the workpiece [W/m2 ] intensity balance of the plasma plume[W/m2 ] integral threshold transformation time from phase i to j [s] pearlite to austenite transformation time [s] pearlite to austenite threshold transformation time [s] pearlite to austenite minimum transformation time [s] pearlite to austenite maximum transformation time [s] integral activation energy for the martensite to austenite transformation [s] initial point of the re-austenitization [s] thermal conductivity [W/mK] thermal conductivity of the boundary element [W/mK] thermal conductivity of the external element [W/mK] Boltzmann constant [J/K] plume length [m] pearlite average plate spacing within a colony [m] radius of the pearlite colony [m] atomic mass [kg] Mach number of the plasma flow quality of the laser beam material removal rate [mm/layer] critical ion density [m−3 ] number of atoms ion density 1/m3 number of atoms in the ground state number of atoms in the excited state equilibrium (saturated) vapor pressure [P a] boiling pressure [P a] peak power of a single laser pulse [W ] average pulse power [W ] laser beam density power [W/m3 ] energy of a single laser pulse [J] activation energy [kJ/mol] pearlite to austenite activation energy [kJ/mol] activation energy for the martensite to austenite transformation [kJ/mol]

rb R RL RP R(x) R(z) R0 SP tAc1 tAr1 t t0 ts tf T Tb Tp TB TE TMs TMf Ts Tc T EM Jki x0 yi Yi (T ) v vz Z ∆Ci ∆t ∆H δt α αIB αP I αabs γ δ ηq ηp ǫ0 θ θ0 λ λP ν

beam radius [m] gas constant [J/molK] reflectivity of laser radiation reflectivity of self-emission plasma plume radiation beam radius at the x distance from the center [m] beam radius at the z distance from the center [m] beam waist radius [m] spatial distribution of the laser intensity time taken to reach the eutectoid temperature during heating [s] time taken to reach the eutectoid temperature during cooling [s] time [s] time for heat diffusion over a distance equal to the beam radius [s] time start of the phases decomposition [s] time finish of the phases decomposition [s] temperature [K] boiling temperature [K] plasma plume temperature [K] temperature of boundary element [K] temperature of external element [K] martensite start temperature [K] martensite end temperature [K] target surface temperature [K] critical temperature [K] transverse electromagnetic mode of the laser beam solute flux Rayleigh length [m] fraction of the ith decomposing phase at time t maximum transformed fraction at temperature T beam speed [m/s] ablation rate [m/layer] charge state of the ion variation of carbon concentration in the cell time step [s] heat of vaporization per atom, [J/kg] infinitesimal time [s] laser absorption coefficient [m−1 ] Bremsstrahlung coefficient [m−1 ] photoionization coefficient [m−1 ] laser absorption coefficient [m−1 ] ratio of the specific heats duty cycle efficiency fraction of the emitted intensity lost in the environment permittivity of free space [F/m] angle between the laser direction and the target surface normal [rad] divergence angle [rad] wavelength [m] decay factor of a radiation laser frequency [Hz]

ω ϕ σ φ10 φ01 ρ ρp τ τυ υ

angular frequency [Hz] phase Stefan’s constant [W m−2 K −4 ] proportionality coefficient proportionality coefficient distance from the laser axis [m] or density [kg/m3 ] radius of irradiation of the plume [µm] pulse duration [s] tempering ratio propagation speed [m/s]

Introduction Nowadays power laser is becoming widely used in industry in various application fields such as cutting, welding, micro-machining, rapid prototyping and surface treatments. Due to the introduction of more reliable laser sources at more competitive prices the laser is becoming more prominent in the industrial context. The advantages presented by this technology are high precision and quality of the products, possibilities to work very different materials, easy process automation, flexibility and high productivity. The laser systems are extremely competitive in the production of small lots of very complex shapes. Models for laser micro-machining and laser surface hardening are presented in this work. A numerical model able to predict the physical phenomena involved in laser ablation of metals was developed where the heat distribution in the work piece, the prediction of the velocity of the vapor/liquid front and the physical state of the plasma plume were taken into account. The model is fully 3D and the simulations make it possible to predict the ablated workpiece volume and the shape of the resulting craters for a single laser pulse or multiple pulses, or for any path of the laser spot. A numerical model able to predict the austenitization of hypoeutectoid steels during very fast thermal cycle such as in laser hardening was developed. The model takes into account the phase transformation and the resulting microstructures according to the laser parameters, the workpiece dimensions and the physical properties of the workpiece. The numerical models were implemented in C++ code and present a graphic output developed using Open GLT M libraries. The Finite Difference Method (FDM) was used to solve the heat transfer and the carbon diffusion equations for a defined workpiece geometry. Experiments were carried out by means of Nd:YAG and Yb:glass solid state lasers and CO2 laser. The code capacities and the good agreement between the theoretical and experimental results are presented in this thesis.

Summary Chapter 1 This chapter introduces the basic principles of laser operation and the properties of the laser beam radiation. The optical characteristics of the laser beam and the different beam delivery systems were analyzed. Chapter 2 Chapter 2 introduces the basic principles of the most common laser sources for industrial application. The characteristics of various existing architectures and the different sources used in industry for laser hardening and micro machining application were analyzed. CO2 , Nd:YAG, diode and fiber lasers were described in detail. Chapter 3 The third chapter describes the laser surface hardening process. The physic of this process and the numerical simulation models in literature were analyzed and discussed. Chapter 4 In Chapter 4 an original approach to the laser hardening simulation is developed. LS (Laser Simulator) and in particular the LHS (Laser Hardening Simulator) submodule is described in detail. LHS is able to predict the austenization of hypo-eutectoid steels during very fast heat cycles such as laser hardening. With the aim to develop a suitable tool for industrial environment by predicting the results for the most widely used classes of materials as hypo-eutectoid carbon steels with the carbon percentage comprises between 0.3 - 0.8%. All the models in literature usually generate a predicted hardness profile into the material depth with an on-off behavior or very complicated and time consuming software simulators. A new approach based on a new austenization model for fast heating processes based on the austenite transformation time parameter Ip→a is proposed. By means of the Ip→a parameter it is possible to predict the typical hardness transition from the treated surface to the base material. At the same time, this new austenization model reduces the calculation time. Taking into account re-austenitization of the martensite during multi tracks laser trajectories an integral energy force Im→a and a tempering factor Im→mt are proposed in the model. Im→a gives the overheating for the martensite transformation and it depends on the heat cycle while Im→mt gives the temperig time factor for the martensitic transformation. Ip→a , Im→a and Im→mt are determined by experimental tests and it is postulated to be constant for low-medium carbon steels. Several experimental examples are proposed to validate the assumptions and to show the accuracy of the model. Chapter 5 Chapter 5 describes the laser micro machining process. The physic of this process and the numerical simulation models in literature were analyzed.

Chapter 6 In this chapter the LAS (Laser Ablation Simualtor) submodule for the laser micromaching simulation is shown and discussed. The software system has been developed to simulate the micro-manufacturing process using solid state lasers with pulse width in the range of 10-100 ns. The system can simulate the effects of the laser beam on the workpiece, keeping into account the surface conditions, the evolution of the workpiece temperature field, the phase changes in the material and the plasma plume effects. Simplifications concerning fluid dynamic and energy dispersions of the plasma plume are proposed. In particular, two empirical tuning parameters are considered: the first one is a global dispersion factor that keeps in account the fraction of energy lost in the environment by the plume; the second one is a spreading factor that permits to model the irradiated energy of the laser beam hitting the workpiece. The direct and coupled effects of these two parameters are evaluated and discussed. The model is fully 3-D and the simulations allow to predict the ablated workpiece volume and the shape of the resulting craters for a single laser pulse or multiple pulses, or for any linear or circular paths. Chapter 7 Chapter 7 presents a laser surface micro-machining process planning system. In this system, based on a regression model approach, the empirical coefficients, that provide the material removal rate, are automatically generated by a specific software according to the different materials that have to be processed. This software is called AP S (Automated Parameter Setup). Numerical models generally presents some limits due to the elevated calculation time requested to simulate the laser Micro-machining of industrial features especially when transient solutions are considered and, for this reason, to carry out a useful industrial tool for the evaluation of the material removal rate, the regression model represents the best solution. The presented statistical method, avoiding physical considerations, correlates the material removal rate with the process parameters in a very short calculation time. The automatic procedure for the generation of the coefficients of the regression polynomial permits to easily extend the regression model to any working material and system configuration allowing to determine the best process parameters in a very short time.

1. FUNDAMENTAL OF LASER THEORY

Chapter one

Fundamental of laser theory

Fundamental of laser theory

Introduction This chapter introduces the basic principles of laser operation and the properties of the laser beam radiation. The optical characteristics of the laser beam and the different beam delivery systems were analyzed.

1.1 The nature of light and the electromagnetic waves The word laser is an acronym that stands for light amplification by stimulated emission of radiation. In order to understand how a laser works the concept of light is fundamental. Light is a transverse electromagnetic wave. The electromagnetic waves are energetic waves in which the energy delivered is equally distributed between an electric field E and a magnetic field B time and space varying. Light is a transverse wave because the electric and magnetic fields are waving in a direction transverse to the direction of propagation. Figure 1.1 shows an electromagnetic wave propagates in x direction, vectors E and B remains perpendicular during the wave propagation.

1.0 0.5 0.0

0

Ez

-0.5 2 -1.0 1.0

x

0.5

4

0.0 6

-0.5

By

-1.0

Fig. 1.1: A generic electromagnetic wave

The result is unpolarized light in which the electric field oscillates in all random directions. The polarization of light is the direction of oscillation of the electric field, the light is plane polarized when the electric field oscillates only in one plane. The light is a collection of many waves: some polarized vertically, some horizontally, and some in between. The time space dependence of E is analytically described by the Eqn. 1.1: 17

Chapter 1

E = Ez0 cos in which:



 2π (υt − x) + ϕ j λ

(1.1)

• Ez0 maximum amplitude of the electric field; • λ wavelength; • ϕ phase; • υ propagation speed; Mathematically, the expression in 1.2: υ = λf

(1.2)

relates the velocity of any wave to its frequency, f , and wavelength λ. The light can propagate through a vacuum because, unlike sound waves or water waves, it does not need a medium to sustain it. If the light wave is propagating in a vacuum, it moves at the speed of light c = 3.0 × 108m/s while it moves less rapidly in a transparent medium like glass or water. This reduction in velocity occurs because the electrons in the medium interact with the electric field in the light and slow it down. The amount of this reduction depends by the refractive index of the material. The index is defined as the ratio of light’s velocity in a vacuum to its velocity in the medium. The electromagnetic radiations are classified on the basis of their wavelength and the behavior of the waves in different portions of the electromagnetic spectrum varies radically. Visible light is only a small portion of the electromagnetic spectrum diagrammed in Fig. 1.2. Radio waves, light waves, and gamma rays are all transverse electromagnetic waves, differing only in their wavelength.

Fig. 1.2: The electromagnetic spectrum

The most common laser sources used in mechanical industry [1] emits a radiation in the infrared region, so the laser beam is not visible to the naked 18

Fundamental of laser theory eye. The electromagnetic wave has a duality nature, sometimes it behaves as if it was composed of waves, and other times it behaves as if it was composed of particles. In 1905, Albert Einstein proposed that light is composed of tiny particles called photons, each photon having energy as described by the Eqn. 1.3: Ep = hf

(1.3)

in which: • Ep photon energy; • h Planck constant ( 6.63 × 10−34 [Js] ); • f photon frequency; So the light behaves as a undulating electric and magnetic field with a wavelength and a undulating period and also as collection of photons moving at the speed of light, and each photon has energy Ep = hf = hc/λ. 1.1.1 Atoms, molecules and energy levels The quantum mechanic predicts that energy is stored in atoms and molecules and that energy can be added to or taken from an atom or molecule only in discrete quantity. That is, the energy stored in an atom or molecule is quantized [2]. The basic structure of an atom is composed of a positively charged nucleus surrounded by a cloud of negative electrons moving in its own orbit around the nucleus as shown in Fig. 1.3.

Fig. 1.3: The atom model

When the electrons absorb energy they move faster, or in different orbits. The fundamental point is that only certain orbits are possible for a given electron, so the atom can absorb or lose only certain amounts of energy. The energy levels for the atom are represented schematically in Fig. 1.4. An atom in the ground state has energy e0 , while an atom in the first excited state has energy e1 , and so on. When an atom moves from energy level 1 to level 0 loses energy Ep = e1 − e0 and it cannot lose any other quantity of energy. The same concept occurs when the atom in the ground state absorb energy to skip at level 1, it can absorb only the energy e1 − e0 and move to the first excited state. The atom can absorb energy by photon absorption but the energy of the 19

Chapter 1

Fig. 1.4: The allowed energy levels for an atom

photon must correspond exactly to the energy difference between two levels of the atom. If the atom has initial energy e0 it can absorb a photon of frequency f10 only if the excited state at energy level e1 is allowed as described by the Eqn. 1.4. e1 = e0 + ef10 = e0 + hf10

(1.4)

An atom in an excited state can lose its energy in several ways. The energy can be transferred to other atoms, or it can be emitted as light. If it is emitted as light, the wavelength of the emitted light will correspond to the energy lost by the atom. There are two mechanisms by which the light can be emitted: spontaneous emission and stimulated emission. The spontaneous emission is shown in Fig. 1.5, a photon with exactly the same energy needed by the atom to elevate from its ground state to its first excited state is absorbed.

Fig. 1.5: The spontaneous emission of a photon

The atom will stay in this excited state for a period know as spontaneous lifetime of the order of some nanoseconds or microseconds. Then the atom will spontaneously emits the photon in a random direction and return to its ground state The process of stimulated emission is shown in Fig. 1.6. A second photon with exactly the same energy as the absorbed photon interacts with the excited atom and stimulates it to emit a photon. The second photon is not absorbed by the atom, but its presence causes the atom to emit a photon. The light is emitted in the direction defined by the stimulating photon, so both photons have the same direction. The stimulating photon has the same energy as the emitted photon so the emitted light has the same wavelength, the same phase and polarization as the stimulating light. 20

Fundamental of laser theory

Fig. 1.6: The stimulated emission of two photons

1.1.2 Population inversion The behavior of a collection of atoms depends on the energy distribution among the individual atoms. For example when a light passes through the collection of atoms inside a gas it could be amplified or dampened. The light is amplified if the stimulated emission phenomena is predominant in the gas while it is dumped if the absorption prevail. The stimulated emission is predominant if the gas is in a particular energetic condition called population inversion. To understand the concept of population inversion it is useful to consider a very simple assembly of atoms forming a gas medium with infinitesimal length dx and undefined transversal section as shown in Fig. 1.7.

Fig. 1.7: Population inversion

Assume there are a group of N atoms, each of which is capable of being in one of two energy states, the ground state with energy e0 and the excited state with energy e1 . The number of these atoms which are in the ground state is given by N0 , and the number in the excited state N1 . If the gas is hit by a group of photons the flux balance in the medium is given by the Eqn. 1.5: Fout = Fin + 21

∂F dx ∂x

(1.5)

Chapter 1 in which: • Fin photon flux in; • Fout photon flux out; In order to determine if the medium is an amplifier or a damper is necessary to calculate the photon flux generated per unit length with the Eqn. 1.6. ∂F ∂Fst ∂Fabs = − ∂x ∂x ∂x

(1.6)

in which: • Fst photons emitted by stimulated emission; • Fabs photons absorbed by the medium; The number of photons per unit time emitted by stimulated emission is proportional to the number of photons at the energy level e1 as reported in the Eqn. 1.7. dN1 = −φ10 N1 dt

(1.7)

in which: • φ10 proportionality coefficient; The proportionality coefficient φ10 depends on the energy gap e1 − e0 and on the photon flux Fin so it is possible to obtain the Eqn. 1.8. ∂Fst dN1 =− ∂t dt

(1.8)

By analog consideration for the photon absorption is possible to obtain the flux balance with the Eqn. 1.9. ∂F ∂Fst ∂Fass = − = φ10 N1 − φ01 N0 ∂t ∂t ∂t

(1.9)

On the basis of thermodynamic consideration Einstein demonstrate that in thermal equilibrium φ10 = φ01 so if N1 < N0 the medium is a dumper while if N1 > N0 is a photon amplifier. If the group of atoms is in thermal equilibrium, it can be shown from thermodynamic that the ratio of the number of atoms in each state is given by a Boltzmann distribution described by the Eqn. 1.10:   N1 e1 − e0 = exp − (1.10) N0 kB · T in which: • T temperature of the medium [K]; • kB Boltzmann constant ( 1.381 × 10−23 [JK −1 ] ) ; 22

Fundamental of laser theory The energy distribution of atoms/molecules under thermodynamic equilibrium at normal temperatures implies that N1 is always less then N0 and the medium appears to be a damper. To realize a photons amplifier we must reject the thermodynamic equilibrium realizing the population inversion with N1 > N0 , a medium with these characteristics is called active medium. A medium becomes active only if a big quantity of atoms passes from the energy level e0 to e1 , so in order to obtain the population inversion is necessary to give energy to the medium. This operation is called energy pumping. The effectiveness of a medium as an amplifier of photons depends on the stability of the higher energy level. Only in the presence of a metastable excited levels the probability of the stimulated emission becomes high enough to achieve amplification. The amplification is the basis of the laser action.

1.2 Laser pumping The laser consists of a cavity containing a medium (solid, liquid or gaseous) in which the atoms and/or the molecules are particularly sensitive to the stimulated emission [3]. In the cavity is introduced energy in the form of light or electric current of varying frequency, this phase is called laser pumping. Laser pumping is the act of energy transfer from an external source into the medium of a laser. The energy is absorbed in the medium, producing excited states in its atoms. When the number of particles in one excited state exceeds the number of particles in the ground state or a less-excited state, population inversion is reached. In this condition, the mechanism of stimulated emission can take place and the medium can act as a laser or an optical amplifier. The energy pumping devices used to obtain the population inversion are of two types on the basis of the laser medium: electrical devices and optical devices. With the electrical pumping an electric discharge is generated in a tube containing the gaseous laser medium, similar to the discharge in a fluorescent lamp. A population inversion is created in the atoms when they absorb energy from the current. Several types of high-power gas lasers such as carbide dioxide laser (CO2 ) are pumped in this way. In other common lasers, such as neodymium doped YAG laser (Nd:YAG), the atoms are embedded in a solid material instead of being in gaseous form. These lasers cannot easily be pumped by an electrical current or an electron beam. Instead, they are optically pumped. The laser material is irradiated with photons whose energy corresponds to the energy difference between the ground level and the excited level. The atoms absorb energy from the pump photons and are excited. 1.2.1 Optical resonance and laser resonator The population inversion and the stimulated emission are the starting point to generate the laser light but the crucial device that permits to obtain a significant amount of laser light is the resonator [4]. The laser resonator consists of two mirrors which are placed parallel to each other to form an optical oscillator as shown in Fig. 1.8, that is, a chamber in which light oscillate between the mirrors forever. The photons are reflected back and forth for many passes through the cavity, stimulating more and more emission on each pass. When the pumping device is turn on in the medium begin the population inversion, in some points of the 23

Chapter 1

Fig. 1.8: Scheme of a laser resonator

cavity take place the spontaneous emission while in others start the stimulated emission of photons in a random direction inside the cavity. The amplification effect increases when the cavity length is a multiple of the semi-wavelength of the laser beam. The photons that lay in the normal direction to the mirrors are reflected back and forth through the cavity generating new amplifications while the others are dumped and deleted. In a very short time a stream of photons of high intensity traveling between the mirrors is generated. One of the two mirrors is partially transparent to allow some of the oscillating power to emerge as the operating laser beam. The shape of the resonator can vary within a multitude of configuration. Instead of flat mirrors can be also used concave or convex elements that are easier to adjust and align. Some curvature is also used to prevent the laser radiation is released prematurely in the resonator.

1.3 Laser beam properties Laser light has some unique characteristics that don’t appear in the light generated from other sources. 1.3.1 Monochromaticity, Directionality and Focusability Laser light has greater purity of color than the light from other sources. That is, all the light produced by a laser is monochromatic. Another unique characteristic of laser light is its high degree of directionality. All the light waves produced by a laser leave the laser traveling in very nearly the same direction, this property permits to focus the laser to a very small spot. The waves inside a laser beam have very nearly the same wavelength, the same direction and the same phase. Together, these three properties make the light coherent, and this coherence is the property of laser light that distinguishes it from all other types of light. 1.3.2 Spatial energy distribution and resonator modes The resonator modes describe the spatial distribution of stored light energy between the laser mirrors [5]. The energy is not stored uniformly in a resonator. There are two types of modes: transverse and longitudinal. The transverse 24

Fundamental of laser theory mode of a laser represents the energy distribution along a plane transverse to the laser axis while the longitudinal mode is the distribution of energy in a plane parallel to the resonator axis. In order to determine the resonator mode is necessary to analyze the shape of the output beam because the pattern inside the resonator moves out through the mirror and becomes the shape of the beam. The beam can have different number of profiles characterized by the identifier T EMmn (Transverse Electromagnetic Mode) in which m and n represents the minimum power density in the the two orthogonal direction x and y. Figure 1.9 shows some examples of T EM mode for a laser beam. The T EM00 mode has a spatial profile without minimum and with only a maximum in the axis center while the T EM10 has a minimum only in x direction . The T EM00 mode is smaller in diameter than any other transverse mode.

Fig. 1.9: The shapes of transverse laser modes and its energy distribution

1.3.3 Gaussian Beam propagation The T EM00 mode is so important that there are several names for it in laser technology: Gaussian mode, fundamental mode or the diffraction-limited mode. Figures 1.10 and 1.11 show the geometry of the Gaussian beam and the intensity profile on laser axis inside the resonator. The laser beam has a convergencedivergence geometry, it converges to the minimum radius R0 , the beam waist radius, and diverge with angle θ0 . The divergence angle is a constructor parameter of the laser source and its value is of the order of some milliradians. The intensity of a Gaussian beam on a plane orthogonal to the x axis at the distance ρ is given by the Eqn. 1.11: I(x, ρ) = I0 in which:



R0 R(x)

2

ρ

exp−2( R(x) )

2

(1.11)

• I0 intensity of the laser source at the waist position R(x) is the beam radius at the x distance from the center given by the Eqn. 1.12. s  2 λx R(x) = R0 1 + (1.12) πR02 25

Chapter 1 RHxL

2R0 R0 -2x0

-x0

Θ0

x0

-R0

2x0

x

-2R0

Fig. 1.10: The geometry of a Gaussian beam inside the laser cavity IH0, ΡLI0 1 0.75 0.5 0.25 -2x0

-x0

x0

2x0

x

Fig. 1.11: The intensity profile of a Gaussian beam

The Rayleigh length x0 of the laser beam is the distance from the beam waist (in the propagation direction) where the beam radius is increased by a factor of the square root of 2 and is given by the Eqn. 1.13. For a circular beam, this means that the mode area is doubled at this point so the intensity is half of I0 . πR02 (1.13) λ At a distance from the waist equal to the Rayleigh range x0 , the width R of the beam is given by the Eqn. 1.14 x0 =

√ R(x0 ) = R0 2

(1.14)

The distance between these two points is called the confocal parameter or depth of focus of the beam DOF and is given by the Eqn. 1.15: 2πR02 (1.15) λ Figure 1.12 shows the depth of focus of the Gaussian beam. So is possible to rewrite the Eqn. 1.12 as function of the Rayleigh distance: s  2 x R(x) = R0 1 + (1.16) x0 DOF = 2x0 =

The maximum intensity value is on the beam axis and decreases away from the focal position, while the width of the distribution R(x) increases with the 26

Fundamental of laser theory

R0

-2x0

2 R0

-x0

0

x0

2x0

x

2x0

Fig. 1.12: The depth of focus of the gaussian beam

same trend. The evolution of the intensity on the axis with the position is given by the Eqn. 1.17: I(x, 0) =

I0 1 + (x/x0 )2

(1.17)

The beam width varies along the axis according to Eqn.√ 1.12. At the Rayleigh distance the beam diameter is increased by a factor 2 so the beam section area is two time bigger and the intensity is an half smaller. At distance |x| >> x0 is possible to approximate the variation of beam radius as function of the distance x from the center with the Eqn. 1.18. R0 x = θ0 x (1.18) x0 The parameter R(x) approaches a straight line for x >> x0 . The angle between this straight line and the central axis of the beam is called the divergence of the beam and it is given by the Eqn. 1.19. R(x) ≈

λ (1.19) 4R0 In which the k parameter is a constant that depends on the spatial distribution of the beam, for the Gaussian beam is kg = 4/π so the minimum divergence for a laser beam is given by the Eqn. 1.20 θ0 = k

θ0 =

λ πR0

(1.20)

1.3.4 Beam quality In industrial practice the laser beam generated by a commercial laser source deviates from the Gaussian beam. In particular, the divergence will be bigger than the ideal values θ0 of the Gaussian beam. In order to define a quality factor for a laser beam is necessary to compare the actual beam divergence θact with the divergence from a Gaussian beam with the same initial waist, θ0 . In laser technology this quality factor is called M 2 and it is given by the Eqn. 1.21. M2 =

θact k π = =k θ0 kg 4

(1.21)

The best possible beam quality is achieved for a Gaussian beam, having M 2 = 1. This value is closely approached by some lasers, in particular by solid 27

Chapter 1 state laser and by fiber laser. On the other hand many high-power lasers can have a very large M 2 of more than 100. 1.3.5 Temporal energy distribution The output of a laser source may be a continuous constant amplitude output (known as CW or continuous wave); or pulsed P W ( pulsed wave), by using the techniques of Q-switching , flash lamp or mode locking . In the continuous mode of operation, the output of a laser is relatively constant with respect to time as shown in Fig. 1.13. The population inversion required for lasing is continually maintained by a steady pump source. In the pulsed mode of operation the energy from a pulsed laser is compressed into little concentrated packages and much higher peak powers can be generated.

Fig. 1.13: Modes of operation of the laser sources

The pulse repetition rate or the frequency f is a measurement of the number of pulses emitted per second by the laser. The period T of a pulsed laser is the amount of time from the beginning of one pulse to the beginning of the next. It is the reciprocal of the frequency. The duty cycle δ of a laser is the fractional amount of time that the laser is producing output, the pulse duration τ divided by the period as shown in the Eqn. 1.22, if the duty cycle is 1 the laser source emits in continuous wave CW . τ (1.22) T The peak power Ppk of a single laser pulse is the maximum power reached by the laser during the pulse duration τ while the average pulse power is given by the Eqn. 1.23. Z Qpulse 1 τ PH = P (t)dt = (1.23) τ 0 τ δ = fτ =

in which Qpulse is the energy of a single laser pulse. The average power Pav of a pulsed laser source is given by the Eqn. 1.24. 28

Fundamental of laser theory

τ (1.24) T There are a number of methods to achieve the pulsed wave mode of operation: flash lamp, Q-switching and mode locking. The first method of achieving pulsed laser operation is to pump the laser material with a source that is itself pulsed such as through electronic charging in a flash lamps, or another laser which is already pulsed. The pulse duration in these lasers is in the order of 10−4 seconds and it can never be operated in CW mode. With the Q-switch device the energy is stored in the population inversion until it reaches a certain level, and then it’s released very quickly in a giant pulse. In a Q-switched laser, the population inversion is allowed to build up by making the cavity conditions unfavorable for lasing. Then, when the pump energy stored in the laser medium is at the desired level, the Q (that stands for the quality of the resonator) is adjusted (electro- or acousto-optically) to favorable conditions, releasing the pulse. This results in high peak powers packed into a shorter time frame (nanoseconds). The extra energy in the population inversion is obtained by blocking or rotating one of the laser mirrors as shown schematically in Fig. 1.14. Pav = f Qpulse =

Fig. 1.14: A scheme of a Q-Switch device

A modelocked laser emits extremely short pulses on the order of tens of picoseconds down to less than 10 femtoseconds. With these lasers is possible to achieve extremely high powers. The modelocked laser is a most versatile tool for researching processes happening at extremely fast time scales also known as femtosecond physics, femtosecond chemistry and ultrafast science and in ablation applications.

1.4 The laser spot size In order to manipulate the beam, to guide it to the workplace and shape it there are many optical devices, the simple laws of geometric optics are sufficient to understand how they will work [6]. The laser becomes the ‘invisible tool’ for the industry only when it is focused onto the work plate with an optical device. There are two methods to focus the laser: with a transmissive optics such as a lens or with a reflective reflective optics such as a mirror. The choice between 29

Chapter 1 the two solutions depends on the laser power. In order to calculate the precise spot size of the laser beam focused with a single lens [7] is necessary to refer to the concepts of diffraction and aberration. 1.4.1 Diffraction As described in the previous paragraph the laser beam has a divergence convergence geometry, in case of a Gaussian beam it converges to the minimum diameter d0 (beam waist) and diverges with the angle θ0 . This geometry is approximately an hyperboloid of revolution. When the laser beam goes out from the resonator with dr diameter the divergence is low and is possible to approximate dr ∼ = dl , dl is the diameter of the beam incident on the lens. A second hyperboloid with a minimum diameter ds and divergence θ is generated when the laser passes through a lens. The minimum diameter is usually called the laser spot. A beam of finite diameter is focused by a lens onto a plate as shown on Fig. 1.15.

Fig. 1.15: The diffraction limited spot size

The singles parts of the beam striking the lens are point radiators of a new wavefront and these rays interfere each others on the focal plane. When two rays arrive at the screen half a wavelength out of phase they will destructively interfere and the light intensity will fall. The central maximum will contain approximately the 86 per cent of all the power in the beam. The diameter of this central maximum diameter is usually called the laser spot diameter ds . The first interference fringe is the negative when: dl sin(θ) 2 From the trigonometry is possible to obtain: OC − AC = λ/2 =

ds = f tan(θ) 2 30

(1.25)

(1.26)

Fundamental of laser theory When θ is small is possible to assume θ ≈ 0 and so sin(θ) ≈ tan(θ) and: ds = k

λf dl

(1.27)

k is a correction factor and for a Gaussian beam 4/π so the equation of the diffraction limited spot size ds,g becomes: ds,g =

4 λf 4λ = π dl πθ

(1.28)

in which: • f focal length; • dl diameter of the lens; • λ wavelength; • θ divergence; Combining the Eqn. 1.21 with 1.24 is possible to obtain this equation. ds = k

λf λf = kg M 2 = ds,g M 2 dl dl

(1.29)

Equation 1.30 gives another definition of the quality factor M 2 as the comparison between the spot diameter of the actual beam and a Gaussian beam. M2 =

ds ds,g

(1.30)

The size of the focal spot is proportional to the wavelength and inversely proportional to the divergence. In order to obtain small focal spot should be used short wavelength and a lens with small focal length while to generate a very directional beam is necessary a short wavelength with a large focus diameter. In practice a laser beam with T EMmn has the minimum spot diameter as given by the Eqn. 1.31. ds =

4 λf (2m + n + 1) π dl

(1.31)

The depth of focus DOF of the laser beam focused with a lens of focal length f is given by the Eqn. 1.32. dof = 0.08π

D02 M 2λ

(1.32)

1.4.2 Aberration The lenses used in laser technology are composed of elements with spherical surfaces. Such elements are made with a spherical shape since this can be accurately manufactured without too much cost and the alignment of the beam is not so critical. The geometry of the commercial lenses differs from the ideal spherical shape because many lenses are affected by the spherical aberration. Figure 1.16 shows a comparison between a perfect lens and a real lens affected 31

Chapter 1 by spherical aberration. A perfect lens focuses all incoming rays to a point on the optic axis, all light rays would be guided through one and only one focal point. A real lens with spherical aberration focuses rays more tightly if they enter it far from the optic axis than if they enter closer to the axis.

Fig. 1.16: Comparison between the perfect lens and the real lens with spherical aberration

The result is that the spot diameter of the beam focused with a spherical lens is bigger then the ideal spot from the perfect lens and is given by the Eqn. 1.33. d3r (1.33) f2 in which ksb is a correction factor related to the lens material. The most common lenses in laser technology are biconvex, meniscus or plane convex realized in Zinc Selenide (ZnSe), Gallium Arsenide (GaAS), Germanium (Ge) or Cadmium Telluride (CdT e), the ksb parameter for each material and type of lens is reported in table 1.1. dsb = ksb

Material ZnSe GaAs Ge CdTe

Plane convex lens 0.0187 0.0114 0.0087 0.0155

Meniscus lens 0.0286 0.0289 0.0295 0.0284

Tab. 1.1: ksb parameter for different type of lens

So the final equation for the spot diameter is the sum of two terms: diffraction and aberration as given by the Eqn. 1.34. ds = ddif f raction + daberration = 32

4 λf d3 + ksb r2 π dl f

(1.34)

Fundamental of laser theory

1.5 Beam delivery systems 1.5.1 Thermal lensing effect In low power lasers the beam is directly focused onto the workpiece by a transmissive optic such a lens but when the power is high there are many problems due to the high temperature. The heating of the medium traversed by the beam produces a lens effect that tends to increase the divergence of the beam and alter the refractive index and the shape of the lens. This effect is called the thermal lensing effect. It makes difficult to use transmissive optics to transport and focus the beam onto the workpiece whit high power laser sources. Transmissive optics can only be cooled from the edge or by blowing filtered, dry air onto the lens surface. As mentioned before in order to reduce the focal spot is necessary to decrease the focal length of the lens but this is in contrast with some problems of sputter that would ultimately make the laser virtually unusable for industrial uses. So it is necessary to deliver the laser onto the workplace by reflective optical devices such as mirrors. 1.5.2 Mirrors The high specific power of the laser beam makes it difficult to use transmissive glass optics to transport and focusing the beam. The losses through the optical glass increase the temperature to unacceptable values for the distortions that are introduced and for the integrity of those lenses. In order to prevent these effects is possible to use metal mirrors (plane or parabolic) as reported in Fig. 1.17 to deliver the beam onto the workpiece. The reflectivity of a mirror is a function of the material. Therefore, most mirrors are made of a good conductor coated with gold for infrared radiation. The cooling is usually achieved by water but maybe by air blast.

Fig. 1.17: Various ways of focusing using mirrors (plane or parabolic)

1.5.3 Beam expander The beam expander or collimator is a transmissive optical system designed to increase the diameter of a laser beam and decrease the divergence for long beam path. It is also used in laser devices where the laser produces such a small beam diameter that is difficult to focus without having the lens very close to the work piece and therefore subject to spatter. The beam expander is designed to take a small diameter beam as input and produce a larger diameter collimated output beam, thus reducing the divergence of the beam. There are two basic types of 33

Chapter 1 beam expander as reported in Fig. 1.18. The Keplerian beam expander consists of a positive input lens and a positive objective, the Galilean beam expander consists of a negative input lens and a positive objective. In both cases, the expansion factor is the ratio of the focal length of the two lenses. The general principle is that the new beam size will be D2 = D1 f2 /f1 .

Fig. 1.18: Beam expanders: Galilean and Keplerian

Figure 1.19 shows an example of the beam path inside a solid state laser source (Nd:YAG).

Fig. 1.19: The laser beam path inside a solid state laser

1.5.4 Focus with fiber As mentioned in the previous section the output of the laser must be focuses onto the material surface. The conventional beam delivery systems utilize lenses and mirrors to accomplish this purpose. The difficulties with this type of system 34

Fundamental of laser theory stay in part from a basic characteristic of the laser light: it expands or diverges through space. This expansion causes two difficulties: • For delivery over long distances, the beam can become very large, requiring commensurate increases in the diameters of the optical elements. In the case of the objective lens, increasing the diameter limits the minimum focal length, and may introduce aberrations in the optical performance. Both of these factors increase the minimum focused spot size. • As the distance between the laser and the objective lens changes, the focused spot size also changes. The only way to maintain a constant spot size is to keep the optics fixed, and move the material. • Inflexibility: changing the relative positions of any of the elements can cause misalignment problems Nowadays there is an increasing market for optical fiber delivery systems for solid state laser [8]. The use of fiber optics to transport the laser beam has the obvious advantage to eliminate problems of alignment and positioning between the laser source and the user. The characteristics of this system are: • Constant beam diameter over a range of distances • Flexibility (position and orientation) in positioning the focused spot • Complete enclosure of the beam, for safety reasons. The fibre is made from extremely pure silica and its structure consist of core, the sorrounding cladding of lower refractive index and an outer plastic protective coating. The light is confined to the core by total internal reflection at the core-cladding interface. There are two types of fibre: step index fibre and granded index fibre, Fig. 1.20 shows an example of a step index fibre.

Fig. 1.20: Step index fiber (top) and graded index fiber (down)

Step-index fibers have a uniform core with one index of refraction, and a uniform cladding with a smaller index of refraction. When plotted on a graph as a function of distance from the center of the fiber, the index of refraction 35

Chapter 1 resembles a step-function. The figure to the left illustrates how the index of refraction varies with location in a cross-section of a step-index fiber. An optical fiber with a core having a refractive index that decreases with increasing radial distance from the fiber axis is called graded-index fiber. The most common refractive index profile for a graded-index fiber is very nearly parabolic. The core diameter varies from 3 µm for the femtosecond pulsed laser to 400 - 1000 µm for the nanosecond pulsed and continuous wave lasers. The output laser beam delivered by an optical fiber diverges and to focus it on the workpiece are necessary two lens: the collimation lens and the focal lens as shown in Fig. 1.21.

Fig. 1.21: Focal system of the optical fiber

The spot diameter of the laser beam is given by the Eqn. 1.35. So the smaller fiber diameter leads to smaller spot size. The construction limit is given by the laser diameter out from the resonator, if it is bigger then the fiber the junction is not possible. In order to deliver a very high power laser, up to 5-10 kW is possible to fraction the laser in many fibres that are finally coupled with an unique focal lens onto the workpiece [9]. ds = df

ff fr

(1.35)

Nowadays many high powered solid state lasers are sold only with fiber optic. The most important advantage of the fiber is that the laser can be in its own room some distance away and be used to serve several workstation all in separate enclosures [10].

36

BIBLIOGRAPHY

[1] W. M. Steen. Laser Material Processing. Springer-Verlag London Limited, third edition, 2003. [2] A. Einstein. On the quantum theory of radiation. Journal of Applied Physics, 18(121):63–77, 1917. [3] J.J. Ewing B. Hitz and J. Hecht. Introduction to laser technology. IEEE press, New York, third edition, 2003. [4] H. Kogelnik and T. Li. Laser beams and resonators. Journal of Applied Physics, 5(10):1550–1567, 1966. [5] J. Fischer H.J. Eicher, B. Eppich. Laser Physics and Applications. Springer, first edition, 2005. [6] P. Drude. Theory of Optics. Longmans, Green and Co. Inc, first edition, 1922. [7] ISO Standard 11146-1. Lasers and laser-related equipment. Test methods for laser beam widths, divergence angles and beam propagation ratios. International Organization for Standardization, 2005. [8] E. Capello. Le lavorazioni industriali mediante laser di potenza. Libreria Clup scrl, first edition, 2003. [9] H.P. Weber and W. Hodel. Industrial Laser Annual Handbook. Laser Institute of America, first edition, 1987. [10] R. Walker. Fibreoptic beam delivery leads to versatile systems. Industrial Laser Review, first edition, 1990.

Chapter 1

38

2. TYPES OF INDUSTRIAL LASER

Chapter two

Types of industrial laser

Types of industrial laser

Introduction This chapter introduces the basic principles of the most common laser sources for industrial application. The characteristics of various existing architectures and the different sources used in industry for laser hardening and micro machining application were analyzed.

2.1 Types of Industrial Lasers 2.2 CO2 Laser The carbon dioxide CO2 laser [1] is composed of a bulb containing a mixture of He(78%), N2 (13%) and CO2 (10%) at low pressure (about 0.5 ≈ 0.7 atm). The standard technique for creating a population inversion in CO2 is to apply an electric discharge through the gas that brings the whole mixture to the plasma state. Inside this plasma the CO2 molecules have three different quantum states that correspond to three different vibration modes each with its own quantized energy as shown in Fig. 2.1: the symmetric stretching mode, e1 ; the bending mode, e2 ; and the asymmetric stretching mode, e3 .

Fig. 2.1: Major vibrational modes of carbon dioxide molecules

The spontaneous transition between the upper energy level e3 = 4.96×10−20 J and e2 = 3.08 × 10−20 J generates a photon of light in the infrared region of 10.6 µm in wavelength traveling in any direction dictated by chance. One of these photons, again by chance, will be moving along the optic axis of the cavity and will start oscillating between the mirrors. During this time it can be absorbed by a molecule in the bending mode state, it can be diffracted out of the resonator or it will hit a molecule which is already excited, in the e3 energy level. At this moment this photon stimulates that excited molecule to emit a photons traveling in the same direction and with the same phase. The process leads to the population inversion inside the resonator and the laser beam is generated from the CO2 molecule. The addition of other gases, N2 and He, aids in energy transfer to and from CO2 molecules. The nitrogen molecules have only one vibrational mode with the same energy as the upper laser level 41

Chapter 2 of CO2 , these transfer their energy to CO2 molecules, forcing the population to remain in the higher quantum state and increasing the probability of the stimulated emission. Helium is added to the gas mixture in a CO2 laser because its thermal conductivity is much higher than CO2 , so it can efficiently remove heat from the gas mixture. The quantum efficiency of the carbon dioxide laser is given by the Eqn. 2.1. ηq =

e3 − e2 ≈ 0.38 e3 − e0

(2.1)

The commercial CO2 lasers usually generate a continuous wave beam (CW ) between milliwatts (mW ) and hundreds of kilowatts (kW ), but they also can be pulsed by modulating the discharge voltage with the Q-Switch device with a rotating mirror or an electro-optic switch, giving peak powers up to gigawatts (GW ). The architecture of CO2 laser cavity is oriented to maintain the gas within the cavity cold to get a good coupling N2 − CO2 , so in order to achieve it there are three types of structure for the carbon dioxide laser: Slow Flow Lasers (SF), Fast Axial Flow Lasers (FAF) and Transverse Flow Laser (TF). 2.2.1 Slow Flow Lasers In this type of configuration the cooling of the medium is through the walls of the cavity. Figure 2.2 shows the construction scheme of this type of device. The direction of the cooling mixture coincides with that of the laser beam.

Fig. 2.2: Costruction of a slow flow laser

The mixture is cooled by heat exchange with a glycol solution that circulates through a pipe concentric with that of the mixture. The output power is not usually grater than 2 kW . This configuration has a very good focusability and stability of the beam. 2.2.2 Fast Axial Flow Lasers This is the most widely used type of CO2 laser, in which the gas flows along the axis of the optical cavity as shown in Fig. 2.3. Axial flow allows the depleted 42

Types of industrial laser gas to be replaced rapidly. Laser beam powers of up to 4 kW of continuous wave output can be achieved. Typically the gases flow at 300-500 ms−1 through the discharge zone.

Fig. 2.3: Costruction of a fast axial flow laser

The key variables in flowing-gas CO2 lasers are the speed and direction of flow. Typically flow is along the length of the laser cavity or longitudinal. Pumps or turbines provide fast axial flow, improving heat transport and allowing higher power levels. Pumping can be by DC, AC or RF discharge. 2.2.3 Transverse Flow Laser At the highest power levels used for industrial lasers, gas flow is transverse to the laser axis or across the laser tube. In these high-power systems the electrical excitation discharge is applied transverse to the length of the laser cavity as shown in Fig. 2.4. Because this gas flows through a wide aperture, it does not have to flow as fast as in a longitudinal-flow laser. Typically the gas is recycled, with some fresh gas added. Cooling is more effective than in FAF laser and very compact high power laser can be build.

2.3 Nd:YAG Laser The Nd:YAG laser is a solid-state laser [2] that consists of a passive host crystal of yttrium aluminium garnet (Y3 Al5 O12 ) and an active ion of neodymium (N d3+ ) added as impurity [3]. The population inversion is created in the N d ion, and this ion generates the photon of laser light of about 1.064 µm in wavelength. Figure 2.5 shows the energy levels of the N d ions. The ions absorbs on specified absorption bands which decay to a metastable state from which lasing action can occur and thus the atoms reach the final state. The final state requires cooling in order to reach the ground state. The quantum efficiency is high because the gap between the energy level e2 = 22.69 · 10−20 and e1 = 3.98 · 10−20 is high, and it is given by the Eqn. 2.2. 43

Chapter 2

Fig. 2.4: Costruction of a transverse flow laser

ηq =

e3 − e2 22.69 − 3.98 = ≈ 0.49 e3 − e0 36.0

(2.2)

The total efficiency is affected by the low gain of the pumping system. There are two different types of pumping devices for the solid state lasers: flash lamps and diodes. Figure 2.6 shows the general construction of a Nd:YAG laser optical chamber pumped with flash lamps. The resonator is an elliptical chamber coated with gold metal or ceramic, in one of the two foci is positioned a krypton flash lamp that leads to the activation of Nd ions and provides the pumping energy while in the other focus is positioned the YAG rod. There are different crystal geometries such as discs, slabs and tubes. In flash lamp pumped Nd:YAG lasers only a few per cent of the flash lamp power is absorbed by the N d ions. This means that considerable energy has to be pumped into the crystal rod to obtain the laser action and this leads to serious cooling problem and distortion of the rod. The operating efficiency of this pumping device is low approximately 2 % and their lifetime is very low. A more effective pumping system is obtained by using diodes of the appropriate frequency that pump the Nd with greater precision. The grater advantages of diode pumping are: the lifetime of the diodes, which is longer than that of lamps (1000 hours for lamps compared to 10000 hours for diode) and the lower cooling requirements [4]. Mounted inside the optical cavity is an aperture for mode control and a Q-switch for rapid shuttering (24-27 M Hz) of the cavity to generate fast pulses of high power. The modulation can achieve high power for short periods. For example, a Nd:YAG of 20 W can generated pulses of few nanoseconds with a power of 100 kW , a pulse repetition rate between 0-50 kHz [5]. Figure 2.7 shows the general construction of a Nd:YAG laser source. For many applications, the infrared light is frequency-doubled or tripled using nonlinear optical materials such as lithium triborate to obtain visible (532 nm, green) or ultraviolet light (265 nm). These devices, if swamped in photons, will absorb two or more photons to rise to higher energy states. This energy 44

Types of industrial laser

Fig. 2.5: Major vibrational modes of neodymium molecules

Fig. 2.6: Nd-YAG laser resonator

can be released in one step and it is twice the photon energy with half the wavelength. Other common host materials for neodymium are: Y LF (yttrium lithium fluoride, 1047 and 1053 nm ), Y V O4 (yttrium orthovanadate, 1064 nm), and glass. A particular host material is chosen in order to obtain a desired combination of optical, mechanical, and thermal properties.

2.4 Diode Laser Semiconductor lasers [6], or diode lasers as they are often called, are currently the most efficient devices for converting electrical into optical energy. A laser diode, like many other semiconductor devices, is formed by doping a very thin layer on the surface of a crystal wafer. The crystal is doped to produce an ntype region and a p-type region, one above the other, resulting in a p-n junction or diode. In a diode laser the excited state is that of the electrons in the conduction band compared to those in the valence band of a semiconductor material. The laser is formed by the junction (p-n) of two dissimilar types of semiconductor (GaAs, GaAlAs or InGaAs) [7] and the light emerges from the edge of the block, coming directly from the junction. A current flow induces 45

Chapter 2

Fig. 2.7: Nd:YAG laser source (Sintec Otronics Pte Ltd)

electrons to move from the conduction band to the valence band and give up the energy difference as a radiation. Just as in any semiconductor p-n junction diode, this forward electrical bias causes the two species of charge carrier - holes and electrons - to be injected from opposite sides of the p-n junction. Holes are injected from the p-doped and electrons from the n-doped. When an electron and a hole are present in the same region, they may recombine with the result being a spontaneous emission, the electron may re-occupy the energy state of the hole, emitting a photon with energy equal to the difference between states of the electron and hole involved. The radiation is amplified through multiple reflections from the polished ends of the semi-conducting medium making it strong enough for induced emission to occur in the p-n junction. Above a certain threshold current (determined by the particular semiconductor diode) the radiation field in the junction is great enough such that the induced emission rate exceeds the spontaneous recombination process. A single p-n junction is not sufficient to generate a laser beam suitable for industrial application; in order to increase the power more junctions are combined to form a stack of diodes that can emit a laser line at each junction. Stacking such arrays can give a few kilowatts of power from a very compact laser source. Figure 2.8 shows the general arrangement for a cavity diode laser. The optical junction of the stacks is obtained by means of particular mirrors, the laser beam generated has a rectangular section in the order of some millimeters with high divergence of about 30 - 40 degrees. The most common laser materials are the GaAs and GaAlAs with a band gap energy of about 1.35 eV which correspond to a wavelength between 750 and 900 nm. The wavelength of a GaAlAs laser can be changed by altering the relative amounts of gallium and aluminum and arsenic in the crystal. Pumping other solid state lasers, but also welding and heat treatment are main applications and uses of diode lasers. 46

Types of industrial laser

Fig. 2.8: General arrangement for a cavity diode laser

2.5 Yb:glass fiber laser Ytterbium (Y b) is a chemical element belonging to the group of rare earth metals. In laser technology, it has acquired a prominent role in the form of the trivalent ion Y b3+ , which is used as a laser-active dopant in a variety of host materials, including both crystals and glasses [8] [9]. The great advantage of the Y b is that it can be highly dopes the glass, so is possible to extract more power per volume unit if compared with the Nd:YAG lasers. High-power fiber lasers are built around dual-core fibers as shown in Fig. 2.9. The inner core, with the highest refractive index, is doped with light-emitting rare-earth elements such as ytterbium and erbium, which may be concentrated in the central part of the core. The outer core (sometimes called the inner cladding) has an index intermediate between the inner core and the outer cladding. External diode lasers pump the outer core, which confines the pump light and guides it so it passes through the inner core and excites the light-emitting atoms. The outer cladding has a lower refractive index, and passively confines pump light inside the outer core. A big advantage of fiber lasers is the relatively large surface area per unit volume, which aids dissipation of waste heat that could cause beam distortion. Fiber lasers also benefit from inherently high efficiency if the light emitters and pump lines are carefully matched. Thus, a 1 kW pump source can produce 800 W of output from an ytterbium-doped fiber, leaving only 200 W of heat to be dissipated. IPG Photonics (Oxford, MA) holds the record for raw power, produced by combining light from multiple ytterbium-doped fibers to produce a multimode beam. Figure 2.10 shows a 10 kW IPG laser.

47

Chapter 2

Fig. 2.9: General arrangement for a Yb fiber laser

Fig. 2.10: IPG 10 kW laser

48

BIBLIOGRAPHY

[1] C.K.N. Patel. Continuous-wave laser action on vibrational-rotational transition of co2. Physical Review, 136(5):1187–1193, 1964. [2] W. Koechner. Solid-state laser engineering. Springer-Verlag, second edition, 1988. [3] J.E. Geusic, H.M. Marcos, and L.G. Van Vitert. Laser oscillations in nddoped yttrium aluminum, yttrium gallium and gadolinium garnets. Applied Physic, 10(4):182–184, 1964. [4] P. Lacovare et al. Room-temperature diode-pumped yb:yag laser. Opt. Lett., 16(14):1089–1095, 1991. [5] W. M. Steen. Laser Material Processing. Springer-Verlag London Limited, third edition, 2003. [6] E. Wintner. Semiconductor lasers, handbook of the Eurolaser Academy vol. 1. D. Schuocker Chapman and Hall, first edition, 1996. [7] R.N Hall, G.E. Fenner, and J.D. Kingsley et al. Coherent light emission from ga-as junctions. Physical Review Letters, 9(9):366–369, 1962. [8] D.C. Hanna et al. Continuous-wave oscillation of a monomode ytterbiumdoped fiber laser. Electron. Lett., 16(24):1111–1118, 1988. [9] L.D. DeLoach et al. Evaluation of absorption and emission properties of yb3+ doped crystals for laser applications. J. Quantum Electron., 4(29):1179–1185, 1993.

Chapter 2

50

3. LASER HARDENING

Chapter three

Laser hardening

Laser hardening

Introduction This chapter introduces an important laser application: laser surface hardening. The physic of this process and the numerical simulation models in literature were analyzed.

3.1 Laser surface hardening Laser heat treatment is becoming a very widely used technology especially in surface hardening processes for wear reduction. The benefits attributed to the use of laser are that it provides localized heat input, negligible distortion, the ability to treat specific areas, access to confined areas and short cycle times. Laser hardening is used to increase the surface hardness of different kinds of mechanical components such as gears, pistons, cylinder liners, piston rings, spindles, bearing races and valve seats [1] [2] without affecting the softer, tough interior of the part. It is used exclusively on low alloy steels with a carbon content of more than 0.2 percent [3]. To harden the workpiece, the laser beam usually warms the outer layer of the component and the temperatures must rise to values above the critical transformation Ac1 but less than the melt temperature (about 1100 to 1600 K). The temperature gradient is of the order of 1000 K/s. Once the desired temperature is reached, the laser beam starts moving. As the laser beam moves, it continuously warms the surface in the processing direction. The high temperature causes the iron atoms to change their position within the metal lattice (austenitization). As soon as the laser beam moves away, the hot layer is cooled very rapidly by the surrounding material in a process known as self-quenching. Rapid cooling prevents the metal lattice from returning to its original structure, producing a very hard metal structure called martensite. The hardening depth of the outer layer is typically from 0.1 to 1.5 millimeters, on some materials it may be 2.5 millimeters or more. Relatively low power densities are needed for hardening, between 103 and 104 W/mm2 . The hardening process involves the eating of extensive areas of the workpiece surface. That is why the laser beam is shaped so that it irradiates an area that is as large as possible. The irradiated area is usually rectangular. Scanning optics are also used in hardening in order to move a laser beam with a round focus back and forth very rapidly ( 5 - 50 mms−1 ), creating a line on the workpiece, this technique leads to precise numerical control and automation in industrial application. The ideal power distribution is that gives a uniform temperature over the area to be treated. To obtain a uniform power distribution is necessary to spread the beam on the surface to treat with optical arrangements. There are many methods of beam spreading such as unfocused beam [4], beam integrator, kaleidoscope, toric mirror and others. Figure 3.1 shows a beam integrator, the system is composed of several mirrors that divide the beam and uniform its distribution on the workpiece.

3.2 Laser sources for laser hardening Theoretically all the laser sources are suitable for the hardening process but the most common sources used in industry are the solid state one such as Nd:YAG and fiber and also the CO2 gas lasers. There are many differences in the heat 53

Chapter 3

Fig. 3.1: Laser beam integrator

treatment process by using these type of sources. Carbon dioxide lasers are usually used as they can provide hundreds of kilowatts of power output which increases the rate of heat addition to the workpiece. However, their 10.6 micron wavelength often makes it difficult for absorption in metals. The metals absorptivity at the CO2 laser light is about 10 percent so this type of laser is not appropriate for this application. Considering also that the CO2 sources are inefficient (about 10 per cent) it follows that the hardening treatment with these sources is very inefficient (about 1 per cent). In order to improve the treatment efficiency with the CO2 laser source is necessary a surface pretreatment of the material to increase its absorptivity. Another problem is that in metals this absorptivity coefficient is not constant on the surface but varies with the roughness, the oxidation state and with the presence of dirt or oil on the surface as shown in Fig. 3.2.

Fig. 3.2: Variation of the laser hardened zone with the optical absorptivity (A)

So the thermal field and the resulting hardness profile are not uniform inside the material because an alternation of fused zones and not hardened zones can take place. The objective of the pretreatment is not only to increase the absorptivity but also to align the surface characteristics of the material. The most commonly used pretreatments for CO2 lasers are the phosphatation and graphitization. Until recently, most application of laser transformation hardening used a CO2 laser system but the solid state laser (Nd:YAG and fiber) has been significantly improved over the last few years. Compared with the CO2 laser hardening some advantages can be obtained by using a Nd:YAG laser system. It is easily automated, can be guided by optical fiber, costs less, is easily to maintain, and applies local heat treatment with only small distortion. The Nd:YAG sources 54

Laser hardening used for the laser hardening operate in continuous wave mode (CW ) up to 2 kW output power. The optical absorption of metals at the wavelength of 1.06 micron of the Nd:YAG lasers greatly increases and therefore the surface pretreatment is not required. The main advantage in the use of Nd:YAG source lays in the possibility to move the beam with high frequency scanning system in order to cover a great area. So it is possible to harden very complex geometry with an ”‘integral”’ spot. Because of its square beam, the high power diode laser is particularly wellsuited for large-surface applications in surface treatment [5] [6]. Compared to CO2 lasers, the diode laser benefits from its short wavelength (808 nm or/and 940 nm), which leads to increase absorption so that the usuals pretreatments are not required. And compared to the Nd:YAG laser, the advantages due to the high efficiency of the diode laser are its beam profile, clearly lower investment and running costs. Moreover the rectangular spot is very suitable to cover a large surface of the material and obtain a uniform hardness profile inside the material. Traditionally used hardening processes are induction hardening, arc hardening and electron beam hardening. When compared with these processes laser hardening presents great advantages, it causes little deformation of the part so that post machining is practically eliminated. The energy input is more efficient, because only the part undergoing treatment is heated. But the main advantage is that the process does not need a quenching media as water or oil. The resultant microstructure is often better than that produced by other methods.

3.3 Metallurgy of laser hardening of low alloy steels The most common materials for laser transformation hardening are low alloy steels, and are therefore Fe-based alloys. Their metallurgy follows the F eC phase diagram shown in Fig. 3.3. According to the eutectic pearlite phase at 0.8%, we can divide them into hypoeutectic and hypereutectic steels, below and above this Carbon concentration, respectively. The basic metallurgical structure of normalized steel consists of a non homogeneous distribution of carbon, pearlite and proeutectoid ferrite [7]. The pearlite is a mixture of alternate strips of eutectoid ferrite and cementite in a single grain. Cementite is a very hard intermetallic compound consisting of 6.7 % carbon and the remainder iron, its chemical symbol is F e3 C. Cementite is very hard, but when mixed with soft ferrite layers its average hardness is reduced considerably. The distance between the plates and their thickness is dependant on the cooling rate imposed to the material during its production. Fast cooling creates thin plates that are close together and slow cooling creates a much coarser structure possessing less toughness. A fully pearlitic structure occurs at 0.8 % in Carbon content. The fundamental metallurgical phases of steel are α ferrite and γ austenite. The ferritic phase has a Body Centre Cubic structure (BCC) which can hold very little carbon, typically 0.0001 % at room temperature. The austenitic phase is only possible at high temperature. It has a Face Centre Cubic (FCC) atomic structure which can contain up to 2 % carbon in solution. A low Carbon steel can be laser hardened by a thermal cycle during which it remains above the Ac3 temperature for sufficiently long. On rapid heating the pearlite colonies first transform to austenite [8] [9]. Then 55

Chapter 3

Fig. 3.3: Fe-C phase diagram

carbon diffuses outwards from these transformed zones into the surrounding ferrite increasing the volume of high carbon austenite. In order to complete the austenitic transformation, it is necessary to maintain the material above the Ac3 temperature for a time sufficient to allow the carbon diffusion and the formation of austenite grains. In all cases, the speed which austenite is formed is controlled by carbon diffusion, a process which can be accelerated a great deal by increasing temperature. For example, the time for complete austenitization in a plain carbon steel of eutectoid composition with an initial microstructure of perlite can be decreased from approximately 400 s ( at an austenitization temperature of 730 C ) to about 30 s ( at an austenitization temperature of 750 C), as shown in Fig. 3.4. So at high enough temperatures austenite forms in a fraction of second. If steel is cooled rapidly from austenite, the FCC structure rapidly changes to BCC leaving insufficient time for the carbon to form pearlite. This results in a distorted structure that has the appearance of fine needles, it is called martensite. On rapid cooling the austenite regions with a carbon content greater then 0.005 % will quench to martensite. There is no partial transformation associated with martensite, it either forms or it doesn’t. However, only the parts of a section that cool fast enough will form martensite; in a thick section it will only form to a certain depth, and if the shape is complex it may only form in small pockets. The hardness of martensite is solely dependant on carbon content, it is normally very high. Figures 3.5 show some micrographs of the basic microstructures of low alloy steels . The required cooling rate to obtain martensite is indicated by the constant cooling curves (CCC curves) [11]. Figure 3.6 shows the constant cooling transformation diagram for a low alloy steel. 56

Laser hardening

Fig. 3.4: Effects of austenitizing temperature on rate of austenite formation from pearlite in a eutectoid steel [10]

Fig. 3.5: Perlite - Austenite and Martensite micrograph for a low alloy steel C 0.4 % (courteously DolTPoMs Dept. University of Cambridge UK http://www.flickr.com/photos/core-materials )

If the cooling curve intercepts the lines Ms and Mf the austenite transforms totally into martensite while if the curve is above the martensitic transformation and below the pearlite reaction the austenite decomposes into another eutectoid microstructure of ferrite and cementite called bainite. It has a different grain morphology than pearlite. There is upper bainite and lower bainite that differs in the grain morphology as well. Figure 3.7 shows the micrography of a medium carbon low alloy steel consists of ferrite platelets in a pearlite/bainite matrix. In laser hardening the cooling rate is very high (about 800-1000 Ks−1 ) so the steel will self quench to martensite. The metallurgical transformation that takes place in steels during the laser hardening are similar to those for furnace or induction treated steels [12]. However, the greater temperature gradient imposed into the material by the laser process generates a more fine martensite and a more homogeneous treated zone. Moreover the hardness value may be slightly higher than that found for conventional treatment. Figure 3.8 shows a typical hardness profile for a AISI 1040 steel. When the areas to be treated are big compared to the laser spot, multiple laser paths are needed. Multiple passes limit the applicability of the laser hardening because the overlapping trajectories lead to a softening of the hardened 57

Chapter 3

Fig. 3.6: CCC curves for a low alloy steel

zone. To reduce this effect, extending the applicability of this process, the laser power is high so that, according to the laser speed, the spot diameter can be increased avoiding the surface melting and reducing the number of the laser paths. Anyway typical laser spot diameters, when circular spot are used are of the order of 10 mm so that multiple passes are usually required. So an optimal laser path strategy is necessary to define for containing the hardness reduction and increasing the overall process speed. The extent of the hardness variation for different overlap between successive passes is shown in Fig. 3.9.

58

Laser hardening

Fig. 3.7: Microstructure consists of ferrite platelets in a pearlite/bainite matrix (courteously DolTPoMs Dept. University of Cambridge UK http://www.flickr.com/photos/core-materials ) 800

Hardness HV1000

700 600 500 400 300 200 0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

Position @mmD

Fig. 3.8: Variation of micro-hardness with depth for a AISI1040 steel with a single laser pass

Fig. 3.9: Plot of surface hardness with variation in overlap between two consequent passes

59

Chapter 3

3.4 Literature review: Laser Hardening models for low Alloy Steels The simulation of conventional ( i.e. in owen) heat treatments is well assessed and many references can be found in literature, a synthetic but exhaustive review on this argument can be found in [13]. These models cannot be directly applied to the laser processing due to the high differences in heating rate and in the interaction time with respect to the conventional models. The metallurgy of a laser surface heat treatment is strongly governed by local diffusion processes that in turn are driven by thermal and chemical gradients. In literature there are many excellent numerical and analytical models for laser hardening transformation of low alloy steels. These models are able to predict the heat conduction and the metallurgical transformation that occur inside the material during the laser hardening process. Several researchers proposed theoretical models in an attempt to establish a relationship between laser processing parameters and temperature, which was then related to a corresponding hardness distribution. The first step in modelling the heat treatment of steel is to consider the phase transformation occurring upon heating, because the state of the microstructure after heating has a great influence upon the kinetics of the phase transformation during cooling and on the subsequent mechanical properties of the steel. In [14] and [15] the authors developed a one-dimensional transient model for predicting the temperature distribution in the proximity of a moving laser spot. In [16] and [17] a thermal model in 3-D form for a semi-infinite plate under a Gaussian laser beam is presented. A 2-D heat flow model with the temperature dependence of surface absorptivity and the thermal properties of the material were presented for cylindrical bodies [18] . A first microstructural approach to the laser hardening was developed by M.F. Ashby and K.E. Easterling in 1984 in [19] for hypo-eutectoid steels and in [20] for hyper-eutectoid ones. Ashby and Easterling used a two dimensional analytical solution for the heat flow. They consider a diffuse beam with a Gaussian energy distribution, tracking in the x direction with velocity v. If the velocity v of the beam is high, it can be treated as a line source, of finite width in the y direction but infinitesimally thin in the x direction. At a point below the center of the beam, the temperature field T (z, t) is given by the Eqn. 3.1. T (z, t) = T0 +

Aq/v 2πk [t(t + to )]

1/2

· exp −

(z + z0 )2 4Dt

(3.1)

where q is the laser beam power, k is the thermal conductivity, D the thermal diffusivity, A the absorptivity and t is time. The constant t0 measures the time for heat to diffuse over a distance equal to the beam radius rb and is given by the Eqn. 3.2 t0 =

rb2 4α

(3.2)

The length z0 measures the distance over which heat can diffuse during the beam interaction time. The heat cycle T (t) at the depth z causes structural changes. Some of the changes that take place during the heat cycle are diffusion controlled: the transformation of pearlite to austenite, the homogenisation of 60

Laser hardening carbon in austenite and the decomposition of austenite to ferrite and pearlite. In quasi static treatments of hypo-eutectoid steels the austenization process is conducted rising the temperature of the bulk material 50 − 90 above the Ac3 temperature. The material is held at this temperature for a time which depends on the thickness of the workpiece (about few minutes for each millimeters of thickness) in order to obtain the complete austenization of the material and a homogeneous carbon distribution inside the austenitic lattice avoiding grain growth. Rapid heating, as in laser hardening, raises the grain’s temperaturee from room temperature to over the Ac1 eutectoid temperature. At this point the pearlilte transforms to austenite and a microstructure of austenite and proeuctectoid ferrite. The austenitic transformation can be divided in two phases:

‰

1. Intra-granular carbon diffusion into the pearlitic structures. 2. Inter-granular carbon diffusion between pearlitic and ferritic grains. 3.4.1 The intra-granular carbon diffusion into the pearlitic structures Ashby stated that in fast heat cycles when the spacing l between the carbide lamellae inside a perlite grain is short the lateral diffusion of carbon would be sufficient to convert the colony to austenite; but after experimental comparisons between the predicted and the measured overheat temperatures the authors decided to assume that only the diffusion from the end of the lamellae is representative for fast heat treatments and, according to this hypothesis, the pearlite dissolution was calculated by solving Eqn. 3.3. More specific studies about the phenomenological model of carbon diffusion was conducted in [21] . Equation 3.3 represents the Arrhenius-like dependency of the carbon diffusion on the temperature, allows to determine the initial time of the pearlite transformation according to the heat cycle induced by the laser in the pearlitic structure.   Z tAr1 Q Ll = D0 exp − dt (3.3) RT (t) tAc1 where l is the pearlite average plate spacing within a colony, L is the radius of the pearlite colony and is given by the Eqn. 3.4 L=

g 1/3

2fi

(3.4)

where fi is the volume fraction occupied by the pearlite colonies and is approximately equal to C/0.8 (where C is the % carbon content), g is the average grain size, R ( = 8.314 J/mol K) is gas constant, t is time, T (t) is the heating cycle and tAc1 and tAr1 are the times taken to reach the critical temperature (eutectoid temperature Ac1 during heating and cooling, respectively, at a given depth below the surface as shown in Fig. 3.10.

61

Chapter 3 Microstructural properties Pearlite grain spacing Diameter of pearlite grain Austenite grain size Activation energy C-diffusion in austenite Activation energy C-diffusion in ferrite Pre-exponential C-diffusion in austenite Pre-exponential C-diffusion in ferrite

l L g Q Q D0 D0

µm µm µm kJ/mol kJ/mol m2 /s m2 /s

0.5 5 10 135 80 1 × 10−5 6 × 10−5

Tab. 3.1: Technical specification

Fig. 3.10: Temperature distribution inside the material under the laser beam

D0 is the diffusion constant, it is basically a measure for the mobility of a certain chemical element in some different atomic environment, e.g. in crystal lattice or in a liquid of different element. The diffusion constant D0 can depend strongly on the temperature. The main microstructural data for a normalized steel are listed in Table 3.1 [22]. The boundary for complete transformation of pearlite to austenite is the minimum depth (Zd ) at wich the Eqn. 3.3 is satisfied. In [23] a first two-dimensional model for carbon diffusion was proposed. The material micro-structure was divided by cells and the carbon diffusion between adjacent cells with different carbon concentration is evaluated. The temperature for pearlite colonies transformation and for the cementite dissolution is dependent on the heating rate. The micro-structure was characterized by the inter-lamellar spacing and by the size of the pearlite colony supposed to be constants for the whole workpiece material but no relationship between the pearlite dimension and the heat cycles were proposed for the pearlite transformation. In that work carbon diffusion, and, consequentially, the austenization were stopped when the temperature into the workpiece reaches the value of Ac3 at 0% of carbon for rapid heating conditions. Ac1 and Ac3 values for the different heating rate were only suggested and not calculated. The heating rates into the material were numerically estimated and of the order of 105 K/s which seem to be too high. As mentioned before a very accurate model for the description of the formation of austenite from lamellar pearlite during furnace heat treatment was pro62

Laser hardening posed in [21] and subsequently detailed in [24] and [25]. The phenomenological model for the pearlite dissolution into austenite, when the eutectoid temperature is reached, can be outlined as shown in Fig. 3.11. Figure 3.11 shows the intra-granular diffusion into a grain of pearlite, this transformation proceeds by diffusion from the cementite plates into the ferrite plates.

Fig. 3.11: The transformation of pearlite to austenite (near the equilibrium)

It was pointed out that only for heat cycles with low temperature gradient, typically carried out in furnace, the cementite dissolution happens from the end of the carbide lamella. In this case, the austenite (Feγ ) transforms from the ferrite (Feα ) and carbide (Fe3 C) as pictured in Fig. 3.11. Moreover, in [24], it is also postulated that a more appropriate model for fast heat cycle consists in the carbide diffusion into austenite from the lateral side of the lamellae as presented in Fig. 3.12.

Fig. 3.12: The transformation of pearlite to austenite (high overheating)

In [26] and [27] the authors used a three-dimensional model to predict 63

Chapter 3 the workpiece temperature distribution, this model is then coupled to a twodimensional kinetic model to predict the resultant hardness and phase distribution. Both lateral and end diffusion were considered and the evaluation of the pearlite transformation was obtained by solving Eqn. 3.3 which is representative just of the diffusion occurring from the bottom of the cementite lamellae [19]. 3.4.2 Inter-granular carbon diffusion between pearlitic and ferritic grains At the end of the first phase, which is triggered by the rising of the temperature over Ac1 , the material presents a mixture of austenitic grains with a pearlitic composition and carbon free ferritic grains. As the heat treatment carries on and the temperature continues to rise close and above the austenitization temperature Ac3 the austenite homogenization starts and the carbon diffuses outward from the transformed zones into the surrounding ferrite [28], increasing the volume fraction of high-carbon austenite as shown in Fig. 3.13.

Fig. 3.13: The homogenization of a hypoeutectoid steel:the diffusion distances scale as the austenite grain size and the transformation is slow

It is evident that the diffusion distances are grater in this step and so the time to diffuse is big. The pearlite becomes austenite containing ce = 0.8% in carbon content while the ferrite becomes austenite with negligible carbon content cf . The carbon diffusion from the higher to lower concentration region depends on temperature and time of the transformation. In [26] a complete model based on the works of Ashby and Easterling [19] and [21] is proposed, the authors consider in details the two phases of the austenitization process. The author implemented an explicit, finite volume program to solve the thermal and kinetic model simultaneously. In particular, in that work, a two-dimensional solution of the Fick’s equation was proposed and 64

Laser hardening applied on the real initial workpiece micro-structure stored by means of a digitized photomicrograph. Figure 3.14 shows an example of the microstructure discretization, each grid point could be either ferrite (α), pearlite (P ) or ferritepearlite boundary (α/P ). During heating austenite (γ) and austenite-ferrite boundary (α/γ) cells may be formed, the grid size is 5 µm. The phase ferrite (α) and pearlite (γ) are always separeted by an interface cell.

Fig. 3.14: Microstructure discretization during heating

When the eutectoid temperature is reached the transformation of the pearlite starts and the calculation is performed solely over the (P ) and (α/P ) cells. If Eqn. 3.5 is verified the (P ) and (α/P ) cells are transformed to austenite and ferrite-austente cells, indicated with γ and α/γ respectively.   Z t2 Q Ll ≤ 2 D0 exp − dt (3.5) RT (t) t1 Assuming the homogenization of austenite is governed by solute diffusion, Fick’s 2nd law of diffusion, shown in Eqn. 3.6, can be used to describe the kinetics. The homogenization step is performed solely over the (f ), γ and α/γ cells.     ∂Cv ∂ ∂Cv ∂ ∂Cv = Dv + Dv (3.6) ∂t ∂x ∂x ∂y ∂y Where Cv is the solute concentration in the υ phase and Dv the solute diffusivity in the υ phase. The interface cells have three additional variables: Ciγ∗ and Ciα∗ , the solute concentrations at the interface in the γ and the α phases, respectively, and fiα the volume fraction of phase α, see Eqn.4.16. A local equilibrium is assumed at the α/γ interface and Ciγ∗ and Ciα∗ are given by the phase diagram. fiα =

Ciγ∗ − Ci Ciγ∗ − Ciα∗

(3.7)

Ci is the solute concentration at the interface. When fiα is less than zero the interface cell is transformed in γ and the adjacent one is converted in an interface cell α/γ. The solute flux is modeled according to Eqn. 4.17: 65

Chapter 3

4

V

X ∆Ci = hJki ∆t

(3.8)

k=1

∆Ci is the variation of carbon concentration in the cell i, having an edge length h and a surface V , after a time step ∆t when a solute flux Jki is coming over the surrounding k cells. The solute flux Jki can be calculated with the following general Eqn. 4.18

Jki = fα∗ Dα



Ckα∗ + Ciα∗ ,T 2



Ckα∗ − Ciα∗ + (1 − fα∗ )Dγ h



Ckγ∗ + Ciγ∗ ,T 2



Ckγ∗ − Ciγ∗ (3.9) h

with fα∗ given from Eqn.4.19 fiα + fkα (3.10) 2 The diffusion coefficient of carbon in the austenite and ferrite, Dα and Dγ , are calculated by means of the Arrhenius law, see Eqn. 3.11 where T is the current temperature:   Q Dν (T ) = D0ν exp − (3.11) RT fα∗ =

3.4.3 The martensite formation After the homogenization step, according to Ashby all the austenite cells and any other interface cells with carbon content greater than 0.05%, are supposed to be transformed to martensite with their percentage of carbon. The hardness of the martensite/ferrite mixture is calculated by using a rule of mixtures knowing the volume of martensite, fm as shown in Eqn. 3.12 H = fm Hm + (1 − f )Hf

(3.12)

with Hm the hardness of martensite and Hf the hardness of the ferrite (150M P a) [29]. The hardness of treated volume con be predict by means of Eqn. 3.13 on the basis of the mean carbon content Ci : Hm = 1667C − 926

Ci2 + 150 fm

(3.13)

Figure 3.15 show an example of the measured hardness profile compared with those predicted by the thermal-kinetic models in literature. In [30] and in [31] a kinetic model for the description of diffusional transformation in low-alloy hypoeutectoid steels during cooling after austenitization is developed. A fundamental property of the model consisting of coupled differential equations is that by taking into account the rate of austenite grain growth, it permits the prediction of the progress of ferrite, pearlite, upper bainite and lower bainite transformations simultaneously. As proposed in [30, 31] the decomposition of the austenite can be modelled using the Avrami kinetic model of Eqn. 3.14 66

Laser hardening 900

Hardness HV1000

800 700 600 500 400 300 200 0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

Position @mmD

Fig. 3.15: Measured hardness profile compared with the predicted one

h i mi yi (t) = Yi (T ) 1 − e−bi t

(3.14)

where yi is the fraction of the ith decomposing phase at time t ( i=0 for ferrite, i=1 for perlite, i=2 for bainite, ecc... ), Yi (T ) is the maximum transformed fraction at temperature T as obtained experimentally from isothermal transformation. The parameters bi and mi are obtained from the C-curves given TT curves using Eqns. 3.15 and 3.16: ln

Yi i = b i tm s Yi − 0.01Yi

(3.15)

Yi i = b i tm (3.16) f Yi − 0.99Yi It can be outlined that the time start ts and the time finish tf of the phases decomposition occur conventionally when the fractions of the decomposing phase are respectively 0.01 and 0.99. The transformations that occur with a continuous transformation can be calculated by using Eqns. 3.17 and 3.18. ln

t∗k+1 =

 ln 1 −

yik Yi(k+1)

1/mi(k+1)

bi(k+1)

h i mk+1 ∗ yi(k+1) = Yi(k+1) 1 − e−bi(k+1) (tk+1 +∆tk+1 )

(3.17) (3.18)

where the variable at the previous integration time are indicated with k, the current time is indicated with k + 1 and the time step is ∆tk+1 . When the temperature is under TMs , the temperature at which the residual austenite starts to transform in martensite, the fractions of martensite and residual austenite indicated as ym and ya are obtained at each time step tk with Eqns. 3.19    Pn  ymk = (1 − i yik ) 1 − e−0.011(TM s −Tk ) (3.19) Pn  yak = 1 − i yik − ymk This multi-model can be applied to the prediction of isothermal and anisothermal transformation processes as well. The pseudo-autonomous differential equations can be solved only by numerical methods, provided that model 67

Chapter 3 parameters Yi , bi and mi are previously estimated, and given as a function of temperature. The simulation conducted by means of the decomposition model and by means of the microstructural models with carbon diffusion gives similar results under isothermal condition but in fast-austenitization process as in laser hardening the decomposition model is not appropriate because it is based on near equilibrium condition.

68

Laser hardening 3.4.4 The tempering effect When a laser is used in practical application to harden the surface of a mechanical component, it is usually necessary to scan the complete surface with multiple laser passes. The laser beam passes a previous track a small distance away. To extend the applicability of this process, the laser power is high so that, according to the laser speed, the spot diameter can be increased avoiding the surface melting and reducing the number of the laser paths. Anyway for typical laser spot diameters multiple passes are usually required to cover the entire area. This area is exposed to thermal cycle and is tempered during a short time. Multiple passes limit the applicability of the laser hardening because the overlapping trajectories lead to a softening effect of the hardened zone due to the tempering effects on the martensite structures leading to nonuniform hardness profiles and case depth [32]. Tempering is a diffusion type phase transformation from a quenched martensite to a tempered martensitic structure containing ferrite and iron carbides (cementite). In carbon steel, it either forms from austenite during cooling or from martensite during tempering. The precipitation and growth of the cementite is strongly related to tempering time and temperature. Figure 3.16 shows a cross section of a AISI 1040 after three laser passes and the correspondent hardness profile, the effect of tempering on the hardness is pronounced.

Fig. 3.16: Cross section of laser tracks on low-alloy steel and harness profile. (CO2 laser, power 1.2 kW, scan velocity 6 cm/s, spot 5 mm, 50 % overalpping) [33]

Structural softening was studied in literature by predicting the resulting structures due to the martensite transformation [34]. This approach implies the prediction of the metastable structures as a function of temperature and time during the post heating [35] up to the modelling of a re-austenization [24]. In this way the prediction of the hardness depends on the hardness of the resulting micro-structures; the accuracy of the prediction can be high but the required calculation time is very high. For tempering condition obtained in furnace, when the heating happens at constant temperature maintained for a long time, typically of the order of hours, there are many empirical formula which correlates the chemical composition of the alloy, the temperature-time cycle in the oven to the resulting hardness. Unfortunately these formula can not be applied when tempering happens with very high temperature gradients like in laser tempering. In recent years the efforts of the researches are focused on the numerical modeling for back tempering to predict final hardness profiles in multi-track 69

Chapter 3 laser hardening. In [36] the authors investigated on the microstructural evolution during tempering with scanning electron microscopy (SEM) and proposed a kinetic law that correlates the carbide growth and the associated hardness evolution. Figure 3.17 shows a SEM micrograph of a tempered microstructure showing secondary carbides.

Fig. 3.17: SEM micrograph of a tempered microstructure showing secondary carbides [36]

The authors found that only the average sizes of the carbides are influenced by tempering conditions and moreover they observed a strong correlation between the hardness measurement after tempering and the average size of the carbides. For a given tempering time the mean carbide size increases with tempering temperature significantly influencing the mechanical properties of the steel. Figure 3.18 shows the hardness evolutions with tempering time at different temperatures. A sharp decrease of hardness takes place during the initial stage of tempering at each temperature followed by a quasi-linear decrease of hardness. 900

Hardness HV 0.2

800 200 °C

700

300 °C 600 350 °C 500

460 °C

400

600 °C 650 °C

300

700 °C 200 0

1

2 Temepring time @hD

3

4

Fig. 3.18: Hardness evolutions during tempering for different temperatures [36]

As mentioned before tempering is a diffusion transformation from an unstable state (martensite) to a quasi equilibrium state ( ferrite + globular carbides). Therefore there are different tempering condition between these two states each one with its own hardness. So it is possible to define a tempering ratio τυ [36] as shown in Eqn. 3.20. τυ =

Hυ − H0 H∞ − H0 70

(3.20)

Laser hardening where H0 is the hardness after quenching, H∞ the hardness in the annealed state and Hυ the hardness of an intermediate state between the as-quenched state and the annealed state. The higher is the temperature, the grater is the tempering ratio for the same tempering time. The evolution of the tempering ratio with time and temperature is controlled by diffusion mechanism (carbides precipitation and growth) and it is governed by the Johnson-Mehl-Avrami [37] [38] [39] [40] equation. τυ = 1 − exp(1 − (Dt)m )

(3.21)

where t is the tempering time, m the ageing exponent depending on the material and D depends on the temepring temperature and follow the Arrhenius Eqn. 3.11. Introducing Eqn. 3.20 in Eqn. 3.21 it is possible to obtain the tempering hardness with the Eqn. 3.22. Hυ = H∞ + (H0 − H∞ ) exp(−(Dt)m )

(3.22)

But this equation is applicable only to isothermal condition, which is not the case in laser hardening so the authors in [41] adapted the model proposed in [36] in order to predict the hardness changes in fast tempering. The authors adapted the model with some key assumption: • The beam that overlaps the first laser passes tempers the material if the phase in the overlapped zone is martensite and the temperature point T verify this condition: 100

‰ < T < Ac

1

(3.23)

• Tempering may form two phases: - ǫ carbide is formed between 100 and 250 -Tempered martensite is formed between 250

‰

‰ ‰ and 727‰

• At the end of the second pass if the resultant phase fraction of martensite in the overlapped zone is more than the non-martensitic phase fraction the resultant hardness is given by the hardness calculated by the hardening model used for the single track (Eqn. 3.13) otherwise hardness is determined by considering martensite and tempered fractions ǫ-carbide is a transition iron carbide with a chemical formula between F e2 C and F e3 C. It has a hexagonal close-packed arrangement of iron atoms with carbon atoms located in the octahedral interstices. The resultant hardness is calculated from the weighted average of the various phase fractions presents in tempered material with the Eqn. 3.24 H = HMartensite fm + Hǫ−Carbide fǫ + HF errite fα + HCementite fc

(3.24)

Where fm , fǫ , fα and fc are respectively the martensite, the ǫ-Carbide, the ferrite and the cementite phase fractions.

71

Chapter 3

72

BIBLIOGRAPHY

[1] W. M. Steen. Laser Material Processing. Springer-Verlag London Limited, third edition, 2003. [2] V.G. Gregson. Laser Material Processing: Laser Heat Treatment. M. Bass North-Holland, first edition, 1984. [3] R.A. Ganeev. Low power laser hardening of steel. Journal of Materials Processing Technology, 2(121):414–419, 2002. [4] F.M. Dickey and S.C. Holswade. Laser Beam Shaping: Theory and Techniques. M. Dekker, first edition, 2000. [5] B.G. Bryden I.R. Pashby, S. Barnes. Surface hardening of steel using a high power diode laser. Journal of Materials Processing Technology, 1(139):585– 588, 2003. [6] E.Kennedy, G. Byrne, and D.N. Collins. Review of the use of high power diode laser in surface hardening. International J. of Material Processing, 156(10):1855–1860, 2004. [7] ASM Handbook Committe. Metallography and microstructures, Vol 9. ASM, fifth edition, 1992. [8] K. E. Easterling B. Bengtsson, W-B Li. Phase transformation in solids. Tsakalakos Th, New York, first edition, 1983. [9] P.G. Shewman. Diffusion in solids. Mc Graw-Hill, New York, first edition, 1963. [10] G.A. Roberts and R.F. Mehl. Effects of austenitizing temperature on rate of austenite formation from pearlite in a eutectoid steel. Trans. ASME, 31:613–623, 1943. [11] A.G. Gray H.E. Boyer. Atlas of Isothermal Transformation and Cooling Transformation Diagrams. ASM International. Metals Park, first edition, 1977. [12] S.L. Semiatin S. Zinn. Elements of induction heating. ASM International, sixth edition, 2002. [13] ASM Handbook Committe. Heat Treating, Vol 4. American Society of Metals, fourth edition, 1992. [14] O.A. Sandven. Report of avco everett metalworking lasers. In Proc. of SPIE 1979 International Conference, 1979.

Chapter 3 [15] V. Gregson. Laser Heat Treatment in Laser Materials Processing. NorthHolland, first edition, 1983. [16] H.E. Cline and T.R. Anthony. Heat treating and melting material with scanning laser or electron beam. J. Applied Physics, 48(9):3895–3900, 1977. [17] D.J. Sanders. Temperature distributions produced by scanninggaussian laser beams. Applied Optics, 23(1):3895–3900, 1977. [18] S. Kou and D.K. Sun. Heat flow during the laser transformation hardening of cylindrical bodies. Physical Metallurgy and Materials Science, 14(9):3895–3900, 1983. [19] M.F. Ashby and K.E. Easterling. The transformation hardening of steel surface by laser beam - i hypo-euctectoid steels. Acta metall., 32(11):1935– 1948, 1984. [20] W.B. Li, M.F. Ashby, and K.E. Easterling. The transformation hardening of steel surface by laser - ii hyper-euctectoid steels. Acta metall., 34(8):1533–1543, 1986. [21] A. Jacot and M. Rappaz. A two-dimensional diffusion model for the prediction of phase transformation: application to austenization and homogenization of hypoeutectoid fe-c steels. Acta materialia, 45(2):575–585, 1997. [22] C.J. Smithells. Metals reference book. Plenum Pr, fourth edition, 1967. [23] E. Ohmura and K. Inoue. Computer simulation on structural changes of hypoeutectoid steel in laser transformation hardening process. JSME International Journal, 32:45–53, 1989. [24] A. Jacot and M. Rappaz. Modeling of reaustenization from the perlite structure in steel. Acta materialia, 46(11):3949–3962, 1998. [25] A. Jacot and M. Rappaz. A combined model for the description of austenization, homogenization and grain growth in hypoeutectoid fe-c steel during heating. Acta materialia, 47(5):1645–1651, 1999. [26] S. Skvarenina and Y. C. Shin. Predictive modeling and experimental results for laser hardening of aisi1536 steel with complex geometric features by a high power diode laser. Surface & Coatings Technology, 46:3949–3962, 2006. [27] R. Patwa and Y. C. Shin. Predictive modeling of laser hardening of aisi5150h steels. International Journal of Machine Tools & Manufacture, 46:3949–3962, 2006. [28] H.K.D.H Bhadesia. Diffusion of carbon in austenite. Metal Science, 15:477– 479, 1981. [29] W.C. Leslie. The physical metallurgy of steels. McGraw-Hill, New York, first edition, 1982. [30] T Reti, Z Fried, and I. Felde. Computer simulation of steel quenching process using a multi-phase transformation model. Computational Materials Science, 22(18):261–278, 2001. 74

Laser hardening [31] S. Denis, D. Farias, and A. Simon. Mathematical model coupling phase transformations and temperature. ISIJ International, 32(3):316–325, 1992. [32] Y. Iino and K. Shimoda. Effect of overlap pass tempering on hardness and fatigue behaviour in laser heat treatment of carbon steel. Journal of Material Science, 6(10):1193–1194, 1987. [33] H.J.Hegge, H. De Beurs, J. Noordhuis, and J. Th.M. De Hosson. Tempering of steel during laser treatment. Metallurgical Transaction, 21A:987–995, 1990. [34] J.H. Hollomon and LD. Jaffe. Time-temperature relations in tempering steel. Trans. AIME, 162:223–249, 1945. [35] Y. Wang, S. Denis, B. Appolaire, and P. Archambault. Modelling of precipitation of carbides during tempering of martensite. J. of Physics IV France, 120:103–110, 2004. [36] Z. Zhang, D. Delagnes, and G. Bernhart. Microstructure evolution of hotwork tool steels during tempering and definition of a kinetic law based on hardness measurements. Material Science and Enginering A, 380(1-2):222– 230, 2004. [37] W.A. Johnson and R.F. Mehl. Reaction kinetics in processes of nucleation and growth. Trans. Am. Inst. Metall. Pet. Eng., 135:416–458, 1939. [38] M. Avrami. Kinetics of phase change i-iii. J. Chem. Phys., 7:1103–1112, 1939. [39] M. Avrami. Kinetics of phase change i-iii. J. Chem. Phys., 8:212–224, 1949. [40] M. Avrami. Kinetics of phase change i-iii. J. Chem. Phys., 9:177–184, 1941. [41] R. S. Lakhkar, Y.C, Shin, and M.J.M. Krane. Predictive modelling of multitrack laser hardening of aisi 4140 steel. Material Science and Enginering A, 480(1-2):209–217, 2008.

75

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76

4. A MODEL FOR LASER HARDENING OF HYPO-EUTECTOID STEELS

Chapter four

A model for laser hardening of hypo-eutectoid steels

A model for laser hardening of hypo-eutectoid steels

Introduction This section presents a model able to predict the austenization of hypo-eutectoid steels during very fast heat cycles such as laser hardening. Laser surface hardening is a process highly suitable for hypo-eutectoid carbon steels with carbon content below 0.6% or for low alloy steels where the critical cooling rate is reached by means of the thermal inertia of the bulk. As proposed by many authors, the severe heat cycle occurring in laser hardening leads to the pearlite to austenite microstructures transformation happening to a temperature much higher than the eutectoid temperature Ac1 and, afterwards, all the austenite predicted during the heating phase become martensite during quenching. Anyway, all these models usually generate a predicted hardness profile into the material depth with an on-off behavior or very complicated and time consuming software simulators. A new approach based on a new austenization model for fast heating processes based on the austenite transformation time parameter Ip→a is proposed. By means of the Ip→a parameter it is possible to predict the typical hardness transition from the treated surface to the base material. At the same time, this new austenization model reduces the calculation time. Ip→a is determined by experimental tests and it is postulated to be constant for low-medium carbon steels. Several experimental examples are proposed to validate the assumptions and to show the accuracy of the model. Two different approaches were analyzed: the microstructural and the fast-austenitization. The model takes into account the phase transformation and the resulting micro-structures according to the laser parameters, the workpiece dimensions and the physical properties of the workpiece. The numerical model was implemented in C++ code and present a graphic output developed using Open GLT M libraries. The Finite Difference Method (FDM) was used to solve the heat transfer and the carbon diffusion equations for a defined workpiece geometry. With the aim to develop a suitable tool for industrial environment by predicting the results for the most widely used classes of materials as hypo-eutectoid carbon steels with the carbon percentage comprises between 0.3 - 0.8%.

79

Chapter 4

4.1 The thermal model Laser surface hardening is based on the target surface heating by means of a low power density laser beam. Low power density beams allow to use wider spots reducing the numbers of scanning tracks and, as a consequence, the tempering phenomena of martensite. Anyway, both situations such as single laser track or multiple passes require an accurate temperature/time prediction into workpiece during the process. The time-dependent temperature distribution through the target material is governed by the heat-flow Fourier equation shown in Eqn. 4.1: Cp ρ in which:

 ∂T ¯ k ∇T ¯ −∇ = q¯ ∂t

(4.1)

• ρ is the density of the material of the workpiece [kg/m3 ] • Cp is the temperature dependent specific heat of the material [J/kgK] • k is the temperature dependent thermal conductivity [W/mK] • T = T (x, y, z) is the resulting three-dimensional time dependent temperature distribution in the material [K] • t is time [s] • q(x, y, z, t) = I(x, y, z, t) is the rate at which heat is supplied to the solid per unit time per unit volume [W/m3 ], it depends on laser parameters and physical and optical properties of material irradiated. Laser energy transmission in the target material is governed by the Beer Lambert law: I(z) = I0 exp−αz

(4.2)

Where z is the distance from the surface, I0 (x, y, t) is the laser radiation intensity at the material surface (z = 0) and α is a coefficient which takes into account the amount of laser beam absorbed into the material in a distance z from the surface. In metals it is about 10 nm. If RL is the reflectivity of the work piece surface depending on the type of material, surface temperature and type of laser beam the Eqn. 4.3 gives the laser energy transmitted to the material at depth z: I(x, y, z, t) = I0 (x, y, t) cos θ(1 − RL )(1 − exp(−αz))SP (x, y)

(4.3)

θ is the angle between the laser direction and the target surface normal as show in Fig. 4.1. SP (x, y) is the spatial distribution of the laser intensity (see Chapter 1), so the Eqn. 4.3 becomes Eqn. 4.4 for a Gaussian power distribution and Eqn. 4.5 for a Uniform distribution. 

R0 I = I0 (x, y, t) cos θ(1 − RL )(1 − exp(−αz)) R(z) 80

2

ρ

2

exp−2( R(Z) )

(4.4)

A model for laser hardening of hypo-eutectoid steels

Fig. 4.1: Laser beam spreading inside the target material

I = I0 (x, y, t) cos θ(1 − RL )(1 − exp(−αz))



R0 R(z)

2

(4.5)

The physical parameters of the workpiece material such as Cp , ρ and k are function of the temperature while, in each point of the domain, the laser intensity q is a time depending function according to the beam shape and the target surface scanning strategy. Because of the importance of the diffusion/heat equation to a wide variety of fields, there are many analytical solutions of that equation for a wide variety of initial and boundary conditions. However, one very often runs into a problem whose particular conditions have no analytical solution, or where the analytical solution is even more difficult to implement than a suitably accurate numerical solution. The selected solution technique was the finite difference method (FDM) where the integration time is dynamically chosen in order to guarantee the stability criterion. FDM method is known as the best solution for the study of no stationary phenomena with variable boundary condition like in laser applications with moving spot. Examples can be found in [1–3]. The time-dependent temperature distribution through the target material T (t, x, y, z) in the three-dimensional form for a generic grid is obtained from Eqn. 4.6 [4] [5] (See appendix for more details).

∂T ∂ Cp ρ = ∂t ∂x

      ∂T ∂ ∂T ∂ ∂T k + k + k +q ∂x ∂y ∂y ∂z ∂z

In which: 81

(4.6)

Chapter 4

  ∂ ∂T ∂k ∂T ∂2T k = +k 2 = ∂x ∂x ∂x ∂x ∂x  2 (x − xi−1 ) (ki+1 − k) + (xi+1 − x)2 (k − ki−1 ) · (x − xi−1 )(xi+1 − x)(xi+1 − xi−1 )  (x − xi−1 )2 (Ti+1 − T ) + (xi+1 − x)2 (T − Ti−1 ) · + (x − xi−1 )(xi+1 − x)(xi+1 − xi−1 )   Ti−1 Ti Ti+1 + 2k − + (xi+1 − xi−1 )(xi − xi−1 ) (xi+1 − xi )(xi − xi−1 ) (xi+1 − xi−1 )(xi+1 − xi ) (4.7)   ∂ ∂T ∂k ∂T ∂2T k = +k 2 = ∂x ∂y ∂y ∂y ∂y  (y − yi−1 )2 (ki+1 − k) + (yi+1 − y)2 (k − ki−1 ) · (y − yi−1 )(yi+1 − y)(yi+1 − yi−1 )  (y − yi−1 )2 (Ti+1 − T ) + (yi+1 − y)2 (T − Ti−1 ) · + (y − yi−1 )(yi+1 − y)(yi+1 − yi−1 )   Ti−1 Ti Ti+1 + 2k − + (yi+1 − yi−1 )(yi − yi−1 ) (yi+1 − yi )(yi − yi−1 ) (yi+1 − yi−1 )(yi+1 − yi ) (4.8)   ∂T ∂k ∂T ∂ 2T ∂ k = +k 2 = ∂z ∂z ∂z ∂z ∂z  2 (z − zi−1 ) (ki+1 − k) + (zi+1 − z)2 (k − ki−1 ) · (z − zi−1 )(zi+1 − z)(zi+1 − zi−1 )  (z − zi−1 )2 (Ti+1 − T ) + (zi+1 − z)2 (T − Ti−1 ) · + (z − zi−1 )(zi+1 − z)(zi+1 − zi−1 )   Ti−1 Ti Ti+1 + 2k − + (zi+1 − zi−1 )(zi − zi−1 ) (zi+1 − zi )(zi − zi−1 ) (zi+1 − zi−1 )(zi+1 − zi ) (4.9) These three terms are the volumetric accumulation rates of energy due to the variation of the three-dimensional temperature field. Those terms depend on both the magnitude of the thermal gradient and the temperature dependence of the thermal conductivity. The model necessities the discretization of space and time such that there is an integer number of points in space and in time at which the field variable(s), in this case just the temperature, is calculated. Figure 4.2 shows a part of a discretization of a generic target domain with hexahedron mesh elements and the relative standard nomenclature. In order to calculate the temperature from the governing equation using the FDM scheme the temperature at node (i, j, k) at time t + dt is expressed in terms of the temperatures of the surrounding nodes at time t (explicit formulation). The convergence of the algorithm is assured by the stability criterion [5] shown in Eqn. 4.10: 82

A model for laser hardening of hypo-eutectoid steels

Fig. 4.2: Three-dimensional finite difference grid

0≤

∆t · φi,j,k ≤1 ρCp

(4.10)

in which:

φi,j,k = 2k



1 1 1 + + 2 2 ∆x ∆y ∆z 2



(4.11)

Equation 4.10 is calculated for each element and the lowest value of the ratio (∆t φi,j,k )/ρCp is considered for the stability criterion. The values ∆x2 , ∆y 2 and ∆z 2 are the minimum distances between the central element of the mesh i, j, k and the surrounding elements in each direction i, j and k respectively. Clearly, for a given ∆x, ∆y and ∆z the allowed value of ∆t must be small enough to satisfy Eqn. 4.10. This stability criterion is applied only to specific difference equations, and hence the result pertains directly to this specific equation. As long as ∆t · φi,j,k ρCp ≤ 1 the error will not grow for subsequent marching steps in t, and the numerical solution will proceed in a stable manner. While if the stability equation is not satisfied the error will progressively become larger and will eventually cause the numerical marching solution to blow up on the computer.

83

Chapter 4

4.2 LS Laser Simulator The thermal model described in the previous section was implemented in a software package called Laser Simulator (LS). LS is divided in two submodules: LHS (Laser Hardening Simulator) and LAS (Laser Ablation Simulator). LAS will be described in details in chapter six. The two modules have in common the thermal model able to predict the temperature history inside the material. The main features of LS are: • To simulate laser spots with general spatial distribution in order to be applied to every laser source • To simulate every temporal distribution and different pulse conditions • To simulate every kinematic condition of the laser spot • To evaluate the temperature behavior of every point of interests • To deal with multiple overlapping passes taking into account the already treated material The LS System simulates the laser material interaction and physical parameters like conduction, reflectivity and others which should vary following the temperature and the changes of phase. The model was implemented in C++ using the Object Oriented paradigm. When the geometry is simple the discretization of the domain is directly chosen by the user by selecting the number of rows, columns and planes according to the stability criterion and the laser spot dimension. The brick element can have different side lengths in the x,y and z directions. Figure 4.3 shows the implementation of the target discretization in the code and shows an example of the laser-material interaction on a plane surface and the correlated austenite generation.

Fig. 4.3: Austenite generation during a laser linear path ( yellow color → complete austenization) [6]

A pre processor was implemented in order to import complex geometries generated from CAD softwares, the meshing of the components is demanded to CUBIT 11.0 developed from Sandia. The CAD model of the component to 84

A model for laser hardening of hypo-eutectoid steels be processed is imported into CUBIT environment and meshed, afterward the coordinates of nodes exported in an appropriate format (Abaqus *.inp, Step *.stp, Fluent *.msh..) are imported in LHS. An example of the output Abaqus style mesh file is reported in Fig. 4.4. *HEADING *cubit(C:/cubo.inp): 02/10/2010: **NODE * 1, 0.000000e+000, 0.000000e+000, * 2, 0.000000e+000, 0.000000e+000, * 3, 0.000000e+000, 5.000000e+000, * 4, 0.000000e+000, 5.000000e+000, . . **ELEMENT, TYPE=C3D8R, ELSET=EB1 *1, 1, 2, 3, 4, 5, 6, 7, 8 *2, 2, 9, 10, 3, 6, 11, 12, 7 *3, 4, 3, 13, 14, 8, 7, 15, 16 . .

14:00:03 1.000000e+001 5.000000e+000 5.000000e+000 1.000000e+001

Fig. 4.4: Mesh output file in Abaqus style

The file contains the coordinates of each node in the mesh and the correlation between the nodes and the hexahedral volumes. Figure 4.5 shows an example of a complex geometry meshed with CUBIT and imported in LS. LS system loads the mesh file and fill the three main topological structures of the code: Node, Face and Volume. Each node knows which faces and volumes belong to, each volume knows its eight nodes and six faces, and each face knows its four nodes and the one or two volumes that share it (the external faces of the geometry share only one volume). Figure 4.6 shows the generic topology construction of a single mesh element in LS. Once the mesh file is loaded all the topology elements are classified in Internal or External. When the laser beam hits the geometry surface some elements becomes Irradiated. Figure 4.7 shows the state of all the elements in LS during the laser movement, ρ is the distance between a node and the laser axes, if ρ ≤ Rz the node is irradiated and the external faces sharing it become irradiated. Figure 4.8 shows the pseudo C++ code to calculate the irradiance that hits an external face. The heat equation 4.6 solved in the simulator by the Finite Difference Method requires the knowledge of the conductivity k overall in the domain. In practical during calculation of the heat flux between two elements the conductivity of both the elements is required in order to evaluate the spatial derivative of it. Figure 4.9 shows a case of an external element with temperature TE and conductivity kE facing to virtual element added to the mesh called boundary element with temperature and conductivity TB and kB , the distance between the elements is ∆x 85

Chapter 4

Fig. 4.5: A complex geometry meshed with CUBIT and imported in LHS

In this situation it is quite easy to impose two kinds of boundary conditions: Perfect insulator : the boundary condition is TB = TE and kB = 0.0, there is not heat flux trough the boundary. Perfect cooler : kB = kE and the boundary element does not change its temperature acting as an ideal quenching medium. The real boundary conditions cannot be treated with that method because it is not possible to treat the boundary layer as an ideal surface of separation. From an engineering point of view real cases are treated by means of the heat transfer coefficient at the boundary hB that represent the power intensity due to a given temperature gradient. • Air: 10 to 100 W/m2 K • Water: 500 to 20000 W/m2 K The thickness of the thermal barrier is generally unknown, if the material surrounding the part is a fluid the value of hB depends by convection. The rules to apply an effective boundary condition in the FDM code is expressed by Eqn. 4.12 hB =

∆x + kB )

1 2 (kE

(4.12)

where ∆x is the distance between the elements at the mesh boundary. The conductivity kB requested by the code is obtained by Eqn. 4.13. kB =

2∆x − kE hB 86

(4.13)

A model for laser hardening of hypo-eutectoid steels

Fig. 4.6: The geometrical topology of the Laser Simulator

This is a fictitious conductivity, in most cases in presence of metallic material surrounded by liquid or gas the conductivity kB can be a meaningless negative number that acquires a physical sense only when used in Eqn. 4.12. LS allows to store data output in .txt and .png files. In particular, .txt files store the temperature values, the micro-structures and the correspondent hardness calculated during the simulation in the region of the work-piece selected by the user by means of the probes, while .png files store images during the simulation. As shown in Fig. 4.10 the blue segments represent the probes set into the component. Figure 4.11 shows a plot of the temperature time inside the material in longitudinal direction. Finally, by setting the laser path, the simulation is ready to be run. The scanning trajectory of the laser spot is described using the ISO standard language to write a part program of the laser spot, considered as a tool in conventional cutting. Figure 4.12 shows a part program to move the laser on a cylindrical surface.

87

Chapter 4

Fig. 4.7: Node irradiated during laser movement

88

A model for laser hardening of hypo-eutectoid steels /// For each mesh elements if( pVol->checkStatus( VOLUMEIRRADIATED ) ) { /// Loop on the 6 faces of the volume for ( if = 0; if < 6; if++ ) { pFace = pVol->getFace( if ); if ( pFace->checkStatus( FACEIRRADIATED ) ) { /// Loop on the 4 nodes of the face for ( in = 0; in < 4; in++ ){ pNode = pFace->getNode(in); if ( pNode->checkStatus( NODEIRRADIATED ) ){ pFace->getNode(in)->getCoords( xl ); /// Evaluate the intensity at the node position I += beam.intensity( xl ); } } /// Evaluate an average value of the intensity [W/m2] that hits the face I = 0.25*I*pFace->getLaserIncidence(); /// The energy density dqa += I*(1-R)*(1-exp(-alpha dz) } Fig. 4.8: The pseudocode of the simualtor engine

Fig. 4.9: The boundary conditions in the Finite Difference Method

89

Chapter 4

Fig. 4.10: LS probes to evaluate the temperature and hardness in specific mesh points

8Temperature-Time
Ip→a,max

(4.24)

1.2 1.0

fa

0.8 0.6 0.4 0.2 0.0

I p®a, min

I p®a, max I p®a

Fig. 4.31: The approximated uniform distribution of Ip→a correlated to the austenite fraction.

With this approach the laser surface treatment appears as in Fig. 4.32, the material over the “Ip→a,max ” curve is completely austenized, below “Ip→a,min ” no austenite is present while in the middle there is a continuous distribution of the austenite fraction that will generate, after quenching, a continuous distribution of martensite and consequently of hardness. This approach permits, in a simplified way, with only two parameters, to simulate the smooth hardness transition below the surface that, in laser treatment, can reach the 50% of the transformed depth. The two threshold values Ip→a,min and Ip→a,max was evaluated by means of an experimental campaign. The austenite homogenization is not considered into the model. 4.4.2 Experimental Results and Discussion In order to determine the material constants Ip→a,min and Ip→a,max and to show the accuracy of the proposed model several experimental tests were done. Experiments were carried out by means of a continuos 3 kW FAF CO2 laser source with a diameter of the laser beam equal to 6 mm located on the upper surface of the specimen. The material was AISI 1045 carbon steel plate with a chemical composition of: C = 0.4%, Si = 0.20%, M n = 0.8%, the plates were 15 mm thickness, 70 mm length and 65 mm width in order to minimize the boundary effects in the thermal field; the scheme of the test together with 105

Chapter 4

Fig. 4.32: A scheme of distributed austenization in surface treatment

specimen dimensions is presented in Fig. 4.33. All the tests are a single laser pass test, the specimen were then polished and etched and the results, in terms of hardness and micro-structures, were measured. A typical shape of the treated area is also presented in Fig. 4.33 reported in yellow. Different tests were carried out by varying the laser power and the scanning velocity. In particular, three laser power levels were used: 1.2 kW , 1.4 kW and 1.8 kW combined with two velocity sets to obtains six different test conditions. The levels for the first set of scanning velocity were: 0.3, 0.5 and 0.6 m/min while for the second they were 0.8, 0.9 and 1.1 m/min. In this way each laser power was used with two different velocity, the laser material interaction time was varied and, as a consequence, also the energy delivered to the workpiece was varied. Each test was replicated two times. An example of what happens in the material is presented in Fig. 4.34 in which the temperature-time behavior in the material depth is presented during a test conducted with a laser power of 1.2 kW and a scanning speed of 300 mm/min. The graph clearly shows that on the surface the material reaches the melting temperature Tm . The first millimeter in depth is subjected to a high overheating respect the transformation temperature Ac1 while the time spent above that temperature is very short. The hardness measurements were obtained in the center of the laser track, as outlined in Fig. 4.33 by the dashed line, by means of Vickers’s tests with a load of 1000 g applied for 15 s. For each trial different hardness profiles with 200 µm step were measured, the profiles started from the workpiece surface in the depth direction, and each hardness test were repeated four times so that the average hardness profile together with the standard deviation were calculated. In Fig. 4.37 to 4.42 the comparisons between the experimental and the theoretical results were done for each test. In particular, the continuous thick blue lines are the average measured hardness comprises between the two thin grey lines representing the ±3σ deviations. The dashed red lines are the predicted results obtained by simulating the test with a software implementing the austenization 106

A model for laser hardening of hypo-eutectoid steels

Fig. 4.33: The scheme of a test sample.

model proposed in Eqns. 4.23 and 4.24. The hardness is evaluated by means of Eqn. 4.25 in which fm is the fraction of martensite obtained, while Hm and Hb are the hardness of respectively the obtained martensite and the base material. H = fm Hm + (1 − fm )Hb

(4.25)

The values of Ip→a,min and Ip→a,max that best fit the overall results are obtained by minimizing the error between tests and simulation. m s The overall error is obtained by Eqn. 4.26 in which Hij and Hij are the th th measured and the simulated hardness of the j point in the i test, N is the number of tests, Mi the number of measured points in the ith test. Error =

N X Mi X m H − H s ij

ij

(4.26)

i=1 j=1

The overall error was evaluated at different threshold values, in particular for 0.1 · 10−6 ≤ Ip→a,min ≤ 1.1 · 10−6 and 3 · 10−6 ≤ Ip→a,max ≤ 10 · 10−6 , the error surface response is shown in Fig. 4.35. The parameters that minimize the errors are Ip→a,min = 0.8 · 10−6s and Ip→a,max = 5.8 · 10−6s and Fig. from 4.37 to 4.42 show the results obtained with this distribution. 107

Chapter 4

Tm

1500 0 mm Temperature °C

-0.4 mm -0.8 mm 1000 Ac3 Ac1 500

0 0

1

2

3 time @sD

4

5

6

Fig. 4.34: The temperature-time behavior in the material depth.

Figure 4.36 represents an example of the simulation results elaborated by the code in terms of martensite prediction into the workpiece after a single laser track. It has been calculated for a laser power P=1.2 kW and a scanning rate v=300 mm/min; the domain discretization was obtained by means of a grid of 175 µm in the depth direction z and 750 µm along x and y directions. The predicted hardness related to this process simulation is presented in Fig. 4.37. For the rake of simplicity, the simulations results for the rest of process parameters are omitted and only the predicted hardness are reported in the following Figs. 4.38-4.42. By analyzing the comparisons in Fig. from 4.37 to 4.42 some considerations can be done. The first consideration regards to the accuracy of the model in the prediction of the hardness in the transition zone. The accuracy of the model is high in fact the predicted slope of the hardness values are very similar to the experimental ones and the predicted extension of the transition hardness is also good. The second consideration regards to the prediction of the hardness values which can be considered satisfied because, as showed in the Fig.4.37 to 4.42, they are almost comprises between the measurement errors or very close to these curves, the only values that are not included in the measurement errors is that of Fig. 4.37. The previous considerations can be summarized in the following statements: • the pearlite to austenite transformation time parameter Ip→a allows to easily take into account the non homogeneity at the microstructural level. This is a simplified and useful model for the pearlite austenization during very fast heating. • the microstructural behavior of the material is considered without meshing the part at the µm level with a great increment of the numerical performances. • the on-off behavior in hardness prediction of the previous models is eliminated and the correct hardness transition between the hardened area and the base material is predicted. 108

A model for laser hardening of hypo-eutectoid steels

2350 10. 2050 Error 1750

9. 8.

1450 0.1

7.

I p®a, max

6.

0.3 0.5

I p®a, min

5. 0.7 4. 0.9 1.13.

Fig. 4.35: The error surface response at different levels of Ip→a,min and Ip→a,max .

• the pearlite to austenite transformation time Ip→a can be considered as a ”physical” parameter of the material and can be considered a constant for any laser process parameters are used. Finally, due to the fact that the transition hardening in laser surface heat treatment can be high, up to the 50% of the hardened area, it cannot be neglected during modeling, this is even more evident when multi-tracks laser hardening have to be processed.

109

Chapter 4

Fig. 4.36: Martensite fraction predicted by the software. Power=1.2 kW, d=6mm, F=0.3 mmin 800 700

HV,1000

600 500 400 300 200 100 0.0

0.2

0.4

0.6 0.8 Position @mmD

1.0

1.2

1.4

Fig. 4.37: Power = 1.2 kW, d = 6mm, F = 300 mm/min. Power=1.4 kW, d=6mm, F=0.6 mmin 800 700

HV,1000

600 500 400 300 200 100 0.0

0.2

0.4

0.6 0.8 Position @mmD

1.0

1.2

1.4

Fig. 4.38: Power = 1.4 kW, d = 6mm, F = 600 mm/min.

110

A model for laser hardening of hypo-eutectoid steels

Power=1.8 kW, d=6mm, F=0.9 mmin 800 700

HV,1000

600 500 400 300 200 100 0.0

0.2

0.4

0.6 0.8 Position @mmD

1.0

1.2

1.4

Fig. 4.39: Power = 1.8 kW, d = 6mm, F = 900 mm/min.

Power=1.2 kW, d=6mm, F=0.5 mmin 800 700

HV,1000

600 500 400 300 200 100 0.0

0.2

0.4

0.6 0.8 Position @mmD

1.0

1.2

1.4

Fig. 4.40: Power = 1.2 kW, d = 6mm, F = 500 mm/min.

111

Chapter 4

Power=1.4 kW, d=6mm, F=0.8 mmin 800 700

HV,1000

600 500 400 300 200 100 0.0

0.2

0.4

0.6 0.8 Position @mmD

1.0

1.2

1.4

Fig. 4.41: Power = 1.4 kW, d = 6mm, F = 800 mm/min.

Power=1.8 kW, d=6mm, F=1.1 mmin 800 700

HV,1000

600 500 400 300 200 100 0.0

0.2

0.4

0.6 0.8 Position @mmD

1.0

1.2

1.4

Fig. 4.42: Power = 1.8 kW, d = 6mm, F = 1100 mm/min.

112

A model for laser hardening of hypo-eutectoid steels

4.5 The tempering model In the previous section the problems concerning the austenitization of the initial pearlite-ferrite micro structures and the influence of the carbon content on the austenite transformation was faced. The results were obtained when a single laser pass was carried out on the material surface but no considerations have been done about the influences of multiple passes on the previous hardened area. The laser beam trajectories have to be chosen with the aim to minimize the interaction between the multiple passes but, when surfaces larger than the laser beam spot must to be treated, softening effects on martensite are always present and they must be taken into account. For tempering condition obtained in furnace, when the heating happens at constant temperature maintained for a long time, typically of the order of hours, there are many empirical formula which correlates the chemical composition of the alloy, the temperature-time cycle in the oven to the resulting hardness. Unfortunately these formula can not be applied when tempering happens with very high temperature gradients like in laser tempering. In this work a polynomial expression for the prediction of the hardening in tempering is proposed. An energy factor which allow to estimate the termodynamic condition for the beginning of the martensite transformation as proposed in [15] for the pearlite dissolution into austenite is considered. A numerical optimization carried out by means of an hardening test on a C40 steel allowed to determine the un-known physical variables to be used into the model for fast transformation. This tempering model completes the Laser Hardening Simulator which is able to predict the extension of the treated area, the resulting micro structures and the hardness for every combination of laser source parameters and laser beam path strategy [19] [20] [21]. Several simulations are presented in order to validate the model. The LHS software was able to predict the resulting micro-scrutures after quenching and the extension of the treated area according to the workpiece material, the laser source parameters, the laser scanning trajectories and the initial type and coarsening of the micro-sctructures. LHS was developed for a single laser path and the hardness was calculated by means of the following Eqn. 4.27 being fm the volume fraction of the martensite and Hm and Hf the hardness of the martensite and ferrite respectively.

H = fm Hm + [1 − fm ]Hf

(4.27)

The tempering model presented in this work is based on the prediction of the hardness variation in the structures obtained after quenching. No microstructures transformation are predicted during the tempering as in [22] and [17]. The prediction of the micro-structure transformations is very time consuming and the development of a routine devoted to this topic into LHS would lead to an useless software for industrial applications due to the elevated calculation time. In furnace heat treatment the prediction of the tempering hardness of quenched Low-Alloy Steels can be obtained as proposed in [23] by means of Eqn. 4.29 for the martensite. 113

Chapter 4

HVM

= − −

−74 − 434C − 368Si − 25M n + 37N i 103 335M o − 2235V + (260 + 616C + 321Si Pc 21M n − 35N i − 11Cr + 352M o + 2354V )

(4.28)

As reported in Eqn. 4.29 the parameter Pc controls the coarsening of the resulting microstructures at room temperature according to heat cycle applied to the workpiece.  −1 1 nR t − · log (4.29) Pc = T Ha t0 Ha is the activation enthalpy of the microstructural transformation during the tempering and it depends on the chemical composition of the alloy. Equation 4.29 can be applied to the tempering processes carried out in furnace where the process temperatures T are constant for the all process time t, but it cannot be applied in laser hardening where the tempering depends on the overlapping of two subsequent laser paths and where the temperature gradients are very high, the temperatures are very different into the workpiece and they can vary from temperature room up to temperatures above the austenite transformation. To solve this problem, two topics have to be faced: • the re-austenitization of the martensite • the not constant tempering temperature Regarding to the re-austenitization of the martensite, it must be noted that it can be considered to be diffusion controlled and, for this reason, the extent of changes depends on the number of the diffusive phenomena occurring during the heat cycle T (t). On the other hand the diffusive phenomena are influenced from the rapidity of the heating. To taking into account this effect on the martensite transformation an integral activation energy Ima is proposed as in Eqn. 4.30. Im→a =

Z

t2

exp−

Qm→a RT (t)

dt

(4.30)

t1

Qm→a is the activation energy for the martensite to austenite transformation being t1 the time when the eutectoid temperature is reached and t2 is the current time. R is the gas constant and T (t) time dependent temperature. Im→a gives the threshold limit for the transformation and, as it is clear, it depends on the heat cycle. Equation 4.30 allows to separates the points into the workpiece which have been re-austenitized by means of the overlapping laser path from the points simply tempered. Once the model determines the re-austenitized and tempered areas in the workpiece, the evaluation of the hardness can be performed. The re-austenitized micro-structures are quenched, LHS determines fm and fb after quenching, and the hardness is calculated by means of Eqn. 4.27. Few consideration must be done for the tempered micro-structures. 114

A model for laser hardening of hypo-eutectoid steels

Fig. 4.43: Hardness variation in two different time tk and tk+1 for a generic tempered point (x, y, z)

In order to apply Eqn. 4.27 also for a tempering induced by the overlapping laser beam, Hm and Hb have to be calculated by means of Eqn. 4.29 for evaluating the softening effects induced on the martensite volume fm . To do this, in the model a tempering time parameters τk is proposed when the martensite start temperature TMs is overtaken. The τk parameter allows the softening of the micro-structures to be calculated as a function of the time as presented in Eqn. 4.31. τk+1 = 1 −

(Hv k − Hv k+1 ) Hv k

(4.31)

Hv k and Hv k+1 are the hardness variation in correspondence of the two subsequent instant tk and tk+1 during the tempering. The tempering factor τk+1 is the coefficient which allows to calculate the hardness Hvjk of a generic phase j at the instant tk as the sum of the softening contributions obtained at discrete temperature values, supposed to be constant for an infinitesimal time δt = (tk - tk+1 ), starting from the initial hardness Hj0 as presented in Eqn. 4.32. Hvjk = Hvj0

k Y

τj

(4.32)

j=0

Increasing δt means that the temperature gradients are lower during the tempering, the process tends to a furnace tempering and the value Hvjk → HVM calculated by Eqns. 4.29. In order to achieve a complete software package for the prediction of the overlapping laser paths effects two considerations must be done with respect to the material properties. Figure 4.44 shows the typical effects on the hardening when two overlapped laser paths are considered. The laser beam is supposed entering into the figure and a qualitative profile of the hardness due to the first path is pictured with the the dash line. The second path causes a decrease of the extension of the treated area and a lower maximum hardness value. At the same time the second treated area is bigger due to the fact that during the second laser path the workpiece is already heated. The final results of the two paths are pictured with the continuos line. The first consideration regards to the evaluation of the integral activation energy Im→a as defined in Eqn. 4.30. Im→a determines the initial point of the 115

Chapter 4

Fig. 4.44: The back tempering effect: a qualitative effect on hardness

re-austenitization and it can be represented with the minimum hardness, point Hmin , in Fig. 4.44. Im→a gives the threshold between the tempered and reaustenitization zones so that in area A1 the hardness depends on the tempering while in area A2 the hardness variation is governed by the quenching after the re-austenitization.The value of the Im→a depends on the chemical composition of the alloy and on the heat cycle T (t). If Im→a increases the influence of the multiple passes on the hardness decreases. The second consideration regards to the evaluation of Qm→a in Eqn. 4.30. It represents the activation energy of the carbon diffusion into the austenite. Coefficient Qm→a and the integral activation energy Im→a are numerically evaluated by means of code runs: the code choose the best values for the couple Im→a and Qm→a by minimizing the difference between the predicted and exeprimantal position of the minimum hardness value Hm for a given surface treatment. In this work the experimental comparison has been done on a C40 steel treated by means of a CO2 laser with a power P =1100 W a scanning velocity v=300 mm/min a beam spot diameter d=8 mm and a second path 50% overlapped. The optimal simulation results have been obtained by setting Qm→a = 2000 J/mol and Im→a = 0.5 s as showed in Fig. 4.43 where the blue line is the experimental hardness measured on the beneath of the irradiated surface in direction x in Fig. 4.45, and the red line represents the predicted ones. 4.5.1 Model validation In order to validate the proposed model and to show the capabilities of the software for laser surface hardening, several experimental tests have been carried out on C40 steel. A CO2 laser source with a laser spot d=8 mm were used for all the trials. Fig. 4.46 and Fig. 4.47 report the results of the obtained hardness when three overlapped trajectories are considered. In particular, in Fig. 4.46 the overlapping of the second and third paths is 70% while in the test reported in Fig. 4.47 the overlapping between the laser paths is 75%. The laser parameters are: P =1200 W and v=400 mm/min for both the trials. As evident, with an 116

A model for laser hardening of hypo-eutectoid steels 800

Hardness HV1000

600

400

200

0 0

2

4

6 Position @mmD

8

10

12

Fig. 4.45: An example of test used for the evaluation of Qm→a and Im→a

overlapping of 75% the third laser path strongly influences the hardness profile obtained with the first trajectory. 800

Hardness HV1000

600

400

200

0 0

2

4

6 Position @mmD

8

10

12

Fig. 4.46: Hardness comparison in the substrate layer: blue dotted line experimental hardness, red dashed line theoretical hardness. 70% overlapping

The hardness in the tempered area are evaluated by means of Eqn. 4.29 with Ha = 50000 J/mol while for the austenitized area is calculated according to Eqn. 4.27. The predicted martensite hardness in the third laser path is always higher than the experimental, this is due to the fact that in the proposed model residual austenite, which very often occur in laser hardening, is not considered. Fig. 4.48 shows the comparison between the experimental test proposed in Fig. 4.46 and the predicted results obtained with Im→a =0. Im→a =0 means that the overheating is not considered in re-austenitization and martensite transforms 117

Chapter 4 800

Hardness HV1000

600

400

200

0 0

2

4

6

8

10

Position @mmD

Fig. 4.47: Hardness comparison in the substrate layer: blue dotted line experimental hardness, red dashed line theoretical hardness. 75% overlapping

into austenite at the eutecotid temperature. Considering Im→a = 0.5 s the estimated overheating is about 200 K. 800

Hardness HV1000

600

400

200

0 0

2

4

6 Position @mmD

8

10

12

Fig. 4.48: Experimental comparison with Im→a =0 and overlapping of 75%: blue dotted line experimental results, red dashed line theoretical results

118

A model for laser hardening of hypo-eutectoid steels 4.5.2 Model refinement The typical effects of back tempering on martensite after two overlapping laser passes is presented in Fig. 4.44. The final results of the two paths are pictured with the red continuous line where A1 represents the locus of the tempered points and A2 are the points re-austenitezed and then retransformed in martensite after the second pass. The threshold Im→a,th determines the initial point of the re-austenitization and it was represented with the minimum hardness point Hmin in Fig. 4.44. Im→a,th was assumed to be a material property and equal to 0.5 s with Qm→a =2000 J/mol as calcualted in the previous paragraph, it also determines the overheating for the martensite re-austenization. The model is then refined to simulate the two diffusive phenomena during tempering: the ǫ carbide and the tempered martensite formations [24]. Both phenomena are carbon diffusion controlled and they can be modeled with an equation similar to equation 4.22 if the appropriate activation energies are used. In this way, by knowing the integral transformation time threshold Ij→i,th of both transformations, i refers to the j phase transformation, when Eqn. 4.33 and 4.34 are verified the martensite transforms to ǫ carbide and ǫ carbide phase transforms to tempered martensite. Im→ǫ ≥ Im→ǫ,th

(4.33)

Iǫ→mT ≥ Iǫ→mT ,th

(4.34)

To further simplify the model, only one activation energy Qm→mT and one transformation time threshold Im→mT ,th for both micro-structure transformations is considered. The diffusive equation governing the physical phenomena of softening in laser hardening becomes as presented in Eqn. 4.35, where tMs is the time when the martensite start temperature is reached and t2 is the current time, and the threshold for the initial transformation is expressed in Eqn. 4.36.   Z t2 Qm→mT exp − dt (4.35) Im→mT = RT (t) tMs Im→mT ≥ Im→mT ,min

(4.36)

Knowing the T (t) function, once the inequality 4.36 is verified, the martesite is transformed into a tempered martensite. The transformation overheating can be also estimated. In Fig. 4.44 the meaning of Im→mT ,min can be explained: it represents, in fact, the left border of the tempered area A1 . The techniques adopted to determine the values of the transformation time thresholds and Qm→mT are explained in the following paragraph. 4.5.3 The transformation time and the activation energy evaluation As written in the previous paragraph the two diffusive phenomena governing the martensite softening during tempering are the ǫ carbide and the tempered martensite formations. These phenomena, being controlled by the carbon diffusion are temperature-time dependent and, for this reason, the hysteresis effects must be considered. The proposal of this model is to control them by means of Eqn. 4.35 for an appropriate value of Qm→mT considering the threshold in 119

Chapter 4 Eqn. 4.36. The minimum threshold allows to predict, according to the heat cycle, the initial temperature of tempering or the minimum hardness reduction. Anyway the maximum threshold is also required in order to predict the maximum tempering temperature where the maximum softening is obtained. This threshold con be thought as the last point tempered into the workpiece: the adjacent point is considered re-austenitized. An hardness softening effect due to the tempering is introduced by a parameter fh . A linear behavior of the transformation time Im→mT between Im→mT ,min and Im→mT ,max is proposed as presented in Fig. 4.49: when Im→mT = Im→mT ,max fh = 1 while for Im→mT = Im→mT ,min is possible to obtain fh = 0. By means of Eqn. 4.37, knowing fh and the martensite volume fraction the hardness of the softening structures can be calculated. 1.2 1.0

fh

0.8 0.6 0.4 0.2 0.0

Im® mT , min

Im® mT , max Im® mT

Fig. 4.49: The linear distribution of the transformation time Im→mT .

The effect of Im→mT ,min and Im→mT ,max on the tempered zone prediction is presented in Fig. 4.50 and 4.51. Decreasing Im→mT ,min leads to decrease the initial tempering temperature while increasing Im→mT ,max means that the tempering transformation needs more energy, it happens at higher temperature, the tempered zone moves towards right and the minimum hardness moves towards the first laser path, as presented in Fig. 4.51. H = fm [fh (Hm − Hb ) + Hb ] + (1 − fm )Hb

(4.37)

The Im→mT ,min and Im→mT ,max thresholds were determined by means of experiments carried out on a C67 steel plate whose chemical composition is reported in Table 4.3 treated by of continuos 3 kW CO2 FAF laser source with a T EM 01∗ beam and a spot diameter equal to 6.5 mm located on the surface of the specimen 3 mm thick, 70 mm length and 65 mm width. In order to prove that the thresholds can be considered non dependent on laser parameters only one laser configuration was considered: 1.2 kW , two laser passes 20% overlapped with a speed of 0.5 m/min for both passes. Three hardness measurement repetitions were done by means of Vickers test with a load of 1000 g applied for 15 s. For each trial the hardness measurement were done in the horizontal direction every 200 µm, 250 µm on the beneath the workpiece sur120

A model for laser hardening of hypo-eutectoid steels ImT ,Thmin =1.0*10-6s; ImT ,Thmax =4.4*10-2s 1000

HV,1

800

600

400

200 0

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8

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Fig. 4.50: Effect of the threshold values Im→mT ,min and Im→mT ,max , Im→mT ,min = 1.0 · 10−6 , Im→mT ,max = 4.4 · 10−2 .

Tab. 4.3: THE MATERIAL CHEMICAL COMPOSITION.

Element C Mn P S

Weight % 0.60-0.70 0.60-0.70 0.04 (max) 0.04 (max)

face transversally respect the laser path and in the vertical direction on the centerline of the second track. The results in the vertical and the horizontal direction are presented in Fig. 4.52 and 4.53 respectively, the vertical hardness refers to approximate centerline of the second pass. The continuous thick blue lines are the average measured hardness comprises between the two thin grey lines representing the ±3σ deviations. By means of numerical simulations the best fit curve between the predicted and experimental hardness was obtained with Im→mT ,min = 1.0 · 10−6 s and Im→mT ,max = 4.4 · 10−2 s and Qm→mT = 20000 J/mol as presented in Fig. 4.54 and 4.55. The red dashed lines with circles are the calculated hardness for both measurements, vertical and horizontal. These values of the thresholds were used for all the experimental tests described in next paragraph in order to prove that they can be considered a property material and not dependent on the process parameters. 4.5.4 Experiments Different tests were carried out by varying the laser power and the scanning velocity. In particular, two laser power levels were used: 1.2 kW and 1.8 kW combined with different velocities in order to obtain different laser power densities. For the lower laser power, a scanning velocity of 0.7 m/min was used 121

Chapter 4 ImT ,Thmin =1.0*10-7s; ImT ,Thmax =1.0*10-2s 1000

HV,1

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Fig. 4.51: Effect of the threshold values Im→mT ,min and Im→mT ,max , Im→mT ,min = 1.0 · 10−7 , Im→mT ,max = 1.0 · 10−2 .

while for the second laser level three different scanning velocity were considered: 0.9, 1.1 and 1.3 m/min, the specimen have the same dimensions reported in the previous paragraph. For every test, the cross-sectional area of the specimen was polished and etched with a Nital solution, the hardened, unhardened and the transition region in the overlapped zone are clearly recognizable in Fig. 4.56. Four Vickers hardness measurement repetitions were made in the approximate center of the second track and along with the hardened zone 250 µm below the surface. All the comparisons are reported in the following Fig. 4.57–4.64, the continuous thick blue lines are the average measured hardness, the two thin grey lines are the ±3σ deviations of the measurements and the red dashed lines represent the predicted hardness. For every comparison, the first laser pass is always reported in the right of the figure and its velocity is named F1 in the label on the top of the figure and the all the comparisons were done by considering the results after 17s simulation. The comparisons show the good accuracy of the model to predict the hardness profile in multi track laser hardening. The extension of the treated area in both directions, vertical and horizontal, can be predicted with high precision especially for short interaction time. The results for 1.2kW experiments are shown in Fig. 4.57 and 4.58, the maximum hardness, dept ah and width of the treated area are in good accordance with experiments. The back tempered area extension, the minimum hardness and its position, indicating the last tempered point before re-austenization, are calculated with high accuracy. The extension of the complete martensite zone in vertical direction, see Fig. 4.57, shows a little discrepancy with the measurements even if the transition area between the martensite zone and base material is predicted with good accuracy. Figures 4.59 and 4.60 refer to tests carried out at 1.8 kW with two differents laser speed: F1=0.5 m/min for the first track and F2=0.9 m/min for the second track. The hardness prediction has high accuracy in vertical and horizontal directions and in the overlapped region. Small discrepancies are shown in Fig. 4.59– 4.64 for hardness profile calcula122

A model for laser hardening of hypo-eutectoid steels 1000

Hardness HV,1

800

600

400

200 0.0

0.5

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1.5

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Fig. 4.52: Hardness measurement in the centerline of the second pass in the vertical direction. 1000

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Fig. 4.53: Hardness measurement in the horizontal direction 250 µm below the workpiece surface.

tions in the back tempered zone. These cases refer to the highest laser velocities in the second pass, 1.1 and 1.3 m/min respectively. In particular, it seems that the model over estimates the extension of the heat affected zone of the second laser track on the first, the martensite extension areas generated by the second path are wider. This result leads to a bigger extension of second track hardened zone with respect to the first one and a higher value of the minimum hardening, this means that lower values of Im→mT ,min and Im→mT ,max are required when the interaction time between laser and material are shorts, otherwise the model over estimates the initial tempering temperatures and the tempered area are smaller. Good accuracy in maximum hardness predictions and extensions of treated areas were still observed also for high laser speeds. The validated model has been applied in real industrial cases.

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Test II, P=1.2 kW, d=6.5mm, F=0.5 mmin, t=17.s 1000

HV,1

800

600

400 Numerical Experimental ±3Σ

200 0.0

0.5

1.0 1.5 Position @mmD

2.0

2.5

Fig. 4.54: Hardness comparison in the centerline of the second pass in the vertical direction, P = 1.2kW d = 6.5mm F = 0.5m/min.

Test II, P=1.2 kW, d=6.5mm, F=0.5 mmin, t=17.s 1000

HV,1

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400 Numerical Experimental ±3Σ

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Fig. 4.55: Hardness comparison in the horizontal direction 250 µm below the workpiece surface, P = 1.2kW d = 6.5mm F = 0.5m/min.

Fig. 4.56: A cross-sectional area of a specimen after the laser treatment. P=1.2 kW ; F1=0.5 m/min; F2=0.5 m/min.

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Test III, P=1.2 kW, d=6.5mm, F=0.7 mmin, t=17.s 1000

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400 Numerical Experimental ±3Σ

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Fig. 4.57: Hardness comparison in the approximate center of the second pass in the vertical direction, P = 1.2kW d = 6.5mm F = 0.7m/min.

Test III, P=1.2 kW, d=6.5mm, F=0.7 mmin, t=17.s 1000

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Fig. 4.58: Hardness comparison in the horizontal direction 250 µm below the workpiece surface, P = 1.2kW d = 6.5mm F = 0.7m/min.

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Test IV, P=1.8 kW, d=6.5mm, F=0.9 mmin, t=17.s 1000

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Fig. 4.59: Hardness comparison in the approximate center of the second pass in the vertical direction, P = 1.8kW d = 6.5mm F = 0.9m/min.

Test IV, P=1.8 kW, d=6.5mm, F=0.9 mmin, t=17.s 1000

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Fig. 4.60: Hardness comparison in the horizontal direction 250 µm below the workpiece surface, P = 1.8kW d = 6.5mm F = 0.9m/min.

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Test V, P=1.8 kW, d=6.5mm, F=1.1 mmin, t=17.s 1000

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Fig. 4.61: Hardness comparison in the approximate center of the second pass in the vertical direction, P = 1.8kW d = 6.5mm F = 1.1m/min.

Test V, P=1.8 kW, d=6.5mm, F=1.1 mmin, t=17.s 1000

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Fig. 4.62: Hardness comparison in the horizontal direction 250 µm below the workpiece surface, P = 1.8kW d = 6.5mm F = 1.1m/min.

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Test VI, P=1.8 kW, d=6.5mm, F=1.3 mmin, t=17.s 1000

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Fig. 4.63: Hardness comparison in the approximate center of the second pass in the vertical direction, P = 1.8kW d = 6.5mm F = 1.3m/min.

Test VI, P=1.8 kW, d=6.5mm, F=1.3 mmin, t=17.s 1000

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Fig. 4.64: Hardness comparison in the horizontal direction 250 µm below the workpiece surface, P = 1.8kW d = 6.5mm F = 1.3m/min.

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4.6 Industrial cases 4.6.1 Laser hardening of large cylindrical martensitic stainless steel surface The results of a large surface hardening simulation in an industrial component obtained in AISI420B are presented [25] [26]. In particular, by predicting the temperature distribution into the work-piece, the martensite formation and the subsequent hardness can be calculated. The virtual spot technique is adopted. The first step for the simulation of the treatment is the discretization of the component. This is obtained by means of hexagonal finite elements into CUBIT environment starting from a file elaborated by a CAD, both format .step and .iges can be used. The component to be treated is presented in Fig. 4.65.

Fig. 4.65: The work-piece discretization: the hexagonal discretization in CUBIT.

Figure 4.66 shows the work-piece discretization in CUBIT. The component has 72 mm diameter, a thickness of 4 mm and a length of 60 mm, the surface to be treated is the external cylindrical surface which must have 52-54 HRC for a depth of 500 µm along the 60 mm length. After a format conversion, the file of the node coordinates is exported into LHS, see Fig. 4.67. The boundary condition set into the simulator were: • no convection and radiating heat flux toward the environment; • the component is supposed insulated, in adiabatic condition, due to the predominant conduction heat flux toward the bulk. LHS allows to store data in .txt and .png files. In particular, .txt files store the temperature values and the micro-structures calculated during the simulation in the region of the work-piece selected by the user by means of the probes, while .png files store images during the simulation as presented in Fig. 4.67. The blue segments represent the probes set into the component. In particular, in this case, 6 probes where considered in order to store the radial and longitudinal temperatures into the component. Finally, by setting the laser path, the simulation is ready to be run. In order to treat a large surface like in this case, the well known technique of 129

Chapter 4

Fig. 4.66: The work-piece to be treated

virtual spot is used. It consists in creating a high temperature ring, typically above the eutectoid temperature, all around the cylindrical surface and in propagating it by combining high rotating speed of the work-piece and high laser power density typically used in welding. By means of this technique, large surface can be hardened also by laser, even if a quenching medium can be necessary because the cooling temperature can be slow. Due to the fact that AISI420 B is a self-hardened steel, the martensite can be obtained in the region where the eutectoid temperature is reached without any quenchant. According to this assumption, several simulations were carried out in order to define the correct laser trajectory which allows to reach an uniform temperature along the cylindrical surface higher than the austenitization temperature supposed equal to 1300 K. The laser path simulation can be divided by two: a first part for the virtual spot generation where the laser is fixed and the part is rotated, and a second part for the virtual spot propagation along the cylindrical surface where helicoidal path is programmed. The aim of the first simulation part is to determine the number of component rotations required for reaching the austenization temperature along the external circle where the beam is focused (virtual spot), according to the laser power, laser spot and the rpm of the component, while the aim of the second simulation part is to determine the axial velocity of the laser which allows to propagate the thermal field (1300 K at external surface). The optimal solution were obtained with the following parameter: • Laser power = 2kW • Laser spot diameter = 1.2 mm • Rotational velocity of the component= 900 rpm • Laser axial feed per revolution = 0.5 mm According to this process parameters, LHS predicts a 280 component rotations, 18.5 sec, for the virtual spot generation. The simulation is stopped after 130

A model for laser hardening of hypo-eutectoid steels

Fig. 4.67: The work-piece discretization exported into LHS. The blue lines are the probes

19.5 sec corresponding to a 10 mm axial path of the laser. The laser material interaction starts at 3.5 mm from the border in y direction (axial direction) at the upper side of the surface corresponding to the coordinates x=0 and z=36 mm. In Fig. 4.68 a .png file elaborated by LHS after 1.5 sec is presented.

Fig. 4.68: The simulation after 1.5 sec

As presented in Fig. 4.69 and 4.70, the temperature reached in radial direction (z direction) is higher than 1300 K all along the external surface of the component after 280 rotations or 18.5 sec. After this threshold the temperature slightly decrease due to the laser displacement. Finally, the laser was turned off after 10 mm run in axial direction. In Fig. 4.71 4.72 4.73 4.74 the temperature at the end of the simulation, after 19.5 sec, calculated at the position of 5 mm in 131

Chapter 4 axial direction are presented. As it can be seen, also in this case the temperature is practically uniform as it is indicated by the 4 longitudinal probes. Finally, by knowing the time dependent temperature into the workpiece, applying Eqn. 4.22 the pearlite to austenite transformation can be predicted, while the preeutectoid ferrite is transformed to austenite with 0 % carbon content when Ac3 is reached. During quenching the austenite is transformed to austenite with no variation of the carbon content, 0.8 % of the austenite, as the carbon diffusion can be neglected for fast heat cycle. Temperature Probe ð1 @KD

AISI 420 B HP=2 kW, n=900 rpmL 1400 1200

TMAX=1323.15

1000 800

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Fig. 4.69: Probe 1: temperature evolution during the virtual spot generation at x=0; y=3.5; z=36

Temperature Probeð2 @KD

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1000 800

Tmin =1223.15

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Fig. 4.70: Probe 2: temperature evolution during the virtual spot generation at x=36; y=3.5; z=0.

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Temperature Probeð3 @KD

AISI 420 B HP=2 kW, n=900 rpm, 20% OverlapL 1400 1200 TMAX =1323.15

1000 800

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Fig. 4.71: Probe 3: temperature evolution during the virtual spot generation at x=0; y=5; z=36.

Temperature Probeð4 @KD

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1000 800

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Fig. 4.72: Probe 4: temperature evolution during the virtual spot generation at x=36; y=5; z=0

Temperature Probeð5 @KD

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1000 800

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Fig. 4.73: Probe 5: temperature evolution during the virtual spot generation at x=0; y=5; z=-36

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Temperature Probeð6 @KD

AISI 420 B HP=2 kW, n=900 rpm, 20% OverlapL 1400 1200 TMAX =1323.15

1000 800

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Fig. 4.74: Probe 6: temperature evolution during the virtual spot generation at x=-36; y=5; z=0

134

BIBLIOGRAPHY

[1] N.M. Bulgakova and A.V. Bulgakov. Pulsed laser ablation of solid: transition from normal vaporization to phase explosion. Applied Physics A, 73(2):199–208, August 2001. [2] Sushimita R, Franklin, and R.K. Thareja. Simplified model to account for dependence of ablation parameters on temperature and phase of the ablated material. Applied Surface Science, 222(1-4):293–306, 2004. [3] T. Dobrev, D.T. Pham, and S.S. Dimov. A simulation model for crater formation in laser milling. In Elsevier (Oxford), editor, 4M 2005 - First International Conference on Multi-Material Micro Manufacture, 2005. [4] J. C. Tannehill, A. D. Anderson, and R. H. Pletcher. Computational Fluid Mechanics and Heat Transfer. Taylor and Francis, 1997. [5] T.J. Chang. Computational Fluid Dynamic. Cambridge University Press, 2002. [6] L. Orazi, A. Fortunato, G. Cuccolini, and G. Tani. An efficient model for laser surface hardening of hypo-eutectoid steels. Applied Surface Science, 256:1913–1919, 2010. [7] G. Tani, A. Ascari, and L. Orazi. Metallurgical phases distribution detection through image analysis for simulation of laser hardening of carbon steels. In Proc.of MSEC2007, 2007. [8] L. Orazi, A. Fortunato, G. Tani, G. Campana, and A. Ascari. 3d modelling of laser hardening and tempering of hypo-eutectoid steels. In Proocedings of LPM2007, 2007. [9] G. Tani, L. Orazi, A. Fortunato, and G. Campana. 3d transient model for c02 laser hardening. In Proceedings of FLAMN07, 2008. [10] G. Tani, L. Orazi, A. Fortunato, G. Campana, G. Cuccolini, and A. Ascari. Laser hardening simulation for 3d surfaces of medium carbon steel industrial parts. In Proocedings of LIM2007, 2007. [11] G. Tani, L. Orazi, A. Fortunato, G. Campana, and G. Cuccolini. Laser hardening process simulation for mechanical parts. In High Energy/Average Power Lasers and Intense Beam Applications, 2007. [12] S. Skvarenina and Y. C. Shin. Predictive modeling and experimental results for laser hardening of aisi1536 steel with complex geometric features by a high power diode laser. Surface & Coatings Technology, 46:3949–3962, 2006.

Chapter 4 [13] L. Orazi, A. Fortunato, G. Cuccolini, and G. Tani. A new computationally efficient model for martensite to austenite transformation in multi-tracks laser hardening. Journal of Optoelectronics and advanced materials, 12(3), 2010. [14] L. Orazi, A. Fortunato, G. Tani, G. Campana, A. Ascari, and G. Cuccolini. A new computationally efficient method in laser hardening modeling. In Proceedings of the 2008 International Manufacturing Science and Engineering Conference, 2008. [15] M.F. Ashby and K.E. Easterling. The transformation hardening of steel surface by laser beam - i hypo-euctectoid steels. Acta metall., 32(11):1935– 1948, 1984. [16] A. Jacot and M. Rappaz. A two-dimensional diffusion model for the prediction of phase transformation: application to austenization and homogenization of hypoeutectoid fe-c steels. Acta materialia, 45(2):575–585, 1997. [17] A. Jacot and M. Rappaz. Modeling of reaustenization from the perlite structure in steel. Acta materialia, 46(11):3949–3962, 1998. [18] A. Jacot and M. Rappaz. A combined model for the description of austenization, homogenization and grain growth in hypoeutectoid fe-c steel during heating. Acta materialia, 47(5):1645–1651, 1999. [19] A. Fortunato G. Tani, L. Orazi, G. Campana, A. Ascari, and G. Cuccolini. Optimization strategies of laser hardening of hypo-eutectoid steel. In Proc. of Manufacturing Systems and Technologies for the New Frontier Conference, 2008. [20] G. Tani, L. Orazi, and A. Fortunato. Prediction of hypo eutectoid steel softening due to tempering phenomena in laser surface hardening. CIRP Annals, 57(1):209–212, 2008. [21] G. Tani, L. Orazi, A. Fortunato, G. Campana, and A. Ascari. 3d modelling of laser hardening and tempering of hypo-eutectoid steels. Journal of Laser Micro Nanoengineering, 3:124–128, 2008. [22] S. Denis, D. Farias, and A. Simon. Mathematical model coupling phase transformations and temperature. ISIJ International, 32(3):316–325, 1992. [23] ASM Handbook Committe. Heat Treating, Vol 4. American Society of Metals, fourth edition, 1992. [24] L. Orazi A. Fortunato and G. Tani. A new computationally efficient model for tempering in multi-tracks laser hardening. In Proc. of the ASME 2009 International Manufacturing Science and Engineering Conference (MSEC2009), 2009. [25] A. Fortunato G. Tani, L. Orazi, G. Campana, A Ascari, and G. Cuccolini. Laser hardening of 3d complex parts: industrial applications and simulation results. In 9th AITeM Conference - Enhancing the Science of Manufacturing - Proceedings, 2009. 136

A model for laser hardening of hypo-eutectoid steels [26] G. Campana A. Fortunato, L. Orazi. Laser hardening of large cylindrical martensitic stainless steel surfaces. In Proc. of the Fifth International WLTConference on Laser in Manufacturing 2009, 2009.

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5. LASER MICRO MACHINING

Chapter five

Laser micro machining

Laser micro machining

Introduction This chapter introduces an important laser application: laser micro machining. The physic of this process and the numerical simulation models in literature were analyzed.

5.1 Laser micro machining Laser micro machining is based on the interaction of laser light with matter. The beam from a pulsed laser source can readily be focused on a solid material to cause sufficient heating to give surface evaporation. As a result of this complex process, small amounts of material can be removed from the surface of a workpiece. This physical process is called laser ablation [1]. Depending on the energy density delivered to the workpiece, the removal process can happen with or without the melting of the workpiece: laser radiations with long pulse width, of the order of nanoseconds, generates materials melting before the vaporization occurs, while, laser radiations with short pulse width, of the order of picoseconds or better femto seconds, causes vaporization of the target surface and no heat transmission into the bulk, for this reason it is sometimes called cold ablation. The physical interaction phenomena between the laser and the target material are clear for both the processes, but, in industrial environment, only the nanosecond laser systems are widespread utilized even if the quality of the processed parts is higher by using the femto second lasers [2] that still currently present high instability. Laser systems with long pulse width are commonly utilized for operations of marking and engraving when the workpieces are processed to obtain artistic shapes or when no particular geometric tolerances are required. Removal material operations when deep penetrations, high accuracy and complicated shapes must be realized are usually realized by electrical discharge machining (EDM). In molds manufacturing the finishing operations are typically performed by EDM, they are realized after the conventional cutting operations and they can require some hours. It must be outlined that the fabrication of EDM electrodes in cases of very complex features can be extremely time expensive. Laser sources allows to successfully realize operations like engraving, texturing, pocketing small features and other, with the same accuracy of EDM but with higher manufacturing rate and, for this reason, they are always more often substituting EDM in mold fabrication. Laser sources can also be used like conventional tools in the same machining centers used for obtaining the overall geometry of the molds and for this reason laser removal material can be assimilated to conventional milling machining. Moreover, there is no contact between tool and work pieces and for this reason there are no cutting forces or tool wear. Some examples of laser milling on molds are shown in Fig. 5.1. The lasers normally used are solid state lasers as Nd:YAG and Ytterbium fiber with Q-Switch apparatus that generates giant pulse with frequency ranging from 0 to 150 kHz and a duration in the range of 5 - 80 ns, the average powers are between 20 and 400 W . The laser is delivered to the workpiece with optical fiber and moved with two single-axis galvanometer scanners placed perpendicular to each other [3]. The optimization of laser ablation is quite a complex activity due to the high number of parameters involved and nowadays the most common way of optimizing the process, in industrial environments, is based 141

Chapter 5

Fig. 5.1: Examples of laser micro machining application: molds for plastic bottles, molds for buttons and artistic features

on a ”trial and error” activity. During the last few years, numerous numerical and analytical models have been developed by many authors to simulate laser-matter interaction phenomena in laser ablation. This task involves the understanding of many physical problems such as energy absorption, energy transfer to the lattice, phase transformations in the target material, ablation mechanisms and properties of the induced plasma and its interaction with the incident laser beam.

142

Laser micro machining

5.2 Literature review: physical models In pulsed laser material removal systems, it is very important to understand the physical phenomena that take place during laser ablation process. The pulse duration and the relatively small material removal rates makes an experimental investigation of all factors influencing the process very difficult. Consequently, simulation models are considered important tools for a better understanding and optimization of laser ablation parameters especially when laser milling is applied for machining micro features. In order to control the laser-material interaction and optimize the processes, it is necessary to understand the energy transport process between the laser and the target, the material removal mechanism and the transport process of the laser beam in the laser induced plasma plume. The starting point in all the models in literature is the heat conduction equation solved either analytically or numerically using finite difference schemes or by finite elements methods. The time-dependent temperature distribution through the target material T (t, x, y, z) is governed by the heat-flow equation Eqn. 4.1 with the additional terms of the recession velocity of the ablated front. So the Eqn. 4.1 becomes Eqn. 5.1 for the laser ablation model:       ∂T ∂ ∂T ∂ ∂T ∂ ∂T Cp (T )ρ(T ) = k + k + k + ∂t ∂x ∂x ∂y ∂y ∂z ∂z   ∂z ∂T Cp (T )ρ(T ) + I0 (x, y, t) cos θ(1 − RL )(1 − exp(−αz))SP (x, y) ∂t z≈0 ∂z (5.1) In which: • T is the temperature, K • Cp is the heat capacity, J/kgK • ρ is the density, kg/m3 • α is the absorption coefficient of laser radiation inside the target m−1 • Io (x, y, t) is the laser intensity incident onto the surface of the vaporizing front, W/m2 • t is time, s • SP (x, y) is the spatial distribution of the laser intensity • RL is the reflectivity of the material The first step in laser micro machining is laser absorption. A part of laser beam energy entering the target is absorbed by its surface layer. The incident light is absorbed by electronic transitions in the solid. In a metal or semiconductor the light produces excited electrons which subsequently interact with the atoms. In an insulator the light is absorbed by interband transitions or transitions from impurity levels for photon energies which exceed the energy of the bandgap or the impurity level. Insulating materials are transparent for photons of energy smaller than that of the band gap. The absorbed photons 143

Chapter 5 are almost instantly converted into heat, in a time comparable to the energy relaxation time of crystal lattice, causing surface heating. Energy relaxation time of metal is of the order of magnitude of 10−13 s. The thickness of the surface layer where interaction takes place is comparable to the optical depth of the target material in question 1/α, where α is the optical absorption coefficient. In case of metals, the conduction electrons absorb the laser photons and are excited resulting in an increase of their kinetic energy. For insulators, energy is absorbed via multi photon ionization or impurities and defects leading to generation of free electrons. The excited electrons transfer their energy to the lattice via thermal collisions within a few picoseconds and heating begins with in the optical absorption depth of the material. If the thermal diffusion length, given by lt = 2(Dτ )1/2 , where D is the thermal diffusion constant and τ the pulse length, is smaller than 1/a, the bulk will be heated down to 1/a, independent of the pulse width [4]. However, in metals 1/α