A simple methodology to optimize shot-peening ...

Int J Adv Manuf Technol DOI 10.1007/s00170-016-9532-1

ORIGINAL ARTICLE

A simple methodology to optimize shot-peening process parameters using finite element simulations R. Seddik 1,2 & A. Bahloul 1,2 & A. Atig 1,2 & R. Fathallah 1,2

Received: 3 July 2016 / Accepted: 25 September 2016 # Springer-Verlag London 2016

Abstract Shot peening is a mechanical surface treatment widely used in the automotive and aerospace industries to improve the fatigue performance of metallic parts. This treatment extends the fatigue life by (i) retarding the crack growth due to the induced compressive residual stresses and (ii) inhibiting the crack initiation through the surface work hardening. However, the effect of shot peening on the fatigue performance is mainly influenced by the choice of the process’s parameters. The aim of this research paper is to propose a simple methodology for optimizing the shotpeening surface’s process parameters taking into account the redistribution of the initial shot-peening properties after cyclic loading. For this purpose, the response surface methodology coupled with finite element analysis is implemented. Moreover, the effects of shot velocity, shot diameter, and peening coverage (duration of treatment) and their interactions on the fatigue performance of shot-peened parts subjected to cyclic loadings are discussed. This analysis can be considered as a very helpful tool for designer engineers in shot-peening parameter optimization. Keywords Shot peening . Residual stresses . Plastic deformation . Damage . Fatigue polycyclic . Design of experiments

* R. Seddik [email protected]

1

Laboratory of Mechanics of Sousse, National Engineering School of de Sousse, BP 264 Erriadh, 4023 Sousse, Tunisia

2

University of Sousse, Sousse, Tunisia

1 Introduction Controlled shot peening is a cold surface treatment widely used in the automotive and aerospace industries to improve the fatigue behavior of metallic mechanical components [1, 2]. Compressive residual stresses, work hardening, and superficial defects can be identified as the main changes induced by this process in the near-surface layers. Shot-peening results depend on both the process conditions (shot velocity, shot type, impact angle, coverage, etc.) and the component material. Frequently, shot peening is considered as an effective method for improving the fatigue behavior of mechanical components [3–5]. The beneficial effects of this process are attributed to the compressive residual stress fields and the surface work hardening [3, 4]. Indeed, these induced compressive residual stresses impart crack closure stress, effectively retarding the fatigue crack initiation time and reducing the driving force of the crack propagation. The work hardening allows delaying the crack nucleation stage [6, 7]. However, in few cases, when the shot-peening parameters are not welloptimized (high velocities, large shot, over-peening, etc.), an unfavorable effect, characterized by a significant degradation of the fatigue behavior can be observed [3, 4]. Thus, the improvement of the shot-peened fatigue strength is linked to the balance between the beneficial and detrimental effects of shotpeening treatment on the surface quality. Therefore, the effect of such surface treatment on the fatigue strength of mechanical components depends mainly on the correct choice of the peening operating parameters such as shot size, Almen intensity, peening coverage, impact angle, etc. However, the multiplicity of the process operating parameters makes its control and repeatability very difficult. The selection of optimum shot-peening parameters to achieve an expected level of the

Int J Adv Manuf Technol

fatigue life is always a matter of question in the designer mind. Accordingly, the control of the shot-peening operating parameters appears very substantial. To predict the effect of shot-peening parameters on the fatigue behavior of metallic components, a significant number of interesting works have been published [8–14]. T. Dorr et al. and M. Obata et al. [8, 9] discussed the effect of the shot size and the peening intensity on the surface hardness and surface residual stress. Based on the elastic-plastic numerical approach, Shivpru et al. [10] studied the effect of shot-peening parameters on the induced compressive residual stress. Rodopoulos et al. [11] studied the optimization of the fatigue strength of 2024-T351 aluminum alloy by controlling shotpeening parameters. The obtained results showed that shot peening improves surface hardness and induces a gradient of compressive residual stresses. On other hand, Mahagaonkar et al. [12] studied the effect of the shot type, the exposure time, the nozzle distance, and the pressure and their interactions on the micro-hardness of steel using the full factorial design technique. Recently, A. A. Aymen [13] investigated the influence of some shot parameters on the induced compressive residual stress, micro-hardness, and wettability and corrosion behavior of AISI 316L steel. Later, Yong-Seog Nan [14] et al. studied the effects of four shot-peening parameters, nozzle distance, pressure, impact angle, and exposure time, on the compressive residual stress and micro-hardness of an aluminum 2124T851. They used the Box-Behnken design to estimate the empirical models in terms of the selected shot-peening parameters. Although shot-peening treatment can improve significantly the fatigue behavior of materials, the initial shot-peened surface proprieties such as compressive residual stress cannot be directly used for fatigue analysis. In fact, the initial shotpeening surface conditions can undergo a significant change during life time [15–20]. The main change takes place in the first few applied cycles. This quasi-static stage is called elastic shakedown step due, principally, to a rebalance of the applied stress loading to the initial induced residual stresses, which is followed by further gradual relaxation during the life time due to cyclic softening [19]. When the applied tensile stress was approaching the yield strength, the relaxation was drastic and distinct. So, it is very important to predict this first stage of relaxation which is more significant when the loading level is important. In order to reach this objective, numerous empirical models were developed from experimental investigation results [19, 21–24]. Nevertheless, these models cannot take into account the influence of all parameters. For this reason, different FE models have been proposed [18, 25–28]. The advantage of these models is to simulate the cyclic-hardening behavior of the surface layers which represents the main phenomenon of residual stress relaxation.

Therefore, the integration of shot-peening initial surface properties in the fatigue strength predictive approach, without considering their redistribution during cyclic fatigue loading, leads to inaccurate results for the reliability of mechanical components. Indeed, the change of the initial shot-peening surface properties due to the cyclic loading can reduce the beneficial effects of shot-peening treatment. However, the majority of the proposed studies discussed the optimization of shot-peening parameters without taking into account the change of the initial shot-peening surface properties during the applied cyclic loading. This paper aims to optimize the after-fatigue shot-peening surface proprieties: compressive residual stress, plastic deformation, and superficial damage variable, by the controlling of shot-peening operating conditions. The design of experiments with three levels is implemented to determine and analyze the effect and the interaction between the different parameters and their influence on the shot-peening stabilized surface properties. This approach will be very useful for designers to choose the optimal shot-peening operating conditions taking into account the after-fatigue changes of the initial shot-peened surface proprieties. The principal steps of the suggested approach can be summarized as follows: (i) Development of an improved 3D random dynamic FE model based on the previous works of Frija [29] and H.Y. Miao [30], by including the repetitive random process of the shot impacts and the cyclic work-hardening behavior of the treated material in order to characterize as better as possible the complex cyclic surface work-hardening mechanisms during the peening process and after the first applied loading cycles. (ii) The second step consists in simulating the first applied loadings on the pre-stressed shot-peened target by means of a FE method, in order to predict the first elastic shakedown step. (iii) Generating of DoE methodology and launching of numerical simulations. (iv) Optimizing the shot-peening conditions.

2 Theoretical background: Response Surface methodology Response surface (RS) methodology is an experimental technique developed to find the optimal response within specified ranges of the factors [31, 32]. These designs are capable of fitting a second-order prediction polynomial for the response based on the results obtained by DOE. The quadratic response surface has the form:


y ¼ b0 þ

n X

n−1 n X X

bii X2i þ

i¼1

bij Xi Xi þ ε

ð1Þ

i¼1 j¼iþ1

where ε represents the model error; bi, bii, and bij are the regression coefficients; and n is the number of parameters. Equation (1) can be expressed in matrix notation as Y ¼ X *B þ ε

ð2Þ

where Y is the vector of observations, ε represents the vector of errors, X is the matrix of the values of the design variables, and B is the vector of tuning parameters. The regression coefficients are calculated by the leastsquares regression: −1 B̂ ¼ X T X X T Y

ð3Þ

Fig. 1 a 3D shot-peening finite-element model; b extracted part; c mesh

Then, the fitted regression is given by Ŷ ¼ X B̂

ð4Þ

The goodness of fit can be evaluated by the coefficient of determination given by 2 X yi − yî i R2 ¼ 1− X

yi − ̅ yi

2

ð5Þ

i

where yi, yî , and ̅ yi are the observed value, the approximated value, and the mean of observed values, respectively. The response surface model is generally collected using the design of experiments (DoE) procedure [33, 34].


3 FE shot-peening process model The shot-peening FE simulation has been carried out using the FE commercial code ABAQUS 6.10 [35]. An explicit solver has been used to take into consideration the shot-peening dynamic effects [35]. In order to automatically generate the model with particular inputs (shot-peening conditions, target constitutive model, boundary conditions, type of shots…), a numerical code is developed in the basis of Python script. The FE analysis is established by employing a damping coefficient [36] in order to reduce stress oscillations and to avoid uncontrolled post-impact oscillations in the FE model [36]. The proposed 3D model allows predicting the indepth evolution of compressive residual stress, plastic deformation, the surface integrity, and micro-geometrical imperfections. 3.1 Target geometry and boundary conditions The target component has been modeled as a rectangular body with a width of 2 mm, a length of 2 mm, and a height of 5 mm (Fig. 1). It was meshed by means of eight-node linear brick solid elements with reduced integration [35]. In order to avoid the border effects and to improve the results’ precision, the target consists of two square regions in the X–Yplane and two layers in the depth direction (Z-direction) [37]. Region 1 is the total target. Region 2, with dimensions 1 × 1 × 0.3 mm3, is the treated region. To improve the accuracy of the FE solutions, a refiner mesh has been used in the treated region. In fact, different mesh sizes are used to investigate mesh sensitivity for the treated region. As the mesh size increases, the obtained results become more and more stable and the gap between experimentalX1

3.2 Material model of shot peening The shot-peening loading is assumed to be a particular and complex cyclic loading [38]. Then, the appropriate shotpeened behavior law of the treated material has to consider the effects of the cyclic loading and the type of the cyclic work hardening: isotropic and kinematic. In this context, the nonlinear isotropic/kinematic hardening model [39, 40] coupled with damage law is used. This plasticity model is capable of characterizing the material behavior during cyclic loading considering the Baushinger effect, ratcheting, mean stress relaxation, and cyclic hardening. 3.2.1 Isotropic-kinematic constitutive model In this model [39, 40], the yield criterion of Von Mises is defined as f σ; X ; R ¼ J 2 σ− X −R−σy0 ≤ 0 ð6Þ ¼ ¼ ¼ ¼ The nonlinear hardening component X , which describes ¼ the translation of the yield surface in the stress space through the back stress, is defined by p 2 dX ¼ C dε −γ X dp ¼ ¼ ¼ 3

2X1

ð7Þ

X1

Y1

Fig. 2 Random position of the shot centers

numerical compressive residual stress profiles increases. A finer mesh with small elements of 0.01 mm × 0.01 mm × 0.01 mm provides stable results in good correlation with the experimental ones. For the boundary condition, the bottom surface of the target has been fixed.

Y1

2Y1

Randomly shot centers


The isotropic hardening component R describes the change of the equivalent stress defining the size of the yield surface as a function of plastic deformation: dR ¼ bðQ−RÞdp ð8Þ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi where dp ¼ 23 dεp : dεp indicates the increment of the ¼ ¼¼ equivalent plastic strain and dεp is the plastic flow law, which ¼ is defined as p

dε ¼ λ ¼

δf δ¼ σ

ð9Þ

The coefficients depending on the material are the initial yield stress σy0 ; two coefficients to represent the evolution of the isotropic hardening, b and Q; and two coefficients to represent the evolution of the kinematic hardening, C and γ. 3.2.2 Damage The shape and the size of the shot-peening defects can be considered as discontinuities of the material at the first affected layers 3. To predict the shot-peening superficial damage, Lemaitre and Chaboche’s [41] three-dimensional ductile plastic model of damage has been used in its integrated form. It is expressed as follows: " ! # Dc 2 σH 2 D≅ p ð1 þ υÞ þ 3ð1−2υÞ −εD ð10Þ εR −εD σeqVM 3 where ν is Poisson’s ratio, σH is the hydrostatic stress of the applied stress tensor, σeqVM is the Von Mises equivalent stress, Fig. 3 Mechanical cyclic loading modeling

Table 1 Material

Mechanical properties [45–46] E (GPa) σy(MPa) υ

C (MPa) γ

AISI 316L 196

220

0.29

30,000

AISI 2205

632

0.3

192,777

192.5

Q(MPa) b

60 150 575

-23

1 13

εD is the initial critical deformation for damage, εR is the deformation at rupture, Dc is the critical damage value, and p is the cumulated plastic strain. In the present study, the damage parameter is calculated from the degree of cumulus of plastic strain. The elasticplastic calculation was made incrementally using the Von Mises criterion. After each increment, the damage variable D is determined, and Young’s modulus E is updated as follows: E tþΔt ¼ E t ð1−Dt Þ

ð11Þ

where Et + Δt is Young’s modulus at the instant t + Δt and Et and Dt are respectively Young’s modulus and the damage value at the instant t. 3.3 Shot stream impact simulation The shot stream impacts randomly the target specimen with a large number of identical shots at normal incidence angle (Fig. 2). The following initial parameters have been similarly assigned to all shots: diameter D, velocity in Z-direction V, impact angle, and initial position. The friction between the shots and the treated surface has been characterized by the Coulomb friction model.

Int J Adv Manuf Technol Table 2

Damage parameters [45–46]

Material

εR

εD

Dc

AISI 316L

0.8

0.02

0.5

AISI 2205

0.75

0.02

0.8

F f ¼ μ Fn

ð12Þ

where Ff is the friction force, Fn is the normal force, and μ is the friction coefficient. The friction coefficient μ, which is difficult to identify experimentally, is determined by calibration of the finite element calculated and the X-ray diffraction analyzed residual stress profiles. The number of shots used in our proposed 3D random dynamic FE model and their random locations are related to the shot size, the representative impacted surface and the peening duration. 3.4 The micro-geometrical imperfections Shot-peening surface treatment is generally aimed at enhancing the resistance of metallic mechanical components. However, in many cases, there is a risk of deteriorating or changing the integrity of the treated surface by inducing superficial defects such as scales, micro cracks, overlaps, and surface roughness imperfections [3, 4], which can induce significant decrease of fatigue strength [42, 43]. According to the standard ISO 4287 [44], the surface finish imperfections are classified into three classes: the surface form errors, the

Fig. 4 Steady loops of the strain–stress law of the AISI 316L steel under strain-controlled tests(Rε = − 1): a Δεt/2 = 0.3%, b Δεt/2 = 0.5%, c Δεt/2 = 0.7%, and d Δεt/2 = 1.0% [45]

waviness including the more widely spaced deviations of a surface from its nominal shape, and the roughness and metal wrenching. In this study, we are only interested in the second case. In fact, the second-order defects are considered as a succession of shot-peening indentations. The typical indentation geometrical defect is assumed to have a penetration depth equal to the mean waviness Wt defined as the maximum peak-to-valley height of the leveled waviness profile. The numerical mean waviness Wt was assessed using the vertical displacements of the surface nodes.

4 Modeling of the first applied loading cycles on the shot-peened target The change of the compressive shot-peening residual stresses during fatigue loading depends principally on (i) the applied loading and (ii) the cyclic mechanical properties of the treated material. Two stages have been observed: (i) a significant relaxation of the residual stresses during the first cycles, in which the relaxation is proportional to the magnitude of the applied loading, and (ii) The residual stresses decrease linearly as a function of Ln (N) (where N is the number of cycles) and the rate of the evolution is proportional to the amplitude of loading; in this second stage, the slow relaxation is due principally to the evolution of the mechanical properties under cyclic loading. In order to determine the stabilized surface properties after the first few applied loading cycles (i.e., first stage of residual


stress relaxation), a simulation of cyclic loading has been carried out on the pre-stressed shot-peened target. The shotpeened specimen was subjected to tension loading, uniformly distributed on one of the X-normal vertical faces. The opposite X-normal vertical face was fixed in the X-direction (i.e., the displacement in the X-direction is constrained) (Fig. 3). The Abaqus load function is used to introduce the amplitude, the type, and the number of cycles of the applied loading. To verify the effect border on the stress distribution, the applied stress tensor is compared to the stress tensor obtained in the central region of the nontreated target after cyclic loading. Coherent results have been obtained. The number of the applied cycles must lead to quasi-stabilized residual stresses’ profiles. The relaxed residual stresses, plastic deformations, damage variable, and mean waviness have been determined.

5 Applications As discussed above, the proposed approach can be used to optimize the shot-peening operating parameters, taking into account the effect of the first applied cycles on the initial induced shot-peening surface conditions, for all kinds of metal materials. In this study, an application has been carried out on AISI 316L steel and AISI 2205. The mechanical proprieties [45, 46] (Table 1) and the damage parameters (Table 2) [45, 46] of such materials have been largely discussed in the open literature [45, 46]. The stress strain curves of AISI 316L and AISI 2205 materials are presented by Figs. 4 and 5 [45, 46], respectively.

Fig. 5 Monotonic and cyclic behavior of the material AISI 2205 ( ε⋅ ¼ 0:00085 s−1 ) [46]

Table 3

Input factors and their levels

Parameter

Shot size (mm) Shot velocity (m/s) Peening coverage (%) Load (MPa)

Notation

level −1

0

+1

D V C

0.2 40 100

0.4 60 200

0.6 80 300

L

1 2 σy

σy

3 2 σy

Moreover, the in-depth residual stress profiles and the FWHM have been analyzed by the X-ray diffraction method [13]. 5.1 Application 1: validation of the FE shot-peening model In order to validate the accuracy of the proposed finite-element shot-peening model, the shot-peening operating conditions used by A. A. Ahmed’s experimental investigations [13] for the case of AISI 316L are considered in this application: (i) ceramic shots with 0.8 mm of size, (ii) shot velocity equal to 40 ms−1 (corresponds to the Almen intensity 0.22 mmA), (iii) peening coverage of 100 %, and (iv) impingement angle equal to ≃90°. The μ friction coefficient between the shots and the treated surface during the contact is estimated to be equal to 0.1. This coefficient, which is difficult to identify experimentally, is determined by calibration of the finite elements calculated and the X-ray diffraction analyzed residual stress profiles. The n material parameter, which is identified using the initial and ultimate stress strain values, is closer to 0.043.


a

[13]

b 400

AISI 2205 (S230, 40m/s, 100%, 90°)

Residual Stress (MPa)

200 0

Depth (mm) 0

0.1

0.2

0.3

0.4

0.5

0.6

-200 -400 -600 -800

[46]

-1000

Fig. 6 Calculated and analyzed X-ray residual-stress profiles in-depth of shot-peened: a for AISI 316L [45]; b for AISI 2205 [46]

For the case, the shot-peening operating conditions used by Pedro Sanjurjo’s experimental investigations [46] for the case

of AISI 2205 are considered in this application: (i) shot type S230, (ii) shot velocity equal to 40 ms−1 (corresponds to the


Almen intensity 0.22 mmA), (iii) peening coverage of 100 %, and (iv) impingement angle equal to ≃90°. The μ friction coefficient between the shots and the treated surface during the contact is estimated to be equal to 0. 2. This coefficient, which is difficult to identify experimentally, is determined by calibration of the finite elements calculated and the X-ray diffraction analyzed residual stress profiles. The n material parameter, which is identified using the initial and ultimate stress strain values, is closer to 0.3. In the present work, the velocity of the shot is assumed to be constant during the impact. Its value has been determined using the available curves [3, 4] giving the Almen arc height with shot velocity for a specific shot. The developed FE model is validated by comparing the averaged in-depth compressive residual stresses over the treated zone with the experimental results available in open literature. 5.2 Application 2: optimization of shot-peening conditions using FE analysis and RS methodology The design of experiments (DOE) is an interesting tool to engineering problem-solving. It represents a systematic approach to understand the response surface evolution of various industry products and process as a function of their input parameters. The DOE procedure allows studying not only the effect of changing the level of each parameter but also their interaction on the desired response. All possible combinations can be treated. In the present study, four parameters and their significance were investigated which are shot size, shot velocity, impact angle, and the applied load level, aiming at linking their effects to the fatigue performance after the change of the surface conditions during the first applied loading cycles. Each factor was tested at three different levels, highest (1), middle (0), and lowest (−1). Their respective levels in actual and coded values are shown in Table 3.

Fig. 7 Appearance of the shot-peened strip for AISI 316L (Pa)

Indeed, the design required 81 runs with 3 levels. The used experiment matrix is established following a central composite design for the four studied factors (shot size, shot velocity and impact angle, load level). The responses corresponding to the different studied combination cases of the experiment matrix generated by the DOE with RS methodology are analyzed with Minitab® V14 statistical software.

6 Results and discussion 6.1 Validation of the FE shot-peening model Figure 6 shows a comparison between the investigated X-ray diffraction and the computed compressive residual stress profiles obtained in-depth of the peened AISI 316L part. A satisfactory correlation between the computed results (Fig. 7) and the experimental values is observed, particularly in the first outer layers where the X-ray analyses are generally more precise than in the deeper layers. The calculated in-depth Von Mises’s plastic deformation profile induced by shot peening is presented in Fig. 8. It shows a qualitative agreement with the full width at half maximum (FWHM) of the X-ray diffraction peak profile [13]. Figure 9 shows the effect of the peening duration on the second-order defects. It is well observed that the waviness parameter increases with the peening duration. These results are coherent with physical observations. Comparing with the experimental results obtained by the X-ray diffraction analysis [13], the 3D dynamic random FE model proposed in the present study shows a good correlation for predicting the initial compressive residual stress profiles for the AISI 316L material. This result proves the plasticity model’s performance (i.e., nonlinear combined isotropickinematic hardening) for describing the material behavior of the affected layers, submitting to the complex shot-peening loading. This cyclic behavior law can be considered as an


Von Mises equivalent plasc strain

0.35

AISI 316L ( 0.8, 40m/s, 100%, 90°)

0.3 0.25 0.2 0.15 0.1 0.05 0

0

0.1

0.2 0.3 Depth (mm)

0.4

0.5

Fig. 8 Von Mises equivalent plastic strain profiles in-depth of shotpeened AISI 316L

the longitudinal (σxx) direction than in the transversal (σyy) direction. These obtained results are in good agreement with those published in the literature [14–17]. It is noted that the residual stress relaxation is more important in the outer layers than in the deep ones. For example, for two different depths having the same initial compressive residual stress value, the observed relaxation is higher for the outer layer (Fig. 11). This observation can be explained by the nonuniformity of the in-depth cumulated plastic deformations and the damage variable; both of them are much more significant in the outer layers. 6.3 Optimization of shot-peening conditions 6.3.1 Optimization

interesting and effective choice to predict as much as possible the change of the initial shot-peening surface conditions (compressive residual stress, plastic strain and damage) with the peening duration. Furthermore, it is worth noticing that the suggested model has the advantage to predict as well the plastic strain damage and waviness parameter variables in-depth of the shot-peened part which are very important on the fatigue performance of the treated parts. 6.2 Relaxation of compressive residual stress Figure 10 shows the change of the residual stress profiles, in the X-direction (σxx) and in the Y-direction (σyy) in-depth of the shot-peened part after the first applied cycles (30 cycles) of purely alternate X-direction tension (Rσ = − 1) for different loading amplitude levels (σa ¼ 12 σy , σa = σy, and σa ¼ 32 σy ). It is observed, here, that the residual stress relaxation depends on the applied loading level and its absolute value is greater in

The impact of each shot-peening parameter can be presented clearly by means of the response graphs. These graphs show the change in the response, when the parameters change their level from −1 to level 1. The response graphs for the studied shot-peening parameters are presented in Fig. 11. Figure 11a shows the main effect of input factors on the superficial compressive residual stress. All the selected shotpeening parameters have a significant effect on the superficial compressive residual stress. It is observed that the amplitude of the applied loading factor has the highest significant effect. In the other side, the shot velocity has a nonlinear effect on the superficial compressive residual stress in which its highest intensity is obtained for the level 0 (correspond to 60 m/s). On other hand, the obtained results show also that the superficial compressive residual stress increases with the increasing of the shot velocity. However, if this velocity exceeds the

Fig. 9 Vertical displacement of the surface nodes after shot-peening treatment for AISI 316L material: a peening coverage 100 %, b peening coverage 200 %, c peening coverage 300 %

Int J Adv Manuf Technol Fig. 10 Relaxation of residual stress after tension cyclic loading for AISI 316L material: a longitudinal 11-direction; b transversal 22-direction

optimal level (shot velocity limit value), the induced residual stresses relax and the damage variable increases significantly. The obtained result can be explained by the important accumulated energy at the superficial affected layers caused by the excessive impacts. As a result, a deterioration of the fatigue behavior can be observed for shot velocities greater than the limit value. Figure 11b shows the main effect of the input factors on the superficial damage variable generated by shot-peening process. It can be deduced that the shot diameter, shot velocity, and peening duration have a significant effect on the superficial damage arising from the shot-peening successive impacts. However, the level of applied loading has no very notable effect. The obtained results reveal that (Fig. 11), if the peening coverage exceeds the optimal level, a case of over-peening

will be detected, resulting in critical local plastic deformations which can encouraged the crack initiations. Figure 12 illustrates the interaction effect plots between the input factors on the induced residual stress and the superficial damage variable. It is possible to visualize graphically the importance of an interaction effect by comparing the relative slope of the lines. It is observed that all the combination interactions induce an important effect on the superficial compressive residual stress and the superficial damage variable, essentially the interaction between the shot diameter and the shot velocity. In addition, the contour plots of the residual stress and the superficial damage in terms of different input parameters are presented to illustrate the variation of both residual stress and superficial damage variable induced by the shot-peening process as a function of combined

Int J Adv Manuf Technol Fig. 11 Main effect plot after tension cyclic loading, for the case of AISI 316L material, on a residual stress and b damage variable

a Data Means C (%)

D(mm)

V(m/s)

load(MPa)

100

Mean

0

-100

-200

-300 -1

0

1

-1

0

1

-1

0

1

-1

0

1

b Main Effects Plot for Damage (z=0) Data Means C (%)

D(mm)

V(m/s)

load(MPa)

0.6

Mean

0.5

0.4

0.3

0.2

0.1 -1

0

1

parameters. Three contour plots of the superficial residual stress and the superficial damage variable are presented, corresponding to the interactions of “peening coverage” × “shot diameter,” “peening coverage” × “shot velocity,” and “shot velocity” × “shot diameter.” From Fig. 13, it can be seen that the maximum superficial residual stress is obtained for a peening coverage of 100 %, a small shot diameter, and a shot velocity closer to the mean value. Figure 14 shows that a small shot diameter, the mean

-1

0

1

-1

0

1

-1

0

1

velocity, and a peening coverage of 100 % decrease the superficial damage. In this work, we have two responses that need to be optimized: superficial damage variable and superficial compressive residual stress. The superficial compressive residual stress should be maximized in its absolute value, and the superficial damage variable should be minimized. The desirability function approach is one of the most commonly used methods to simultaneously optimize multiple responses. It

Int J Adv Manuf Technol Fig. 12 Interaction effect plot after tension cyclic loading, for the case of AISI 316L material: a residual stress and b damage variable

a Interacon Plot for S11 (z=0) Data Means -1

0

1

-1

0

1

0

C (%)

-200

C (%) -1 0 1

-400

D(mm) -1 0 1

0

D(mm)

-200 -400

0

V (m/s)

-200

V (m/s) -1 0 1

-400

load(MPa) -1 0 1

0

load(MPa)

-200 -400 -1

0

1

-1

0

1

b Interacon Plot for Damage (z=0) Data Means -1

0

1

-1

0

1 0.8

0.4

C (%)

C (%) -1 0 1

0.0

0.8

0.4

D(mm) -1 0 1

D(mm)

0.0

0.8

0.4

V (m/s)

V (m/s) -1 0 1

0.0

0.8

0.4

load(MPa)

load(MPa) -1 0 1

0.0 -1

0

1

consists of transforming a multi-response problem into single response by means of mathematical transformations. Indeed, for each individual response, a desirability function between 0 and 1 noted di is constructed. It is obtained by specifying the goals: minimize, target, or maximize the response. Then, the overall desirability function, which is defined as the weighted average of the individual desirability functions, should be maximized. Using the Minitab response

-1

0

1

surface optimizer function, the optimal parameter combination to maximize the superficial residual stress in its absolute value and minimize the damage variable is a shot velocity distance of 62 m/s, shot size of 0.2 mm, and peening coverage of 100 %, as shown in Fig. 15 for the case of the treated part submitted to cyclic loading. However, for the case of the shotpeened part without the application of cyclic loading, the optimal parameter combination is a shot velocity distance of 67,


a

Contour Plot of Damage (z=0) vs D(mm); C (%) Contour Plot of S11 (z=0) vs D(mm); C (%)

1.0 Damage (z=0) < 0.1 0.1 – 0.2 0.2 – 0.3 0.3 – 0.4 0.4 – 0.5 0.5 – 0.6 > 0.6

1.0

D(mm)

0.5

0.0

Hold Values V (m/s) 0 load(MPa) 0

0.5

D(mm)

S11 (z=0) < -300 -300 – -275 -275 – -250 -250 – -225 -225 – -200 -200 – -175 -175 – -150 > -150

0.0

Hold Values V (m/s) 0 load(MPa) 0

-0.5 -0.5

-1.0 -1.0

-1.0 -1.0 -0.5

0.0

0.5

-0.5

1.0

0.0

0.5

1.0

C (%)

C (%)

Contour Plot of Damage (z=0) vs V (m/s); C (%)

b

1.0 Damage (z=0) < 0.15 0.15 – 0.27 0.27 – 0.39 0.39 – 0.51 0.51 – 0.63 0.63 – 0.75 > 0.75

Contour Plot of S11 (z=0) vs V (m/s); C (%) 1.0

V (m/s)

0.5

Hold Values D(mm) 0 load(MPa) 0

0.0

0.5

V (m/s)

S11 (z=0) < -200 – -170 – -140 – -110 – -80 – -50 > -50

-200 -170 -140 -110 -80

0.0

Hold Values D(mm) 0 load(MPa) 0

-0.5 -0.5

-1.0 -1.0 -1.0 -1.0

-0.5

0.0

0.5

-0.5

0.0

0.5

1.0

C (%)

1.0

C (%)

Contour Plot of Damage (z=0) vs V (m/s); D(mm) 1.0

c

Damage (z=0) < 0.2 0.2 – 0.3 0.3 – 0.4 0.4 – 0.5 0.5 – 0.6 0.6 – 0.7 > 0.7

Contour Plot of S11 (z=0) vs V (m/s); D(mm) S11 (z=0) < -250 – -210 – -170 – -130 – -90 – -50 > -50

-250 -210 -170 -130 -90

V (m/s)

0.5

Hold Values C (%) 0 load (MPa) 0

0.0

0.5

V (m/s)

1.0

0.0

Hold Values C (%) 0 load(MPa) 0

-0.5

-0.5

-1.0 -1.0

-0.5

0.0

0.5

1.0

D(mm) -1.0 -1.0

-0.5

0.0

0.5

1.0

D(mm)

Fig. 13 Contour plot of residual stress in terms of different input parameters D, V, and C for the case of AISI 316L material

Fig. 14 Contour plot of damage variable in terms of different input parameters D, V, and C for the case of AISI 316L material

Int J Adv Manuf Technol Fig. 15 Simultaneous optimization of damage variable and residual stress after tension cyclic loading for the case of AISI 316L material

Optimal High D: 0.9287 Cur Predict Low

C (%) 1.0 [-1.0] -1.0

D(mm) 1.0 [-1.0] -1.0

V (m/s) 1.0 [0.1717] -1.0

load(MPa L (MPa) 1.0 [-1.0] -1.0

Composite Desirability D: 0.9287

Damage ( Minimum y = 0.0603 d = 0.98387

S11 (z=0 Minimum y = -462.6667 d = 0.87668

shot size of 0.2 mm, and peening coverage of 100 %, as shown in Fig. 16. From Fig. 15, it can be observed that, when (shot velocity, shot size, peening coverage) = (62 m/s, 0.2 mm, 60, 100 %), the estimated compressive residual stress is −462 MPa with individual desirability d = 0.8766 and damage variable equal to 0.06 with d = 0.9838. The overall desirability is D = (0. 8766 + 0.9838)/2 = 0.9287. The estimated compressive residual stress and the damage variable are considered to be satisfactory.

Fig. 16 Simultaneous optimization of damage variable and residual stress before cyclic tension cyclic loading for the case of AISI 316L material

Optimal High D: 0.9150 Cur Predict Low

Composite Desirability D: 0.9150

Damage ( Minimum y = 0.0692 d = 0.97501

S11 (z=0 Minimum y = -924.4817 d = 0.85874

This difference between the optimal shot-peening operating parameter before and after cyclic loading can justify the importance of taking into account the redistribution of the initial shot-peening surface properties (compressive residual stress, damage variable, plastic strain, surface imperfections, etc.) for the optimizing of shot-peening conditions. So it should be taken into account the redistribution of the initial shot-peening surface properties to optimize the shot-peening operating parameters.

C(%) 1.0 [-1.0] -1.0

D(mm) 1.0 [-1.0] -1.0

V(m/s) 1.0 [0.3535] -1.0


6.3.2 Confirmation tests

3.

To ensure the reproducibility of the parameter combination obtained from the finite element results, a confirmation test is carried out under the optimal shot-peening operating parameters (shot velocity, shot size, peening coverage) = (62 m/s, 0.2 mm, 60, 100 %). Under this optimal condition, the superficial compressive residual stress is equal to −458 MPa and the damage variable is equal to 0.07.

4.

5.

6.

7.

7 Conclusion 8.

The obtained results can be summarized as follows: –

–

–

–

An improvement 3D random dynamic model has been proposed to simulate the shot-peening process via the FE method. Such improvement consists in including the repetitive random process of the shot impacts and the cyclic work-hardening behavior coupled to the damage of the treated material. The compressive residual stress, the plastic strain, the waviness parameter, and the damage variable in-depth of the affected layers, for different shotpeening conditions, can all be predicted using our proposed model. The second step of our approach consists in modeling the first stage of residual stress relaxation (the elasticshakedown stage) for the case of purely alternate tension loading. It leads to predicting the change of the initial shot-peening surface properties (compressive residual stress, plastic strain, damage) after the first applied fatigue loading cycles. In the third step of our approach, a simple methodology for optimizing the shot-peening surface’s process parameters taking into account the redistribution of the initial shot-peening properties after cyclic loading is proposed. The response surface methodology coupled with finite element analysis is implemented in this purpose. The cases of over-peening due to high velocity or/and excessive treatment duration are clearly noticed. This approach is very interesting for engineering designers to predict the fatigue behavior of mechanical shot-peened components and to better discuss the effect of shotpeening parameters on the fatigue behavior of metal parts.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

21.

References 1. 2.

Society of Automotive Engineers Handbook, SAE Publications, 1964. O’Hara P (1984) Developments in the shot peening process. Mater Des 5(4):161–166

22.

23.

Fathallah R, Sidhom H, Braham C, Castex L (2003) Effect of surface properties on high cycle fatigue behavior of a shot peened ductile steel. Mater Sci Technol 19:1050–1056 Gentil B, Desvignes M, Castex L (1987) Analyse des surfaces grenaillées: Fissuration, rugosité et contraintes résiduelle. Matériaux et Techniques 75:493–497 Eleiche AM, Megahed MM, Add-allah NM (2001) The shot peening effect on the HCF behavior of high-strength martensitic steels. J Mater Process Technol 113:502–508 De los Rios ER, Trull M, Levers A (2000) Modelling fatigue crack growth in shot peened components of Al 2024-T351. Fatigue Fract Eng Mater Struct 23:709–716 Guagliano M, Vergani L (2004) An approach for prediction of fatigue strength of shot peened components. Eng Fract Mech 71: 501–512 Dorr T, Hilpert, Beckmerhagan MP, Kiefer A, Wagner L (1999) Influence of shot peening on fatigue performance of high-strength aluminum-and magnesium alloys. Proceedings of the ICSP-7 conference, Warsaw Obata. M, Sudo. A (1993) Effect of shot peening on residual stress and stress corrosion cracking for cold worked austenitic stainless steel. Proceedings of the ICSP-5 conference, Oxford Shivpuri R, Cheng X, Mao Y (2009) Elasto-plastic pseudo-dynamic numerical model for the design of shot peening process parameters. Mater Des 30:3112–3120 Rodopoulos CA, Curtis SA, de los Rios ER, SolisRomero J (2004) Optimisation of the fatigue resistance of 2024-T351 aluminium alloys by controlled shot peeningmethodology results and analysis. Int J Fatigue 26:849–856 Mahagaonkar SB, Brahmankar PK, Seemikeri CY (2008) Effect of shot peening parameters on microhardness of AISI 1045 and 316L material: an analysis using design of experiment. Int J Adv Manuf Technol 38:563–574 Ahmed AA, Mhaede M, Basha M, Wollmann M, Wagner L (2015) The effect of shot peening parameters and hydroxyapatite coating on surface properties and corrosion behavior of medical grade AISI 316L stainless steel. Surface & Coatings Technology 280:347–358 Nam YS, Jeong YI, Shin BC, Byun JH (2015) Enhancing surface layer properties of an aircraft aluminum alloy by shot peening using response surface methodology. Mater Des 83:566–576 Torres MAS, Voorwald HJC (2002) An evaluation of shot peening residual stress and stress relaxation on the fatigue life of AISI 4340 steel. Int J Fatigue 24:877–886 Dalaei K, Karlsson B, Svensson LE (2011) Stability of residual stresses created by shot peening of pearlitic steel and their influence on fatigue lifetime. Mater Sci Eng A 5282:1008–1015 Denkena B, Köhler J, Breidenstein B, Mörke T (2011) Elementary studies on the inducement and relaxation of residual stress. Procedia Eng 19:88–93 Liu J, Yuan H (2010) Prediction of residual stress relaxations in shot-peened specimens and its application for the rotor disc assessment. Mater Sci Eng A 527:6690–6698 Zaroog OS, Aidy A, Sahari BB, Zahari R (2011) Modeling of residual stress relaxation of fatigue in 2024-T351 aluminium alloy. Int J Fatigue 33:279–285 Xie L, Wen Y, Zhan K, Wang L, Jiang C, Ji V (2016) Characterization on surface mechanical properties of Tie6Ale4V after shot peening. J Alloys Compd 666:65–70 Zhuang WZ, Halford GR (2001) Investigation of residual stress relaxation under cyclic load. Int J Fatigue 23:31–37 Seungho H, Lee T, Shin B (2002) Residual stress relaxation of welded steel components under cyclic load. Mater Technol (Steel Res) 73:414–420 Maximov JT, Duncheva GV, Mitev IN (2009) Modeling of residual stress relaxation around cold expanded holes in carbon steel. J Constr Steel Res 65:909–917

Int J Adv Manuf Technol 24.

Zaroog OS, Aidy A, Sahari BB, Zahari R (2009) Modeling of residual stress relaxation: a review. J Sci Technol 17:211–218 25. Arbab Chirani, S (1998) Méthodologie pour la prise en compte des contraintes résiduelles dans un calcul prévisionnel de durée de vie en fatigue de pièces en aluminium. PhD thesis. France: Université de Technologie de Compiègne 26. Gong K, Milley A, Lu, J (2001). Design tool on fatigue for 3D components with consideration of residual stresses. SAE 2001 World Congress, Fatigue Research & Applications (Part A&B), Detroit, MI, USA, 1–6 27. Smith DJ, Farrahi GH, Zhu WX, McMahon CA (2001) Experimental measurement and finite element simulation of the interaction between residual stresses and mechanical loading. Int J Fatigue 23:293–302 28. Boyce BL, Chen X, Peters JO, Hutchinson JW, Ritchie RO (2003) Mechanical relaxation of localized residual stresses associated with foreign object damage. Mater Sci Eng A349:48–58 29. Frija M, Hassine T, Fathallah R, Bouraoui C, Dogui A (2006) FEM modelling of shot peening process: prediction of the compressive residual stresses, the plastic deformations and the surface integrity. Mater Sci Eng 426:173–180 30. Miao HY, Larose S, Perron C, Lévesque M (2009) On the potential applications of a 3D random finite element model for the simulation of shot peening. Adv Eng Softw 40:1023–1038 31. Myers RH, Montgomery DC (2002) Response surface methodology, 2nd edn. Wiley, New York 32. Kartal ME, Basaga HB, Bayraktar A (2011) Probabilistic nonlinear analysis of CFR dams by MCS using response surface method. Appl Math Model 35:2752–2770 33. Zahraee SM, Hatami M, Yusof NM, Rohani M, Ziaei F (2013) Combined use of design of experiment and computer simulation for resources level determination inconcrete pouring process. Jurnal Teknologi 64(1):43–49 34. Montgomery D (2009) Basic experiment design for process improvement statistical quality control. Wiley, USA 35. ABAQUS Theory Manual (2011) Version 6.10. Hibbitt, Karlsson and Sorensen Inc, USA

36.

Taehyung K, Hyungyil L, Minsoo K, Sunghwan J (2012) A 3D FE model with plastic shot for evaluation of equi-biaxial peening residual stress due to multi-impacts. Surf Coat Technol 206: 3981–3988 37. Gariépy A, Larose S, Perron C, Lévesque M (2011) Shot peening and peen forming finite element modelling—towards a quantitative method. Int J Solids Struct 48:2859–2877 38. R. Fathallah (1994). Modélisation du Procédé de Grenaillage: Incidence des Billes et Taux de Recouvrement. PhD thesis ENSAM Paris 39. Armstrong, P.J and Frederick, C.O (1966). A mathematical representation of the multi-axial Bauschinger effect. Technical Report RD/B/N731, CEGB 40. Chaboche J-L (1977). Sur l’utilisation des variables d’état interne pour la description de la viscoplasticité cyclique avec endommagement. In Problèmes Non Linéaires de Mécanique, Symposium Franco-Polonais de Rhéologie et Mécanique, 137–159 41. Lemaitre J, Chaboche, J.L (2002). Mécanique des matériaux solides. Dunod (Edition 2), ISBN 2 10 005662X 42. Sidhom N, Laamouri A, Fathallah R, Braham C, Lieurade H (2005) Fatigue strength improvement of 5083 H11 Al-alloy T-welded joints by shot peening: experimental characterization and predictive approach. Int J Fatigue 27:729–745 43. Wagner L (1999) Mechanical surface treatments on titanium, aluminum and magnesium alloys. Mater Sci Eng A 263:210–216 44. ISO 4287 (1997). Geometrical product specifications (GPS), surface texture: profile method-terms, definitions and surface texture parameters. Ed. International Organization for Standardization (ISO) 45. Laamouri A, Sidhom H, Braham C (2013) Evaluation of residual stress relaxation and its effect on fatigue strength of AISI 316L stainless steel ground surfaces: experimental and numerical approaches. Int J Fatigue 48:109–121 46. Sanjurjo P, Rodríguez C, Peñuelas I, García TE, Javier Belzunce F (2014) Influence of the target material constitutive model on the numerical simulation of a shot peening process. Surface & Coatings Technology 258:822–831