Metal Science and Heat Treatment, Vol. 55, Nos. 5 – 6, September, 2013 (Russian Original Nos. 5 – 6, May – June, 2013)
THERMOCHEMICAL TREATMENT UDC 621.785.52
CONTROL OF HEAT-RESISTANT STEEL CARBURIZED LAYER STRUCTURE. PART II M. Yu. Semenov1 Translated from Metallovedenie i Termicheskaya Obrabotka Metallov, No. 6, pp. 32 – 37, June, 2013. In the first part of the article, published in the previous issue of this journal, on the basis of studying features of the process a physical and mathematical model is presented of carbide formation during heat-resistant steel vacuum carburizing based on the example of VKS-5. In the second part of this article on the basis of analyzing the calculation model physical features are presented for formation of cementite type carbide phase taking account of steel VKS-5 alloying with chromium and nickel, and also temperature. Simultaneously, features of special molybdenum, tungsten, vanadium and niobium carbide formation are considered. The expediency of increasing chromium content in a new generation of heat-resistant steels alloyed with nickel is substantiated.
Key words: vacuum carburizing, heat-resistant steel, carbide formation, crystal structure defects, generation.
where Ni is number of possible generation areas by the adopted mechanism; h is Planck constant; k is Boltzmann constant; T is temperature; DGH is supercritical size of nucleus formation activation energy; Dg* is energy for transition of an atom through a phase interface; r is radius of growing (dissolving) particle; Ka is carbon activity coefficient; CC and CCr are carbon and chromium concentration in solid solution respectively; CCp is carbon concentration with
RESULTS AND DISCUSSION Features of Carbide Phase Formation during Heat-Resistant Steel Carburizing It has been shown in [1] that the shape of excess phase particles formed, as also their size, depends on the degree of solid solution supersaturation, and correspondingly on Gibbs energy of chemical compound formation. With a reduction in carbide-forming alloying element concentration, and also slow impregnation, there is an increase the size of particles formed. These results also follow from the combined solution of relationships describing the rate of alloyed cementite particle generation and growth [2]: h æ DGH + Dg * ö I i = Ni exp ç ÷; kT kT è ø dr = Ka DCC dr = 1
Cr DCr
CC - CCð CCCem - CC
CCr - CCrmin Cem CCr - CCr
which at a given temperature an amount of chromium cementite particle generation commences; CCCem is carbon concentration in cementite; CCrmin is amount of chromium not participating in carbide formation, established by experiCem ment; CCr is measured chromium concentration in Cr are diffusion coefficients for carbon cementite; DCC and DCr and chromium in austenite. Activation energy in expression (1) for nucleus formation of a supercritical size equals [2]:
(1)
dt; DGH = Ki dt,
(1¢ )
16pVC2 s 3gC 3 (g g - gC )2
,
(2)
where Ki (0 < Ki < 1) is some coefficient with a dislocation mechanism for generation depending on the relationship (gg – gC )/sgC and being dimensionless with a value equal to
N. É. Bauman Moscow State Technical University, Moscow, Russia (e-mail:
[email protected]).
316 0026-0673/13/0506-0316 © 2013 Springer Science + Business Media New York
Control Of Heat-Resistant Steel Carburized Layer Structure. Part II
317 b g à C g C g
q sgC g
sgg sC C sg
g
c sgC
q
Fig. 2. Diagram of heterogeneous excess phase (C) particle generation mechanisms: a) at dislocations within an austenite g grain; b ) at an austenite grain boundary; c) at a metal surface.
à
50 mm
b
50 mm
c
50 mm
Fig. 1. Structure of carbide areas of model alloy diffusion layers, carburized at 950°C: a) Fe + 1% Cr; b ) Fe + 3% Cr; c) Fe + 3% Cr + 3% Ni.
0.4 – 0.7, decreasing with an increase in (gg – gC ); VC is volume of carbide phase necessary for one atom of carbon; sgC is carbide and austenite interface surface energy, known from published data; (gg – gC ) is difference in solid solution and carbide phase Gibbs free energy, necessary for one carbon atom, which in this work was calculated proceeding from the principle of additive contribution of the corresponding specific fields of iron and chromium atoms to formation energy of a corresponding carbide. The contribution of chromium to the energy of carbide formation of reaction, necessary for one atom (or one mole) exceeds the corresponding contribution of iron by more than factor of 25 (data in [3] for 950°C was used in the calculation). In view of this, according to Eq. (2), with a reduction in chromium concentration there is a reduction in energy entering the carbide formation reaction, there is an increase in energy for nucleus formation, and as a consequence from Eq. (1) there is a slowdown in new phase particle generation. Simultaneously, saturation of solid solution with low concentration of chromium as a result of the small number of centers for new phase growth, leads to an increase in the size of precipitated particles due to acceleration of their diffusion growth. In addition, an increase in particle size promotes a slowdown in impregnation of solid solution with carbon, since there is a reduction in the degree of supersaturation, and consequently the energy output of the carbide forming reaction. Simultaneously, with a reduction in carbide forming element concentration (chromium in the case in question) instead of equiaxed particles of spherical and cubic shape, typical for processes occurring with a high value for change in free energy, there is formation of dendrites and fibers at grain boundaries [1]. According to data in [4] these structures, vi-
sible in a microsection of impregnated metal, may be two-dimensional flat shapes within a real volume. Numerical and actual experiments carried out lead to a similar conclusion, aimed at studying particle generation of alloyed cementite in model alloys based on iron with a different chromium concentration. Model alloys of the iron-chromium system (containing 1 and 3% chromium, balance iron), and also of the iron – chromium – nickel system (3% Cr and 3% Ni, balance iron) were carburized with the aim of establishing features of carbide formation in the absence of strong carbide forming elements (W, Mo, V, etc.) present in heat-resistant steels. It has been established that with a content in these steels, as in heat-resistant steels, of chromium less than 3% during carburizing there is formation of a carbide network along grain boundaries (Fig. 1a ). An increase in chromium concentration to 3% provides preparation during carburizing of carbide particles of favorable globular shape at dislocations (Fig. 1b ), instead of a cementite network (films) along grain boundaries. It is well known that the dislocation mechanism of nucleus formation (Fig. 2a ), connected with a reduction in activation energy DGH for generation of a supercritical nucleus compared with generation in a defect-free region of a crystal, is one of the theoretically based heterogeneous generation mechanisms in a solid phase, whose homogeneous (defectfree) generation is almost impossible [2]. The priority of a dislocation mechanism for carbide phase formation with an increase in chromium content in an iron alloy (and equally within heat-resistant steel) is connected with an increase in the energy output of carbide formation reaction (gg – gC ), providing the possibility of nucleus formation at a linear packing defect (dislocation) instead of predominantly particle generation at a two-dimensional defect (grain boundary). Simultaneously, as shown above, with an increase in steel alloying with chromium, as a result of acceleration of nucleation and correspondingly an
318
M. Yu. Semenov dav , mm à 1.5
1.0
0.5 0
2
4
6 Cr, %
Cr, % 5
b
Dislocation 3
Boundary 1 900
950
1000
t, °C Fig. 3. Effect of alloying with chromium on carbide formation: a) effect of chromium concentration on calculated mean square alloyed cementite particle diameter (at 940°C, duration of impregnation stage ti = 2 min, diffusion stage td = 10 min, N = 20); b ) effect of chromium concentration and temperature on preferred nucleus formation mechanism.
increase in the number of alloyed cementite particles, there is a reduction in their average size (Fig. 3a ). The advantage of a dislocation mechanism with an increase in energy output of the reaction over a grain boundary mechanism is due first to the greater number of areas of potential generation at dislocations, than at grain boundaries. Second, as indicated above, reflecting acceleration of nucleation rate by a dislocation mechanism, coefficient Ki from expression (2) depends on dislocation parameters and specific volumetric transformation energy [2]. According to Cahn theory it decreases with an increase in the value of energy output of the reaction (gg – gC ) by a rule a rule close to linear; correspondingly there is a reduction in the energy threshold for supercritical nucleus formation. With a grain-boundary mechanism for carbide formation this coefficient only depends on the ratio of specific surfaces energies of austenite grain boundaries sgg and phases interfaces sgC (Fig. 2b ) [2]): Ki =
3ù é 1 ê 3s gg æç s gg ö÷ ú . + 22 ê 3s gC çè 2s gC ÷ø ú ë û
(3)
Here sgg /2sgC = cos q, where q is angle between the tangent to a surface of a growing particle and an intergranular
boundary line. Values of sgg and sgC are comparable with values in [5], which is due to the physical similarity of austenite and cementite, within which according to [6] the bond between atoms of a single sort (carbon or iron) is stronger than between atoms of impurity and metal (carbon and iron). As a consequence, austenite and cementite have similar values of normal elasticity modulus (on average about 210 and 200 GPa respectively), and determine to a considerable extent the value of surface energy, which also depends little on temperature. In view of this coefficient Ki in a grain boundary generation mechanism is close to constant, and almost does not depend on steel chromium content. Thus, an increase in carbide forming element concentration, leading to an increase in (gg – gC ), gives rise to a reduction in carbide particle generation activation energy by a grain-boundary mechanism in proportion to (gg – gC ) to a second degree, and by a dislocation mechanism almost to a third degree. As shown above, the value of Ki for nucleus formation by a grain-boundary mechanism depends little on chromium concentration, consequently, the priority mechanism for generation is determined by a change in Gibbs volumetric energy (gg – gC ). With presence of nickel in steel, which as is well known stabilizes austenite, there is a reduction in the degree of solid solution supersaturation, and as a consequence a predominantly grain-boundary mechanism of carbide formation in the form of networks is provided (see Figs. 1c and 2b ). In [7] attention is drawn to the fact that spherical particles contribute to solid solution greater distortion energy than disk-shaped (flat) particles. From this situation it is possible also to conclude that formation of globular (spherical and rarely cubic) precipitates is only possible with greater energy output of phase transformation for supersaturated solid solution, i.e., with an increase in chromium content. With an increase in temperature for carburizing above 980°C even with alloying steel with 3% chromium apart from coarsening of carbide particles, due to an increase in diffusion coefficient, and correspondingly acceleration of their growth in accordance with expression (1¢ ), there is also formation of a network of excess phase along grain boundaries (see Figs. 1a and 3b ). In our opinion this is connected with acceleration of carbon diffusion into the depth of metal from a surface area, which is caused by a reduction in degree of solid solution saturation with carbon, causing preferred formation of carbides by a grain-boundary mechanism. In addition, an increase in temperature accelerates annihilation of dislocations, leading to a reduction in areas of possible alloyed cementite particle growth within grains, and also prevents occurrence of fluctuations of carbon concentration, which are fundamental for forming new phase nuclei by any mechanism. The danger of forming a grain-boundary carbide network even with an insignificant increase in temperature compared with that recommended for carburizing (not more than 940 – 960°C), considerably increases for carburizing new
Control Of Heat-Resistant Steel Carburized Layer Structure. Part II
special heat-resistant steel VKS10 (10Kh3N3M2VFB-Sh), developed on the basis of steel VKS-5. This is caused by the increase in content in steel VKS-10 (up to 3%), which as shown above, as a result of its capacity to stabilize austenite, causes formation of a cementite network. In view of this during further development of heat-resistant steels grades it is proposed to increase chromium concentration within them up to 4 – 4.5% with the aim of stabilizing cementite, and providing its formation in the form of particles of favorable globular shape. Research of the effect of tungsten, vanadium, and molybdenum on carbide formation in heat-resistant steels has been studied on alloys of model composition: 99% Fe and 1% W, 99% Fe and 1% V, 99% Fe and 1% Mo, which were also carburized. These alloys are characterized by carbide formation in heat-resistant steels with exclusion of the effect on it of chromium and nickel. With a content in these model alloys of strong carbide forming elements: V, W, Mo, and equally Nb, exhibiting greater affinity for carbon than iron and chromium, form very fine particles of spherical shaped carbides (Fig. 4). During carburizing of model alloys, containing tungsten and molybdenum, there is regular location of fine carbide particles in the form of typical chains. This phenomenon is probably explained by an increase in concentration of the alloying elements indicated at crystal structure defects, such as grain boundaries and dislocations, caused by significantly different atomic radii of these elements and iron, on which alloying element atom bond energy with crystal structure defects depends [8]: U=8
1+ m 2 , G (RFe – RMe )R Fe 1– m
(4)
where m is Poisson’s ratio; G is shear modulus; RFe and RMe are iron and alloying element atomic radii respectively. Taking account of atom bond energy for substitution impurities with defects U and average atomic concentration of alloying element CMe , it is possible to calculate the average saturation of substitution impurity atom defects by an equation [8]:
D C Me
æU ö CMe exp ç ÷ è kT ø . = æU ö 1– CMe + CMe exp ç ÷ è kT ø
(5)
Atomic fractions of alloying elements of the test steel, and also results of calculation by Eqs. (4) and (5) at 950°C are provided in Table 1. It should be noted that as a result of the closeness of iron and chromium atomic radii, and also nickel atoms, chromium and nickel are distributed almost uniformly in solid solution based on iron. In addition, chromium exhibits a capacity for good dissolution in iron compounds, in particular
319
50 mm
à
b
50 mm
c
50 mm
Fig. 4. Structure of molybdenum alloy diffusion layer carbide zones, subjected to carburizing at 950°C: a) Fe + 1% V; b ) Fe + 1% W; c) Fe + 1% Mo.
cementite. The atomic radii of other alloying elements, within the composition of heat-resistant steels, differs markedly from the sizes of matrix atoms (see Table 1). In view of this the concentration of vanadium atoms (to a lesser extent), tungsten, molybdenum, and particularly niobium at crystal structure defects differ from the average content of these elements in heat-resistant steel VKS-5. These concentrations correspond to a significantly more uniform vanadium carbide distribution observed by experiment in carburized iron alloy with 1.0% V, whose saturation of defects with atoms according to calculation by Eqs. (4) and (5) is 4.2%, than for molybdenum and tungsten carbides in corresponding model alloys based on iron (Fig. 4). According to calculations in alloys containing respectively 1.0% Mo and W impregnation of defects with atoms of these
TABLE 1. Atomic Radii, Average Concentration, and Alloying Element Segregation Formation Parameters at Steel VKS-5 (16Kh3NVFMB-Sh) Crystal Structure Defects Element
Fe Cr Ni W Mo V Nb
RMe , nm
0.126 0.128 0.124 0.139 0.139 0.134 0.146
CMe
– 0.028 0.013 0.008 0.005 0.0045 0.0015
U, 10 – 20 J
D C Me
– 0.616 0.616 4.001 4.001 2.462 6.153
– 0.039 0.019 0.090 0.051 0.019 0.054
Note. Average values are provided for steel alloying element concentration (in tenths).
320
elements is 9.8%, which exceeds by almost a factor of ten their average content in the model alloy. Segregations of strong carbide-forming elements are areas of more intense special carbide particle generation. In [1] a similar effect of nucleus formation at segregations of impurity atoms has been described in the case of internal oxidation of copper-silicon alloy. According to rough calculation, the formation energy for special carbides exceeds by more than a factor of twenty the formation energy for cementite alloyed with 5 – 6% Cr (with a total chromium content in steel or alloy based on iron equal to 3%) from the calculation for one metal atom. The energy output for special carbide formation of strong carbide-forming elements is so high that for their particles, outside the dependence on the area of their generation, uniaxial point morphology is typical (see Fig. 4). This particle shape is provided due to very high rate of generation. In view of this, nuclei form more as a result of a slowdown in diffusion growth of these particles, which as follows from expression (1¢ ), is caused by the high concentration of atoms of strong carbideforming elements in corresponding special carbide, with a low value of diffusion coefficient for their atoms in iron. Formation of cementite carbides at the surface of impregnated metal with prolonged active impregnation in the form of a flat surface film is caused by the following reasons (see Fig. 2c ). After absorption of carbon atoms from a dissociating carbon-containing gas they form a flat layer of carbon black, itself characterized by high surface energy. In addition, the specific energy of the outer surface g-Fe (sg ) exceeds by about a factor 2 – 3 the intergranular boundary energy sgg [5]. Thus, requirements are created for forming a flat interface between generating cementite and austenite particles (sC ), and also the outer surface of this particle outside the dependence on volumetric transformation energy (gg – gC ) both in steels alloyed with chromium and in unalloyed steel. The rate of this heterogeneous generation is determined by the value of cos q, as shown above proportional to the ratio of surface energies. Even after transfer of all chromium into carbide phase of the cementite type at a surface, further conversion of supersaturated austenite into cementite does not cease, since carbon atoms continue to be absorbed from an active medium. In practice this means the possibility of forming a continuous carbide film, formed by an external carburizing mechanism. It should be noted that formation of carbides with transfer of all alloying elements into excess phase should slow down as a result of a reduction in the energy effect of supersaturated austenite transformation. As indicated above, this slowdown leads to preparation of coarse carbides, orientated in defect planes, and in this case external boundaries. It should be noted that unalloyed cementite may only form as a thin surface skin, whose thickness is determined by the area of crystal structure surface defects, or internal defects, emerging at a surface. This situation is caused by absence of a carbon concentration gradient with achievement
M. Yu. Semenov
of its solubility limit, equal to carbon potential. Qualitatively another situation arises in the presence of a sufficient amount of chromium, partly redistributed in carbides. A negative free chromium gradient in solid solution (chromium concentration decreases towards a surface as a result of presence within it of a maximum amount of carbides) causes upward diffusion of carbon into the depth of a layer. Supersaturation with carbon for deeper alloys in steel alloyed with chromium causes an increase in the extent of a region for possible formation of chromium cementite, and correspondingly an active carbide zone. Thus, development of a mathematical model for vacuum carburizing of complexly alloyed steel taking account of formation of carbide phase of complex composition presents a possibility of reliable prediction of chemical composition and structure of a diffusion layer in these steels with a different combination of production factors. The possibility of carrying out numerical experiments is especially noticeable taking account of a requirement for planning vacuum carburizing of gear wheels, whose supporting capacity is determined by different ratios of operating properties: – contact fatigue; – wear resistance; – jamming resistance; – resistance to fatigue fracture i bending. In order to provided these operating properties within prescribed limits it is necessary to monitor both saturation distribution of a layer strengthened with carbon, and the volume faction and size-quantitative distribution of excess phase particles. In turn, the problem of monitoring these properties of cementite layer structure is resolved by calculating them for a known steel chemical composition and production factors of vacuum carburizing using the physical and mathematical models proposed. CONCLUSIONS 1. On the basis of experimental studies and theoretical presentations a physical model has been developed for carbide formation during vacuum carburizing of heat-resistant steels, including formation of an excess phase of the cementite type by external (and internal) type I carburizing mechanisms, and also special carbides of strong carbide-forming elements by a type II internal carburizing mechanism. 2. The assumptions made for a physical model are reflected in the mathematical model developed, which has been implemented with application software making it possible with satisfactory accuracy to calculate chemical and phase composition of a diffusion layer at any instant of vacuum carburizing. 3. A solution has been analyzed for the problem of describing carbide phase particle generation and growth. The effect has been established of alloying and production factors on the preference of a dislocation mechanism for carbide
Control Of Heat-Resistant Steel Carburized Layer Structure. Part II
particle formation of globular shape over a grain-boundary mechanism of cementite network precipitation mechanism. A value of alloying with chromium in an amount of not less than 3% is shown in order to obtain a developed excess phase structure of acceptable shape during carburizing. Features are revealed fro forming special vanadium, molybdenum, and tungsten carbides in heat-resistant steels. 4. Means are proposed for resolving the problem of monitoring the eutectoid zone structure of carbide layers for heat-resistant steels based on performing a numerical experiment. This work was carried out within the framework of the Federal target program “Research and development of priority development areas of the scientific and technological complex of Russia for 2007 – 2013,” in accordance with state contract No. 16.523.11.3010 on the theme “Creation of a complex of vacuum and ion-vacuum technology of chemical heat treatment for machine components with preparation of a diffusion layer nanostructured condition.”
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