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Influence of phase transformations on the mechanical properties of austenitic stainless steels
International Journal of Plasticity 16 (2000) 749±767 www.elsevier.com/locate/ijplas
In¯uence of phase transformations on the mechanical properties of austenitic stainless steels A.A. Lebedev *, V.V. Kosarchuk National Academy of Sciences of Ukraine, Institute for Problems of Strength, 2, Timiryazevskaya str., 252014, Kiev, Ukraine Received in ®nal revised form 11 November 1999
Abstract The martensitic transformation in austenitic stainless steels type 18±10 can be induced by plastic deformation at room and low temperatures. In this study we conducted a systematic series of experiments to assess the in¯uence of both temperature and stress state type on kinetics of martensitic transformation. An attempt has been made to correlate the mechanical properties with the microstructural changes. The results of present studies make it possible to estimate the eect of stress state type on martensitic transformation kinetics in metastable chromiumnickel steels under isothermal loading. # 2000 Elsevier Science Ltd. All rights reserved. Keywords: Phase transformations; Isothermal loading; Austenitic stainless steels
1. Introduction A complete constitutive description of material behavior requires information about a material's response as a function of strain, stress state, strain rate, and temperature. Consequently the simulation of plastic deformation is one of the most complex and topical problems of the mechanics of solids. This is especially true for ``non-classical'' materials, in particular structurally unstable materials which undergo phase transformations subjected to thermal and mechanical loading. The mechanical properties of metastable materials, in particular Fe±Cr±Ni steels, have been the subject of experimental and theoretical studies for a long time. The reason is that these materials are quite often used in modern engineering. * Corresponding author. 0749-6419/00/$ - see front matter # 2000 Elsevier Science Ltd. All rights reserved. PII: S0749-6419(99)00085-6
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However, their mechanical properties are not fully investigated, because the character and the intensity of phase transformations depend on many factors, such as strain rate and strain level, stress state and regime of mechanical loading, and temperature. In this paper we examine the mechanical behavior and the evolution of phases in 18Cr±10Ni austenitic stainless steels as a function of the strain level, stress state and temperature. We consider the microstructural evolution as the key information for eventual understanding of the plastic ¯ow and failure behavior. Martensite formation resulting from plastic deformation of metastable austenite is of great interest for producing high strength and ductility in austenitic stainless steels. Substantial strengthening can be obtained in metastable austenitic stainless steels by plastic deformation below Md temperature (Md is the highest temperature at which the martensitic transformation can be induced by plastic deformation) to produce cubic body centered 0 and hexagonal closed packed " martensite. The transformation of cubic face centered austenite to 0 and " martensite depends on the alloy composition, stacking fault energy, degree of deformation, temperature etc. On the other hand, the fraction of the phases in the metal has a signi®cant eect on the character of its strain-hardening and its strength and ductility characteristics. Early studies (Eichelman and Hull, 1953; Bannykh and Kovneristyi, 1969; Hirayama and Ogirima, 1970; Pavlov et al., 1979) presented investigations of phase transitions in several pure and commercial Fe±Cr±Ni alloys under the in¯uence of plastic deformation at room and sub-zero temperatures. One of the main conclusions made in these studies was that the rate of martensite transformation depends signi®cantly on the chemical composition of the steel, with Ni, Cr and C having a particularly strong eect on the phase transition process. The total eect of the main alloying elements on the martensitic transition is evaluated from the nickel equivalent (Hirayama and Ogirima, 1970) Niequ %Ni 0:65%Cr 0:98%Mo 1:05%Mn 0:35%Si 12:6%C: Martensitic transformations in austenitic stainless steels have been studied extensively in uniaxial tension at low strain rates (static loading) (Angel, 1954; Langeborg, 1964; Wigley, 1971; Olson and Cohen, 1975; Tamura, 1982; Reed, 1983; Chappuis et al., 1984; Seetharaman, 1984). The in¯uence of the stress (strain) state on the phase transformation has received, however, very little attention (Kato and Mori, 1976; Hecker et al., 1982; Piwecki, 1986; Kosarchuk et al., 1989; Marketz and Fischer, 1995; Lebedev et al., 1999). Current achievements in transformationinduced plasticity are analyzed in paper by Fischer et al., 1996). Continuum thermomechanical theory of martensitic phase transformations in elastoplastic materials is presented by Levitas (1997, 1998). Interaction between phase transformation and plasticity at the micro level was studied by Leblond et al. (1989), Leblond (1989), Cherkaoui et al. (1998), Marketz and Fischer (1995) and Idesman et al. (1999).
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2. Experimental procedure Two commercial type 18Cr±10Ni austenitic stainless steels were studied, and their composition is given in Table 1. The nickel equivalent for steels A and B is 22.46 and 26.73%, respectively. The lower value of Niequ for steel A is evidence of its greater metastability with respect to the martensite transformation. Mechanical tests (uniaxial tension and compression, torsion, and biaxial loading with dierent principal stress ratios ) at temperatures of 293, 173, and 77 K were conducted on a hydraulic testing machine SNT-5PM with a computer-aided control system (Pisarenko et al., 1984). The loading rate was kept constant in all of the tests (about 15 MPa/s). Two types of specimens were used for the tests: thin-walled tubular specimens (external diameter 26 mm, wall thickness 0.5 mm, working length 75 mm, gage length 20 mm) made of steel A, and solid cylindrical specimens (6 mm diameter, working length 25 mm, gage length 10 mm) made of steel B. The specimens were made from hot-rolled bars of steels A and B 45 and 20 mm in diameter, respectively, in the conditions as received. After machining, the specimens were heat-treated as follows: heating to 1350 K in a vacuum, 40 min holding, and slow cooling. The specimens were deformed in stages. After each loading stage we conducted a phase analysis of the material and determined the plastic strains. The plastic longitudinal "pz and transverse "p strains of the tubular specimens were measured with an accuracy of 0.02%, while the radial strain "pr was determined to within 0.2%. Structural changes in the deformed steel were studied by the methods of X-ray diraction and optical metallography. We recorded the (111) X-ray lines of austenite and the (110) and (101) lines of the 0 and " martensite, respectively, to determine the volumetric fraction of retained austenite and strain induced martensite in the steels. Here, we used a diractometer DRON-2,0 with scintillation recording. The phase composition of the material was determined by comparing the integral intensities of X-ray interference with allowance for repetition factors. A well-known method was used to do this (Lysak and Khandros, 1953). The microstructure of the working surface of the specimens was studied with a ``Neophot-2'' optical microscope after preliminary mechanical and electrolytic polishing of the specimens. The specimens were etched electrolytically in a chromium-acetate Morris reagent (Morris, 1946) consisting of 133 ml of glacial acetic acid, 25 g of chromic anhydride, and 7 ml of water. The electrolytic etching regime was as follows: current density 0.1 A/cm2, temperature 17 C. The microstructure was studied at magni®cation of 200, 800, and 2000. The microstructure of the austenite after the heat treatment consists of light Table 1 Chemical composition (wt%) of steels investigated Type
C
Cr
Ni
Mn
Ti
Si
Mo
V
Cu
Fe
A B
0.07 0.07
16.4 15.4
9.6 12.3
1.03 1.45
0.67 0.41
0.39 0.43
0.11 1.91
0.06 0.05
0.04 0.12
Balance Balance
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equiaxed grains of solid solution with characteristic annealing twins. Mean grain size is about 44 mm. 3. Results and discussion 3.1. Uniaxial tension The stress±strain curves of the steels under dierent temperatures are shown in Fig. 1 (i and "i are von Mises equivalent stress and strain). The stress±strain curves of steels A and B at room temperature are similar to the typical tension curves of polycrystalline alloys with an fcc lattice and exhibits a regular form. The authors of several works (Medvedev et al., 1979; Skibina et al., 1979 etc.) noted that the deformation of steels of the 18±10 type at room temperature is not accompanied by phase transitions up to the fracture. Bannykh (1969) and Firks (1970) showed that the metal should be deformed to a very high strain to form strain induced martensite at room temperature. Phase transitions caused by plastic deformation, however, occur also at room temperature and start at relatively low strains in the conducted tests with steel A. A detectable amount of martensite (a0 -phase) is already present at "pi > 10% (Fig. 2a).
Fig. 1. Stress±strain curves for steels A (1, 2, 3) and B (4, 5) at temperatures of 293 K (1, 4), 173 K (2), and 77 K (3, 5). (The dashed lines are stress±strain curves in the case of staged loading, while the solid curves are for continuous loading.)
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The largest amount of martensite (up to 40%) is observed in the neck region of fractured specimens deformed to 55±60%, while the amount of martensite formed in the region of uniform plastic strain (about 35%) is not high (up to 25%), and its contribution to strain-hardening is insigni®cant (see Fig. 1).
Fig. 2. Dependence of the volume fraction of 0 -phase (a) and e-phase (b) in steels A and B on strain at temperatures of 77, 173 and 293 K.
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For the more stable steel B, no martensitic transformation was observed at room temperature up to fracture. The dierence is evidently attributed to the chemical composition of the steels, particularly the reduced nickel content of steel A. It was noted (Bannykh and Kovnerstyi, 1969; Reed, 1983) that the formation of the mechanical properties of chromium-nickel austenitic steels in low-temperature deformation is aected not only by the strain induced martensite, but also by the temperature induced martensite formed during cooling of the initial structure below the martensite start temperature Ms . The temperature Ms for steels A and B, calculated from an empirical formula proposed Eichelman and Hull (1953), is 140 and 8 K, respectively. Despite the possible error in the determination of Ms , it should be expected that the cooling of steel A to 77 K will lead to the formation of temperature induced martensite. The dependence of the kinetics of phase transformations on the temperature, duration of holding under ®xed load, number of thermal cycles and type of stress state has been examined. The studies have demonstrated that the martensitic transformations are related to thermal stresses and are little aected by the duration of the holding at a constant low temperature without load. Thus, for example, seven thermal cycles (cooling to 77 K and heating to 293 K) performed either in 15 min or 250 h (the duration of each cycle was about 36 h in this case) resulted in about the same quantity (about 8%) of 0 -martensite (Fig. 3a and 3b). The cooling and heating rates were 6 and 3 K/s, respectively. As the number of thermal cycles increases, the amount of the 0 -phase formed per cycle decreases monotonically, and temperature induced martensite volume fraction saturates (see Fig. 3a and 3c). The holding at low temperature under plastic deformation contributes to a greater extent to the phase transition than the holding in elastic domain or under zero load condition does. The long rest during 2 months activate phase transformations (point C on curves). A small amount of "-martensite (up to 6%) was observed on the diraction patterns simultaneously with the 0 -phase. The presence of the "-martensite was ®xed in the form of an interference re¯ection from the {101} plane. It is believed (Firks, 1968; Startsev et al., 1975; Reed, 1983) that the "-phase is an intermediate phase in the
! 0 transition. The results obtained on chromium±nickel steels at low temperatures con®rm this (Sokol, 1974; Chappuis et al., 1984; Singh, 1985). Nevertheless, this may not be the only possible transformation scheme (Bogachev and Egolaev, 1973; Sipos et al., 1976; Murr et al., 1982). Martensitic transformation begins with the formation of several parallel-phase plates in octahedral {111} planes of austenite grains. An increase in the number of thermal cycles is accompanied by fragmentation of the initial austenite grains as a result of the intersection of "-martensite plates at angles of 60 and 120 . The 0 phase martensite is seen at a magni®cation of 800 in the form of a large accumulation of points located in the "-phase plates. It follows from the above results and data of optical study stabilization of the process of martensite transformation is evidently connected with complete ®lling of plates of the "-phase by 0 -martensite crystals. Preliminary deformation in tension promotes the initial stage of the process of thermal induced martensite formation, as it is evident from data on martensite
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transformation kinetics of steel A prestrained at room temperature to "pi 20%(see Fig. 3b and c). Deformation at low temperatures is accompanied by intensive strain-hardening of the steel, the character of which is aected by the phase transitions (solid lines in Fig. 1). The stress±strain curves of steel A at 173 and 77 K dier somewhat in the rate of strainhardening even in the region of relatively small strains (3±9%). This is connected with the dierences in kinetics of martensite transformation at these temperatures.
Fig. 3. Dependence of the volume fraction of 0 -phase on number of cooling cycles.
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According to Reed (1983), Pavlov et al. (1979), the "-phase exerts a softening eect, which reduces strain-hardening. An increase in strain is accompanied initially by some increase in the amount of "-martensite (the latter reaches 6.5% at "pi 2:6%) followed by decrease in "-martensite (see Fig. 2b). At "pi > 13% no "-phase is seen on the diraction patterns. The increase in strain-hardening at "pi > 13% is evidently connected with the predominant eect of the 0 -phase, which grows with an increase in strain (see Fig. 2a). Despite the small dierence in the chemical composition of the investigated steels, the stress±strain curves at 77 K dier considerably (see Fig. 1). This is connected with features of the martensite transitions. The formation of strain induced martensite ( 0 -phase) in steel B starts at a larger (about 5%) strain than in steel A. The transition takes place more slowly, and the maximum amount of martensite (about 100%) is reached at strains of 40±45% (see Fig. 2a). In contrast to steel A at 77 K, parallel with the ! 0 transition in steel B, austenite is transformed to the hcp "-phase (Fig. 2b). The presence of this phase aects the character of strain±hardening, especially at small (5±15%) strains (see Fig. 1). Thus, the greater stability of the austenite in steel B lowers the rate of its strainhardening, which is consistent with the results of Startsev et al. (1975); Nizhnik (1980); Reed and Mikesell (1960). Twinning and slip occur during the initial stages of deformation, as is it evident from the appearance of a large number of slip traces in the austenite grains. An increase in the strain is accompanied by the appearance of numerous zones with an extremely unhomogeneous strain distribution leading to the formation of microreliefs connected with distortion of the crystalline lattice. The slip bands form broad blocks which intersect with martensite needles. The strain traces are heavily distorted and masked by numerous martensite plates at the stage of deformation preceding fracture. As follows from Fig. 1, staged deformation (i.e. sequence loadings with intermediate unloadings) leads to additional strain-hardening of the material caused by two factors. On the one hand, it is related to the strain-hardening eect of the martensite formed during repeated cooling. On the other hand, it is connected with the change in the properties of the steel as a result of recovery. A comparison of the stress±strain curves at 77 and 173 K (temperature induced martensite is not observed at the latter temperature) shows that the eect of temperature induced martensite is predominant. This is con®rmed by the fact that after unloading and subsequent loading without holding (point VII'' in Fig. 1), no additional strain-hardening eect is observed. Holding the unloaded specimen for 3 h at 77 K (point VII'') leads to a slight amount of additional strain-hardening. Quantitative description of the eects observed will require the realization of special experiments. It is known (Bannykh and Kovneristyi, 1969; Sokol, 1974) that transformation of austenite to martensite is accompanied by a change in volume. Volume increases in the ! 0 transition and decreases in the ! " transition. The kinetics of the phase transition in steel A at 173 and 77 K is re¯ected by the dierent character of
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Fig. 4. The lateral strain factor versus the degree of plastic strain (steel A).
the change of the coecient of transverse plastic deformation "p ="zp with an increase in the amount of prestrain "pi (Fig. 4). At a temperature of 77 K, the coecient of transverse plastic deformation initially increases rapidly, reaching a maximum value of 0.49. Then it decreases monotonically. Comparison of Figs. 2a and 4 indicates that a remarkable change in volume during plastic deformation starts at a strain "pi 5%, which corresponds to a martensite fraction of 45%. It should be noted that the eect of strain induced martensite on at 173 K begins to be manifested as well at a volume fraction of 0 -phase of about 45%. Fig. 5 shows the dependence volume change, characterized by the ÿ of the relative mean plastic strain "f0 1=3 "pz "p "pr ; on the volume fraction of strain induced martensite (we considered the total fraction of the 0 and " phases) in deformed steel A. It can be seen that the change in volume depends to a signi®cant extent on the test temperature. Whereas the value of "f0 is nearly linearly dependent on the martensite fraction at 77 K, a more complex pattern is seen at 173 K. The value of "f0 decreases slightly during the initial stages of deformation and then increases fairly
Fig. 5. Dependence of the mean plastic strain on total volume fraction of martensite (steel A).
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rapidly. Such a character of the relation "f0 ÿ Vm is evidently connected with the competing eects of the 0 and " phases at small strains. Thus, the results obtained provide evidence of a clear correlation between the strain-hardening of chromium±nickel austenitic steels and the kinetics of martensite transformation under uniaxial tension. 3.2. Compression and torsion Experimental and theoretical (Kato and Mori, 1976; Hecker et al., 1982; Piwecki, 1986; Kosarchuk et al., 1989; Marketz and Fischer, 1995; Lebedev et al., 1999) investigations showed that, together with the temperature, the type of the stress state has a signi®cant in¯uence on the processes of phase transformations in metastable steels. However, too few experimental data do not allow a quantitative evaluation of the in¯uence of the type of the stress state on the intensity of the martensite transformation in the course of plastic deformation. This section presents the results of an investigation of the kinetics of the phase transformations in steel B in tension, compression, and torsion. The samples were deformed in load steps. After each load step a phase analysis of the material was performed, and the microhardness and residual deformations of the specimens were determined. The axial and transverse deformations were determined in tension and compression with an accuracy of 0.05%, and the angle of twist in torsion related to a length of 25 mm with an accuracy of 0.5%. The hardening of the deformed steel was evaluated by measurement of the microhardness. The working surface of the specimens was indented with a load of 100 g. Each experimental point was determined by averaging the microhardness readings of 10 indentations. The mechanical tests were made at 293 and 77 K. The room-temperature tests indicate that, regardless of the type of the stress state, the plastic deformation of the given steel is not accompanied by phase transformations up to the failure. A cooling to 77 K without any deformation does also not lead to a martensite transformation even under conditions of a long holding at this temperature. Low-temperature deformation of steel B is accompanied by a martensite transformation. In the deformed steel hexagonal "-phase is observed together with 0 martensite. Figs. 6a and 6b present the relation between the volume fraction of 0 - and "martensite and the strain for the three types of loading: tension, torsion, and compression. A comparison of the curves shows that, depending on the type of loading, the process of the martensitic transformation occurs with dierent intensities. Tension causes more intense formation of "-phase than torsion and especially than compression. The V ÿ "pi curves in torsion and compression have a smaller slope than in tension, and the maximum amount of 0 -martensite, which also depends on the mode of loading, is reached with higher degrees of straining. The kinetics of the ! " transformation diers signi®cantly from the kinetics of formation of the 0 -martensite (Fig. 6a and b).
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The hexagonal "-martensite is already formed in the early stages of deformation (traces of "-phase are observed at deformations of 1%), while the ! 0 transformation still does not up to 5% deformation. As follows from Fig. 6b, the volume fraction of "-martensite depends to a signi®cant extent on the type of loading, especially at large deformations. The maximum "-phase fraction is approximately the same (8±9%) for all types of loading, but the range of deformations in which it is observed is signi®cantly higher for compression than for tension. In the prefailure state and in the failed specimens, "-phase was not observed.
Fig. 6. The volume fraction of 0 -phase (a) and "-phase (b) in steel B versus the plastic strain intensity under tension (1), torsion (2), and compression (3).
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The reason for the observed dierences in the kinetics of the phase transformations with the type of loading is related to the sign of volume change due to the formation of martensite (Ilyichev et al., 1968; Bannykh and Kovneristyi, 1969). It is known that the ! 0 transformation is accompanied by an increase in volume and the ! " transformation by a decrease in volume. Therefore, tension promotes the ! 0 transformation and suppresses the formation of "-phase. In compression the reverse eects are observed. Phase transformations possess a signi®cant in¯uence on the strain hardening of chrome-nickel austenitic steels, the degree of which may be judged from the microhardness H (Fig. 7), (see e.g. Bannykh and Kovneristyi, 1969; Reed, 1983). There is a steady increase in microhardness related to strain hardening at room temperature during tension as a result of work hardening of austenite. Some reduction in microhardness with large degrees of deformation (>40%) may apparently be explained by softening of the material in the prefailure stage. At low temperature (77 K) tension of steel leads to a signi®cant increase in the strain hardening of the material, which is related to the occurrence of phase transformations. On the H -"pi curves (see Fig. 7) three characteristic stages may be conditionally distinguished. For example, in tension a rapid increase in microhardness occurs in the ®rst stage, caused by work hardening of the austenite as well as by the formation of coarse dispersed "-martensite, the hardness of which exceeds the hardness of austenite by 40%. In the second stage ("pi =6±12%) the rate of strain hardening decreases since there is practically no more increase in the volume fraction of "-phase, and the ®nely dispersed 0 -martensite, formed in a small quantity, makes an insigni®cant contribution to hardening of the investigated steel. This may p explain the appearance ÿ p of a bend on the H ÿ "i curve (see Fig. 7). The third stage "i > 12% shows strong hardening of the steel, which occurs primarily as the result of intense formation of the -phase.
Fig. 7. The microhardness of steel B versus the plastic strain intensity in the case of tension (1, 3) and compression (2) at 77 K (1, 2) and 293 K (3).
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In compression the features of strain hardening of the steel under low-temperature conditions are preserved but less pronounced. Comparing the H ÿ "pi relationship for tension and compression with the corresponding curves of the change in volume fraction of the phases (Figs. 6a and 6b) may lead to the conclusion that the main features of strain hardening of the steel in these types of loading are related to dierent intensities of the processes of formation of 0 - and "-phases. 3.3. Plane stress state A study of martensitic transformation kinetics under biaxial stress state at low temperatures showed that the intensity of its development depends markedly on the principal stress ratio k z = . In these tests we used the thin-walled tubular specimens of steel A. The change in volume fraction of martensite during low-temperature deformation of steel A with values k z = is illustrated in Fig. 8. The amount of 0 -phase decreases for a ®xed value of plastic strain with the change-over from uniaxial tension to balanced biaxial tension. It is possible to estimate the in¯uence of stress state on the intensity of phase transformations by applying the stress triaxiality parameter K 0 =i , where i is the equivalent stress and 0 is the hydrostatic stress (Pisarenko and Lebedev, 1976; Marketz and Fischer, 1995; Iwamoto et al., 1998).
Fig. 8. Dependence of volume fraction of -martensite in steel A at 173 K on the amount of strain with dierent ratios of principal stresses: 1 ÿ k 1; 2 ÿ k 0:5; 3 ÿ k 1; 4; 4 ÿ k 1.
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This in¯uence is connected with volume increase during 0 -martensite formation. An increase in stress triaxiality leads to an increase in the elastic volumetric strain which should stimulate the 0 transformation. However, in the present work an opposite eect was obtained: with an increase in parameter K from 1/3 (uniaxial tension) to 2/3 (balanced biaxial tension) the rate of 0 -phase formation decreases with strain. By comparing the results considered above, we see that K is not the only parameter of the stress state aecting martensitic transformation. One may suggest a dependence of martensitic transformation kinetics also on the stress deviator which is characterized by the Lode's parameter 22 ÿ 1 ÿ 3 = 1 ÿ 3 . Both K and describe the trajectory of simple (proportional) loading path in the stress space. A decrease in the rate of martensitic transformation with a change-over from uniaxial to balanced biaxial tension may be explained by the prevailing eect of parameter on the phase transition which in this case varies from ÿ1 to 1. The amount of 0 -phase at some ®xed plastic strain "pi is greater for higher value of R j"p1 ="p3 j where "p1 and "p3 are the maximum values of plastic tensile strain and plastic compressive strain, respectively. In the case of similarity of stress and strain deviators " , the value of R is equal to 2 for ÿ1; for 0 it is 1, and for 1 it is 0.5. A very perfect [111] texture (Burgers and Klosterman, 1965) may have an activating eect on the process of martensite formation under uniaxial tension ÿ1. The retarding eect of a second stress component on the martensitic transformation is explained by formation of a more complex stressed austenite structure with an increased structural defect density (Istomina and Nizhnik, 1973). Thus, the correlation established between the stress triaxiality parameter K , Lode's parameter, , and the rate of phase transformation caused by plastic deformation makes it possible to present the volume fraction of martensite in austenitic stainless steels under proportional loading by the following function relation: ÿ 1 Va f "pi ; s ; Ks ; T The experimental results (see Figs. 2, 6, 8) have made it possible to specify function (1) for the case of isothermal loading as Table 2 Parameters of Eq. (2) with various ratios of principal stresses Stress state parameters
Steel A at T=173 K
Steel B at T=77 K
k
K
n
"0
n
"0
1 1.4 1.0 2 ÿ1.0 ±
1/3 0.62 2/3 1 0 ÿ1/3
ÿ1 0.45 1 0 0 1
49.1 46.0 28.1 46.9 ± ±
0.93 0.88 0.80 0.88 ± ±
1.78 2.01 1.95 1.88 ± ±
0 0 0 0 ± ±
31 ± ± ± 10 6
1.04 ± ± ± 0.9 1.1
1.81 ± ± ± 1.43 1.45
0.047 ± ± ± 0.05 0.07
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ÿ n V 1 ÿ exp ÿ "p1 ÿ "p0i ;
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2
where "p0i is the martensitic start strain (it depends on the degree of steel stability); , and n are coecients which are functions of stress state parameters , and K . Numerical values of these coecients for steels A and B are given in Table 2. Curves ÿ V "pi , calculated from Eq. (2), are depicted in Figs. 2a, 6a and 8. In Fig. 9, surfaces were plotted in the three-dimensional space V ÿ ÿ K based on Eq. (2) and data of Table 2, qualitatively re¯ecting the eect of stress state parameters on the amount of 0 -martensite at certain ®xed values of "pi . As can be seen from Fig. 9, with an increase in K and a reduction in Lode's parameter the process of martensitic transformation intensi®es. The has a predominant eect on the ! 0 transition due to the shear components of transformation stress. The phase transformations strongly aect the mechanical properties of steels under biaxial testing at low temperatures. A discrepancy of the eective stress±strain curves with the ratio of principal stresses k z = is observed (Fig. 10). The strain-hardening rate curves (Fig.11) exhibits changes in concavity and two in¯ection points.
Fig. 9. Dependence of volume fraction of martensite on stress state stiness parameter and Lode's parameter at dierent levels of plastic strain: 1 ÿ "pi 5%; 2 ÿ "pi 10%; 3 ÿ "pi 15%.
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Fig. 10. Stress±strain curves for steel A at 173 and 293 K at various ratios of principal stresses: 1 ÿ k 1; 2 ÿ k 1; 4; 3 ÿ k 0; 5; 4 ÿ k 1.
Fig. 11. Strain-hardening rate curves for steel A at 173 K (a) and 293 K (b) at dierent ratios of principal stresses: 1 ÿ k 1; 2 ÿ k 1:4; 3 ÿ k 0:5; 4 ÿ k 1.
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Thus, the results of the present studies allow to estimate qualitatively and quantitatively the eect of the loading type on martensitic transformation kinetics in metastable austenitic stainless steels with isothermal proportional loading. The experimental data may be used as a basis to formulate some constitutive relations for metastable materials. Furthermore, they can be used for optimization of technological processes connected with plastic forming and thermomechanical strengthening of austenitic stainless steels. 4. Conclusions 1. The rate of martensitic transformation depends signi®cantly on the chemical composition of the steel. 2. Deformation by tension causes more intense formation of both 0 - and " martensite than deformation by torsion and especially by compression. 3. Tension, causing an increase in the volume, promotes the ! 0 transformation and suppresses the formation of "-phase. In compression the reverse eect is observed. 4. With an increase in the stress triaxiality parameter and a reduction of Lode's parameter the ! 0 transformation intensi®es. The Lode's parameter has a predominant eect on the martensitic transformation. 5. The results demonstrate a clear correlation between the strain-hardening of austenitic stainless steels and the kinetics of martensitic transformation under various types of loading. Acknowledgements We are indebted to Professor V.V. Levitas (Texas Tech University, Lubbock) for helpful discussions and his help with preparing this article. References Angel, T., 1954. Formation of martensite in austenitic stainless steels. J. Iron & Steel Inst. 177, 165. Bannykh, O.A., Kovneristyi, Y.K., 1969. Steels for operation at low temperatures. Metallurgiya, Moscow (in Russian). Bogachev, I.N., Egolaev, V.F., 1973. Structure and properties of iron-manganese alloys. Metallurgiya, Moscow, (in Russian). Burgers, W.Y., Klosterman, J.A., 1965. In¯uence of the direction of deformation on the transition of austenite into martensite. Acta Met. 13, 669. Chappuis, G., Naja®-Zadeh, A., Harmelin, M., Lehr, P., 1984. Contribution of martensitic transformations to the plastic behavior and the mechanical properties of Cr, Ni austenitic stainless steels. Mat. Res. Soc. Symp. Proc. 21, 699. Cherkaoui, M., Berveiller, M., 1998. Micromechanical modeling of the martensitic transformation induced plasticity (TRIP) in austenitic single crystals. Int. J. Plasticity 14, 597. Eichelman, G.H., Hull, T.C., 1953. The eect of composition on the temperature of spontaneous transformation of austenite to martensite in 18-8 type stainless steel. Trans. Amer. Soc. Met. 45, 77.
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Firks, H.J., 1968. Mechanische Eigenschaften asustenitischer Cr±Ni-StaÈhle nach ! und ! " ! Umwandlung. Neue HuÈtte 13, 668. Firks, H.J., 1970. Verformungs±Temperature±Umwandlungs±Diagramme von austenitischen kohlenstoarmen Cr±Ni±StaÈhlen. Neue HuÈtte 15, 300. Fischer, F.D., Sun, Q.-P., Tanaka, K., 1996. Transformation-induced plasticity. Appl. Mech. Rev. 49, 317. Hecker, S.S., Stout, M.G., Staudhammer, K.P., Smith, J.L., 1982. Eect of strain rate on deformationinduced transformation in 304 stainless steel. Part 1. Magnetic measurements and mechanical behavior. Metallurgical Trans. 13A, 619. Hirayama, T., Ogirima, M., 1970. Eect of chemical composition on martensite transformations in Fe± Cr±Ni stainless steels. J. Japan Inst. Metals 361, 507. Idesman, A.V., Levitas, V.I., Stein, E., 1999. Elastoplastic materials with martensitic phase transition and twinning at ®nite strains: numerical solution with the ®nite element method. Comp. Meth. in Appl. Mech. and Eng. 173, 71. Ilyichev, V.Y., Ul'Yanov, R.A., Skibina, L.V., 1968. The in¯uence of packing defects on phase transformations in Fe±Cr±Ni alloys in low temperature deformation. Metallo®zika 23, 78. Istomina, E.S., Nizhnik, S.B., 1973. Features of the development of strain-induced texture in austenitic steel with a plane stressed state. Izv. Adad. Nauk SSSR, Ser. Metallurgiya 3, 157. Iwamoto, T., Tsuta, T., Tomita, Y., 1998. Investigation on deformation mode dependence of straininduced martensitic transformations in TRIP steels and modeling of transformation kinetics. Int. J. Mech. Sci. 40, 173. Kato, M., Mori, T., 1976. Stress-induced martensite in single crystals of an Fe±23Ni±5Cr Alloy. Acta Met. 24, 853. Kosarchuk, V.V., Zaitseva, L.V., Lebedev, A.A., Kovalchuk, B.I., 1989. Eect of stress state parameters on phase transformation kinetics in austenitic steels with plastic deformations. Strength of Materials 21, 60. Langeborg, R., 1964. The martensite transformation in 18% Cr±8% Ni steels. Acta Met. 12, 823. Lebedev, A.A., Kosarchuk, V.V., Gudramovich, V.S., 1999. Micro- and macrostructural aspects of plastic deformation of metastable steels. In: Bruhns, O.T., Stein, E. (Eds.), Micro- and Macrostructural Aspect of Thermoplasticity, Proc. of the IUTAM Symp. 25±29 Aug. 1997. Kluwer Academic Publishers, Bochum, Germany, pp. 355±362. Leblond, J.B., 1989. Mathematical modeling of transformation plasticity in steels II: coupling with strain hardening phenomena. Int. J. Plasticity 5, 573. Leblond, J.B., Devaux, J., Devaux, J.C., 1989. Mathematical modeling of transformation plasticity in steels I: case of ideal-plastic phases. Int. J. Plasticity 5, 551. Levitas, V.I., 1997. Phase transitions in elastoplastic materials: continuum thermomechanical theory and examples of control. Parts I and II. J. Mech. Phys. Solids 45, 923 and 1203. Levitas, V.I., 1998. Thermomechanical theory of martensitic phase transformations in inelastic materials. Int. J. Solids and Structures 35, 889. Lysak, L.I., Khandros, L.G., 1953. Change in residual austenite during the deformation of steel U12A. Dokl. Akad. Nauk Ukr. SSR 4, 236. Marketz, F., Fischer, F.D., 1995. A mesoscale study on the thermodynamic eect of stress on martensitic transformation. Metall. Mater. Trans. 26A, 267. Medvedev, E.M., Lavrent'ev, E.F., Kurmanova, T.M., 1979 Martensitic transformations occurring with low-temperature thermal cycling and features of their eect on the yield point of steels OKh18N10T and 03Kh18N8. In: Martensitic Transformations in Metals and Alloys, Naukova Dumka, Kiev, 119± 122 (in Russian). Morris, C.E., 1946. Electropolishing of steel. Met. Prog. 56, 696. Murr, L.E., Staudhammer, K.P., Hecker, S.S., 1982. Eect of strain rate on deformation-induced transformation in 304 stainless steel. Part 2. Microstructural study. Metallurgical Trans. 13A, 627. Nizhnik, S.B., 1980. Stress±strain curves of stable and metastable two-phase steel in relation to the structure and volume content of the phases. Probl. Prochn. 3, 57. Olson, G.B., Cohen, M., 1975. Kinetics of strain-induced martensitic nucleation. Metallurgical Trans. 6A, 791.
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Pavlov, I.M., Bannykh, O.A., Mekhed, G.I., Chulanov, O.B., 1979. Stress±strain curves of steels with dierent types of martensitic transformations. In: Plastic Deformation of Metals and Alloys. Nauka, Moscow, pp. 63±67 (in Russian). Pisarenko, G.S., Lebedev, A.A., 1976. Deformation and strength of materials under complex stress state. Naukova Dumka, Kiev (in Russian). Pisarenko, G.S., Lebedev, A.A., Kovalchuk, B.I., 1984. Experimental study of the eect of the type of stress state on plastic strain in structural materials at low temperatures. Acta Astronautica 11, 483. Piwecki, M. 1986. Strain induced austenite transformation in stainless steels in uniaxial and biaxial tension. Arch. Budowy Maszyn, 33, 415 (in Polish). Reed, R.P., 1983. Martensitic transformation in Fe±Cr±Ni stainless steels. In: Reed, R.P., Horiuchi, T. (Eds.), Austenitic Steels at Low Temperatures (Proc. Joint. Int. Croygen. Eng. Conf. & Int. Cryogen. Mater. Conf., May 1982, Kobe, Japan). Plenum Press, New York±London, pp. 41±67. Reed, R.P., Mikesell, R.P., 1960. The stability of austentic stainless steels at low temperatures as determined by magnetic measurements. Advances in Cryogenic Engineering 4, 84. Seetharaman, V., 1984. Deformation and martensitic transformations. Bull. Mater. Sci. 6, 703. Singh, J., 1985. In¯uence of deformation on the transformations of austenitic stainless steels. J. Material Sci. 20, 3157. Sipos, K., Remy, L., Pineau, A., 1976. In¯uence of austenite predeformation on mechanical properties and strain-induced martensitic transformations of a high manganese steel. Metallurgical Trans. 7A, 857. Skibina, L.V., Ilyichev, V.Y. 1979. Martensitic transformation and its eect on the mechanical properties of single crystals of stainless alloys. In: Martensitic Transformations in Metals and Alloys. Naukova Dumka, Kiev, 84±88 (in Russian). Sokol, I.Y., 1974. Two-phase steels. Metallurgiya, Moscow (in Russian) Startsev, V.I., Ilyichev, V.Y., Pustovalov, V.V., 1975. Plasticity and strength of metals and alloys at low temperatures. Metallurgiya, Moscow (in Russian). Tamura, I., 1982. Deformation-induced martensitic transformation and transformation-induced plasticity in steels. Metal. Sci. 16, 245. Wigley, D.A., 1971. Mechanical properties of materials at low temperatures. Plenum Press, New York± London.
In¯uence of phase transformations on the mechanical properties of austenitic stainless steels A.A. Lebedev *, V.V. Kosarchuk National Academy of Sciences of Ukraine, Institute for Problems of Strength, 2, Timiryazevskaya str., 252014, Kiev, Ukraine Received in ®nal revised form 11 November 1999
Abstract The martensitic transformation in austenitic stainless steels type 18±10 can be induced by plastic deformation at room and low temperatures. In this study we conducted a systematic series of experiments to assess the in¯uence of both temperature and stress state type on kinetics of martensitic transformation. An attempt has been made to correlate the mechanical properties with the microstructural changes. The results of present studies make it possible to estimate the eect of stress state type on martensitic transformation kinetics in metastable chromiumnickel steels under isothermal loading. # 2000 Elsevier Science Ltd. All rights reserved. Keywords: Phase transformations; Isothermal loading; Austenitic stainless steels
1. Introduction A complete constitutive description of material behavior requires information about a material's response as a function of strain, stress state, strain rate, and temperature. Consequently the simulation of plastic deformation is one of the most complex and topical problems of the mechanics of solids. This is especially true for ``non-classical'' materials, in particular structurally unstable materials which undergo phase transformations subjected to thermal and mechanical loading. The mechanical properties of metastable materials, in particular Fe±Cr±Ni steels, have been the subject of experimental and theoretical studies for a long time. The reason is that these materials are quite often used in modern engineering. * Corresponding author. 0749-6419/00/$ - see front matter # 2000 Elsevier Science Ltd. All rights reserved. PII: S0749-6419(99)00085-6
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However, their mechanical properties are not fully investigated, because the character and the intensity of phase transformations depend on many factors, such as strain rate and strain level, stress state and regime of mechanical loading, and temperature. In this paper we examine the mechanical behavior and the evolution of phases in 18Cr±10Ni austenitic stainless steels as a function of the strain level, stress state and temperature. We consider the microstructural evolution as the key information for eventual understanding of the plastic ¯ow and failure behavior. Martensite formation resulting from plastic deformation of metastable austenite is of great interest for producing high strength and ductility in austenitic stainless steels. Substantial strengthening can be obtained in metastable austenitic stainless steels by plastic deformation below Md temperature (Md is the highest temperature at which the martensitic transformation can be induced by plastic deformation) to produce cubic body centered 0 and hexagonal closed packed " martensite. The transformation of cubic face centered austenite to 0 and " martensite depends on the alloy composition, stacking fault energy, degree of deformation, temperature etc. On the other hand, the fraction of the phases in the metal has a signi®cant eect on the character of its strain-hardening and its strength and ductility characteristics. Early studies (Eichelman and Hull, 1953; Bannykh and Kovneristyi, 1969; Hirayama and Ogirima, 1970; Pavlov et al., 1979) presented investigations of phase transitions in several pure and commercial Fe±Cr±Ni alloys under the in¯uence of plastic deformation at room and sub-zero temperatures. One of the main conclusions made in these studies was that the rate of martensite transformation depends signi®cantly on the chemical composition of the steel, with Ni, Cr and C having a particularly strong eect on the phase transition process. The total eect of the main alloying elements on the martensitic transition is evaluated from the nickel equivalent (Hirayama and Ogirima, 1970) Niequ %Ni 0:65%Cr 0:98%Mo 1:05%Mn 0:35%Si 12:6%C: Martensitic transformations in austenitic stainless steels have been studied extensively in uniaxial tension at low strain rates (static loading) (Angel, 1954; Langeborg, 1964; Wigley, 1971; Olson and Cohen, 1975; Tamura, 1982; Reed, 1983; Chappuis et al., 1984; Seetharaman, 1984). The in¯uence of the stress (strain) state on the phase transformation has received, however, very little attention (Kato and Mori, 1976; Hecker et al., 1982; Piwecki, 1986; Kosarchuk et al., 1989; Marketz and Fischer, 1995; Lebedev et al., 1999). Current achievements in transformationinduced plasticity are analyzed in paper by Fischer et al., 1996). Continuum thermomechanical theory of martensitic phase transformations in elastoplastic materials is presented by Levitas (1997, 1998). Interaction between phase transformation and plasticity at the micro level was studied by Leblond et al. (1989), Leblond (1989), Cherkaoui et al. (1998), Marketz and Fischer (1995) and Idesman et al. (1999).
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2. Experimental procedure Two commercial type 18Cr±10Ni austenitic stainless steels were studied, and their composition is given in Table 1. The nickel equivalent for steels A and B is 22.46 and 26.73%, respectively. The lower value of Niequ for steel A is evidence of its greater metastability with respect to the martensite transformation. Mechanical tests (uniaxial tension and compression, torsion, and biaxial loading with dierent principal stress ratios ) at temperatures of 293, 173, and 77 K were conducted on a hydraulic testing machine SNT-5PM with a computer-aided control system (Pisarenko et al., 1984). The loading rate was kept constant in all of the tests (about 15 MPa/s). Two types of specimens were used for the tests: thin-walled tubular specimens (external diameter 26 mm, wall thickness 0.5 mm, working length 75 mm, gage length 20 mm) made of steel A, and solid cylindrical specimens (6 mm diameter, working length 25 mm, gage length 10 mm) made of steel B. The specimens were made from hot-rolled bars of steels A and B 45 and 20 mm in diameter, respectively, in the conditions as received. After machining, the specimens were heat-treated as follows: heating to 1350 K in a vacuum, 40 min holding, and slow cooling. The specimens were deformed in stages. After each loading stage we conducted a phase analysis of the material and determined the plastic strains. The plastic longitudinal "pz and transverse "p strains of the tubular specimens were measured with an accuracy of 0.02%, while the radial strain "pr was determined to within 0.2%. Structural changes in the deformed steel were studied by the methods of X-ray diraction and optical metallography. We recorded the (111) X-ray lines of austenite and the (110) and (101) lines of the 0 and " martensite, respectively, to determine the volumetric fraction of retained austenite and strain induced martensite in the steels. Here, we used a diractometer DRON-2,0 with scintillation recording. The phase composition of the material was determined by comparing the integral intensities of X-ray interference with allowance for repetition factors. A well-known method was used to do this (Lysak and Khandros, 1953). The microstructure of the working surface of the specimens was studied with a ``Neophot-2'' optical microscope after preliminary mechanical and electrolytic polishing of the specimens. The specimens were etched electrolytically in a chromium-acetate Morris reagent (Morris, 1946) consisting of 133 ml of glacial acetic acid, 25 g of chromic anhydride, and 7 ml of water. The electrolytic etching regime was as follows: current density 0.1 A/cm2, temperature 17 C. The microstructure was studied at magni®cation of 200, 800, and 2000. The microstructure of the austenite after the heat treatment consists of light Table 1 Chemical composition (wt%) of steels investigated Type
C
Cr
Ni
Mn
Ti
Si
Mo
V
Cu
Fe
A B
0.07 0.07
16.4 15.4
9.6 12.3
1.03 1.45
0.67 0.41
0.39 0.43
0.11 1.91
0.06 0.05
0.04 0.12
Balance Balance
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equiaxed grains of solid solution with characteristic annealing twins. Mean grain size is about 44 mm. 3. Results and discussion 3.1. Uniaxial tension The stress±strain curves of the steels under dierent temperatures are shown in Fig. 1 (i and "i are von Mises equivalent stress and strain). The stress±strain curves of steels A and B at room temperature are similar to the typical tension curves of polycrystalline alloys with an fcc lattice and exhibits a regular form. The authors of several works (Medvedev et al., 1979; Skibina et al., 1979 etc.) noted that the deformation of steels of the 18±10 type at room temperature is not accompanied by phase transitions up to the fracture. Bannykh (1969) and Firks (1970) showed that the metal should be deformed to a very high strain to form strain induced martensite at room temperature. Phase transitions caused by plastic deformation, however, occur also at room temperature and start at relatively low strains in the conducted tests with steel A. A detectable amount of martensite (a0 -phase) is already present at "pi > 10% (Fig. 2a).
Fig. 1. Stress±strain curves for steels A (1, 2, 3) and B (4, 5) at temperatures of 293 K (1, 4), 173 K (2), and 77 K (3, 5). (The dashed lines are stress±strain curves in the case of staged loading, while the solid curves are for continuous loading.)
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The largest amount of martensite (up to 40%) is observed in the neck region of fractured specimens deformed to 55±60%, while the amount of martensite formed in the region of uniform plastic strain (about 35%) is not high (up to 25%), and its contribution to strain-hardening is insigni®cant (see Fig. 1).
Fig. 2. Dependence of the volume fraction of 0 -phase (a) and e-phase (b) in steels A and B on strain at temperatures of 77, 173 and 293 K.
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For the more stable steel B, no martensitic transformation was observed at room temperature up to fracture. The dierence is evidently attributed to the chemical composition of the steels, particularly the reduced nickel content of steel A. It was noted (Bannykh and Kovnerstyi, 1969; Reed, 1983) that the formation of the mechanical properties of chromium-nickel austenitic steels in low-temperature deformation is aected not only by the strain induced martensite, but also by the temperature induced martensite formed during cooling of the initial structure below the martensite start temperature Ms . The temperature Ms for steels A and B, calculated from an empirical formula proposed Eichelman and Hull (1953), is 140 and 8 K, respectively. Despite the possible error in the determination of Ms , it should be expected that the cooling of steel A to 77 K will lead to the formation of temperature induced martensite. The dependence of the kinetics of phase transformations on the temperature, duration of holding under ®xed load, number of thermal cycles and type of stress state has been examined. The studies have demonstrated that the martensitic transformations are related to thermal stresses and are little aected by the duration of the holding at a constant low temperature without load. Thus, for example, seven thermal cycles (cooling to 77 K and heating to 293 K) performed either in 15 min or 250 h (the duration of each cycle was about 36 h in this case) resulted in about the same quantity (about 8%) of 0 -martensite (Fig. 3a and 3b). The cooling and heating rates were 6 and 3 K/s, respectively. As the number of thermal cycles increases, the amount of the 0 -phase formed per cycle decreases monotonically, and temperature induced martensite volume fraction saturates (see Fig. 3a and 3c). The holding at low temperature under plastic deformation contributes to a greater extent to the phase transition than the holding in elastic domain or under zero load condition does. The long rest during 2 months activate phase transformations (point C on curves). A small amount of "-martensite (up to 6%) was observed on the diraction patterns simultaneously with the 0 -phase. The presence of the "-martensite was ®xed in the form of an interference re¯ection from the {101} plane. It is believed (Firks, 1968; Startsev et al., 1975; Reed, 1983) that the "-phase is an intermediate phase in the
! 0 transition. The results obtained on chromium±nickel steels at low temperatures con®rm this (Sokol, 1974; Chappuis et al., 1984; Singh, 1985). Nevertheless, this may not be the only possible transformation scheme (Bogachev and Egolaev, 1973; Sipos et al., 1976; Murr et al., 1982). Martensitic transformation begins with the formation of several parallel-phase plates in octahedral {111} planes of austenite grains. An increase in the number of thermal cycles is accompanied by fragmentation of the initial austenite grains as a result of the intersection of "-martensite plates at angles of 60 and 120 . The 0 phase martensite is seen at a magni®cation of 800 in the form of a large accumulation of points located in the "-phase plates. It follows from the above results and data of optical study stabilization of the process of martensite transformation is evidently connected with complete ®lling of plates of the "-phase by 0 -martensite crystals. Preliminary deformation in tension promotes the initial stage of the process of thermal induced martensite formation, as it is evident from data on martensite
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transformation kinetics of steel A prestrained at room temperature to "pi 20%(see Fig. 3b and c). Deformation at low temperatures is accompanied by intensive strain-hardening of the steel, the character of which is aected by the phase transitions (solid lines in Fig. 1). The stress±strain curves of steel A at 173 and 77 K dier somewhat in the rate of strainhardening even in the region of relatively small strains (3±9%). This is connected with the dierences in kinetics of martensite transformation at these temperatures.
Fig. 3. Dependence of the volume fraction of 0 -phase on number of cooling cycles.
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According to Reed (1983), Pavlov et al. (1979), the "-phase exerts a softening eect, which reduces strain-hardening. An increase in strain is accompanied initially by some increase in the amount of "-martensite (the latter reaches 6.5% at "pi 2:6%) followed by decrease in "-martensite (see Fig. 2b). At "pi > 13% no "-phase is seen on the diraction patterns. The increase in strain-hardening at "pi > 13% is evidently connected with the predominant eect of the 0 -phase, which grows with an increase in strain (see Fig. 2a). Despite the small dierence in the chemical composition of the investigated steels, the stress±strain curves at 77 K dier considerably (see Fig. 1). This is connected with features of the martensite transitions. The formation of strain induced martensite ( 0 -phase) in steel B starts at a larger (about 5%) strain than in steel A. The transition takes place more slowly, and the maximum amount of martensite (about 100%) is reached at strains of 40±45% (see Fig. 2a). In contrast to steel A at 77 K, parallel with the ! 0 transition in steel B, austenite is transformed to the hcp "-phase (Fig. 2b). The presence of this phase aects the character of strain±hardening, especially at small (5±15%) strains (see Fig. 1). Thus, the greater stability of the austenite in steel B lowers the rate of its strainhardening, which is consistent with the results of Startsev et al. (1975); Nizhnik (1980); Reed and Mikesell (1960). Twinning and slip occur during the initial stages of deformation, as is it evident from the appearance of a large number of slip traces in the austenite grains. An increase in the strain is accompanied by the appearance of numerous zones with an extremely unhomogeneous strain distribution leading to the formation of microreliefs connected with distortion of the crystalline lattice. The slip bands form broad blocks which intersect with martensite needles. The strain traces are heavily distorted and masked by numerous martensite plates at the stage of deformation preceding fracture. As follows from Fig. 1, staged deformation (i.e. sequence loadings with intermediate unloadings) leads to additional strain-hardening of the material caused by two factors. On the one hand, it is related to the strain-hardening eect of the martensite formed during repeated cooling. On the other hand, it is connected with the change in the properties of the steel as a result of recovery. A comparison of the stress±strain curves at 77 and 173 K (temperature induced martensite is not observed at the latter temperature) shows that the eect of temperature induced martensite is predominant. This is con®rmed by the fact that after unloading and subsequent loading without holding (point VII'' in Fig. 1), no additional strain-hardening eect is observed. Holding the unloaded specimen for 3 h at 77 K (point VII'') leads to a slight amount of additional strain-hardening. Quantitative description of the eects observed will require the realization of special experiments. It is known (Bannykh and Kovneristyi, 1969; Sokol, 1974) that transformation of austenite to martensite is accompanied by a change in volume. Volume increases in the ! 0 transition and decreases in the ! " transition. The kinetics of the phase transition in steel A at 173 and 77 K is re¯ected by the dierent character of
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Fig. 4. The lateral strain factor versus the degree of plastic strain (steel A).
the change of the coecient of transverse plastic deformation "p ="zp with an increase in the amount of prestrain "pi (Fig. 4). At a temperature of 77 K, the coecient of transverse plastic deformation initially increases rapidly, reaching a maximum value of 0.49. Then it decreases monotonically. Comparison of Figs. 2a and 4 indicates that a remarkable change in volume during plastic deformation starts at a strain "pi 5%, which corresponds to a martensite fraction of 45%. It should be noted that the eect of strain induced martensite on at 173 K begins to be manifested as well at a volume fraction of 0 -phase of about 45%. Fig. 5 shows the dependence volume change, characterized by the ÿ of the relative mean plastic strain "f0 1=3 "pz "p "pr ; on the volume fraction of strain induced martensite (we considered the total fraction of the 0 and " phases) in deformed steel A. It can be seen that the change in volume depends to a signi®cant extent on the test temperature. Whereas the value of "f0 is nearly linearly dependent on the martensite fraction at 77 K, a more complex pattern is seen at 173 K. The value of "f0 decreases slightly during the initial stages of deformation and then increases fairly
Fig. 5. Dependence of the mean plastic strain on total volume fraction of martensite (steel A).
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rapidly. Such a character of the relation "f0 ÿ Vm is evidently connected with the competing eects of the 0 and " phases at small strains. Thus, the results obtained provide evidence of a clear correlation between the strain-hardening of chromium±nickel austenitic steels and the kinetics of martensite transformation under uniaxial tension. 3.2. Compression and torsion Experimental and theoretical (Kato and Mori, 1976; Hecker et al., 1982; Piwecki, 1986; Kosarchuk et al., 1989; Marketz and Fischer, 1995; Lebedev et al., 1999) investigations showed that, together with the temperature, the type of the stress state has a signi®cant in¯uence on the processes of phase transformations in metastable steels. However, too few experimental data do not allow a quantitative evaluation of the in¯uence of the type of the stress state on the intensity of the martensite transformation in the course of plastic deformation. This section presents the results of an investigation of the kinetics of the phase transformations in steel B in tension, compression, and torsion. The samples were deformed in load steps. After each load step a phase analysis of the material was performed, and the microhardness and residual deformations of the specimens were determined. The axial and transverse deformations were determined in tension and compression with an accuracy of 0.05%, and the angle of twist in torsion related to a length of 25 mm with an accuracy of 0.5%. The hardening of the deformed steel was evaluated by measurement of the microhardness. The working surface of the specimens was indented with a load of 100 g. Each experimental point was determined by averaging the microhardness readings of 10 indentations. The mechanical tests were made at 293 and 77 K. The room-temperature tests indicate that, regardless of the type of the stress state, the plastic deformation of the given steel is not accompanied by phase transformations up to the failure. A cooling to 77 K without any deformation does also not lead to a martensite transformation even under conditions of a long holding at this temperature. Low-temperature deformation of steel B is accompanied by a martensite transformation. In the deformed steel hexagonal "-phase is observed together with 0 martensite. Figs. 6a and 6b present the relation between the volume fraction of 0 - and "martensite and the strain for the three types of loading: tension, torsion, and compression. A comparison of the curves shows that, depending on the type of loading, the process of the martensitic transformation occurs with dierent intensities. Tension causes more intense formation of "-phase than torsion and especially than compression. The V ÿ "pi curves in torsion and compression have a smaller slope than in tension, and the maximum amount of 0 -martensite, which also depends on the mode of loading, is reached with higher degrees of straining. The kinetics of the ! " transformation diers signi®cantly from the kinetics of formation of the 0 -martensite (Fig. 6a and b).
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The hexagonal "-martensite is already formed in the early stages of deformation (traces of "-phase are observed at deformations of 1%), while the ! 0 transformation still does not up to 5% deformation. As follows from Fig. 6b, the volume fraction of "-martensite depends to a signi®cant extent on the type of loading, especially at large deformations. The maximum "-phase fraction is approximately the same (8±9%) for all types of loading, but the range of deformations in which it is observed is signi®cantly higher for compression than for tension. In the prefailure state and in the failed specimens, "-phase was not observed.
Fig. 6. The volume fraction of 0 -phase (a) and "-phase (b) in steel B versus the plastic strain intensity under tension (1), torsion (2), and compression (3).
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The reason for the observed dierences in the kinetics of the phase transformations with the type of loading is related to the sign of volume change due to the formation of martensite (Ilyichev et al., 1968; Bannykh and Kovneristyi, 1969). It is known that the ! 0 transformation is accompanied by an increase in volume and the ! " transformation by a decrease in volume. Therefore, tension promotes the ! 0 transformation and suppresses the formation of "-phase. In compression the reverse eects are observed. Phase transformations possess a signi®cant in¯uence on the strain hardening of chrome-nickel austenitic steels, the degree of which may be judged from the microhardness H (Fig. 7), (see e.g. Bannykh and Kovneristyi, 1969; Reed, 1983). There is a steady increase in microhardness related to strain hardening at room temperature during tension as a result of work hardening of austenite. Some reduction in microhardness with large degrees of deformation (>40%) may apparently be explained by softening of the material in the prefailure stage. At low temperature (77 K) tension of steel leads to a signi®cant increase in the strain hardening of the material, which is related to the occurrence of phase transformations. On the H -"pi curves (see Fig. 7) three characteristic stages may be conditionally distinguished. For example, in tension a rapid increase in microhardness occurs in the ®rst stage, caused by work hardening of the austenite as well as by the formation of coarse dispersed "-martensite, the hardness of which exceeds the hardness of austenite by 40%. In the second stage ("pi =6±12%) the rate of strain hardening decreases since there is practically no more increase in the volume fraction of "-phase, and the ®nely dispersed 0 -martensite, formed in a small quantity, makes an insigni®cant contribution to hardening of the investigated steel. This may p explain the appearance ÿ p of a bend on the H ÿ "i curve (see Fig. 7). The third stage "i > 12% shows strong hardening of the steel, which occurs primarily as the result of intense formation of the -phase.
Fig. 7. The microhardness of steel B versus the plastic strain intensity in the case of tension (1, 3) and compression (2) at 77 K (1, 2) and 293 K (3).
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In compression the features of strain hardening of the steel under low-temperature conditions are preserved but less pronounced. Comparing the H ÿ "pi relationship for tension and compression with the corresponding curves of the change in volume fraction of the phases (Figs. 6a and 6b) may lead to the conclusion that the main features of strain hardening of the steel in these types of loading are related to dierent intensities of the processes of formation of 0 - and "-phases. 3.3. Plane stress state A study of martensitic transformation kinetics under biaxial stress state at low temperatures showed that the intensity of its development depends markedly on the principal stress ratio k z = . In these tests we used the thin-walled tubular specimens of steel A. The change in volume fraction of martensite during low-temperature deformation of steel A with values k z = is illustrated in Fig. 8. The amount of 0 -phase decreases for a ®xed value of plastic strain with the change-over from uniaxial tension to balanced biaxial tension. It is possible to estimate the in¯uence of stress state on the intensity of phase transformations by applying the stress triaxiality parameter K 0 =i , where i is the equivalent stress and 0 is the hydrostatic stress (Pisarenko and Lebedev, 1976; Marketz and Fischer, 1995; Iwamoto et al., 1998).
Fig. 8. Dependence of volume fraction of -martensite in steel A at 173 K on the amount of strain with dierent ratios of principal stresses: 1 ÿ k 1; 2 ÿ k 0:5; 3 ÿ k 1; 4; 4 ÿ k 1.
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This in¯uence is connected with volume increase during 0 -martensite formation. An increase in stress triaxiality leads to an increase in the elastic volumetric strain which should stimulate the 0 transformation. However, in the present work an opposite eect was obtained: with an increase in parameter K from 1/3 (uniaxial tension) to 2/3 (balanced biaxial tension) the rate of 0 -phase formation decreases with strain. By comparing the results considered above, we see that K is not the only parameter of the stress state aecting martensitic transformation. One may suggest a dependence of martensitic transformation kinetics also on the stress deviator which is characterized by the Lode's parameter 22 ÿ 1 ÿ 3 = 1 ÿ 3 . Both K and describe the trajectory of simple (proportional) loading path in the stress space. A decrease in the rate of martensitic transformation with a change-over from uniaxial to balanced biaxial tension may be explained by the prevailing eect of parameter on the phase transition which in this case varies from ÿ1 to 1. The amount of 0 -phase at some ®xed plastic strain "pi is greater for higher value of R j"p1 ="p3 j where "p1 and "p3 are the maximum values of plastic tensile strain and plastic compressive strain, respectively. In the case of similarity of stress and strain deviators " , the value of R is equal to 2 for ÿ1; for 0 it is 1, and for 1 it is 0.5. A very perfect [111] texture (Burgers and Klosterman, 1965) may have an activating eect on the process of martensite formation under uniaxial tension ÿ1. The retarding eect of a second stress component on the martensitic transformation is explained by formation of a more complex stressed austenite structure with an increased structural defect density (Istomina and Nizhnik, 1973). Thus, the correlation established between the stress triaxiality parameter K , Lode's parameter, , and the rate of phase transformation caused by plastic deformation makes it possible to present the volume fraction of martensite in austenitic stainless steels under proportional loading by the following function relation: ÿ 1 Va f "pi ; s ; Ks ; T The experimental results (see Figs. 2, 6, 8) have made it possible to specify function (1) for the case of isothermal loading as Table 2 Parameters of Eq. (2) with various ratios of principal stresses Stress state parameters
Steel A at T=173 K
Steel B at T=77 K
k
K
n
"0
n
"0
1 1.4 1.0 2 ÿ1.0 ±
1/3 0.62 2/3 1 0 ÿ1/3
ÿ1 0.45 1 0 0 1
49.1 46.0 28.1 46.9 ± ±
0.93 0.88 0.80 0.88 ± ±
1.78 2.01 1.95 1.88 ± ±
0 0 0 0 ± ±
31 ± ± ± 10 6
1.04 ± ± ± 0.9 1.1
1.81 ± ± ± 1.43 1.45
0.047 ± ± ± 0.05 0.07
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ÿ n V 1 ÿ exp ÿ "p1 ÿ "p0i ;
763
2
where "p0i is the martensitic start strain (it depends on the degree of steel stability); , and n are coecients which are functions of stress state parameters , and K . Numerical values of these coecients for steels A and B are given in Table 2. Curves ÿ V "pi , calculated from Eq. (2), are depicted in Figs. 2a, 6a and 8. In Fig. 9, surfaces were plotted in the three-dimensional space V ÿ ÿ K based on Eq. (2) and data of Table 2, qualitatively re¯ecting the eect of stress state parameters on the amount of 0 -martensite at certain ®xed values of "pi . As can be seen from Fig. 9, with an increase in K and a reduction in Lode's parameter the process of martensitic transformation intensi®es. The has a predominant eect on the ! 0 transition due to the shear components of transformation stress. The phase transformations strongly aect the mechanical properties of steels under biaxial testing at low temperatures. A discrepancy of the eective stress±strain curves with the ratio of principal stresses k z = is observed (Fig. 10). The strain-hardening rate curves (Fig.11) exhibits changes in concavity and two in¯ection points.
Fig. 9. Dependence of volume fraction of martensite on stress state stiness parameter and Lode's parameter at dierent levels of plastic strain: 1 ÿ "pi 5%; 2 ÿ "pi 10%; 3 ÿ "pi 15%.
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Fig. 10. Stress±strain curves for steel A at 173 and 293 K at various ratios of principal stresses: 1 ÿ k 1; 2 ÿ k 1; 4; 3 ÿ k 0; 5; 4 ÿ k 1.
Fig. 11. Strain-hardening rate curves for steel A at 173 K (a) and 293 K (b) at dierent ratios of principal stresses: 1 ÿ k 1; 2 ÿ k 1:4; 3 ÿ k 0:5; 4 ÿ k 1.
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Thus, the results of the present studies allow to estimate qualitatively and quantitatively the eect of the loading type on martensitic transformation kinetics in metastable austenitic stainless steels with isothermal proportional loading. The experimental data may be used as a basis to formulate some constitutive relations for metastable materials. Furthermore, they can be used for optimization of technological processes connected with plastic forming and thermomechanical strengthening of austenitic stainless steels. 4. Conclusions 1. The rate of martensitic transformation depends signi®cantly on the chemical composition of the steel. 2. Deformation by tension causes more intense formation of both 0 - and " martensite than deformation by torsion and especially by compression. 3. Tension, causing an increase in the volume, promotes the ! 0 transformation and suppresses the formation of "-phase. In compression the reverse eect is observed. 4. With an increase in the stress triaxiality parameter and a reduction of Lode's parameter the ! 0 transformation intensi®es. The Lode's parameter has a predominant eect on the martensitic transformation. 5. The results demonstrate a clear correlation between the strain-hardening of austenitic stainless steels and the kinetics of martensitic transformation under various types of loading. Acknowledgements We are indebted to Professor V.V. Levitas (Texas Tech University, Lubbock) for helpful discussions and his help with preparing this article. References Angel, T., 1954. Formation of martensite in austenitic stainless steels. J. Iron & Steel Inst. 177, 165. Bannykh, O.A., Kovneristyi, Y.K., 1969. Steels for operation at low temperatures. Metallurgiya, Moscow (in Russian). Bogachev, I.N., Egolaev, V.F., 1973. Structure and properties of iron-manganese alloys. Metallurgiya, Moscow, (in Russian). Burgers, W.Y., Klosterman, J.A., 1965. In¯uence of the direction of deformation on the transition of austenite into martensite. Acta Met. 13, 669. Chappuis, G., Naja®-Zadeh, A., Harmelin, M., Lehr, P., 1984. Contribution of martensitic transformations to the plastic behavior and the mechanical properties of Cr, Ni austenitic stainless steels. Mat. Res. Soc. Symp. Proc. 21, 699. Cherkaoui, M., Berveiller, M., 1998. Micromechanical modeling of the martensitic transformation induced plasticity (TRIP) in austenitic single crystals. Int. J. Plasticity 14, 597. Eichelman, G.H., Hull, T.C., 1953. The eect of composition on the temperature of spontaneous transformation of austenite to martensite in 18-8 type stainless steel. Trans. Amer. Soc. Met. 45, 77.
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Firks, H.J., 1968. Mechanische Eigenschaften asustenitischer Cr±Ni-StaÈhle nach ! und ! " ! Umwandlung. Neue HuÈtte 13, 668. Firks, H.J., 1970. Verformungs±Temperature±Umwandlungs±Diagramme von austenitischen kohlenstoarmen Cr±Ni±StaÈhlen. Neue HuÈtte 15, 300. Fischer, F.D., Sun, Q.-P., Tanaka, K., 1996. Transformation-induced plasticity. Appl. Mech. Rev. 49, 317. Hecker, S.S., Stout, M.G., Staudhammer, K.P., Smith, J.L., 1982. Eect of strain rate on deformationinduced transformation in 304 stainless steel. Part 1. Magnetic measurements and mechanical behavior. Metallurgical Trans. 13A, 619. Hirayama, T., Ogirima, M., 1970. Eect of chemical composition on martensite transformations in Fe± Cr±Ni stainless steels. J. Japan Inst. Metals 361, 507. Idesman, A.V., Levitas, V.I., Stein, E., 1999. Elastoplastic materials with martensitic phase transition and twinning at ®nite strains: numerical solution with the ®nite element method. Comp. Meth. in Appl. Mech. and Eng. 173, 71. Ilyichev, V.Y., Ul'Yanov, R.A., Skibina, L.V., 1968. The in¯uence of packing defects on phase transformations in Fe±Cr±Ni alloys in low temperature deformation. Metallo®zika 23, 78. Istomina, E.S., Nizhnik, S.B., 1973. Features of the development of strain-induced texture in austenitic steel with a plane stressed state. Izv. Adad. Nauk SSSR, Ser. Metallurgiya 3, 157. Iwamoto, T., Tsuta, T., Tomita, Y., 1998. Investigation on deformation mode dependence of straininduced martensitic transformations in TRIP steels and modeling of transformation kinetics. Int. J. Mech. Sci. 40, 173. Kato, M., Mori, T., 1976. Stress-induced martensite in single crystals of an Fe±23Ni±5Cr Alloy. Acta Met. 24, 853. Kosarchuk, V.V., Zaitseva, L.V., Lebedev, A.A., Kovalchuk, B.I., 1989. Eect of stress state parameters on phase transformation kinetics in austenitic steels with plastic deformations. Strength of Materials 21, 60. Langeborg, R., 1964. The martensite transformation in 18% Cr±8% Ni steels. Acta Met. 12, 823. Lebedev, A.A., Kosarchuk, V.V., Gudramovich, V.S., 1999. Micro- and macrostructural aspects of plastic deformation of metastable steels. In: Bruhns, O.T., Stein, E. (Eds.), Micro- and Macrostructural Aspect of Thermoplasticity, Proc. of the IUTAM Symp. 25±29 Aug. 1997. Kluwer Academic Publishers, Bochum, Germany, pp. 355±362. Leblond, J.B., 1989. Mathematical modeling of transformation plasticity in steels II: coupling with strain hardening phenomena. Int. J. Plasticity 5, 573. Leblond, J.B., Devaux, J., Devaux, J.C., 1989. Mathematical modeling of transformation plasticity in steels I: case of ideal-plastic phases. Int. J. Plasticity 5, 551. Levitas, V.I., 1997. Phase transitions in elastoplastic materials: continuum thermomechanical theory and examples of control. Parts I and II. J. Mech. Phys. Solids 45, 923 and 1203. Levitas, V.I., 1998. Thermomechanical theory of martensitic phase transformations in inelastic materials. Int. J. Solids and Structures 35, 889. Lysak, L.I., Khandros, L.G., 1953. Change in residual austenite during the deformation of steel U12A. Dokl. Akad. Nauk Ukr. SSR 4, 236. Marketz, F., Fischer, F.D., 1995. A mesoscale study on the thermodynamic eect of stress on martensitic transformation. Metall. Mater. Trans. 26A, 267. Medvedev, E.M., Lavrent'ev, E.F., Kurmanova, T.M., 1979 Martensitic transformations occurring with low-temperature thermal cycling and features of their eect on the yield point of steels OKh18N10T and 03Kh18N8. In: Martensitic Transformations in Metals and Alloys, Naukova Dumka, Kiev, 119± 122 (in Russian). Morris, C.E., 1946. Electropolishing of steel. Met. Prog. 56, 696. Murr, L.E., Staudhammer, K.P., Hecker, S.S., 1982. Eect of strain rate on deformation-induced transformation in 304 stainless steel. Part 2. Microstructural study. Metallurgical Trans. 13A, 627. Nizhnik, S.B., 1980. Stress±strain curves of stable and metastable two-phase steel in relation to the structure and volume content of the phases. Probl. Prochn. 3, 57. Olson, G.B., Cohen, M., 1975. Kinetics of strain-induced martensitic nucleation. Metallurgical Trans. 6A, 791.
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