Effect of Volume Expansion on Transformation Plasticity during Ferrite and Martensite Transformation of Steel

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1 (Journal of the Society of Materials Science, Japan), Vol. 60, No. 10, pp , Oct Original Papers Effect of Volume Expansion on Transformation Plasticity during Ferrite and Martensite Transformation of Steel by Takayuki OTSUKA, Tohru AKASHI, Shigeru OGAWA, Takayuki IMAI and Akira EGAMI Several kinds of carbon steels and Invar alloys are applied to identify the dependence of transformation volume expansion on transformation plasticity for both diffusive and non-diffusive transformation. It is confirmed by the experiments that the notion of Leblond s model (transformation volume expansion over yield stress of mother phase and transformation plastic coefficient has proportional relationship) appears to be good for both ferrite and martensite transformation. In addition, the experimental results of Invar alloys also support the idea that if the transformation volume expansion is significantly small, the transformation plastic strain becomes small accordingly. It is commonly said that Magee effect (selective martensite variant) plays a main role during martensite transformation. However, for steel treated in this paper, Greenwood-Johnson effect (transformation volume expansion) is also significant for martensite transformation. Key words : Transformation plasticity, Transformation strain, Transformation volume expansion, Greenwood- Johnson effect, Magee effect, Martensite transformation, Ferrite transformation, Steel, Invar alloy 1 Introduction In the course of steel producing process, high temperature austenite phase slab is rolled to be product shape and size, and at the same time, cooled down at controlled optimum cooling rate to achieve ferrite, pearlite, bainite and martensite mixed phase depending on steel grades. During phase transformation, when stress is applied even if it is smaller than its yield stress, remarkable strain occurs ; the behaviour is called transformation plasticity. 1) Transformation plasticity is known to play an important role in steel making processes. For example, in the course of heat treatment process, transformation plastic deformation affects products shape and residual stress. 2), 3) Hence, it is extremely important to identify the behaviour of transformation plasticity precisely for given steel grades and cooling rates. However, presently, the behaviour and even its mechanism are not fully understood. Therefore, sometimes it is required to conduct many numbers of experiments to identify the phenomenon. In this paper, several kinds of steel grades are treated to investigate the mechanism of transformation plasticity during both diffusive (ferrite, pearlite) and non-diffusive (martensite) phase transformation. 2 Existing Mechanism for Explaining Transformation Plasticity Presently, the dominant mechanism of transformation plasticity is not fully understood, and therefore, several kinds of mechanism explaining transformation plasticity are proposed. Among these are called Greenwood-Johnson effect, 4) in which the volume expansion during diffusive phase transformation (or contraction during reverse transformation) enhances total macroscopic deformation called transformation plastic strain, and Magee effect, 5) in which particular martensite orientation is selected with small applied stress. For diffusive transformation, according to the Greenwood-Johnson mechanism, Leblond et. al. 6) modelled transformation plasticity represented by following equation. (1) Where, tp th ε ij is transformation plastic strain rate, Δε 1 2 is transformation volume expansion from phase 1 (mother) to phase 2 (new), σ 1 y is a yield stress of phase 1, ξ is volume fraction of phase 2 and s ij is applied deviatoric stress. The case dividing by ξ value is set in order to prevent numerical unstable with taking log near zero. This equation indicates the transformation plastic strain rate depends on the magnitude of volume change during phase transformation Δε 1 2, yield stress of mother phase σ 1 y, applied devia- th toric stress s ij and the rate of volume fraction increase of new phase ξ. This model unveils its good agreement with experimental results. 1) It is also confirmed by finite element simulations carried out by Barbe et. al., 7) that the Greenwood- Johnson effect is certainly one of the greatest reasons for explaining transformation plasticity. It is also confirmed by Inoue et. al. 8) by using simple parallel spring model between two phases. Another well-known model is rather simple phenomenological equation, 2) such that (2) Received Oct. 29, The Society of Materials Science, Japan Member : Technical Development Bureau, Nippon Steel Corporation, Shintomi, Futtsu, Japan Technical Development Bureau, Nippon Steel Corporation, Shintomi, Futtsu, Japan Gifu Research Institute, Japan Ultra-High Temperature Materials Research Institute, Higashi-machi, Tajimi, Japan

2 938 T. Otsuka, T. Akashi, S. Ogawa, T. Imai, A. Egami or following enhanced model that is applicable to multiple transformation. 9) (3) where, K is a transformation plasticity coefficient. On the other hand, for non-diffusive phase transformation, including martensite transformation, it is said that particular martensite orientation (variant) is selected according to applied stress, and it also fosters total macroscopic strain. This effect is called Magee effect. The effect shows good correspondence with martensite transformation of shape memory alloys. 10) Still, the Greenwood-Johnson effect for non-diffusive transformation remains unclear, for no smaller transformation expansion than diffusive transformation occurs during martensite transformation of steels. It seems that the dominant mechanism is dependent on the chemical composition of alloys and condition of transformation. In this paper, the authors aim to unveil the Greenwood- Johnson effect for not only ferrite transformation but also martensite transformation of steel by applying several kinds of steel grades. 3 Experimental Procedure to Identify Transformation Plastic Strain 3. 1 Carbon Steels Tensile machine with heating and cooling system is developed for identifying transformation plasticity. The Ar jet cooling system, which enables high cooling rates for obtaining martensite phase, is installed in the Instron 8802 fatigue testing machine. In this facility, induction heating is adapted to heat up specimens up to It is also important to note that vacuum chamber is necessary for such high temperature ; otherwise, thick layer of oxide scale is generated, which makes it difficult to detect precise temperature. In this paper, the specimen with chemical composition shown in Table 1 with Japanese industrial standard (JIS) code are adopted. They are initially heated up to 900 and keep the temperature for 5 minutes in order to obtain fully austenite phase, which is followed by applying small stress ranging from 10MPa to 50MPa. No sooner stress is applied than the specimens are cooled down rapidly. The cooling rates are 8 and 50 /sec at 700. In the course of cooling procedure, phase transformation from austenite phase to ferrite or martensite phase occurs depending on the cooling rates. During the transformation, one can observe large strain generation depending on the values of applied stress Fe-Ni-Co Invar alloys Two types of Invar alloys with chemical composition summarized in Table 2 are adopted. The aim of using Invar alloys is to take advantage of their extremely small transformation volume expansion 11) to determine the Greenwood-Johnson effect of martensite transformation. Fe-25Ni-20Co Invar alloy has its magnetic transformation point at about 500, and below this temperature, coefficient of thermal expansion decreases significantly. Therefore, the alloy has considerably small transformation volume expansion when it transforms to martensite phase. Another Invar alloy Fe-27Ni-20Co has Ms point below 0. It means that the alloy remains austenite phase at room temperature. Hence, special treatment should be taken to obtain martensite phase ; it is called sub-zero cooling. For the purpose of this, the authors introduced a liquid nitrogen direct cooling system into a tensile testing machine (different from the one for carbon steel) to achieve temperature lower than 100. This temperature is enough lower than Ms point of Fe-27Ni-20Co alloy according to the reference. 11) Maximum cooling rate of this system is about 0.2 /sec. A picture of this apparatus is shown in figure 1. The specimens are cooled down by liquid Nitrogen during loading and strains are measured at the same time. The authors used strain gauge that is applicable to ultra low temperature. The gauge s thermal expansion is identified beforehand, and the resultant strain is calculated by subtracting the gauge s thermal expansion from its original voltage data. This Invar alloy has tremendously small transformation volume expansion (almost zero). This is because, besides its lowness of Ms point, thermal expansion is tremendously small if the temperature is below magnetic transformation point. This alloy has a value of transformation volume expansion much smaller than that of Fe-25Ni-20Co alloy. Table 1 Chemical composition for carbon steels. (wt %) Table 2 Chemical composition of Invar alloys. (wt %) Fig. 1 Apparatus for tensile test under subzero condition.

3 Effect of Volume Expansion on Transformation Plasticity during Ferrite and Martensite Transformation of Steel Results and Discussions 4. 1 Temperature-Strain Curves Obtained temperature-strain curves are depicted in figure 2 (a) for S45C carbon steel with natural cooling (ferrite transformation), in (b) for S45C with intense cooling (martensite transformation), in (c) for Fe-25Ni- 20Co Invar alloy, and in (d) for Fe-27Ni-20Co Invar alloy. Note that ferrite and pearlite transformation are not distinguished in this paper, because they are both diffusive transformation. The difference of those transformations is not the main topic of this paper. From figure 2 (a) and (b), when temperature reaches the phase transformation start point, large strain development is observed. These strain values depend on the magnitude of applied stress, even though the applied stress is below yield stress of mother phase. It should be also noted that the temperature of S45C ferrite (pearlite) transformation in figure 2 (a) rises during phase transformation. This is caused by latent heat generated with phase transformation. The reason why this temperature rising is not observed for martensite transformation in figure 2 (b), (c), is that the cooling rates for those martensite transformation are enormously faster so that the latent heat is not enough to bring temperatures upward. From figure 2 (d), it is observed that the temperature drops below room temperature by liquid nitrogen i.e. sub-zero cooling is performed. The strain value is corrected by subtracting thermal expansion of strain gauge itself, which is preliminary identified. After cooling by liquid nitrogen, temperature returns back to room temperature. During cooling, the phase becomes fully martensite and remains martensite phase even after return back to room temperature. Consequently, the coefficient of thermal expansion during returning back to room temperature (martensite) is different from that of during cooling (austenite). From figure 2 (c) and (d), one can also observe the dependence of applied stress on strain value during phase transformation. This fact says that the Invar alloy shows, although small, transformation plasticity, whereas the transformation expansion is small. As we can see below, the magnitude of transformation plastic strain is one-order smaller than those of carbon steels Stress-Transformation Plastic Strain Relation Transformation plastic strain values for each steel grade can be calculated by figure 2 depending on applied stress value. For example, transformation plastic strain of S45C ferrite transformation is the strain difference at 550 between stress-free strain value and the strain value with small applied stress. This calculation is valid only when every single test is carried out under the same temperature history. This is because transformation volume expansion and thermal strain vary significantly with temperature history such as cooling rate. Relations between applied stress and total transformation plastic (a) S45C carbon steel (ferrite transformation) (b) S45C carbon steel (martensite transformation) (c) Fe-25Ni-20Co Invar alloy (d) Fe-27Ni-20Co Invar alloy Fig. 2 Temperature-Strain curves under various applied stress. strain are shown in figure 3 (a) for S45C (ferrite), (b) for S45C (martensite), (c) for Fe-25Ni-20Co, and (d) for Fe- 27Ni-20Co respectively. Figure 3 shows that the dependence of applied stress on transformation plastic strain is linear when the applied stress is small. In contrast, it is well-known that when applied stress is comparatively high, the strain value is expected to exceed the linear relation. The threshold stress under which this linear relation

4 940 T. Otsuka, T. Akashi, S. Ogawa, T. Imai, A. Egami and total transformation plastic strain can be calculated by integrating equation (1) from transformation start point ξ = 0 to transformation complete point ξ = 1 such that, (4) (a) S45C carbon steel (ferrite) The value K is called transformation plasticity coefficient, 2) which is ideally the same value in equation (2) and (3). An approach for making database of transformation plasticity coefficient K is reported these days. 13) The Leblond model indicates that this coefficient has linear relation with transformation expansion (This will be discussed in following section). Therefore, the transformation plasticity coefficient K can be calculated in two ways. One is by Leblond s model as expressed in equation (4). The other way is using figure 3 and equation (2). By integrating equation (2) from transformation start point ξ = 0 to transformation complete point ξ = 1, one obtains total transformation plastic strain, such that (5) (b) S45C carbon steel (martensite) (c) Fe-25Ni-20Co Invar alloy (d) Fe-27Ni-20Co Invar alloy Fig. 3 Transformation plastic strain under various applied stress for each material. is satisfied is approximately half the value of yield stress of mother phase. 12) The value of transformation expansion can be determined by strain results under 0MPa applied stress. For Fe-25Ni-20Co and Fe-27Ni-20Co Invar alloys, in spite of its smallness of transformation volume expansion, it shows good proportional relationship between applied stress and transformation plastic strain. From the Leblond model, the proportionality factor between applied stress If applied stress is uniaxial, transformation plastic strain can be written in simple form. (6) Therefore, transformation plasticity coefficient K is a slope of figure 3. In this paper, the transformation plasticity coefficients calculated by the latter way (equation 6) are denoted by K P (ferrite, pearlite) and K M (martensite) Yield Stresses Leblond s model indicates that yield stress of mother phase is as important as transformation volume expansion. For the purpose of obtaining stress-strain curves of mother phase of each material, tensile tests under the same temperature history as the tests for transformation plasticity (figure 2) are carried out. The specimens are heated up to 900, and keep the temperature for 5 minutes. After the 5 minutes, the specimens are cooled down as the same manner (i.e. same cooling rate) of the tests for transformation plasticity. Shortly before transformation start point, tensile tests are carried out. The transformation start points can be determined by stress free temperaturestrain curves. The loading points are carefully determined, for it is assumed that the yield stress is dependent on temperature. It is also important to duplicate the cooling rate, because the yield stress is considered to be affected by cooling rate. If the upper yield point is not clear, then 0.2% proof stress is adopted. The stress-strain curves of S45C (ferrite, pearlite), S45C (martensite), Fe-25Ni-20Co, and Fe-27Ni-20Co are drawn in figure 4 (a), (b), (c) and (d) respectively. These experiments are carried out at 0.02 (s 1 ) strain rate Transformation Plasticity Coefficient and its Dependence of Transformation Volume Expansion and Yield stress Ferrite According to the Leblond s model, the proportionality factor between applied stress and total transformation plastic strain is a function of transformation volume

5 Effect of Volume Expansion on Transformation Plasticity during Ferrite and Martensite Transformation of Steel 941 Table 3 Transformation expansion and transformation plasticity coefficient data for each material (ferrite transformation). Cooling rate at 700 is 8 /sec. (a) S45C at 674 Fig. 5 Relation between parameter 2Δε 1 2/σ y and transformation plasticity coefficient. (b) S45C at 340 (c) Fe-25Ni-20Co Invar alloy at 220 (Cooling rate at 700 is 50 /sec.) (d) Fe-27Ni-20Co Invar alloy at room temperature Fig. 4 Stress-strain curves right before transformation start. expansion and yield stress of mother phase. In this section, these relations of alloys treated in this paper are discussed. Transformation expansion can be obtained from temperature-strain curves under stress free condition. Although, strictly speaking, these values are not unique for one steel grade. It is because the transformation expansion is a dependent of cooling rate and obtained phase. This is the reason why one has to be careful when carrying out experiments that the temperature history should be exactly the same throughout the experimental sequence of one type of steel grade. The obtained results of transformation volume expansion, yield stress and transformation plastic coefficient K P are shown in Table 3. From the data in Table 3, relation between the parameter 2Δε 1 2/σ y and transformation plasticity coefficient K P are depicted in figure 5. Figure 5 indicates that the relation between the parameter in equation (1) and transformation plasticity coefficients K P is proportional, although the obtained transformation plasticity coefficients K P are much larger than to be expected by equation (1) Transformation Plasticity Coefficient and its Dependence of Transformation Volume Expansion and Yield stress Martensite Similar to the ferrite transformation, obtained transformation expansion, yield stress and transformation plasticity coefficient K M are shown in Table 4. Along with the data shown in Table 4, the relations between parameter 2Δε 1 2/σ y and transformation plasticity coefficient for martensite transformation K M are depicted in figure 6 as the same manner of ferrite transformation. From figure 6, one can observe the proportional relation between transformation volume expansion over yield stress and transformation plasticity coefficient K M. With smaller transformation volume expansion, we have considerable small value of transformation plasticity coefficient for Fe-25Ni-20Co and Fe-27Ni-20Co Invar alloy. The intercept of the approximate line in figure 5 indicates that the influence of Magee effect, whereas the value is a bit smaller than that of the Greenwood- Johnson effect. From this proportional factor, parameter 2Δε 1 2/σ y for martensite transformation can be calculated by equation (4). Similar to ferrite transformation, the magnitude of the

6 942 T. Otsuka, T. Akashi, S. Ogawa, T. Imai, A. Egami Table 4 Transformation expansion and transformation plasticity coefficient data for each material (martensite transformation). Cooling rate at 700 is 8 /sec. Cooling rate at 700 is 50 /sec. Cooling rate at 0 is 0.09 /sec. Fig. 6 Relation between parameter 2Δε 1 2/σ y and transformation plasticity coefficient. transformation plasticity coefficient K M is slightly larger than that of parameter 2Δε 1 2/σ y. Even though, the proportional relation between the parameter and transformation plasticity is satisfied, i.e. the idea of equation (1) is confirmed to be valid. In addition to that, the relationship is rather clear than that of ferrite transformation, thanks to Invar alloys extreme smallness of transformation volume expansion. 5 Concluding Remarks The authors applied several carbon steel grades and Invar alloys to identify the dependence of volume expansion on transformation plasticity for both diffusive and non-diffusive transformation. For ferrite tranformation, the proportional relation between the parameter 2Δε 1 2/σ y and transformation plasticity coefficient K P is confirmed; however, the proportional factor did not correspond to the model when subtracting intercept of linear approximate line. For martensite transformation, the proportional relation is also confirmed. The proportional factor is slightly smaller than transformation plasticity coefficient K M. The intercept of the approximate line is considered to be a manifestation of the Magee effect. The experimental results for Invar alloys show that if the transformation volume expansion is significantly small, the transformation plastic strain becomes tremendously small accordingly. It is said that Magee effect (selective martensite variant) plays main role during martensite transformation. However, for several steel grades treated in this paper, transformation volume change affects transformation plastic strain significantly. These results indicate that Greenwood-Johnson effect (transformation expansion) is not negligible during martensite transformation. References 1 ) L. Taleb, N. Cavallo and F. Waeckel, Experimental analysis of transformation plasticity, Intl. J. Plasticity, Vol.17, pp.1-20 (2001). 2 ) T. Inoue, Z. G. Wang and K. Miyao, Simulation of Quenching Process of Carburized Steel Gear Wheel under Metallo-thermo-Mechanical Coupling, Proceedings of IUTAM Symposium on Thermomechanical Coupling in Solids, Elsevier Science Publishers, Paris, B. V. North- Holland, pp (1986). 3 ) S. Yamanaka, T. Sakanoue, T. Yoshii and T. Inoue, Influence of Transformation Plasticity on the Distortion of Carburized Quenching Process of Cr-Mo Steel Ring, Journal of the Society of Materials Science, Japan, Vol.48, No.7, pp (1999). 4 ) G. W. Greenwood and R. H. Johnson, The deformation of metals under small stresses during phase transformations, Proceedings of Royal Society, 283A, pp (1965). 5 ) C. L. Magee, Transformation kinetics, Microplasticity and Aging of Martensite in Fe-31Ni, Ph.D. Thesis of Carnegie Institute of Technology (1966). 6 ) J. C. Leblond, J. Devaux and J. C. Devaux, Mathematical modelling of transformation plasticity in steels Case of deal-plastic phases, International Journal of Plasticity, Vol.5, pp (1989). 7 ) F. Barbe, R. Quey and L. Taleb, Numerical modelling of the plasticity induced during diffusive transformation. Case of cubic nuclei, European Journal of Mechanics, A/Solids, Vol.26, pp (2007). 8 ) T. Inoue, On Phenomenological Mechanism Transformation Plasticity and Inelastic Behavior of Steel Subjected to Varying Temperature and Stress, Journal of the Society of Materials Science, Japan, Vol.57, No.3, pp (2008). 9 ) T. Otsuka, Y. Wakasu and T. Inoue, A simple identification of transformation plastic behaviour and some data for heat treating materials, International Journal of Materials and Product Technology, Vol.24, No.1-4, pp (2005). 10) V. P. Panoskaltsis, S. Bahuguna and D. Soldatos, On the thermo mechanical modelling of shape memory alloys, International Journal of Non-Linear Mechanics, Vol.39, pp (2004). 11) A. Shibata, H. Yonezawa, K. Yabuuchi, T. Furuhata and T. Maki, Relation between martensite morphology and volume change accompanying fcc to bcc martensitic transformation in Fe-Ni-Co alloys, Materials Science and Engineering, A , pp (2006). 12) G. C. Videau, G. Cailletaud and A. Pineau, Experimental study of the transformation induced plasticity in a Cr-Ni- Mo-Al-Ti steel, Journal de Physique IV, colloque Cl, Supplèment au J de Physique III, Vol.6, pp (1995). 13) T. Inoue and K. Okamura, Materials Database for Simulation of Metallo-Thermo-Mechanics Fields, Proceedings of 5th International Symposium on Quenching and Distortion Control, ASM, St. Louis, October, pp (2000).