Analysis of Work Hardening Behavior in Ferrite-Martensite Dual-phase Steels Using Micro-grid Method

Abstract

To clarify the contribution of martensite increase to work-hardening during transformation-induced plasticity (TRIP), the changes in local strain distribution with tensile deformation were investigated for dual-phase steels with different volume fractions of martensite in ferrite using the precise marker method. Particular attention was paid to the changes in strain and stress bearing by martensite and ferrite with tensile deformation. The precise marker method is especially useful for local strain analysis of multiphase materials. Three types of steels with volume fractions of 25%, 50%, and 75% martensite were subjected to local strain analysis at several stages of deformation. The important results are as follows: (1) in steels with a large volume fraction of martensite, the contribution of the plastic deformation of martensite to the overall tensile strain is large from the beginning of the tensile deformation, and (2) the difference in strain bearing by martensite and ferrite increases through tensile deformation in both 25% and 50% martensitic steels. Using the constitutive equations for the stress-strain response, the strain distributions in each phase were translated into stress distributions. Then, the stress-strain response was numerically estimated by applying the general rule of mixtures using the average values of strain and stress, and compared with the experimental results. The relationship between the controlled martensitic transformation and tensile deformation behavior in TRIP steel is also discussed.

1. Introduction

Austenitic-ferrite duplex stainless steel is a steel with improved ductility due to TRIP.^1,2) It is well known that work-hardening in the steel is sustained by the sequential generation of martensite as the hard phase due to the transformation of a part of the austenite during plastic deformation.^3,4,5,6) The authors previously compared the plastic deformation behavior of two types of Cr–Mn–N duplex stainless steels with and without TRIP; they found that the difference in the work-hardening ability greatly contributed to the uniform elongation in tensile deformation.⁷⁾ In this paper, the contribution of strain-induced martensite to work-hardening during tensile deformation is discussed based on micromechanics theory, and it is shown that the key mechanism is the occurrence of stress distribution between the successively generated martensite and untransformed austenite.

An important part of the study was the measurement of the local strain distribution by a precise marker method. Experimentally, large strains appeared in the untransformed austenite around the strain-induced martensite with tensile deformation, which accounted for the stress distribution. This method is particularly useful for the plastic strain analysis of multiphase materials and has contributed to explaining the tensile deformation behavior of dual-phase steels such as ferrite-bainite and ferrite-martensitic steels.^8,9) In those papers, the relationship between the measured local strains and the orientation distribution in dual-phase steels is discussed along with the contribution of each phase in the steel to the local deformation in the later stages of tensile deformation.

It has been already mentioned that an increase in strain-induced martensite bearing tensile stress contributes to work-hardening. In TRIP steels, the quantity of strain-induced martensite in the austenite gradually increases with tensile deformation. When martensite is generated, it starts bearing the stress caused by the elastic deformation of martensite. Thereafter, martensite finishes its role as a work-hardening structure when its plastic deformation begins. Subsequently, the newly generated martensite contributes to work-hardening in the same manner. The ratio of the occurrence of martensite to tensile strain, that is, the change in the volume fraction of martensite with tensile strain, depends on the amount of austenite-stabilizing elements. However, in this study using duplex stainless steels, no comparison was made with different amounts of austenite-stabilizing elements. Therefore, it is unclear how changes in the volume fraction of martensite affect the work-hardening behavior.

In this study, to clarify the contribution of the increase in martensite during tensile deformation in TRIP steels, we used dual-phase steels with different martensite volume fractions in ferrite and measured the local strains by the precise marker method. We discussed how each phase bears plastic deformation and contributes to work-hardening during tensile deformation.

2. Experimental Procedure

Three steel grades with different martensite fractions of 25, 50, and 75% were used as the test materials. These steels are referred to as 25%M, 50%M, and 75%M. All of them were prepared by vacuum melting 50-kg ingots, and the composition was adjusted so that the carbon concentrations in the martensite in all of them were almost equal. The composition of each steel is listed in Table 1. The ingots were hot-rolled and cold-rolled to form 1.2-mm sheets. The cold-rolled plates were annealed in a salt bath (1073 K, 1.8 ks) in the ferrite-austenite duplex region, cooled with water, and then tempered at 423 K to obtain dual-phase steels with a specified martensitic fraction.

Table 1. Chemical compositions.

(mass%)
	C	Si	Mn	P	S	Al	N
25%M	0.05	1.5	2.0	0.01	0.002	0.04	0.004
50%M	0.12	1.4	2.0	0.01	0.001	0.04	0.004
75%M	0.18	1.5	2.0	0.01	0.002	0.03	0.004

Small-sized test specimens (Fig. 1) were prepared from each steel plate for SEM observation during tensile deformation. After polishing and smoothing the surface of the specimen, precise markings were made on the entire surface along the gauge length by electron beam lithography.^10,11) The specimens were subjected to a tensile test at room temperature at an initial strain rate of 1 × 10⁻⁴ s⁻¹. The markers were arranged in a rectangle 70-nm wide and with 500-nm spacing (Fig. 2). The displacement of the rectangular apexes was measured at unloading during tensile deformation. From the measured displacements, the Green-Lagrange strain applicable to large deformation was calculated and the equivalent plastic strain based on the Mises yield function was obtained. By assuming a constant volume condition, the strains in the normal direction of the surface were incorporated as a strain change at the surface. As the shape of the specimen used in this study was somewhat unique, as shown in Fig. 1, due to the marker deposition and its SEM observation, the displacement at the deformed area varies considerably from place to place. Indeed, when the deformed section in the specimen was divided into several parts and the true strain was measured both in terms of the length change and the displacement by the markers, there was a large difference in the amount of strain due to the shape of the specimen. Therefore, the strain evaluated from the elongation change of the entire deformed section of the specimen (3.8-mm) has little physical significance. In this study, the average of the equivalent plastic strains over the entire region of the marking was obtained and was defined as the tensile strain.

Fig. 1.

Dimension of specimen for tensile test.

Fig. 2.

Dimension of pattern drawn by marker.

Based on the obtained strain distributions, the corresponding stress distribution during tensile deformation was calculated using the constitutive equations of the stress-strain responses.

3. Experimental Results

Figure 3 shows the stress-strain curves for three kind of steels obtained using the tensile test specimens of JIS standards. The dimension of the specimen was a flat plate (1.2 mm thick) of 60-mm in parallel length and 25-mm in width. The larger the volume fraction of martensite, the greater the tensile strength and the lower the uniform elongation.

Fig. 3.

Stress-strain curves obtained by tensile tests.

Figures 4(a) and 4(b) show SEM images including martensite at 0.26 tensile strain in a steel with 50%M and an equivalent plastic strain distribution obtained from the displacement of the marker, respectively. The tensile strain was determined as the average of the equivalent plastic strain for the view shown in Fig. 4(a). Figure 4(b) shows the strain distribution in the rectangular marker diagram before the deformation, using the color scale of the strain shown on the right side of the figure. The area surrounded by white dashed lines in the figure corresponds to the martensite. Figure 4(a) shows that although the markers are slightly deformed inside the martensite, the distortion of the markers in the ferrite region is very large. Correspondingly, Fig. 4(b) shows a higher strain value inside the ferrite compared to the martensite. In the ferrite region near the interface with the martensite, the strains appear to reach very large values, such as 0.5.

Fig. 4.

Deformation of a martensite-containing region at an equivalent plastic strain of 0.26.

Figures 5(a), 5(b) and 5(c) show SEM images of 25, 50 and 75%M, respectively, at tensile strains of 0.07–0.08. In all the images, the surface appears very rough associated with plastic deformation, and thus, each crystal grain is clearly visible. Some grains appear flatter than their surroundings. Figures 5(d)–5(f) show images of the equivalent plastic strain distribution in the same view as in the previous figures. The areas indicating large strains are connected in the shape of a band, which is inclined at an angle of approximately 45° to the direction of tensile deformation (horizontal direction in the figure). The spacing of these band-like structures corresponding to the strain concentration becomes smaller as the fraction of martensite increases. As shown in Fig. 5(e), there were many areas with large strains of 0.5, especially in 50%M. To clarify the strains bearing by the phases, such as ferrite and martensite, the average strain values were obtained from these strain maps.

Fig. 5.

Deformation behavior and strain distribution at equivalent plastic strain 0.7–0.8. (a) (d) 25%M, (b) (e) 50%M, (c) (f) 75%M.

Figure 6 shows the average strain values for the regions within the red rectangle shown in Fig. 5. The magnitudes of the equivalent plastic strains (corresponding to tensile strains) in the analyzed region were equal to 0.075, 0.078, and 0.073, although the martensitic fractions differed from the 25%, 50% and 75%. The strain averages in ferrite did not vary greatly among the steels, but the strain bearing by ferrite tended to increase slightly with increasing martensitic fractions. In contrast, the strain-averaged values in martensite were shown to increase significantly with increasing martensite fractions. The interface area in the figure corresponds to that between ferrite and martensite, which was included in the rectangle formed by the marker. Therefore, the strains at the interface shown in the figure correspond to the equivalent plastic strains in the vicinity of the interface in the range of maximum 0.5 microns. This value is the largest for steels with a 50% martensite fraction, and the strain at the interface tends to decrease for both smaller and larger martensite fractions.

Fig. 6.

Martensitic fraction dependence of mean equivalent plastic strain for each phase at equivalent plastic strain 0.7–0.8.

Figure 7 shows the changes in the equivalent plastic strain distribution with increasing tensile strain. Figures 7(a)–7(c) show the equivalent plastic strain distributions for regions of deformation corresponding to tensile strains of 0.03, 0.08 and 0.14 in the 25%M. As the tensile strain increased, the area of large strain increased. Rather than a random increase in local strain, a tendency to increase with increasing tensile strain appeared preferentially in regions that once exhibited large strain. The regions of increased strain were connected in this way, resulting in an increase in the region of large local strain. Figures 7(d)–7(f) show the equivalent plastic strain distributions in the region of 0.03, 0.08, and 0.26 in the tensile strain in the 50%M sample. Figures 7(d) and 7(e) show the same tendency as for the 25%M sample. In contrast, as shown in Fig. 7(f), the number of regions with large local strains increased rather than being connected to each other when the amount of deformation was large. Because the tensile strain was 0.26 in Fig. (f), the martensite was considered to have a role in the plastic strain as significantly as ferrite, and strain up to 0.3 appeared locally in martensite. However, the tendency of the strain to preferentially increase in the area where the local strain was large prior to reaching the mentioned above value of strain was similarly independent of the martensite fraction.

Fig. 7.

Local strain distribution in tensile strain corresponding to each equivalent plastic strain, (a)–(c) 25%M, (d)–(f) 50%M.

To investigate how the strains in each microstructure change as the amount of deformation increases, we distinguished between ferrite and martensite within the red rectangle shown in Fig. 7 and calculated the average strains in each microstructure. Figure 8 shows the change in the mean equivalent plastic strain over the entire area and in the ferrite and martensite as the tensile deformation increases in the 25%M and 50%M. I, II and III in the figures correspond to tensile strains of 0.03, 0.08, and 0.14 at 25%M and 0.03, 0.08, and 0.26 at 50%M, respectively. The strains bearing by ferrite significantly increased with tensile strain in all steels. In contrast, the increase in strain bearing in the martensite is small. The arrows in the Fig. 8 indicate the difference between the mean strain value in ferrite and the mean strain value in martensite at each deformation level. This difference tends to increase with increasing tensile strain in both steels. Particularly, in the case of the 50%M, the strain bearing by ferrite is much larger than that by martensite, even in the middle to late tensile deformation range of 0.08 to 0.26.

Fig. 8.

Dependence of the average equivalent plastic strain on tensile strain in each phase, (a) 25%M, (b) 50%M. I, II and III are deformations corresponding to tensile strains of 0.03, 0.08 and 0.14 at 25% M and 0.03, 0.08 and 0.26 at 50% M, respectively.

4. Discussion

4.1. Effect of Local Strain Distribution on Work Hardening in Each Phase

Figure 6 shows that both the strain averages of ferrite and martensite increase with the volume fraction of martensite at equivalent plastic strains of 0.07–0.08. The increase in the strain average of martensite was particularly pronounced, and it was experimentally shown that the contribution of martensite to plastic deformation is greater in steels with a higher volume fraction of martensite. In contrast, the strain average of ferrite slightly increased with martensite content, which may correspond to the amount of plastic deformation that contributed to work-hardening from the beginning of the deformation to this tensile strain. Moreover, the work-hardening ability of each phase of ferrite and martensite may contribute significantly to the work-hardening of dual-phase steel when a large fraction of the phase is included, whereas the effect of stress distribution due to being a composite may be superimposed on this. In other words, when martensite bears a large deformation stress, the amount of plastic deformation in ferrite, which transfers this large stress, should also increase.

The strain average at the interface indicated the maximum value at the 50% martensitic volume fraction. This suggests that the strain-bearing ability of the various parts of the interface in this steel was greater than that in other steels. In 25%M, most of the plastic strain was carried by ferrite after yielding, whereas in 75%M, martensite also carried most of the plastic strain after yielding. In these steels, it is likely that the initial work-hardening depends on the work hardening of ferrite and martensite itself. In contrast, the local strains in the vicinity of the interface in the 50%M increased immediately after yielding, indicating that stress distribution significantly contributed to work hardening. In other words, it suggests that the contribution of being a composite to the development of large work-hardening is considerable in 50%M.

The main feature illustrated in Fig. 8 is that the plastic strain difference between ferrite and martensite increases with the increase in tensile strain, although the strain averages of all phases increased with the increase in tensile strain. This implies that the role of martensite as a reinforcing phase continues even under relatively high strains, where the overall equivalent plastic strain is more than 8%. This may contribute to the persistence of work-hardening with increasing tensile strain.

4.2. The Role of Ferrite and Martensite in Work Hardening

Morooka et al. estimated internal stresses in each phase of dual-phase steels during deformation using by neutron diffraction.¹²⁾ Based on those results, the constitutive equations for the stress-strain response of ferrite and martensite phases were obtained. In this section, to clarify the roles of ferrite and martensite on work-hardening in dual-phase steels, the constitutive equations were used to obtain the stress distribution from the equivalent plastic strain distribution. Using the average stress values in each phase, the SS curves were estimated from the two rules of mixtures and compared with the experimental values.

Figures 9(a)–9(c) show the stress distribution of 25%M at tensile strains of 0.03, 0.08, and 0.14, respectively. The values of the stresses in the figures are calculated based on the equivalent plastic strains, as described above, and correspond to the true stresses which were necessary to generate the equivalent plastic strains. Although the internal stress in the ferrite region was less than 900 MPa for all deformation levels, the stress distribution in martensite was above 1200 MPa even for small deformation. Moreover, Figs. 9(d)–9(f) show the stress distribution of 50%M at 0.03, 0.08, and 0.26 tensile strains, respectively. Even with the same amount of deformation, the stress carried by the martensite was extremely large, approximately 1500–1800 MPa. In both steels, the stresses in both the ferrite and martensite regions increased with increasing deformation level.

Fig. 9.

Dependence of stress distribution on tensile strain, (a)–(c) 25%M, (d)–(f) 50%M. The tensile strains are (a) (d) 0.03, (b) (e) 0.08, (c) 0.14, and (f) 0.26.

The average stresses in the ferrite and martensite phases were determined from these stress distributions. The stress-strain responses of dual-phase steels were estimated by applying the rule of mixtures and inverse rule of mixtures assuming two extreme states of distribution of martensite as a reinforcing phase and using the average stress at each deformation. The results are shown in Fig. 10. In Fig. 10(a), the solid line shows the stress-strain response obtained from the experiment. The stresses at the three points connected by dashed lines are calculated from Eq. (1), and the strains are calculated from Eq. (2).   

$$\sigma =(1-f){\sigma }_F+f{\sigma }_M$$(1)

  

$$\epsilon =(1-f){\epsilon }_{eq.F}+f{\epsilon }_{eq.M}$$(2)

σ, f, σ_F, σ_M, ε, ε_wq.F and ε_wq.M are the nominal stress, volume fraction of martensite, stress average of ferrite, stress average of martensite, nominal strain, strain average of ferrite and strain average of martensite, respectively. The calculated value was obtained by using the rule of mixtures, assuming that the distribution of martensite in the ferrite is parallel to the load direction. Although the stress-strain response of 50%M was close to the experimental results, the stress-strain responses estimated by using the rule of mixtures were closer to the experimental results.

Fig. 10.

Calculated stress-strain curves (broken lines) and experimental values (solid lines) for 25%M and 50%M obtained using the rules of mixtures based on the stress averages of each phase from the strain distribution, (a) assuming general rule of mixtures and (b) assuming inverse rule of mixtures.

In Fig. 10(b), the solid line shows the same experimental values as in Fig. 10(a). The three values forming the dashed lines were calculated by the Eq. (3) for the deformation stress and Eq. (4) for the strain.   

$$\sigma =1/\left\{(1-f)/{\sigma }_F+f/{\sigma }_M\right\}$$(3)

  

$$\epsilon =1/\left\{(1-f)/{\epsilon }_{eq.F}+f/{\epsilon }_{eq.M}\right\}$$(4)

The calculated value was obtained by using the inverse rule of mixtures, assuming that the distribution of martensite in the ferrite was aligned perpendicular to the load direction. The calculated values are very close to the measured values for 25%M. This suggests that the deformation mode in the composite changes with the volume fraction of martensite. That is, martensite contributes to the plastic deformation of 50%M from the beginning of the deformation, while in 25%M, ferrite contributes to plastic deformation until the later stages of deformation. This corresponds to the results estimated from the measured strain distribution. Although martensite continues to contribute to the strengthening of dual-phase steels during plastic deformation, the work-hardening rate tends to be saturated at lower tensile strains in steels with higher martensitic fractions. As mentioned above, the local strain measurements (Fig. 8) suggested that martensite continues to play a role as a reinforcing phase even during plastic deformation.

On the other hand, Fig. 10 shows that the work-hardening rate of the dual-phase steel depends on the martensitic fraction, which corresponds to the results obtained from tensile tests of steels with different martensitic fractions. Considering this and the results obtained in Fig. 6, the effects of each phase on the work-hardening of the dual-phase steel are as follows. The larger the martensite fraction, the greater the role of martensite as a reinforcing phase and the greater the deformation stress, Nevertheless, it is disadvantageous in terms of work-hardening because martensite also assumes an increase in strain immediately after yielding. In order to maintain the work-hardening and increase in tensile elongation, it is advantageous that the martensite fraction is small, as the strain bearing by the martensite is lower. However, this does not fully exploit the role of martensite as an enhancement phase. As show in Fig. 6, when the martensite fraction is approximately 50%, the stress distribution between ferrite and martensite is effective because the martensite/ferrite interface area bears a large strain, Thus, martensite plays an important role as a strengthening phase. This has implications for controlling the amount of residual austenite during martensitic transformation with deformation in TRIP steels. That is, the continued martensitic transformation results in an effective and sufficient stress distribution between martensite and austenite during the deformation. This helps achieve the required tensile elongation and guarantees excellent mechanical properties of TRIP steel.

5. Conclusions

(1) For steels with a large volume fraction of martensite, the contribution of plastic deformation of martensite to the total strain is larger than that of the initial tensile deformation.

(2) Martensite continues to play a role as a reinforcing phase in multiphase steels not only during elastic deformation but also after initiation of plastic deformation, contributing to work-hardening.

(3) Although martensite may contribute to the strengthening of dual-phase steels during plastic deformation, the work-hardening rate tends to be saturated early if the martensite fraction is large and carries more plastic deformation than at the beginning of deformation. This may contribute to the determination of the rate of martensitic transformation during deformation in TRIP steel.

Acknowledgment

This work was supported by JSPS KAKENHI Grant Number JP18K04751.

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