2020 Volume 60 Issue 9 Pages 2083-2089
Digital image correlation was applied to analyze the strain distribution and deformation-induced martensitic transformation of retained austenite in a low alloy transformation-induced plasticity (TRIP) steel plate under tension. The distribution of strain instilled by tensile deformation was inhomogeneous at a microscopic scale. Strain generated by deformation-induced martensitic transformation was successfully visualized and it led to a homogeneous strain distribution. The retained austenite in the high strain region transformed to martensite preferentially, which demonstrates that inhomogeneous strain distribution affects the stability of retained austenite. The high resolution strain distribution exhibited that a certain amount of strain instilled into retained austenites and there are a lot of strain concentration sites at ferrite/austenite interfacial boundaries in high strain region. Therefore, the stress concentration at the ferrite/retained austenite interfacial boundary occurs due to the difference of strain between the ferrite matrix and retained austenite. These strain accumulation in a retained austenite and/or stress concentration at ferrite/retained austenite interfacial boundary may induce martensitic transformation in high strain regions.
Mechanical properties in transformation-induced plasticity (TRIP) steel consisting of metastable retained austenite and a ferrite matrix depends on the stability of retained austenite to deformation. Highly stabile retained austenite transforms into martensite at a late stage of deformation, which provides a good balance of strength and ductility in a TRIP steel.1) The stability of individual retained austenite grains is closely related with test temperature,1) carbon content,2) morphology,3) precipitation site4) and so on. Furthermore, we have previously demonstrated that the retained austenite near the zone normal to <111> along the tensile direction was mechanically stable.5)
Digital image correlation (DIC) has been developed as a conventional strain analysis method, calculating strain from the difference of images before and after deformation.6,7,8,9) It demonstrates an advantage in application to any strain modes or materials, as long as there is a significant contrast in the digital images. The deformation behavior in various metal materials had been visualized by using DIC method.10,11,12,13) We were successful in visualizing strain distribution in a tensile-deformed ferrite single-phase polycrystalline.14) The strain distribution was inhomogeneous at a microscopic scale, even though its microstructure consisted of equiaxed ferrite grains and exhibited a number of movable slip systems. In the case of TRIP steel consisting of dual phases with different strengths, its strain distribution may be rather more inhomogeneous than that of ferrite single-phase. In addition, the martensitic transformation accompanies a volume expansion due to the difference of crystal structure between the austenite and martensite phases, generating strain.15) However, little experimental analysis on the strain generated by deformation-induced martensitic transformation in TRIP steel has been done.
In the present study, DIC was applied to analyze strain distribution instilled by cyclically unloaded tensile tests in a low alloy TRIP steel plate. The secondary electron (SE) images were taken from the unloaded specimen each time, and the effect of strain generated by deformation-induced martensitic transformation on strain distribution was examined. The relationship between strain distribution and deformation-induced martensitic transformation of retained austenite is discussed.
A 0.31C-1.74Si-1.49Mn-0.006P-0.0010S-0.008Al-0.0014N (in mass%) cold-rolled steel plate with a thickness of 2.5 mm was used. The steel was cold-rolled and annealed at 1063 K for 0.3 ks in the ferrite and austenite region, and then austempered at 673 K for 0.6 ks. The initial volume fraction of the retained austenite was 17.2%.5)
2.2. Tensile TestsA sheet-type specimen with a gauge length of 30 mm, width of 4 mm, and thickness of 2.5 mm was cut, so that the longitudinal direction was parallel to the rolling direction (RD).5) The tensile tests were carried out with an initial strain rate of 2.8 × 10−4 s−1 using a mortar-driven tensile test machine at 293 K (in the air) and 193 K (immersed in a cooling alcohol). The stability of retained austenite depends on test temperature, and we clarified that the decrease of retained austenite with increasing strain was different between these temperatures.5) The effect of the amount of martensitic transformation on strain distribution was discussed through strain distribution analysis was carried out at 293 K and 193 K. The detail tensile properties were reported in our previous study.5) The cyclically unloaded tests were carried out in steps from 0.04 nominal strain (measured with an extensometer) up to a total of 0.12 nominal strain at 293 K and 193 K. The most of retained austenite transformed to martensite until 0.12 nominal strain.5) Furthermore, it is difficult to apply DIC analysis to a high strained specimen. Therefore, we analyzed strain distribution until the 0.12 nominal strain.
2.3. Microstructural AnalysesThe microstructure on the surface of the normal-direction (ND) specimen was observed with an SE image using field-emission gun scanning microscopy (FE-SEM). The specimen was electropolished in a 1:9 by volume perchloric acid ethanol at 253 K using a Lectropol 5 with applied voltage of 31 V. The electron backscattered diffraction pattern (EBSD) technique with the FE-SEM was employed to analyze the volume fraction of retained austenite. Data were recorded with a beam scanning step of 50 nm. Data points with a confidence index more than 0.1 were provided for phase identification using the software program OIMTM analysis 7.0.1. The volume fractions of retained austenite were estimated from phase maps.
2.4. Strain Distribution AnalysesThe microstructures of the specimens cyclically unloaded after 0 (unstrained), 0.04, 0.08 and 0.12 strains at 293 K and 193 K were analyzed with the DIC method. The analysis used the software program (VIC-2D) for the SE images under 81 or 31 pixels in subset size and 3 or 2 pixels in step. The SE image taken from the former strained condition in the same specimen was adopted as the reference for the analysis: for example, the SE image in 0.08 strain of the cyclically unloaded specimen was analyzed using that of 0.04 strain as the reference. The strain distribution is consisted of nine SE images. The average strain of nine SE image was 0.04 though that of each SE image was not 0.04. Therefore, the strain distribution in this study exhibits representative deformation behavior in the specimen.
Figure 1 shows SE images of the specimen in 0 (a) and 0.12 (b) strains at 293 K. Retained austenite or martensite which transformed during cooling was dispersed in the ferrite matrix.5) Protrusions had appeared at 0.12 strain aligned along the slip line, as shown with the white arrows. Since EBSD data were acquired four times in the same region in this experiment, and the specimen was exposed to an electron beam a number of times, these protrusions seem to be hydrocarbon contamination deposited on fine protrusions formed by slip deformation on the specimen surface. DIC analysis has limited success when the contrast in digital images between before and after deformation changes dramatically. Therefore, we calculated strain between each strain step: 0 and 0.04, 0.04 and 0.08, 0.08 and 0.12.
Secondary electron images on ND plane after 0 (a) and 0.12 (b) strains at 293 K.
Figure 2 shows phase maps in each tensile strain at 293 K (a)–(d) and 193 K (e)–(h). Red and green colors indicate ferrite and austenite phases, and the black color indicates a point not analyzed by EBSD. These black points increase with increasing strain and are located at retained austenite regions. EBSD analysis becomes difficult when the probe diameter is larger than the grain size. Thus, the unanalyzed region implies generation of deformation-induced martensites consisting of fine grains. The difference in volume fraction of retained austenite before deformation between 293 K (a) and 193 K (e) is an error because we demonstrated that retained austenite is thermally stable at 193 K.5) Retained austenite dramatically decreased up to 0.04 strain at 193 K (f) and then decreased slightly at 0.08 (g) and 0.12 (h) strain. At 293 K, retained austenite decreased monotonically with increasing strain, until 0.07 of retained austenite in volume remains at 0.12 strain (d). Since the volume fraction of retained austenite on the specimen surface and interior was nearly identical at each strain,5) the effect of free surface on stability of retained austenite was not significant in this experiment.
Phase maps strained at 293 K (a)–(d) and 193 K (e)–(h) on ND plane: (a) 0, (b) 0.04, (c) 0.08, (d) 0.12, (e) 0, (f) 0.04, (g) 0.08 and (h) 0.12 strains. (Online version in color.)
Figure 3 shows SEM images before deformation and εxx strain distribution in each strain at 293 K (a)–(d) and 193 K (e)–(h). Subset size and step in the DIC analysis were 81 pixels and 3 pixels, respectively. The color bar indicates strain, and minimum and maximum strain are 0 and 0.08. Reference images in each strain distribution were SE images of former strained specimens, and the average strain was approximately 0.04 in all strain distribution. Strain was instilled as an inhomogeneous distribution at the microscopic scale. The high-strain region was over twice as high as the average strain, and the low strained region was almost zero. The high and low strain regions tended to distribute continuously along 45 degrees from the tensile direction in our previous study.7) In this study, the same trend of strain distribution was confirmed in a strain distribution calculated with the lower magnification SE images. However, the highly strained area was rather randomly detected in the strain distribution calculated from the ten times higher magnification SE images as shown in Fig. 3. Hence, the highly strained and lower strained areas are randomly installed in the high and low strain regions distributed macroscopically along 45 degrees strain distribution, respectively. Strain distribution at 0.04 strain at 293 K (b) was nearly equivalent to that at 0.12 strain at 293 K (d), demonstrating that the inhomogeneity of strain distribution is not reduced, but is rather increased with deformation. On the other hand, in the tensile test at 193 K, strain distribution at 0.04 strain (e) was more homogeneous than that in 0.08 (f) and 0.12 (g). The decrease of retained austenite in 0.04 strain at 193 K was the largest in all test conditions, as shown in Fig. 2. Therefore, deformation-induced martensitic transformation affects strain distribution. The difference of strain distribution between 293 K and 193 K, excepting 0.04 nominal strain, is due to the difference of a retained austenite phase distribution which is a harder phase than ferrite and bainite as discussed later.
εxx strain distributions strained at 293 K (a)–(d) and 193 K (e)–(f): (a) 0, (b) 0.04, (c) 0.08, (d) 0.12, (e) 0, (f) 0.04, (g) 0.08 (h) 0.12 strains. (Online version in color.)
Figure 4 shows phase maps and high resolution εxx strain distribution in a part of Fig. 3 in each strain at 293 K. Subset size and step in the DIC analysis were 31 pixels and 2 pixels, respectively. The retained austenite indicated by the white arrow in the maps remained until 0.04 strain (b), and most of them transformed into martensite at 0.08 strain (c). Strain in the retained austenite region was lower than the average strain at 0.04 strain (f) and over twice as high as the average strain at 0.08 strain (g), and then the strain reduced again at 0.12 strain (h). Strain increased when deformation-induced martensitic transformation occurred, and the strain increment at 0.08 strain corresponds to strain generated by the martensitic transformation of the retained austenite. It has been assumed that 0.05 normal strain along the normal direction of a martensite habit plane and 0.2 shear strain along a martensite habit plane are generated by the transformation from austenite into martensite, accompanying volume expansion.16) According to this assumption, strain along the tensile direction generated by the martensitic transformation can be estimated as a function of the angle (θ) between tensile direction and the normal direction of the martensite habit plane. Figure 5 shows the relation between strain along tensile direction generated by martensitic transformation and θ. The strain is minimum (0.05) at θ = 0° and maximum (0.206) at θ = 76°. The estimated strain from the crystal orientation of the retained austenite in Fig. 4 was approximately 0.1, which was roughly the same as the generated strain (0.058) calculated for the strain difference in the region between 0.04 and 0.08 strain in Fig. 4. There are some potential explanations for the difference between the estimated strain and the measured one: The measured strain includes strain not only in the retained austenite region but also around the ferrite region, strain was released to free surface, and alloy elements affect strain generated by martensitic transformation and so on.
Phase maps and εxx strain distributions in (a), (e) 0, (b), (f) 0.04, (c), (g) 0.08 and (d), (h) 0.12 strains at 293 K. (Online version in color.)
Relation between strain generated by martensitic transformation and angle from tensile direction to normal direction of habit plane. (Online version in color.)
The black markers in Fig. 6 represent the relation between standard deviation and average strain (εavg.) calculated from histograms of εxx strain distribution (Fig. 3). The black line indicates the relation between standard deviation and average strain calculated from ferrite single-phase polycrystalline. All histograms compared to normal distribution; hence, standard deviation represents the width of the histograms as well as the inhomogeneity of the strain distribution in this analysis. The standard deviation in the TRIP steel was higher than that of ferrite single-phase polycrystalline, meaning that strain distribution in the TRIP steel was rather inhomogeneous than that in ferrite single-phase polycrystalline. The standard deviation in the TRIP steel increased linearly in proportional to εavg. except for the data at 0.04 strain at 193 K. Therefore, inhomogeneity of the strain distribution, i.e. the total areas of high and low strain region, were identical among the test conditions excepting 0.04 strain at 193 K. However, the size of each high and low strain region were different between test temperatures from Fig. 3; for example, low strain region at 193 K was finely dispersed compared to that at 293 K as indicated by white arrows in Figs. 3(c) and 3(g). The ferrite phase is hardening with decreasing temperature17) and its slip system is restricted at low temperature.18) These temperature dependences of mechanical property and deformation behavior in the ferrite phase may affect the distribution of the strain at low temperature, but the detail is unclear and further study is necessary.
Standard deviation as a function of average strain or strain in microstructure.
The standard deviation at 0.04 strain at 193 K is lower than that in the other test condition, which means that the strain distribution in 0.04 strain at 193 K is more homogeneous compared to other test conditions. Here, the average strain calculated from the DIC analysis is assumed to be a sum of strain in microstructure (εstruc) and strain generated by martensitic transformation (εtrans). εstruc is the strain generated by only tensile deformation without deformation-induced martensitic transformation. If the martensitic transformation occurs randomly, the average strain generated by martensitic transformation will be 0.1, as calculated from Fig. 5. Therefore, εtrans can be calculated from the decrease of retained austenite from the previous strain (ΔVR) as shown in the following simple equation.
| (1) |
The gray markers in Fig. 6 represent standard deviation as a function of εstruc calculated by subtracting εtrans from εavg. Here, the standard deviation may increase by deformation induced martensitic transformation because the transformation preferentially occurs within the high strain region as discussed in Section 3.3. The difference of decreasing value of retained austenite between high (εavg > 0.04) and low (εavg < 0.04) strain regions until 0.04 strain at 193 K was approximately 1%, and then the generated strain by deformation induced martensitic transformation was 0.001 according to equation (1), which corresponds to increase of width of histogram. Hence, the increasing value of the standard deviation by the martensitic transformation is 0.001 and it is negligibly small. The effect of deformation induced martensitic transformation on the standard deviation did not consider in this study.
The standard deviation and εstruc are clearly linearly proportional for all data including 0.04 strain at 193 K. Thus, reducing strain in microstructure by generating deformation-induced martensite results in a homogeneous strain distribution at 0.04 strain at 193 K. It has been assumed that the deformation induced martensite enhances work hardening due to the martensite possessing much higher hardness compared to ferrite or austenite one and it gives to high elongation by suppressing a necking in the TRIP steel.19) Recently, we had demonstrated this high phase stress of deformation induced martensite in the TRIP steel by using in-situ neutron diffraction measurement during tensile test.20) On the other hands, the reducing strain accumulation in a microstructure by deformation induced martensitic transformation should contribute to a high elongation in the TRIP steel, and it must be one of the improvement mechanisms of elongation by the deformation induced martensitic transformation.
3.3. Relation between Strain Distribution and Deformation-induced Martensitic Transformation of Retained AusteniteFigure 7 shows the volume fraction of retained austenite in each strain class (a) and the ratio of the volume fraction of retained austenite in each strain class to the total retained austenite (Rclass/all) (b) as a function of nominal strain at 293 K. Here, retained austenite in each strain class was defined by comparing the εxx strain distribution in 0.04 strain represented by four classes (Fig. 8(a)) to the phase map (Fig. 8(b)). The boundaries of each strain class at 0.04 strain were used to measure retained austenite at 0, 0.08 and 0.12 strain. The volume fraction of retained austenite in 0.06 < εxx was very small (Vr = 0.008) in Fig. 7(a), which implies that the retained austenite is harder than the ferrite matrix at 293 K, and the deformation proceeds preferentially in the region where the amount of retained austenite is few. In all strain classes, the retained austenite decreases as nominal strain increases, as shown in (a); however, the decrease of the volume fraction of retained austenite differs among strain classes. Rclass/all in 0 < εxx < 0.02 and 0.02 < εxx < 0.04 increase continuously with increasing nominal strain, and in 0.04 < εxx < 0.06 decreases as demonstrated in Fig. 7(b). Retained austenite in the high strain region was preferentially transformed into martensite, which in the low strain region remained until the late stage of deformation. It can be concluded that strain distribution is playing an important role in the stability of retained austenite in the TRIP steel.
Volume fraction of retained austenite (a) and ratio of the retained austenite in each strain class to the total retained austenite (b) as a function of nominal strain in strain at 293 K.
εxx strain distribution represented by four classes (a) and phase map with boundary of each strain class (b) in 0.04 strain at 293 K. (Online version in color.)
Figure 9 shows high resolution εxx strain distribution in low (a) and high (b) strain regions at 0.04 strain at 293 K, and phase maps in 0 (b), (e) and 0.08 (c), (f) strains at 293 K in (a) and (b). Subset size and step in the DIC analysis were 31 pixels and 2 pixels, respectively. Since the resolution of strain distribution depends primarily on subset size in the DIC analysis, Fig. 9 exhibits more detailed strain distribution as compared to Fig. 3. Strains in both the ferrite matrix and the retained austenite were low in the low strain region (Fig. 9(a)), and a part of ferrite/retained austenite interfacial boundary showed a high strain as indicated by the white arrow in Fig. 9(a). In high strain region (Fig. 9(d)), the retained austenite had a certain amount of strain and the ferrite phase had much higher strain compared to austenite one. It has been assumed that the martensitic transformation is induced by stress and/or strain:13) Stress generates the mechanical driving force for martensitic transformation, and strain reduces energy to generate martensite by creating a nucleation site with deformation. The retained austenite at the high strained ferrite/retained austenite interfacial boundary as shown by white arrows in Figs. 9(c) and 9(f) tended to preferentially transform to martensite. These martensitic transformations should be induced by stress because the stress concentration caused by the difference of strain between ferrite and austenite occurs at these interfacial boundaries. On the other hands, comparably high strained austenite as indicated by gray arrow in Figs. 9(d)–9(f) transforms to martensite even though stress concentration at the ferrite/retained austenite interfacial boundary does not occur. This martensitic transformation should be induced by strain. The numbers of high strained retained austenite and stress concentration sites in high strain regions were larger than those in low strain regions, and it must explain why deformation-induced martensitic transformation preferentially occurred in the high strain region. The retained austenite with low strain or at low stained ferrite/retained austenite interfacial boundary as indicated by black arrows in Figs. 9(e) and 9(f) remained until 0.08 strain even in the high strain region, which reasonably supports the hypothesis: both of strain accumulation and stress concentration affect the stability of retained austenite. Figure 10 is a schematic illustration of the relation between strain distribution and stability of retained austenite. The low strained retained austenite surrounded by low strained ferrite is the most stable. The stability of intermediate strained retained austenite is comparatively low because the accumulated strain within retained austenite induces martensitic transformation. The retained austenite surrounded by high strained ferrite is the markedly unstable due to strain accumulation of retained austenite and stress concentration at ferrite/retained austenite interfacial boundary.
High resolution εxx strain distribution in low (a) and high (b) strain regions at 0.04 strain at 293 K, and phase maps in (b), (e) 0 and (c), (f) 0.08 strains at 293 K in (a) and (b). (Online version in color.)
Schematic illustration of relation between strain distribution and stability of retained austenite. (Online version in color.)
Our results demonstrated that strain distribution introduced by deformation affects the stability of the retained austenite in the TRIP steel. However, retained austenite in the low strain region also decreased with increasing nominal strain, as shown in Fig. 7. Hence, other factors such as carbon content, morphology, and precipitation site also affect the stability of retained austenite in this TRIP steel. Inhomogeneous strain distribution is one influential factor in a deformation-induced martensitic transformation, but a comprehensive analysis of the factors is needed to quantitatively evaluate the factors in the stability of retained austenite.
Digital image correlation was applied to analyze strain distribution instilled by cyclically unloaded tensile tests in a low alloy TRIP steel plate, and the effect of strain generated by deformation-induced martensitic transformation on strain distribution was examined. Then the relationship between strain distribution and deformation-induced martensitic transformation of retained austenite was discussed. The main results are summarized as follows:
(1) Strain was instilled with an inhomogeneous distribution on a microscopic scale. The strain in high and low strain regions was over twice the average strain, and almost zero, respectively.
(2) Strain generated by martensitic transformation was successfully visualized. The measured strain was approximated the estimated strain from the general strain generation model in martensitic transformation.
(3) Strain in the microstructure was calculated by subtracting strain generated by martensitic transformation from average strain measured from digital image correlation analysis. The strain was linearly proportional to the standard deviation of strain histogram. Strain generated by deformation-induced martensitic transformation reduces the strain in the microstructure.
(4) The ratio of retained austenite to the total retained austenite in the low strain region increased continuously with nominal strain, and that in the high strain region decreased, meaning that retained austenite in the high strain region is preferentially transformed into martensite.
(5) Retained austenite with high strained austenite and at the high strained ferrite/retained austenite boundary preferentially transformed to martensite from high resolution strain distribution map. Therefore, it can be concluded that strain accumulation in the retained austenite and/or stress concentration at ferrite/retained austenite interfacial boundary may induce martensitic transformation. The difference of numbers of high strained retained austenite and stress concentration sites between high and low strain region must be the reason why the martensitic transformation preferentially occurred in high strain regions.
