Combined Multi-scale Analyses on Strain/Damage/Microstructure in Steel: Example of Damage Evolution Associated with ε-martensitic Transformation

Abstract

We studied damage evolution behavior associated with ε-martensite in a Fe-28Mn alloy. Visible factors of damage evolution associated with ε-martensite are considered to be strain distribution, microstructure, micro-void and crack. Combinatorial use of replica digital image correlation, electron backscattering diffraction, and electron channeling contrast imaging enables to clarify the distributions of strain, microstructure and damage. Through quantitative damage analysis, damage evolution behavior was classified into three regimes: (i) incubation regime, (ii) nucleation regime, and (iii) growth regime. In the incubation regime, an interaction of ε/ε-martensite plates and impingement of ε-martensite plates on grain boundaries caused plastic strain localization owing to plastic accommodation. In the nucleation regime, accumulation of the plastic strain on the boundaries caused microvoid formation. The damage propagated along with the boundaries through coalescence with other micro-voids, but the propagation was arrested by crack blunting at non-transformed austenite. In the growth regime, the arrested damage grew again when a further plastic strain was provided sufficiently to initiate ε-martensite near the damage.

1. Introduction

1.1. Analysis of Damage Evolution Behavior

Theoretical interpretation of fractures associated with plastic deformation requires detailed analyses of microdamage evolution behavior. Important visible factors for microdamage analysis are the strain, microstructure, and cracks/voids. Because all of these factors have hierarchical characteristics depending on the observation scale, multiscale analyses of these three factors and their relationships play key roles in constructing a detailed fracture model.

Because the primary factors causing fracture are crack/void nucleation and growth, it is necessary to quantitatively clarify the amount, size, and distribution of cracks and voids. This study focuses on fracture after plastic deformation; thus, crack/void observation results must be linked to the local plastic strain. The use of post-mortem samples with a plastic strain gradient is reportedly helpful for quantification of crack/void characteristics. More specifically, the damage area fraction, number of damage incidents, and average damage size are useful as quantitative damage parameters when they are plotted against the local plastic strain every 100 μm.^1,2,3) In particular, a diagram of the average damage size can quantitatively and statistically elucidate aspects of the damage evolution behavior corresponding to damage initiation, propagation, and arrest.¹⁾

The underlying mechanism of damage evolution can be clarified from a microstructural viewpoint. To obtain a direct link between statistical data on cracks/voids and microstructure, it is desirable to use a single sample for damage and microstructure observations. Therefore, an observation method with a spatial resolution ranging from several nanometers to several tens of micrometers for a bulk material is needed. Electron backscatter diffraction (EBSD) and electron channeling contrast imaging (ECCI) satisfy these conditions. EBSD analyses can provide the crystal orientation and identify the phase. Thus, EBSD analysis is an effective method of analyzing an interface associated with initiation and growth of cracks/voids.^4,5,6) However, EBSD analysis cannot detect extremely fine microstructure (approximately several nanometers) and dislocation substructure that does not have a large crystallographic misorientation. On the other hand, ECCI can clearly visualize a single dislocation,^1,7,8) thin deformation twin,^9,10,11) cell structure,^9,12) local slip bands,¹³⁾ and so forth, whereas EBSD cannot. The combined use of these observational methods can clarify the microstructure dependence of damage evolution behavior.

Understanding the plastic strain distribution can provide a bridge between the behaviors of microstructure evolution and those of damage initiation/growth. Specifically, plastic strain and microstructure evolution are mainly attributed to dislocation glide, multiplication, and rearrangement. Damage evolution has been reported to have a correlation with the microstructurally-local strain localization.^14,15) To correlate the strain distribution with the microstructure and damage, a spatial resolution of several tens of micrometers (microstructure scale, such as grain size) or less is needed. It is also desirable to use identical regions of the same sample for mapping cracks/voids and microstructure. However, there are two problems with mapping microstructure-scale local plastic strain using the same sample: 1) undeformed microstructure is required to obtain the local strain; 2) the state just before damage initiation is needed in order to correlate crack/void initiation with the strain heterogeneity. For these reasons, a spatially resolved strain map must be taken at several deformation stages across wide observation ranges of the sample. To solve these problems, we developed a method of digital image correlation (DIC) on plastic replicas.¹⁶⁾ DIC analysis of plastic replicas that are sampled at several deformation stages can provide the microstructure-scale strain distribution at each deformation stage. More specifically, because replication copies the surface microstructures in an entire region of the sample, DIC of replicas can clarify the correlation among the plastic strain, microstructure, and damage evolution behavior from initiation to failure in a selected area after a sample fractures.

As stated above, the observation methods for strain, microstructure, and cracks/voids were developed independently. However, these observation methods has not been used together to clarify damage evolution behavior. In particular, the damage evolution mechanism of austenite including ε-martensite has not been clarified owing to its microstructural complexity, although the austenite-based alloy is recognized as a high-performance structural material. In addition, austenite has not been comprehensively analyzed in terms of the strain, microstructure, and cracks/voids on multiple scales. We will explain the importance of damage evolution behavior related to ε-martensite in the following section.

1.2. Fracture Phenomena Related to ε-Martensite

In recent years, the introduction of deformation-induced ε-martensite has drawn attention as an effective method of improving the shape memory effect,^17,18,19) ductility and strength,^20,21,22,23) and low cycle fatigue properties.^24,25,26) For example, ε-martensite enhances the work hardening capacity and thus improves the tensile ductility as long as the plastic instability condition is satisfied.^20,22) Moreover, even though twinning-induced plasticity steels show no ε-martensitic transformation at ambient temperature, cryogenic deformation can provide deformation-induced ε-martensitic transformation. In fact, the ε-martensitic transformation affects the mechanical properties at low deformation temperature.^27,28) Hence, the existence of ε-martensite is not a negligible factor for general applications of various austenitic steels.

In contrast to the advantageous effects, ε-martensite has also been reported to cause damage initiation and propagation.^29,30) Damage evolution degrades the ductility remarkably in some austenitic steels.^29,30,31,32) However, the degree of degradation depends on the amount and morphology of ε-martensite, its chemical composition, and the stress level. In some cases, only the advantageous features appear without any ductility degradation.^22,23,31) Therefore, understanding the damage evolution behavior associated with the ε-martensitic transformation is required to obtain an alloy design that suppresses the ductility degradation.

As described above, the morphology of ε-martensite has various complicated effects on damage evolution behavior. For instance, ε-martensite microscopically affects the crystallographic orientation dependence and local stress concentration and macroscopically affects the work hardening behavior. Therefore, a method of observing the strain, microstructure, and cracks/voids on multiple scales is indispensable for clarifying the damage evolution behavior associated with ε-martensite. In this study, we will discuss the damage evolution mechanism associated with ε-martensite using observation methods that enable us to correlate it with multiple factors on multiple scales.

2. Experimental

2.1. Material and Specimens

An Fe–28.4Mn–0.002C–0.0089S–<0.003P–0.0049O–0.0053N (wt.%) alloy was prepared by vacuum induction melting. A 10 kg ingot was forged and hot rolled at 1273 K; it was then solution treated at 1273 K for 3.6 ks under an argon gas atmosphere and subsequently water quenched to suppress the formation of cementite and ferrite and grain boundary segregation of impurity carbon from the other elements. The solution-treated bar was cut by spark machining to obtain the specimen geometries required for the following experiments (Fig. 1). Tensile tests were conducted at ambient temperature with a crosshead speed of 1.0 × 10⁻² mm/s for two types of plate specimens. The first type of specimen has a gauge dimension of 4 mm^w × 0.5 mm^t × 10 mm^l [Fig. 1(a)]. The second type is an hourglass-shape specimen with a dimension of 14 mm^w × 1.0 mm^t × 30 mm^l and a radius of 5.0 mm [Fig. 1(b)]. The hourglass-type specimen can provide a gradient of the plastic strain corresponding to the width of each location on the specimen. Therefore, the damage and microstructure corresponding to each plastic strain can be observed in a single specimen. An optical micrograph of the initial microstructure was taken after etching with a 15% HNO₃ + 85% C₂H₅OH solution. The initial microstructure is γ-austenite and plate-like thermally induced ε-martensite formed along Mn segregation bands, as shown in Fig. 2. The initial microstructure was used as a random pattern for the DIC measurements. ε-martensitic transformation and dislocation slip are the dominant plastic deformation modes,³¹⁾ and the α′-martensitic transformation does not occur in this alloy.³¹⁾ To remove the Mn segregation bands, lengthy homogenization treatment is required at a temperature range of 1473 to 1573 K. In other words, the heat treatment temperature must be lower than the melting temperature and higher than a temperature enabling significant Mn diffusion. However, Mn in high-Mn steels is desorbed from the surface by heat treatment at a high temperature. Therefore, homogenization treatment to remove the Mn segregation band in high-Mn steels requires a large ingot size that can provide sufficient material even after the Mn-depleted zone is ground. Therefore, for the present bar received, homogenization treatment was difficult. Moreover, complicated heat treatment is not considered to be performed for practical application of high-Mn steels. Therefore, in this study, the sample was not homogenization-treated and therefore includes Mn segregation bands.

Fig. 1.

Sample dimensions used for (a) tensile testing and (b) damage evolution analysis.

Fig. 2.

Optical micrograph showing the undeformed microstructure.

2.2. Multiscale Strain Analysis Method

In this study, “multiscale strain analysis” does not mean strain mapping corresponding to microstructural hierarchy, which has been investigated recently.^7,33,34) Here, strain analyses were conducted on the following three scales with three different purposes.

The first experiment is a tensile test using a specimen having a gauge part. On the basis of the work hardening behavior, we evaluate the occurrence of premature fracture. The relationship between work hardening and premature fracture can be discussed using the following equation.   

$$\sigma \ge \text{d}\sigma /\text{d}\epsilon$$(1)

where σ is the true stress, ε is the true strain, and dσ/dε is the work hardening rate. Equation (1) is known as the criterion for the plastic instability condition, which is reportedly available in high-Mn austenitic steels.^22,27,31,35)

The second experiment is a measurement of the plastic strain gradient of the hourglass-type specimen. Specifically, Vickers indents were introduced on the specimen surface every 100 μm before the tensile test. Then, the local plastic strains were determined by measuring the distances between the indents before and after the tensile test. Various microstructures and damage in different locations of the specimen can be correlated with the local plastic strain measured every 100 μm. Measurement of the mesoscale plastic strain in a single specimen is indispensable to obtaining the damage evolution curves described below.

Third, micro-DIC analysis of plastic replicas was conducted to clarify the correlation between the microstructurally local strain and damage evolution behavior. As mentioned in the introduction, DIC on replicas can be used to analyze the local plastic strain in a selected area where surface cracks are observed on a post-mortem sample by tracking the damage evolution at several deformation stages. An acetyl cellulose film 34 μm in thickness was used for the replication. The replica sheet was immersed in methyl acetate for 3±1 s and pasted on the specimen surface without any external force. After drying, the replica sheet was peeled from the specimen surface. The replica sheet was observed using an optical microscope after sputtering with Pt. The influence of the replica sheet shrinkage must be considered when applying DIC analyses. Hamada et al. reported¹⁶⁾ that the shrinkage ratio of the replica sheet used in this study does not exhibit anisotropy and depends only on the immersion time in methyl acetate. The relationship between the shrinkage ratio β of the replica sheet and the immersion time t is described by the following equations.   

$$\text{Actual length}=\left(1+\beta \right)\times \text{Replica length}$$(2)

  

$$\beta =0.0172t^{0.505}$$(3)

The DIC analyses were performed using VIC-2D (Correlated Solutions, Inc.). The step size and subset size for the DIC analyses were set to 1 pixel and 111 × 111 pixels, respectively. Because the DIC analysis is affected by the contrast of the images, the average contrast of the optical micrographs was adjusted.

2.3. Multiscale Analysis of Damage Evolution Behavior

The specimen for scanning electron microscopy (SEM) was prepared by mechanical polishing for 1.2 ks with colloidal silica to observe deformation-induced cracks/voids in the post-mortem specimen. The damage evolution behavior was quantified by measuring the damage area fraction D_a, number of damage incidents per area n, average damage size d_ave, and average aspect ratio of damage a/b. The damage area fraction D_a was defined as D_a = A_d/A_a, where A_a is the area of the entire region observed, and A_d is the damaged area. The number of damage incidents per area n was defined as n = N/A_a, where N is the number of damage incidents for each region. The average damage size d_ave was defined as d_ave = D_a/n. The definition of the average damage aspect ratio is estimated using test results as described below. The quantitative damage evolution behavior was evaluated by plotting these calculated values against the average local plastic strain corresponding to each observation area.

Microstructural damage analysis was conducted using microstructure characterization as described in the next section. Using the analysis results derived from the correlation between the damage and the microstructure, we constructed a damage evolution model that is consistent with the characteristics of the fracture surface. Fractography was performed at 10 kV by secondary electron imaging.

2.4. Multiscale Observation of Microstructure

The deformation microstructure and phase distribution near damage were examined using the EBSD and ECCI methods. EBSD and ECCI are microstructural observation methods for a bulk specimen. Therefore, a single sample was used for quantitative observation of cracks/voids without changing the state of the sample surface. EBSD analyses were conducted at 15 kV with a beam step size of 100 nm and working distance of 18.0 mm. ECC analyses were conducted at 10 kV with a working distance of 3.0 mm.

3. Results

3.1. Stress–Strain Response and Work Hardening Behavior

Figure 3(a) shows the engineering stress–strain curve of the specimen with a gauge part shown in Fig. 1(a). Figure 3(b) shows the true stress–strain and work hardening rate curves obtained from Fig. 3(a). The intersection point of these curves indicates the plastic instability condition described by Eq. (1). Fracture occurred after the plastic instability condition was satisfied, indicating that premature fracture^30,31,32) resulting from the ε-martensitic transformation did not occur. Therefore, we noted ductile damage evolution behavior associated with ε-martensite in this study.

Fig. 3.

(a) Engineering stress-strain curve of the Fe-28Mn alloy. (b) True stress-strain curve and work hardening rate plotted against true strain.

3.2. Quantitative Analysis of Damage Evolution

Figure 4(a) shows a SEM image of a fractured specimen in which several Vickers indents were introduced before tensile deformation. The local plastic strain was determined by measuring the distances between the indents before and after the tensile test. Figure 4(b) shows the relationship between the local plastic strain and the distance from the fracture part. The damage evolution parameters are plotted against the average local plastic strain obtained from the relationship between the strain and the distance from the fractured part. Figures 4(c)–4(e) show an example of damage observed by SEM. To determine the aspect ratio a/b, first, the vertical length a was measured as shown in the schematic images. Then, the horizontal length b was calculated from an approximate ellipse representing each damage area. The aspect ratio a/b was calculated from the values of a and b.

Fig. 4.

(a) SEM micrograph showing an overview of the fractured specimen. (b) Local plastic strain plotted against distance from fractured part. (c–e) Examples of microdamage incidents.

Figure 5 shows the damage area fraction D_a, number of damage incidents n, average damage size d_ave, and damage aspect ratio a/b plotted against the average local plastic strain. The damage area fraction D_a increased gradually until the average local plastic strain reached 55% and increased rapidly thereafter [Fig. 5(a)]. The number of damage incidents increased with increasing average local plastic strain evolution [Fig. 5(b)]. In contrast, the average damage size increased and then had a constant value [Fig. 5(c)]. Therefore, the damage evolution process is classified into three stages from the curve of the average damage size. Hereafter, these three stages are called the damage incubation stage (5%–30%), damage nucleation stage (30%–55%), and damage growth stage (>55% fracture). The damage aspect ratio was less than one in the damage incubation stage and increased above one with increasing local plastic strain in the damage nucleation stage. Then, the damage aspect ratio decreased gradually with increasing average local plastic strain in the damage growth stage.

Fig. 5.

(a) Area fraction of damage, (b) number density of damage, (c) average damage size and (d) aspect ratio of damage plotted against local plastic strain.

3.3. Replica DIC

Figure 6(a) shows a surface of the fractured specimen. Surface cracks occurred in regions A and B in Fig. 6(a). In addition to these region, in four regions including regions C and D where surface cracks did not occur, the local plastic strain was analyzed by DIC on plastic replicas. Figure 6(b) shows the relationship between the distance from the fracture part and the plastic strain calculated from optical micrographs of the plastic replicas in each deformation stage. Figures 6(c)–6(g) show optical micrographs of the replica showing the specimen surface in each deformation stage. Figures 6(d’)–6(g’) show strain contour maps obtained by analyzing these optical micrographs. These images were modified on the basis of Eqs. (2) and (3) before the DIC analyses. The immersion time of the replicas in methyl acetate for each displacement are (c) 0 mm: 3.25 s, (d) 0.5 mm: 3.24 s, (e) 1.0 mm: 3.62 s, (f) 1.5 mm: 3.23 s, and (g) 2.0 mm: 2.85 s. In this study, grain boundaries and plate-like thermally induced ε-martensite were used as a random pattern for the DIC analyses. Therefore, the spatial resolution of the present DIC analyses is approximately the grain size (50 μm).

Fig. 6.

(a) SEM image at the vicinity of the fractured part. (b) The relationship between plastic strain distribution and displacement. Optical micrographs of the replicas taken at displacements of (c) 0, (d) 0.5, (e) 1.0, (f) 1.5, and (g) 2.0 mm. (c’–g’) Plastic strain maps obtained by replica DIC. (h) Local plastic strain ε_DIClocal plotted against Local plastic strain, ε_Ave.local. (Online version in color.)

The replica image indicates that thermally induced ε-martensite was present at regions A and B where the surface cracks were observed, as shown in Fig. 6(c). On the other hand, regions C and D, without surface cracks, were composed mainly of a single γ-austenite phase. Because Mn reduces the starting temperature of the martensitic transformation, M_s (γ→ε), the non-transformed region corresponds to the Mn-segregated region. Hereafter, we discuss test results assuming that Mn is segregated in the region where thermally induced ε-martensite does not exist. A plastic strain concentration corresponding to the grain size was observed in the region where thermally induced ε-martensite formed. In particular, a relatively large local plastic strain was observed even in the early deformation stage in region A, where surface cracks appeared. A similar large localized strain was also observed in region C, which is composed of γ-austenite. In terms of the presence of thermally induced ε-martensite, the result of replica DIC classifies these regions into four categories: 1) a high plastic strain region with thermally induced ε-martensite (regions A and B), 2) a low plastic strain region with thermally induced ε-martensite, 3) a high plastic strain region without thermally induced ε-martensite (region C), 4) a low plastic strain region without thermally induced ε-martensite (region D). Among these regions, surface cracks initiated in region 1). Furthermore, Fig. 6(h) shows the relationship between the average local plastic strain and local plastic strain analyzed by DIC in each deformation stage. Surface cracks were not observed in region C, which was composed of γ-austenite, although region C showed a larger local plastic strain than region B.

3.4. Microstructure Observation and Fractography

Figure 7 shows an ECC image in the damage incubation stage (5% local plastic strain). In this image, the surface orientation of the austenite phase satisfied Bragg’s condition, so the intensity of backscattered electrons is very low.⁹⁾ Therefore, the austenite parent phase appears as a dark contrast. On the other hand, ε-martensite and the dislocation substructure appear as brighter contrast because of the different crystal structure and elastic strain, respectively. Namely, the plate-like products appearing as bright contrast are ε-martensite, and the mist-like feature indicates evolution of the dislocation substructure. Here, the ε-martensite in the ECC image is thin and is a single variant. In addition, a remarkable contrast change was observed at the intersection of ε-martensite plates and a grain boundary, as shown by a dotted line in Fig. 7.

Fig. 7.

ECCI showing dislocation substructure and thin ε-martensite plates at 5% local plastic strain region.

Figures 8, 9, 10 show examples of the relationship between the damage configuration and microstructure at the damage nucleation stage. Schematics for each image are shown to illustrate the corresponding damage initiation and propagation processes. Figure 8 shows damage nucleation and propagation along a grain boundary. A large amount of deformation-induced ε-martensite was observed near the damage tip. These ε-martensite plates impinged on a γ-grain boundary where the damage nucleated. Figure 8(b) shows microvoids that formed near the damage tip. Figure 8(c) is a magnified image of the rectangular region outlined in Fig. 8(a) and shows development of cell structure. Even if dislocation substructure developed, damage such as a void does not nucleate in the damage nucleation stage if a large amount of ε-martensite does not form. Figure 9 shows that voids nucleated in the region where a large amount of ε-martensite was present and grew along the γ-grain boundary. As shown in Fig. 9, the tensile orientation of austenite in Grain 3 is <111>, which was determined from the crystal orientation of the retained austenite (enclosed by the yellow line). The thick plate-like region oriented in the <100> direction is considered to be an annealing twin in Grain 3. In addition, thin plate-like products are considered to be a thin annealing twin or deformation twin in Grain 3. Another type of damage was observed as a transgranular crack along ε-martensite plates, as shown in Fig. 10. We cannot specify the initial crystal orientation of austenite, as it is difficult to distinguish between an annealing twin and the austenite parent phase using the orientation information of the deformation microstructure obtained by EBSD. However, this zigzag-shaped damage is determined to propagate along some surface traces of four types of {111} planes of the retained austenite, which is clarified from the relationship between the ε and γ crystal orientations.

Fig. 8.

ECCI showing (a) crack and (b) microvoids, and (c) dislocation substructure at 40% average local plastic strain region. (d–f) Schematics demonstrating how the micro voids nucreated, coalesced and propagated.

Fig. 9.

(a) Phase map and (b) RD-IPF map coupled with IQ map showing intergranular damage at 36% average local plastic strain region. (c–d) Schematics demonstrating propagation of the intergranular damage. (Online version in color.)

Fig. 10.

(a) Phase map and (b) RD-IPF map coupled with IQ map showing transgranular crack and at 55% average local plastic strain region. (c–d) Schematics demonstrating propagation of transgranular damage. (Online version in color.)

Figure 11 shows damage after large plastic deformation was provided in the damage growth stage (67% local plastic strain). As shown in Fig. 11(a), a sharp crack tip renucleated at the blunted crack tip (arrow A) in the region where a considerable amount of ε-martensite formed. The tip of the other side of the crack remained blunted (arrow B), and its propagation was stopped in the region where austenite was mechanically stable. The tensile direction of the retained austenite is close to the <100> direction, as shown Fig. 11(b). The schematic image in Fig. 11(c) shows the relationship between asymmetrical damage evolution behavior and the distribution of ε-martensite.

Fig. 11.

(a) Phase map and (b) RD-IPF map coupled with IQ map showing a blunted crack at 67% average local plastic strain region. (c) Schematic demonstrating how the crack propagated in ε-martensite phase and arrested in austenite. (Online version in color.)

Figure 12 shows a fractograph of the tensile-fractured specimen. Here, the fracture surface can be classified into three regions according to their characteristics: 1) a comparatively flat region with shallow surface relief giving evidence of plastic deformation, 2) a region covered with small dimples ranging from approximately several hundreds of nanometers to 1 μm, and 3) a region covered with large dimples 10 μm in size with inclusions.

Fig. 12.

Fractograph showing flat region (red arrow), small dimple (white arrow) and relatively-large dimple with fish eye (yellow arrow). (Online version in color.)

4. Discussion

As mentioned above, the damage evolution process was classified into three stages: the damage incubation stage, damage nucleation stage, and damage growth stage. Hereafter, we classify the deformation and damage evolution behavior into these three stages and discuss the correlations among damage evolution associated with ε-martensite, microstructure evolution, and plastic strain concentration.

4.1. Damage Incubation Stage (5%–30% Local Plastic Strain): Accumulation of ε-Martensite Plates and Plastic Strain Concentration

In the stage with 5%–30% average local plastic strain, damage incidents were observed mainly as voids, which form when an inclusion separates from the austenitic parent phase. Namely, the dominant factors affecting the average damage size in this stage are void initiation at the inclusion and its growth. The damage aspect ratio is less than 1 in this stage, which indicates that the void is stretched along the loading direction. However, void growth is not the main reason for fracture in the present alloy. As described below, ε-martensite plays an important role in the fracture phenomenon.

Note that deformation-induced ε-martensite has already been formed significantly at this stage, as shown in Fig. 7. The ε-martensite observed in Fig. 7 is characterized as thin plates oriented in one direction. These characteristics appear when deformation-induced ε-martensite forms in the early stage of plastic deformation.³⁶⁾ In the same Fe–28Mn alloy, an increase in the amount of ε-martensite with deformation was confirmed by X-ray diffraction.³⁷⁾ ε-martensite reportedly acts as a stress concentration source for the following two reasons. (1) ε-martensite is formed in parallel to {111}_γ//{0002}_ε, in accordance with the Shoji–Nishiyama relation.³⁸⁾ The slip plane of ε-martensite having hexagonal close-packed structure is {0002}_ε. Therefore, the γ/ε interfaces act as a barrier against dislocation motion on other slip planes.^29,39) (2) An ε-martensite tip has a large stress concentration.⁴⁰⁾ Even though the ε-martensitic transformation did not induce damage, the amount of ε-martensite acting as a stress concentration source increases with increasing plastic strain, which is a precursor step to damage initiation in the damage incubation stage. The stress concentration is accommodated through plastic deformation as long as the ε-martensite and γ-austenite have sufficient toughness. Therefore, the stress concentration provides a plastic strain concentration promoting microvoid formation at the intersection of ε-martensite plates and interfaces. Elastic and plastic strain concentrations caused by interaction between ε-martensite and a grain boundary were observed as a local contrast change in the area surrounded by dotted lines in Fig. 7. The plastic strain concentration resulting from the ε-martensitic transformation also appears in the result of DIC analysis in Fig. 6(d’). Because ε-martensite remains after the microstructural plasticity accommodation, the degree of plastic strain concentration increases with increasing plastic strain through repeated stress concentration and plastic accommodation arising from the presence of ε-martensite, as shown in Figs. 6(d’)–6(g’). A considerable amount of thermally induced and deformation-induced ε-martensite formed easily in the region of low Mn content where the stability of austenite is low. Therefore, plastic strain concentration occurs easily in the low Mn content region. Rolling direction–inverse pole figure (RD-IPF) maps indicate that the tensile orientation of retained austenite is near-<100>, as shown in Figs. 9, 10, 11. In particular, <100> is reportedly the non-preferential tensile orientation for deformation-induced ε-martensite.^41,42) In contrast, the <111> tensile orientation is the preferential orientation for the deformation-induced ε-martensitic transformation.^41,42) A large amount of ε-martensite was observed to form in <111>-oriented grains, which is clarified from the crystal orientation of the retained austenite in this observation result. According to the tensile orientation dependence, the result of replica DIC can be explained as follows. The largest plastic strain concentration occurred in a grain oriented to <111>, which is the preferential tensile orientation for the deformation-induced ε-martensitic transformation accompanied by thermally induced ε-martensite (low Mn content region). The second largest plastic strain concentration occurred in a <111>-oriented grain without thermally induced ε-martensite (high Mn content region). To summarize these results in terms of damage accumulation, in the <111>-oriented grain with a low austenite stability, deformation-induced ε-martensite can form easily, causing stress concentration and subsequent plastic strain localization associated with plasticity accommodation. The plastic strain concentration plays an important role in damage initiation related to deformation-induced ε-martensite.

4.2. Damage Nucleation Stage (30%–55% Local Plastic Strain): Microvoid Formation Resulting from ε-Martensite, Damage Coalescence, and Damage Arrest

In the stage of 30%–55% local plastic strain, plate-like damage was observed along an interface intercepting ε-martensite plates in addition to a void originating in an inclusion (Fig. 8). The damage-tip became blunt as spherical microvoids coalesced. These microvoids associated with ε-martensite nucleated through plastic strain concentration, which results from stress concentration and is followed by plastic accommodation. More specifically, the maximal local plastic strain is much more than 60% because of plastic strain concentration at this deformation stage of 30% average local plastic strain (2.0 mm displacement). Namely, the maximal local plastic strain exceeds the total elongation of this alloy. The strain was more localized near the interfaces than in the grain interior, as shown in Fig. 7. Therefore, the actual local plastic strain near the interface intercepting deformation-induced ε-martensite is considered to be higher than the plastic strain obtained by the replica DIC in interfaces. Thus, the plastic strain concentration causes localization of lattice defects such as vacancies arising from dislocation dipole formation near a grain boundary, which induces microvoid formation. When ε-martensite induces microvoid formation, the minimal distance of microvoid formation is several hundreds of nanometers, which corresponds to the distance between ε-martensite plates. The coalescence of neighboring microvoids correspond to surface damage incidents in regions A and B in Fig. 6(a). Nanovoids of approximately several hundreds of nanometers were also observed near the tip of the plate-like damage, as indicated by black arrows in Fig. 8(b). These nanovoids are associated with ε-martensite and represent the damage incident before coalescence occurs. Nakatsu et al. reported that microvoids formed along interfaces such as grain boundaries or thermally induced ε-martensite, where deformation-induced ε-martensite impinged in an Fe–27Mn steel and an Fe–22Mn steel.³¹⁾ Because the plate-like damage has a stress concentration at the tip, coalescence with the nanovoids occurs easily. For this reason, the average damage aspect ratio increased in the damage nucleation stage, as shown in Fig. 5(d). In addition to the increase in the average damage aspect ratio, an important feature is the constant average damage size in this stage, as shown in Fig. 5(c). Although the length of damage increased, the average damage size was constant. This is because the average damage size is calculated using damage incidents including newly formed small voids. The effect of tiny void formation compensates for the effect of microvoid elongation. Moreover, damage is arrested in this stage, decreasing the average damage growth rate significantly. These facts result in the plateau feature in the average damage size–local plastic strain curve. Note the region indicated by arrow B in Fig. 11. Nanovoids did not nucleate in the damage tip in the near-<100>-oriented grain with only a small amount of ε-martensite. Therefore, the driving force of damage propagation is lost, and the damage tip remains blunted, resulting in the low damage growth rate in the damage nucleation stage. In other words, the average damage size depends on the distance between grains that are unfavorable for the deformation-induced ε-martensitic transformation. In most cases, the distance is 1–2 times the grain size (approximately 50–100 μm).

4.3. Damage Growth Stage (Local Plastic Strain Exceeding 55%): Coalescence of Damage Incidents Originating from ε-Martensite and Inclusion, and Subsequent Final Fracture

The plate-like damage observed in the previous stage propagated into the grain interior or along the grain boundary through coalescence with microvoids. Then, the damage was arrested when it reached a grain in which the deformation-induced ε-martensitic transformation is difficult. However, deformation-induced ε-martensite formed when further plastic strain was provided in a damage tip. The ε-martensitic transformation induces microvoid nucleation at the damage tip, causing the arrested damage to start to grow again. Therefore, a sharp damage tip appears again, as shown in region A in Figs. 9 and 11. (In Fig. 11, damage growth was arrested because the ε-martensitic transformation did not occur easily during damage opening.) In this way, damage grows and leads to failure through the following cycle: damage tip blunting → deformation-induced ε-martensitic transformation → nanovoid formation → coalescence of microvoids. Namely, damage growth requires a critical plastic strain for the occurrence of the deformation-induced ε-martensitic transformation in the blunted damage tip, which corresponds to the border separating the damage nucleation and damage growth stages. In the damage growth stage, the damage tip continues to open until the ε-martensite fraction at the damage tip becomes sufficient for nanovoid formation. Therefore, the average damage size increased but the average damage aspect ratio decreased with increasing plastic strain in the damage growth stage, as shown in Figs. 5(c), 5(d).

On the basis of these discussions, the entire damage evolution process is attributed to microvoid formation and coalescence even if sharp cracks apparently form. Therefore, the entire fracture surface is covered by a large number of dimples, as shown in Fig. 12. Here, we explain the characteristics of the fracture surface in this alloy again. The fracture surface can be classified into three regions: 1) a relatively flat region with shallow surface relief indicating plastic deformation, 2) a region covered with small dimples ranging from approximately several hundreds of nanometers to 1 μm, and 3) a region covered with large dimples 10 μm in size with inclusions. As shown by the red arrows in Fig. 12, a relatively flat region was also observed, but the region was not completely flat and had a shallow surface relief associated with plastic deformation. Namely, the region results from coalescence of nanovoids several tens of nanometers in size. A quasi-cleavage-like characteristic has been observed when the γ/ε interfaces separate.^22,29) Thus, the comparatively flat fracture surface is considered to form through growth of the transgranular crack observed in Fig. 10. In Fig. 12, small dimples several hundreds of nanometers to 1 μm in size and a comparatively large dimple of 10 μm with an inclusion were also observed on the fracture surface, as shown by white and yellow arrows, respectively. The diameter of the small shallow dimples corresponds to the microvoid size observed in the interfaces intercepting ε-martensite plates. Retained austenite was also observed between ε-martensite plates even in the region where a large plastic strain was provided. Therefore, these facts imply that the small shallow dimples formed through microvoid growth associated with ε-martensite and/or ductile fracture of the retained austenite. A fish-eye feature was observed at the bottom of the comparatively large dimple. Therefore, these dimples formed through void growth from an inclusion. Finally, we conclude that fracture occurred through coalescence of ε-martensite-related damage and voids originating in inclusions.

5. Conclusions

This study clarified various correlations among the plastic strain concentration, microstructural factors, and damage evolution behavior associated with ε-martensite through combined use of replica DIC, ECCI, and EBSD techniques in the Fe–28Mn alloy. Considering the average damage size and damage aspect ratio, we specified the dominant factors affecting damage evolution in the observed microstructural characteristics. We also classified the damage evolution behavior into three stages based on the average damage size in terms of ε-martensite and proposed a damage evolution mechanism related to the macroscopic fracture. The elucidated damage evolution mechanism in each stage is listed below.

(1) Damage incubation stage (5%–30% local plastic strain): Deformation-induced ε-martensite increased with increasing plastic strain. In the region where ε-martensite formed, a plastic strain concentration related to ε-martensite was observed, which promoted microvoid formation. In this stage, damage was also observed as voids that originated in inclusions separated from the austenite parent phase. Therefore, the damage aspect ratio was less than one.

(2) Damage nucleation stage (30%–55% local plastic strain): The damage evolution behavior associated with ε-martensite dominated the macroscopic damage parameters such as the average damage size. Specifically, many voids nucleated at intersections of ε-martensite plates and γ-grain boundary/ε-martensite. These microvoids grew along the interfaces through coalescence. Then, the damage was arrested in a grain where the austenitic stability was comparatively high. Therefore, the average damage size had a constant value against the plastic strain in this stage. Damage also coalesced and propagated perpendicular to the loading direction. Therefore, the damage aspect ratio became more than one.

(3) Damage growth stage (local plastic strain exceeding 55%): New microvoids nucleated near a crack tip when sufficient further plastic strain was provided to initiate ε-martensite near the crack tip. The arrested damage grew again through coalescence with these microvoids. Thus, the average damage size increased dramatically with increasing plastic strain in this stage. Finally, these damage incidents coalesced with voids originating in inclusions, resulting in final failure.

Acknowledgements

The work was supported by acknowledge Grant-in-Aid for Young Scientists B (Grant Number 15K18235) and ISIJ Research Promotion Grant (2015–2016).

References

• 1)   M.  Koyama,  C. C.  Tasan,  E.  Akiyama,  K.  Tsuzaki and  D.  Raabe: Acta Meter., 70 (2014), 174.
• 2)   C. C.  Tasan,  J. P. M.  Hoefnagels and  M. G. D.  Geers: Scr. Mater., 54 (2010), 316.
• 3)   C. C.  Tasan,  J. P. M.  Hoefnagels and  M. G. D.  Geers: Acta Mater., 57 (2009), 4957.
• 4)   D.  Raabe,  H.  Springer,  I.  Gutierrez-Urrutia,  F.  Roters,  M.  Bausch,  J. -B.  Seol,  M.  Koyama,  P. -P.  Choi and  K.  Tsuzaki: JOM, 66 (2014), 1845.
• 5)   M.  Wang,  C. C.  Tasan,  M.  Koyama,  D.  Ponge and  D.  Raabe: Metall. Mater. Trans. A, 46 (2015), 3797.
• 6)   D.  Sasaki,  M.  Koyama and  H.  Noguchi: Mater. Sci. Eng. A, 640 (2015), 72.
• 7)   D.  Yan,  C. C.  Tasan and  D.  Raabe: Acta Meter., 96 (2015), 399.
• 8)   S.  Yamasaki,  M.  Mitsuhara,  K.  Ikeda,  S.  Hata and  H.  Nakashima: Scr. Mater., 101 (2015), 80.
• 9)   I.  Gutierrez-Urrutia and  D.  Raabe: Scr. Mater., 69 (2013), 53.
• 10)   M.  Koyama,  E.  Akiyama,  K.  Tsuzaki and  D.  Raabe: Acta Meter., 61 (2013), 4607.
• 11)   M.  Koyama,  E.  Akiyama,  T.  Sawaguchi,  D.  Raabe and  K.  Tsuzaki: Scr. Mater., 66 (2012), 459.
• 12)   I.  Gutierrez-Urrutia and  D.  Raabe: Acta Mater., 59 (2011), 6449.
• 13)   M.  Koyama,  H.  Springer,  S. V.  Merzlikin,  K.  Tsuzaki,  E.  Akiyama and  D.  Raabe: Int. J. Hydrog. Energ., 39 (2014), 4634.
• 14)   D.  Yan,  C. C.  Tasan and  D.  Raabe: Acta Mater., 96 (2015), 399.
• 15)   T. R.  Bieler,  P.  Eisenlohr,  F.  Roters,  D.  Kumar,  D. E.  Mason,  M. A.  Crimp and  D.  Raabe: Int. J. Plast. 25 (2009), 1655.
• 16)   S.  Hamada,  T.  Fujisawa,  M.  Koyama,  N.  Koga,  N.  Nakada,  T.  Tsuciyama,  M.  Ueda and  H.  Noguchi: Mater. Charact., 98 (2014), 140.
• 17)   A.  Sato,  E.  Chishima,  K.  Soma and  T.  Mori: Acta Metall., 30 (1982), 1177.
• 18)   H.  Otsuka,  H.  Yamada,  T.  Maruyama,  H.  Tanahashi,  S.  Matsuda and  M.  Murakami: ISIJ Int., 30 (1990), 674.
• 19)   M.  Koyama,  M.  Murakami,  K.  Ogawa,  T.  Kikuchi and  T.  Sawaguchi: Mater. Trans., 48 (2007), 2729.
• 20)   L.  Remy and  A.  Pineau: Mater. Sci. Eng., 28 (1977), 99.
• 21)   Y.  Tomota,  M.  Strum and  J. W.  Morris: Metall. Mater. Trans. A, 17A (1986), 537.
• 22)   M.  Koyama,  T.  Sawaguchi and  K.  Tsuzaki: Mater. Trans., 56 (2015), 819.
• 23)   M.  Koyama,  T.  Sawaguchi and  K.  Tsuzaki: Mater. Sci. Eng. A, 556 (2012), 331.
• 24)   T.  Sawaguchi,  I.  Nikulin,  K.  Ogawa,  K.  Sekido,  S.  Takamori,  T.  Maruyama,  Y.  Chiba,  A.  Kushibe,  Y.  Inoue and  K.  Tsuzaki: Scr. Mater., 99 (2015), 49.
• 25)   T.  Sawaguchi,  L.-G.  Bujoreanu,  T.  Kikuchi,  K.  Ogawa,  M.  Koyama and  M.  Murakami: Scr. Mater., 59 (2008), 826.
• 26)   H.  Li,  M.  Koyama,  T.  Sawaguchi,  K.  Tsuzaki and  H.  Noguchi: Philos. Mag. Lett., 95 (2015), 303.
• 27)   M.  Koyama,  T.  Sawaguchi,  T.  Lee,  C. S.  Lee and  K.  Tsuzaki: Mater. Sci. Eng. A, 528 (2011), 7310.
• 28)   M.  Koyama,  T.  Lee,  C. S.  Lee and  K.  Tsuzaki: Mater. Des., 49 (2013), 234.
• 29)   S.  Takaki,  T.  Furuya and  Y.  Tokunaga: ISIJ Int., 30 (1990), 632.
• 30)   M.  Koyama,  T.  Sawaguchi and  K.  Tsuzaki: Metall. Trans. A, 43A (2012), 4063.
• 31)   H.  Nakatsu and  S.  Takaki: J. Jpn. Inst. Met., 60 (1996), 141.
• 32)   M.  Koyama,  T.  Sawaguchi and  K.  Tsuzaki: ISIJ Int., 52 (2012), 161.
• 33)   N.  Nakada,  M.  Nishiyama,  N.  Koga,  T.  Tsuchiyama and  S.  Takaki: Tetsu-to-Hagané, 100 (2014), 1238.
• 34)   F. D.  Gioacchino and  J. Q.  da Fonsece: Exp. Mech., 53 (2013), 743.
• 35)   M.  Koyama,  T.  Sawaguchi and  K.  Tsuzaki: ISIJ Int., 53 (2013), 323.
• 36)   N.  Bergeon,  G.  Guenin and  C.  Esnouf: Mater. Sci. Eng. A, 242 (1998), 77.
• 37)   M.  Koyama,  S.  Okazaki,  T.  Sawaguchi and  K.  Tsuzaki: Metall. Mater. Trans. A, 47 (2015), 2656.
• 38)   Z.  Nishiyama: Kinzoku-no-Kenkyuu, 11 (1934), 561.
• 39)   A.  Sato,  K.  Soma and  T.  Mori: Acta Metall., 30 (1982), 1901.
• 40)   H.  Nakatsu,  T.  Miyata and  S.  Takaki: J. Jpn. Inst. Met., 60 (1996), 928.
• 41)   E. P.  Kwon,  S.  Sato,  S.  Fujieda,  K.  Shinoda,  K.  Kajiwara,  M.  Sato and  S.  Suzuki: Mater. Sci. Eng. A, 570 (2013), 43.
• 42)   R.  Ueji,  Y.  Takagi,  N.  Tsuchida,  K.  Shinagawa,  Y.  Tanaka and  T.  Mizuguchi: Mater. Sci. Eng. A, 576 (2013), 14.