Physical Properties
Strain Distribution Analysis of Two Perpendicular Planes in SUS310S Austenitic Stainless Steel Using Digital Image Correlation
2021 年 61 巻 1 号 p. 481-486
詳細
2021 年 61 巻 1 号 p. 481-486
We performed a strain distribution analysis of two perpendicular planes in SUS310S austenitic stainless steel using digital image correlation (DIC). Strain bands in both the rolling direction, (RD)-transverse direction and RD-normal direction planes, were connected at an edge, and the formation of a strain plane surrounded by the strain bands in each plane was confirmed. Furthermore, we found that the three-dimensional strain distribution can be inferred by analyzing the strain distribution of two perpendicular planes using DIC. The finite element method (FEM) was used to verify the formation of macro and micro strain bands. The FEM analysis also revealed that the connection of micro strain bands led to the formation of macro strain bands. The angle of macro strain bands to tensile loading direction was dependent on preferential deformation site distribution. In contrast, the angle of micro strain bands was mainly determined by preferential deformation site distribution when the angle of preferential deformation site to tensile loading direction was <50° and by maximum shear stress when it was >50°. From these results, we concluded that (i) the angle of the macro strain bands observed by DIC to tensile loading direction was mainly determined by the preferential deformation site distribution; and (ii) the angle of the micro strain bands was determined by both the preferential deformation site distribution and maximum shear stress.
Detailed investigation of plastic deformation behavior plays an important role in improving the safety and reliability of metals. Deformation behavior has been computationally investigated using the finite element method (FEM)1,2,3) and, more recently, digital image correlation (DIC).4,5,6,7,8,9,10,11) The latter is an innovative noncontact optical technique to measure the strain and displacement in metals.
In some previous studies, DIC has been applied to strain distribution analysis in dual-phase (DP) steel consisting of a soft-ferrite matrix and hard martensite as the secondary phase.4,5,6) For instance, Nakada et al.4) investigated the strain distribution in DP steel using DIC. They suggested that a combination of scanning electron microscopy (SEM) imaging and DIC can be used to evaluate a heterogeneous strain distribution. Yan et al.5) also pointed out the utility of combining these two methods to study damage nucleation in DP steel. In the case of hard vanadium carbide particle dispersion ferritic steel, DIC analysis for tensile-deformed specimens revealed that plastic strain was concentrated around the vanadium carbide particles.9) However, the majority of previous studies using DIC have applied two-dimensional (2D) analysis. For a more precise understanding of deformation behavior, it is necessary to carry out analysis of strain distribution in two perpendicular planes and/or three dimensions in metals.
Only a small number of researchers have performed an analysis of deformation behavior using three-dimensional (3D) analysis.12,13,14) For instance, Toda et al.12) carried out 3D analysis of crack and pore distribution in an aluminum alloy via synchrotron X-ray microtomography. However, it is difficult to evaluate the relationship between crack and pore distribution (i.e., deformation behavior) and microstructure in three dimensions simultaneously using this method. Furthermore, it is also difficult to establish a 3D evaluation method for the relationship between microstructure and strain distribution using DIC.
The number of studies applying two perpendicular plane analysis of strain distribution using DIC is especially limited. However, if the strain distribution of two perpendicular planes (e.g., rolling direction (RD)-transverse direction (TD) and RD-normal direction (ND) planes, RD-TD and ND-TD planes, and RD-ND and ND-TD planes) can be clarified using DIC, we may presume the 3D strain distribution to some extent. Thus, the purpose of the present study was to perform strain distribution analysis of two perpendicular planes in SUS310S austenitic stainless steel using DIC. In addition, the accuracy of the strain distribution in each plane obtained by DIC was verified using 2D FEM analysis.
The material used in the present study was a sheet of SUS310S austenitic stainless steel with a thickness of 1.0 mm. Figure 1 shows the initial microstructure of a specimen after annealing at 1000°C for 15 min. The initial microstructure was observed by SEM. The average diameter of crystal grains in the initial microstructure was approximately 12.5 μm. To investigate the constituent phase of the specimen, an X-ray diffraction (XRD) pattern of specimen without strain was obtained using an X-ray diffractometer with Mo Kα radiation. The XRD pattern of the specimen without strain in Fig. 2 shows that the microstructure of the specimen is austenite single phase.
SEM image of initial microstructure of specimen.
XRD pattern of specimen without strain.
The detailed experimental procedure for DIC of two perpendicular planes is shown in Fig. 3. The specimens were cut into 1.0 (thickness) × 2.0 × 40 mm and polished with silicon carbide paper, diamond paste, alumina powder, and colloidal silica. After the polishing, the microstructures in the RD-TD and RD-ND planes of the etched-specimen were observed by SEM. In addition, the strain distributions in the RD-TD and RD-ND planes of the same area as the SEM observation were also evaluated by DIC (VIC-2D, Correlated Solutions) with a subset size of 43 × 43 pixels and step of 5 × 5 pixels. Specimens were deformed at room temperature (25°C ± 2°C) by tensile straining of 3%, 6%, and 9% at a strain rate of 1.0 × 10−3 s−1. In the tensile tests, loading and unloading were repeated to evaluate the strain distribution at the same area of the same sample at different nominal strains.
Experimental procedure of DIC for two perpendicular planes.
In addition, we performed FEM analysis in plane stress state using a commercial software program (Femtet, Murata Software) to investigate the strain distribution computationally. As shown in Fig. 4, we created a virtual 2D microstructure where second phases as a trigger for deformation (preferential deformation sites) were dispersed in a matrix to express the inhomogeneity of the microstructure, and various angles of preferential deformation site distribution to tensile loading direction were set. The single short side was fixed and the long sides were free, and stress was applied in the direction of the arrow. The numbers of elements and nodes of triangular meshes used for FEM were 8202 and 16705, respectively. The material properties of both phases were summarized in Table 1. The material properties of the matrix were set to that of the austenite phase. The Young’s modulus of preferential deformation sites was set larger than that of the matrix to efficiently apply stress to the preferential deformation site. Furthermore, the yield strength of preferential deformation sites was set lower than that of the matrix to yield preferential deformation sites in the early stage of deformation. As a result, inhomogeneous deformation was observed at these conditions.
Typical virtual microstructure with preferential deformation sites dispersed in a matrix.
| Young’s modulus (GPa) | Yield strength (MPa) | n value | Poisson’s ratio | |
|---|---|---|---|---|
| Matrix | 190 | 190 | 0.39 | 0.3 |
| Preferential deformation site | 201 | 140 | 0.41 |
Figure 5 shows the SEM images and DIC strain maps of the two perpendicular planes in each specimen. In the case of the specimen having 3% strain, strain bands (dashed line) were observed to a small extent in both the RD-TD and RD-ND planes (Fig. 5(a)), forming at an angle of approximately 45° to the tensile loading direction. Figure 6 shows the angular distribution of the strain bands to tensile loading direction in both the RD-TD and RD-ND planes, varying between 40° and 70° with the peak angle distribution appearing at around 45°–55°. The strain bands became more obvious with increasing strain (Figs. 5(b) and 5(c)). Moreover, as shown in Fig. 7, the strain concentration regions corresponded to mainly grain-boundary triple junctions and were preferentially strained with increasing strain. Figure 8 shows two typical 3D SEM images and DIC strain maps in the specimen with 6% strain. The 3D images indicate that the strain bands in each plane were connected at an edge, and a strain plane (dashed line) surrounded by the strain bands in each plane was formed. Figure 9 illustrates the two typical strain planes expected from the results shown in Fig. 8. We found that the 3D strain distribution can be deduced by investigating the strain distribution of two perpendicular planes using DIC.
SEM images and DIC strain maps of two perpendicular planes in specimens consisting strains of (a) 3%, (b) 6%, and (c) 9%.
Distribution of angle of strain band to tensile loading direction.
Two typical strain concentration regions at grain-boundary triple junction.
Two typical 3D SEM images and DIC strain maps in specimen at a strain of 6%.
Schematics showing two typical strain planes expected from the results obtained by DIC.
The reason for this formation of strain bands and strain plane in the early stages of deformation should be discussed. As shown in Fig. 5, the strain bands were formed at an angle of approximately 45° to the tensile loading direction. It is well known that maximum shear stress is forced at this angle; thus, the formation of strain bands in each plane is most likely attributable to the maximum shear stress. For instance, several authors have previously reported the detection of deformation bands in only one plane of DP steel using DIC.15,16,17) Meanwhile, in Herrera-Solaz et al.’s18) investigation of the strain distribution of austenitic stainless steel during tension loading using DIC and FEM, very few obvious strain bands were observed because the region of microstructure observation was narrow. In contrast, we succeeded in observing not only strain bands but also a strain plane in single-phase stainless steel by applying the strain distribution analysis of two perpendicular planes using DIC.
As shown in Figs. 5 and 6, the angle of the strain bands to the tensile loading direction was not exactly 45°. In their study of DP steel, Joo et al.15) demonstrated that several diagonal shear bands were formed in the soft-ferrite phase in the early stages of deformation, and Ghadbeigi et al.16) also reported the formation of deformation bands that initiated inside the ferrite. However, the accuracy of the angle of the deformation bands to tensile loading direction has not previously been discussed. Here, we note that the strain bands in our tests were formed by connecting each strain concentration region. As mentioned above, these regions mainly corresponded with grain-boundary triple junctions. This result implies that the distribution of grain-boundary triple junctions may affect the angle of the strain bands to tensile loading direction.
Figure 10 shows the FEM evaluation of strain distribution in the virtual microstructure at a strain of 4%. The angle of preferential deformation site distribution to tensile loading direction in the virtual microstructure was set to 60°. In this case, crystal plasticity should be taken into consideration for FEM analysis. On the contrary, we assumed that the second phases which triggered deformation (i.e., grain-boundary triple junctions) are dispersed in a matrix to perform a simple FEM analysis. As shown in Fig. 10(a), strain was concentrated at the preferential deformation sites, and macro strain bands were formed by connecting each strain concentration region. The macro strain bands observed by this simple FEM analysis likely correspond with those obtained by DIC. Furthermore, the angle of the macro strain bands to tensile loading direction was approximately 60°. In all cases, the angle of preferential deformation site distribution to tensile loading direction was almost the same as that for the macro strain bands, which indicates that the latter depends on preferential deformation site distribution.
(a) Strain distribution and (b) magnified view of (a) in the virtual microstructure at a strain of 4% as evaluated by FEM (angle of preferential deformation site distribution to tensile loading direction = 60°).
In addition to the macro strain bands, micro strain bands were observed between the preferential deformation sites (Fig. 10(b)). The angle of the micro strain bands to tensile loading direction was approximately 49° and remained almost the same (approximately 50°) when the corresponding angle for the preferential deformation site was >50°. This result suggests that the angle for micro strain bands is mainly determined by the maximum shear stress in this condition. Moreover, it is likely that the connection of the micro strain bands led to the formation of the macro strain bands. Sirinakorn et al.17) reported that, in the case of DP steel, the highest stress concentrations occurred at the ferrite–martensite triple junctions and localized bands appeared at an angle of 45° to tensile loading direction. The localized bands in that study may correspond with the strain bands observed in the present study, but the previous report did not focus on the effect of martensite distribution on the angle of those bands to tensile loading direction. As mentioned above, our findings indicate that the preferential deformation site distribution can affect the angle of the macro strain bands.
Figure 11 shows the relationship between the angle of the micro strain band to tensile loading direction and that for the preferential deformation site. The angles for both the macro and micro strain bands were approximately 42° when the angle for preferential deformation site distribution in the virtual microstructure was set to 42°. In addition, the angle of both types of band to tensile loading direction was almost the same as the preferential deformation site distribution when the angle for the preferential deformation site was <50°. These results indicate that the angles of both the macro and micro strain bands to tensile loading direction were mainly determined by the angle for the preferential deformation site in this condition.
Relationship between angle of micro strain band to tensile loading direction and angle of preferential deformation site to tensile loading direction.
Figure 12 illustrates the changes in the strain distribution with increasing strain. First, the strain was concentrated at the preferential deformation sites (e.g., grain-boundary triple junctions). Second, micro strain bands were formed between the strain concentration regions, and the angle of the micro strain bands to tensile loading direction was approximately 45°. Finally, the connection of the micro strain bands led to the formation of macro strain bands, and the angle of the macro strain bands to tensile loading direction depended on the preferential deformation site distribution.
Schematics showing the changes in strain distribution with increasing strain.
From these findings, we can conclude that (i) the angle of the macro strain bands observed by DIC to tensile loading direction was mainly determined by the preferential deformation site distribution, and (ii) the angle of the micro strain bands was determined by both the preferential deformation site distribution and the maximum shear stress. In the present study, a detailed discussion on the formation mechanism of the strain plane using FEM is not necessarily sufficient. Several authors have demonstrated 3D FEM analysis for characterizing the deformation behavior of DP steels.19,20,21) In the future, the formation mechanism of the strain plane should be investigated using 3D FEM analysis.
We performed a strain distribution analysis of two perpendicular planes (RD-TD and RD-ND planes) in SUS310S austenitic stainless steel using DIC and FEM techniques, obtaining the following results:
(1) Strain bands in both the RD-TD and RD-ND planes were connected at an edge, and the formation of a strain plane surrounded by the strain bands in each plane was confirmed. Furthermore, we found that the 3D strain distribution can be inferred by analyzing the strain distribution of two perpendicular planes using DIC.
(2) FEM analysis verified the formation of both macro and micro strain bands between the preferential deformation sites. In addition, it also revealed that the connection of micro strain bands led to the formation of macro strain bands.
(3) The angle of the macro strain bands to tensile loading direction was dependent on the preferential deformation site distribution. In contrast, the angle of the micro strain bands was mainly determined by the preferential deformation site distribution when the angle of the preferential deformation site to tensile loading direction was <50° and mainly determined by the maximum shear stress when >50°.
