Effects of Specimen Thickness in Tensile Tests on Elongation and Deformation Energy for Industrially Pure Iron

Abstract

Industrial pure iron specimens with a thickness that varied from 0.2 to 2.0 mm were investigated in tensile tests to examine the influence of specimen thickness on the percentage elongation and deformation energy.

Conventionally, the total percentage elongation of a tensile specimen can be converted by Oliver’s equation, which is related to the tensile test specimen thickness. However, in this experiment, it was noticed that there were number of factors which led to the inaccuracy in the result. The total percentage elongation was influenced by the stress triaxiality. The FEM (Finite Element Method) analysis indicated that the stress triaxiality increased significantly with the thinner specimen. This was due to the void growth behavior, observed by SEM (Scanning Electron Microscope) under low voltage. These results revealed that voids nucleation and growth behavior influenced by the stress triaxiality were the main cause for the formula’s incompatibility.

After completing the tensile test, the stress-strain curve can be obtained and categorized into the uniform and local deformation. The uniform deformation energy did not depend on the specimen thickness in contrast to duplex stainless steel, which was examined in our previous research. On the other hand, the local deformation energy lowered with the decrease in specimen thickness as with duplex stainless steel.

These results indicated that the void nucleation and growth behavior had a significant impact on the total percentage elongation.

1. Introduction

Tensile tests are commonly used for evaluating the strength and ductility of materials. The yield stress (YS) and tensile strength (TS) obtained in this study are physical and intensive properties. However, it is necessary to contain five or more crystal grains in the transverse direction for obtaining the constant strengths.¹⁾ On the other hand, the percentage total elongation (El_tot: ratio of gauge length, L₀ and total displacement, ΔL in tensile test), is influenced by the dimension of specimen. In 1880, Barba discovered that the displacement in the uniform deformation is proportional to the gauge length, and the displacement in the local necking deformation is proportional to the square root of the cross-sectional area of the test specimen.²⁾ From the results, Eq. (1) is proposed to predict the El_tot.   

$$\mathrm{E}{\mathrm{l}}_{\mathrm{t}\mathrm{o}\mathrm{t}}=\mathrm{a}+\mathrm{b}\surd {\mathrm{A}}_0/{\mathrm{L}}_0$$(1)

where, a and b are empirical constants based on the material, A₀ is the original cross-sectional area of the test specimen.

Later, Oliver examined the strain distribution of specimen in the tensile direction, whose formula is used to predict the El_tot from the different thickness specimen.³⁾ Thus, the Eq. (2) was adopted by Japanese Industrial Standards (JIS 0202-1987 No. 1152).⁴⁾   

$$\mathrm{E}{\mathrm{l}}_{\mathrm{t}\mathrm{o}\mathrm{t}}{}^{\prime }=\mathrm{E}{\mathrm{l}}_{\mathrm{t}\mathrm{o}\mathrm{t}}{(\mathrm{K}/{\mathrm{K}}^{\prime })}^{\mathrm{n}}\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }(\mathrm{K}={\mathrm{L}}_0/\surd {\mathrm{A}}_0,{\mathrm{K}}^{\prime }={{\mathrm{L}}^{\prime }}_0/\surd {\mathrm{A}}_0{}^{\prime })$$(2)

where, El_tot′ is the total elongation of the desired specimen thickness, L′₀ is the gauge length, A₀′ is the original cross-sectional area of the test specimen, respectively, K is constant defined by L₀, A₀ for reference specimen (based on geometry), K′ is constant defined by L₀′, A₀′ for specimen which we want to predict the El_tot, and n is a material-specific constant.

Oliver’s formula is widely used for calculating the El_tot from the results of different thickness specimens and is used when the ratio of the parallel length and the width of specimen is higher than 5.5. This formula is based on only the difference in the strain distribution in the tensile direction. Therefore, the stress triaxiality, which related to voids nucleation, growth and coalescence (hereinafter referred to as void formation behavior)^5,6,7) in the local deformation region is not considered. Since the void formation behavior can depend on the specimen thickness, the use of Oliver’s formula might result in a significant divergence in the prediction of the El_tot especially for the lower than 1 mm thick specimen, where a large difference of stress triaxiality is expected. In a previous study, concerning duplex stainless steel specimens, we examined the calculation of the El_tot for specimen varying in thickness from 0.2 to 1.2 mm. The results of this study revealed that Oliver’s formula is not applicable for the thinner specimen due to the difference in stress triaxility.⁸⁾ Since duplex stainless steel has two different microstructures, the divergence for the El_tot could not be concluded only by the stress triaxility influenced by the specimen thickness. In this report, a single-phase ferritic industrial pure iron was evaluated in order to report results that stand in contrast to prediction based on Oliver’s formula.

In this study, for analyzing the void formation behavior and its relation to thickness, the internal energy change of the specimen was estimated from the tensile test. The examination of the internal energy change was effective for the following reasons: During the tensile test, the work done (ω) on the test specimen (system) was converted into the internal energy change of the specimen (ΔU) and heat (Δq). The temperature variation was calculated in the duplex stainless steel with thicknesses from 0.2 to 1.2 mm under an initial strain rate of 1×10⁻³/s during the tensile test. Regardless of the thickness, we observed there was a gradual increase in temperature as the tensile test progressed. Since the difference in temperature from 1.5 to 2°C up was not caused by thickness, conclusions from Δq could be ignored.⁸⁾ This finding is applicable to the present study since pure iron has a higher thermal conductivity compared to stainless steel. Accordingly, the internal energy changes of the test specimens in the tensile tests are shown in Eq. (3):⁹⁾   

$$\mathrm{\Delta }\mathrm{U}=\omega =\int {}_{\mathrm{v}}{\sigma }_{\mathrm{i}\mathrm{j}}\mathrm{d}{\epsilon }_{\mathrm{i}\mathrm{j}}=\mathrm{V}\sigma \mathrm{d}\epsilon$$(3)

where, σ is stress, ε is strain, and V is the system volume (in this study, volume in the guage).

Further, nonlinear fracture mechanics afforded energy manipulation of the void growth process in the local deformation area. Gao et al. show in their work that the J-integral value for the energy release rate at the crack tip correlates with the void shape and volume fraction.¹⁰⁾ Nagumo discussed void growth and the crack formation in terms of energy.¹¹⁾ These findings suggest that the energy obtained by the stress-strain curve is useful for evaluation of materials. The authors show experimentally that the uniform deformation energy from the stress-strain curve does not depend on the spacing of Cr precipitates in ferritic single-phase 16% Cr steel. However, the local deformation energy increased with the increase in spacing between precipitates.¹²⁾

In this study, the influences of specimen thickness on the percentage elongation and the deformation energy during tensile testing were investigated by using the industrial pure iron without precipitates. The relationship between void formation behavior and stress triaxiality was evaluated while comparing the results to those of conventional duplex stainless steel.

2. Experimental Methods

2.1. Test Material

The chemical composition of the hot-rolled and annealed industrially pure iron (t=4.0 mm) tested in this study is shown in Table 1. We used the specimen which involves a partially recrystallized structure for this experiment to examine the void formation behavior for both grain boundaries of large and small angles. Microstructural analysis was performed by using electron backscatter diffraction (EBSD) for the longitudinal direction in the center of the 4.0 mm thick plate. The thickness of the specimens varied from 0.2, 0.5, 1.2, to 2.0 mm and the width of the specimens was 3.0 mm. The 30 mm length of the parallel portion of the test specimens was taken from 1/4 sections of the plate thickness that was parallel to the rolling direction. The surfaces finished with 1200 grade emery paper were subjected to a tensile test. In accordance with Oliver’s equation explained previously, the test specimens in this study had a parallel length (L_c) and width (W) ratio (L_c/W) of 5.5 or higher.

Table 1. Chemical composition of industrial pure iron (mass%).

C	Si	Mn	P	S	Al	N
0.0028	0.001	0.16	0.011	0.004	0.001	0.0017

2.2. Tensile Test

Tensile tests were conducted with an initial strain rate of 1.0×10⁻³/s. A 20 mm gauge length mark was made on the parallel portion of the test specimens and the ΔL was photographed with a camera.

2.3. Void Observation

After the tensile test, the fractured specimen perpendicular to the surface was cross-sectional. It was cut with a high-precision cutting machine, embedded in resin, wet-polished using a sequence of 150 to 2000 grade emery paper, and further polished to a mirror finish using alumina buffing, as illustrated in Fig. 3. Surface damage and any contamination was then removed for the scanning electron microscope (SEM) specimen by using a flat milling machine (Hitachi High-Technologies, IM-3000) with an accelerating voltage of 4 kV at a sample incline angle of 80°. Argon sputtering was performed for 180 s with a specimen rotation speed of 25 rpm. Voids were observed using a field emission (FE) -SEM (Carl Zeiss, Ultra55) with an accelerating voltage of 5 kV to obtain the angle selective backscatter (AsB) image. Voids up to 0.1 μm in size can be observed by this method.¹²⁾

Fig. 3.

(a) IPF image and (b) Kernel average misorientation image of base metal obtained by EBSD analysis.

The methodology of measuring plastic strain ε_p is shown in Fig. 1. First, we defined 0 μm line as the bottom of fracture surface in Fig. 1, because the shape of fracture surface was oblique by shear fracturing mode. Second, we measured the width (w) of 6 lines with an interval of 20 μm and 4 lines with an interval of 100 μm from the line 0 μm along X-axis by using SEM image. Further, after cutting the specimen in a half at the part of center, we measured the thickness (t) as the same process of the width along X-axis. In so doing, we adjusted Δx as the line 0 μm in view of a difference caused by the oblique shape fracture surface. Where X-axis is the Rolling direction (RD), Y-axis is Transverse direction (TD) and Z-axis is Normal direction (ND).

Fig. 1.

Calculation method of plastic strain.

The plastic strain value, ε_p was calculated from Eq. (4), where the cross-sectional area from the specimen thickness and width were determined after the tensile test.   

$${\epsilon }_{\mathrm{p}}=\mathrm{l}\mathrm{n}({\mathrm{S}}_0/\mathrm{S})$$(4)

where, S₀ is the cross-sectional area before the tensile test and S are the measured cross-sectional area (which was measured by calculating the width before cutting and the thickness after cutting) for voids observed after the tensile test.

For each measurement area with plastic strain, the voids per standardized unit area were calculated. An example from this study would be 17 × 276 μm² in a region with a plastic strain of 1.73 for thickness of 1.2 mm specimen. Furthermore, the average area for each void taken from the total void area was divided by the number of voids in each test specimen of varying thickness.

Additionally, EBSD analysis was used after the fracture to examine the crystallographic orientation and the void nucleation site.

2.4. FEM Analysis of the Relationship between Stress Triaxiality and Specimen Thickness

Figure 2 shows a finite element method (FEM) by using ABAQUS ver. 6.1.2 in 1/8 scale model of tensile test specimens used to evaluate the relationship between the variation of stress triaxiality and specimen thickness. In this model, the thickness was varied while the material properties were constant in order to extract only the factor of the test specimen shape. The experimental stress-strain curve of a 0.2 mm thick specimen was used as a representative one. The stress-strain curves of the local deformation area following the maximum load point were estimated by using Swift’s formula. A density of 7830 kg/m³, a Young’s modulus of 206 GPa, and a Poisson’s ratio of 0.3 were used for each element.

Fig. 2.

Finite element meshes of tensile test specimen for analyzing stress triaxiality (a) t=0.2 mm, (b) t=1.2 mm.

3. Experimental Results

3.1. Relationship between Strength and Percentage Elongation

Figures 3(a) and 3(b) show the inverse pole figure (IPF) and kernel average misorientation (KAM) images, respectively. The orientation direction was parallel to the rolling direction. The images were obtained by using orientation imaging microscope (OIM). The KAM image revealed portions of the specimen with misorientations of several degrees in high angle grain boundaries. Since the average grain size was about 35 μm, even the thinnest 0.2 mm test specimen had five or more crystal grains in the transverse direction. Fukumaru et al. determined that this is not within the scope of the required thickness and grain size when considering the evaluation of strength.¹⁾

The stress-strain curves from the tensile test are shown in Fig. 4. Figure 4(b) shows the enlarged figure for strain from 0 to 0.010. The relationships of the lower yield stress (LYS) and tensile strength (TS) in the specimen thickness can be found in Fig. 5. A thickness dependency was not observed in either the LYS and the TS.

Fig. 4.

(a): Nominal stress and nominal strain curves of 2.0, 1.2, 0.5, 0.2 mm thickness specimens for industrial pure iron. (b): Enlarged figure for strain from 0 to 0.010.

Fig. 5.

Effects of specimen thickness on lower yield stress (LYS) and tensile strength (TS) for industrial pure iron.

The relationship between the specimen thickness and the El_tot (calculated by Eq. (2)) is shown in Fig. 6. Generally, steels have an n value of 0.3 to 0.4.¹³⁾ In Fig. 6, a reference thickness of 0.2 and 2.0 mm, n value of 0.2 and 0.4 were used. In all cases the equivalent value from the Oliver formula for the El_tot exhibits a discrepancy with the experimental results. These results provide evidence that that Oliver’s equation alone cannot completely account for the effect of specimen thickness on the El_tot.

Fig. 6.

Relationships between elongation and specimen thickness obtained by experiments and converted from the JIS 0202-1987 No. 1152, including experimental data of uniform elongation.

In addition, the uniform elongation obtained by the experiments was a few dependent on the specimen thickness.

3.2. Void Observation

The effects of specimen thickness on the formation behaviors of voids were examined by using SEM. The number and the area of voids were analyzed in the AsB image.⁸⁾ Figures 7(a) and 7(b) show micrographs taken before and after analyzing (Image J analysis software) with an plastic strain (ε_p) equal to 1.50. Figure 7(a) shows the AsB image prior to binarization, and (b) shows the image after binarization to create an image that highlights only the voids. The number of voids 430, 163, 62, 48 were detected in each specimen of 2.0, 1.2, 0.5, 0.2 mm thickness, respectively.

Fig. 7.

Void observation result by SEM for specimen of 0.5 mm thickness at ε_p≒1.50: (a) AsB image, (b) thresholding result of AsB image.

The relationship between the number of voids per unit area and the plastic strain is shown in Fig. 8. The arrows in the figure show the plastic strain confirmed by a void observation in SEM. These values did not change significantly with respect to thickness. The number of voids decreased significantly in the vicinity of the fracture surface. The relationship between the average void area and the plastic strain is shown in Fig. 9. When the specimen thickness was reduced, a significant increase in voids near the fracture surface was observed. These results suggest the stress triaxiality depends on thickness. Further examination of this point is discussed later by evaluating the relationship between thickness and the stress triaxiality in the FEM analysis.

Fig. 8.

Relationships between number of voids and plastic strain for industrial pure iron.

Fig. 9.

Relationships between average void area and plastic strain for industrial pure iron.

Figures 10(a) and 10(b) show results of EBSD analysis for voids located 600 and 700 μm from the fracture surface with plastic strains of 0.79 and 0.71, respectively. The crystal grain orientation map in Fig. 10(a) shows that voids are generated at high-angle grain boundaries. However, Fig. 10(b) shows a void generated from the point where a slight directional contrast is observed. Figure 11 shows the results of OIM analysis of the change in crystal orientation near the void as shown in Fig. 10(b). In Fig. 11, St and F are the starting and end locations of the analysis, respectively. The orientation contrast within one crystal grain is considered to be a point inclined at 2°, since a crystal orientation occurs at the tip of the long axis of the void. Figure 3 also reveals that this test specimen already had a misorientation of a few degrees before tensile testing. For this reason, we hypothesize that a void occurred from this point. It is also important to note that 70% of the formation points were in high-angle grain boundaries.

Fig. 10.

Voids nucreation sites observation results by EBSD micrograph (t=1.2 mm).

Fig. 11.

Crystallographic orientation difference analysis result in Fig. 10(b) (Black field < CI value 0.1).

3.3. Finite Element Method Analysis

The influence of thickness on the growth behavior of voids due to the increase of plastic strain was confirmed in the previous section. This phenomenon could be caused by the stress triaxiality. In each specimen, the stress triaxiality was analyzed by using FEM. The stress triaxiality is a parameter obtained by dividing the average triaxial stress by the equivalent stress, as shown in Eq. (5):   

$$\begin{array}{c}{\sigma }_{\mathrm{h}}/{\sigma }_{\mathrm{e}\mathrm{q}}=(1/3)({\sigma }_1+{\sigma }_2+{\sigma }_3)/(1/2[{({\sigma }_1-{\sigma }_2)}^2\\ {+{({\sigma }_2-{\sigma }_3)}^2+{({\sigma }_3-{\sigma }_1)}^2])}^{1/2}\end{array}$$(5)

where, σ_h is the average triaxial stress, σ_eq is the equivalent stress, and σ₁, σ₂, and σ₃ are the x, y, and z-directional stresses, respectively.

The resulting FEM analyses for the nominal stress-nominal strain curves are shown in Fig. 12(a). The relationship between the stress triaxiality and nominal strain is shown in Fig. 12(b) for specimens with 0.2, 1.2, and 2.0 mm thickness. The same mechanical properties were used for each thickness specimen. The fracture point cannot be extracted from FEM. Instead, the fracture point for each specimen thickness was taken as the stress value at the time of fracture from data shown in Fig. 4. The data input into the mesh was constant regardless of the specimen thickness. However, a thickness dependency was observed for the El_loc and the stress triaxiality. As shown in Fig. 12(b), the stress triaxiality is lower at the time of fracture when the thickness is reduced. These results revealed that the rate of increase in the stress triaxiality is large in the local deformation region with the decrease in thickness. Since mechanical conditions depend on the differences in specimen thickness, the strain in each respective thickness and width direction was organized in correlation to nominal strain as shown in Fig. 13. Figure 13(b) indicates that thickness has very little effect on the strain in the specimen width direction (Δw/w₀: w₀ is the original width of the parallel portion; Δw is width change in the parallel portion of the specimen). However, Fig. 13(a) indicates that the strain in the thickness direction (Δt/t₀: t₀ is the original specimen thickness; Δt is change in thickness at the center of the test specimen) increases rapidly with the start of local deformation (0.16 nominal strain) when the specimen size is 0.2 mm. These results suggest that as the specimen thickness is reduced, it occurred at the start of local deformation. Positive stress is applied by the dimension change of cross section to pincushion configuration. This serves to explain why triaxial stress causes a rapid increase in the start of local deformation for thinner specimen.

Fig. 12.

Nominal stress – Nominal strain curves and stress triaxiality profiles obtained by FEM analysis.

Fig. 13.

Relationships between thickness strain, width strain and nominal strain for industrial pure iron.

4. Discussion

In this work, we examined the thickness dependence of ductile fracture energy and void formation behavior. The dependence of stress triaxiality on thickness is shown in Fig. 12. In the local deformation region where percentage elongation is governed by void formation behavior, it is presumed that the local deformation energy is influenced by specimen thickness. However, there is at present no fundamental relationship between deformation energy and specimen thickness. In this study, deformation energy is divided into uniform and local deformation. The results of examining the thickness dependence are shown in Fig. 14. We calculated deformation energy by stress-strain (load-displacement) curves (change of internal energy in the system of the test specimen) is an extensive property that depends on the shape of the specimen. As such, the influence of specimen thickness as an intensive property where the volume of gauge length is divided by the internal energy change per atom (eV/atom) is discussed. During the uniform deformation (see Fig. 14) a dependence on specimen thickness was not observed for the internal energy change per atom (referred to as uniform deformation energy). However, a significant dependence was observed for the internal energy change per atom in the local deformation (referred to in this paper as local deformation energy).

Fig. 14.

Relationships between uniform deformation energy, local deformation energy and specimen thickness of tensile test for industrial pure iron.

According to the FEM analysis results shown in Fig. 12, when thickness is reduced, the rate of increase of stress triaxiality in the local deformation regions becomes greater. Accordingly, as the specimen thickness is decreased, the increase in stress triaxiality causes growth of voids in regions of low strain. From these results, we can infer a reduction in the local deformation energy. Our previous experimental results revealed that the rate of increase of nano-indentation hardness (H_IT) between voids corresponds to the tensile deformation in the local deformation region of duplex stainless steel lowered with the decrease in specimen thickness, which suggests the amount of plastic deformation also decreases.⁸⁾

Figure 15 shows the nominal stress and nominal strain curves for duplex stainless steel. Compared with the results of the industrial pure iron, thickness dependencies of the El_uni and the El_loc are different compared with pure industrial iron as shown in Fig. 4. Because yield point (YP), TS and Young’s modulus are different in industrial pure iron and duplex stainless steel, the dependency of specimen thickness on deformation energy for pure industrial iron is discussed, comparing the previous results for the duplex stainless steel investigated by our team. The relationship between the specimen thickness and the internal energy change per atom for industrial pure iron and duplex stainless steel⁸⁾ are shown in Fig. 16. The local deformation energy for both industrially pure iron and duplex stainless steel showed signs of thickness dependence. A thickness dependence on uniform deformation energy was observed for duplex stainless steel. However, this thickness dependence was not observed for the industrially pure iron specimens.

Fig. 15.

Nominal stress and nominal strain curves of 1.2, 0.5, 0.2 mm thickness specimens for duplex stainless steel.⁸⁾

Fig. 16.

Relationships between uniform deformation energy, local deformation energy and specimen thickness of tensile test for industrial pure iron and duplex stainless steel.⁸⁾

The relationship between the number of voids per unit area of duplex stainless steel and the plastic strain is shown in Fig. 17.⁸⁾ Compared with the results of industrial pure iron, there was no significant decrease in number of voids. It is thought that in the duplex stainless steel, the significant void coalescence occurred at fracture surface according to Thomason model.⁶⁾ On the other hand, the voids growth and coalescence in industrial pure iron was detected by McClintock model.⁵⁾ It was thought that the difference of this mechanism in two types of steel depends on the voids nucleation site and is discussed as follows: The relationships between the amount of plastic strain for void nucleation (which is indicated by arrows in Figs. 8 and 17) and thickness of duplex stainless steel and industrially pure iron is shown in Fig. 18. Voids nucleated with about the same plastic strain in the industrially pure iron. However, the plastic strain in void nucleation in duplex stainless steel changes according to specimen thickness. Our research group showed this phenomenon is attributed to the large increase in the stress triaxility at beginning of the local deformation in the thinner specimen by using FEM analysis in the previous report.¹⁴⁾

Fig. 17.

Relationships between number of voids and plastic strain for duplex stainless steel.⁸⁾

Fig. 18.

Relationships between plastic strain of void nucleation and specimen thickness for industrial pure iron and duplex stainless steel.⁸⁾

For the most point the occurrence of voids after the maximum load causes necking.¹⁴⁾ However, in ferritic-austenitic duplex stainless steel each phase has different stress-strain curves. In duplex stainless steel, the strain is partitioning between hard and soft phases before attaining the maximum strength.¹⁵⁾ As a result, necking does not necessarily occur at the same time as void nucleation in duplex stainless steel. Recently, Toda et al., observed the void nucleation in duplex stainless steel at a two-phase interphase. They also observed void nucleation before the maximum load was reached.¹⁶⁾ On the other hand, voids nucleation behavior of industrially pure iron is different from that of duplex stainless steel. The relationship between the number of voids and the plastic strain for duplex stainless steel was shown in Fig. 17. These data and the results from Toda et al., suggest voids are likely to form in duplex stainless steel due to a small amount of strain from the reduction in thickness in the uniform deformation area, as shown in Fig. 18. As a result, the uniform deformation energy of duplex stainless steel decreases with decreasing thickness, as shown in Fig. 16. In this study, industrially pure iron is a type of material where voids nucleate in the region near to the maximum load. At the same time, only the local deformation energy from the difference of the void growth in the local deformation region is thought to have strong thickness dependence.

5. Conclusions

Ferritic single-phase industrially pure iron with thicknesses between 0.2 and 2.0 mm was used to examine the applicability of Oliver’s thickness equation to elongation in tensile tests. The effect of specimen thickness on the internal energy change obtained from stress-strain curve in tensile tests was considered from the stress triaxiality and void formation behavior. The main conclusions findings of this research are as follows:

(1) The total elongation in a tensile test did not coincide with the equation according to JIS 0202-1987 No. 1152.

(2) Voids generated from high-angle grain boundaries or from within grains that had a crystal grain misorientation of several degrees regardless of specimen thickness.

(3) As thickness decreased, voids grew rapidly in the vicinity of fracture surface. Furthermore, the effect of specimen thickness on plastic strain of voids generation is small compared with duplex stainless steel.

(4) FEM analysis indicated that as the specimen thickness decreased, the rate of stress triaxiality rises. The differences in the growth behavior of voids near the fracture surface according to specimen thickness correspond with finite element method analysis results.

(5) The uniform deformation energy calculated by the stress-strain curve (internal energy change per atom in a uniform deformation region) in the industrially pure iron is constant with no relationship to specimen thickness. The local deformation energy (internal energy change per atom in a local deformation region) in the industrially pure iron decreases in accordance with the reduction in specimen thickness. These results can be attributed to the low dependence of plastic strain caused by voids on thickness. On the other hand, uniform deformation energy is dependent on the thickness in case of duplex stainless steel where the voids nucleate in the uniform deformation region.

These results indicate that the specimen thickness correction for total elongation requires careful consideration of matters of nucleation, growth, and coalescence behavior of voids caused by the stress triaxiality in local deformation region. Lastly, it was concluded that the local deformation energy is related to the voids formation behavior.

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