The purpose of this study is to clarify the effect of deformation during crack growth on the residual stress of sheared edges. By measuring the residual stress in the thickness direction of the sheared edge, the residual stress of the sheared edge on the scrap side was found to be larger than that on the product side. It was also found that this residual stress difference depends on the shearing clearance, and the difference becomes smaller with greater clearance. By experiments and numerical analysis, it was clarified that the difference in residual stress between the two sheared edges is due to the deformation caused by the Mode II growth of cracks. When the clearance is large, the growth of Mode I cracks increases and that of Mode II decreases, so it is considered that the stress difference between both edges becomes smaller.

This Paper was Originally Published in Japanese in J. JSTP 63 (2022) 101–107.

In recent years, several companies in the automotive industry have actively adopted high-strength steel plates (especially in the structural parts of vehicles) to reduce their environmental impacts and improve their crash safety performance. In many cases, high-strength steel plates can increase the amount of energy absorbed during collisions and strengthen parts while maintaining or decreasing their masses, without increasing plate thicknesses. For this reason, steel plates for 1.5 GPa hot stamping and 1180 MPa high-strength sheet steel for cold forming are being adopted for automotive parts, and steel plates with even higher strengths are being developed [1, 2].

However, press processing of parts using high-strength steel plates has a few technical problems. For example, as the strength of steel plates increases, the occurrence of springback and wrinkles increases, thus making it difficult to maintain the dimensional accuracy of the parts [3]. In addition, as the strength of the steel plates increased, their uniform deformability and fracture limit of the steel plate decreased; this made them less resistant to fracture during the forming process. Furthermore, because molded products are subjected to high-residual stress, a decline in their fatigue properties and hydrogen embrittlement resistance is always a matter of concern. The tensile residual stress was especially high on the fractured surface of the sheared edges. Therefore, there is an urgent need to address the issues caused by residual stress [4].

Generally, when metallic materials are subjected to non-uniform plastic deformation, residual stress remains after unloading. For the most common press forming methods, such as deep drawing, stretch forming, stretch-flange, and bending, various studies have been conducted to elucidate the residual stress generation mechanism using numerical analyses such as elementary analysis and finite element methods. In addition, based on these mechanisms, researchers have proposed methods to control the spring-back behavior of press-formed products [5].

However, few studies have discussed the mechanism behind the generation of residual stress on the edges formed by shearing. Previous experimental investigations have been conducted on the effect of the shape of shearing tools [6], the effect of the coating on the tools [7], and the effect of punching clearance [8], which have demonstrated that trends of residual stress on sheared edges can be reproduced by numerical analysis using finite element methods [6]. However, as these studies did not detail the mechanism of residual stress generated on the sheared edges, many aspects remain unclear. One of the reasons for this is the fact that previous knowledge about other nondestructive press-forming methods cannot be directly applied because the fractured surfaces of sheared edges are formed following the development of ductile fracture cracks.

Therefore, in this study, we examine the effects of crack growth on the residual stress of fractured surfaces. It is known that the stress state of a crack tip changes radically according to the crack growth direction relative to the load direction [9]. Hence, the first step involved the analysis of the influence of the crack growth direction during the formation of a fractured surface. Therefore, we conducted a shearing process by varying the clearances of the tools used. After that, the residual stresses generated on the fractured surfaces were examined. Subsequently, we conducted a numerical analysis using the finite element method to simulate this process and compared the results with the experimental results. This numerical analysis was conducted in two different ways: one considering the deformation caused by crack growth, and the other by excluding it to determine its effect on the residual stress.

We excluded the effect of deformation until cracks that formed the fractured surface were generated so that we could identify only the effect of crack growth on the residual stress of the fractured surface. First, we let the crack develop under a load of mode II (in-plane shear), which is dominant in shearing processes, and then investigated experimentally the stress that remained on the fracture surface. Subsequently, a numerical analysis simulating this crack growth was performed, and the results were compared with the experimental results from the perspective of the crack growth direction. With these analyses, we attempted to elucidate the mechanism of the generation of residual stress owing to deformations caused by crack growth.

A prototype of a test piece of 980 MPa cold-rolled steel plate with a thickness of 1.6 mm has been made. Subsequently, we conducted a tensile test using an Instron-type test machine at a crosshead speed of 3 mm/min (strain rate = 1 × 10⁻³/s). We measured the residual stress along the thickness and orthogonal rolling directions. However, as it was difficult to obtain a test piece along the thickness direction, A JIS No. 5 tensile specimen prescribed in JIS Z 2241 was obtained along the orthogonal direction. The mechanical properties of the test materials are listed in Table 1.

Table 1 Mechanical properties of the material (σ_YP: 0.2% proof strength; σ_TS: ultimate tensile strength; e_t: total elongation).

A rectangular steel plate with a rolling direction length of 50 mm, width of 15 mm, and thickness of 1.6 mm was used as the test piece. Using a punch and die with a right-angle edge, the test piece was split into steel plates with rolling direction lengths of approximately 42 and 8 mm, respectively, with the punching line as a straight line. The punch-to-die clearance and plate thickness ratios (CL/t) were 5, 10, 15, and 20%, respectively. During this process, the punch was lowered at a speed of 100 mm/s using a servo-press machine.

After the shearing process, the sheared edge of the steel plate with an approximate rolling direction length of 42 mm on the left side of the die (hereafter referred to as the “sheared edge of product”) and the sheared edge of the steel plate with an approximate length of 8 mm ejected as scrap (hereafter referred to the “sheared edge of scrap”) were photographed with an optical microscope. Photographs were acquired at the center of the test piece along the width direction.

The residual stress in the width and thickness directions of the sheared edge was measured using X-rays at the center of the width and thickness directions of a test piece with a spot diameter of 0.5 mm. X-rays were irradiated at different angles Ψ between the sample surface and the surface lattice directions. The changes in the diffraction angle of the diffraction line were then measured, and the residual stress was calculated from the slope of the 2θ - sin² Ψ plot [10].

The results observed for the sheared edges of the product and scrap are shown in Figs. 1 and 2, respectively. The sheared edges of both the product and scrap were formed by shear droop, sheared surfaces, and fractured surfaces. No occurrences of secondary sheared edges or excessive burrs were noted.

Fig. 1

Sheared surface of product (CL/t: clearance ratio); (a) CL/t 5%, (b) CL/t 10%, (c) CL/t 15%, (d) CL/t 20%.

Fig. 2

Sheared surface of scrap (CL/t: clearance ratio); (a) CL/t 5%, (b) CL/t 10%, (c) CL/t 15%, (d) CL/t 20%.

The cross-sectional images of the sheared edges of the products are shown in Fig. 3. Although local irregularities were observed, the fracture surface formed a straight line connecting the punch- and die-cutting edges.

Fig. 3

Cross-sectional shape of product (CL/t: clearance ratio); (a) CL/t 5%, (b) CL/t 10%, (c) CL/t 15%, (d) CL/t 20%.

Figure 4 shows the relationship between the percentages of shear droop, and sheared edge and fractured surfaces with respect to the cut surface and as a function of the clearance ratio (CL/t). The shear droop ratio on the sheared edge of the product increased as a function of CL/t. The fractured surface ratio varied between 75% and 85% and peaked when CL/t was 10%. The effects of CL/t on the sheared edge of the scrap were relatively smaller than that on the sheared edge of the product. It also yielded a higher percentage of shear droop and sheared edges than the sheared edge of the product and a smaller percentage of fractured surface. All the residual stress measurements were performed on the fractured surfaces.

Fig. 4

Clearance ratio dependence of shear droop, sheared surface, and fractured surface; (a) Product, (b) Scrap.

The results of the residual stress measurements at the sheared edge are shown in Fig. 5. The residual stress along the thickness direction is shown in Fig. 5(a). As indicated, on the sheared edge of the scrap, the measured tensile residual stress was close to the tensile strength for all CL/t values. The tensile residual stress measured at the shear edge of the product was lower than that measured at the shear edge of the scrap. The difference was particularly large for small values of CL/t and decreased as CL/t increased.

Fig. 5

Results of residual stress measurement; (a) Residual stress in thickness direction, (b) Residual stress in width direction.

The residual stress along the width direction is shown in Fig. 5(b). This shows that the tensile residual stresses measured at the sheared edges of the product and scrap are comparable for all CL/t values. Moreover, the measured residual stress was almost constant, regardless of CL/t.

We also conducted a numerical analysis of shearing using the finite element method (FEM) to analyze the mechanism of residual stress generated on the fractured surface. This analysis focused on the residual stress in the thickness direction of the sheared edge of the product that changed considerably as a function of CL/t. Shearing is a process in which a tool cuts into the sheet material; after the shear droop and sheared edge are formed, a crack generated by the tool edge develops in the thickness direction, thus forming a fractured surface. Therefore, the residual stress generated on the fractured surface was considered to be influenced by the 1) stress distribution at the onset of fracture surface formation, and 2) deformation caused by crack growth during the formation of the fractured surface.

The following verification uses a numerical analysis based on the FEM to examine the changes in the residual stress generated on a fractured surface owing to the deformations caused by the propagation of a crack. That is, after performing an analysis simulating the formation process of the shear droop and sheared edge, we set two different fracture limits between the elements of the punch and die and conducted a numerical analysis that simulated the process of fractured surface formation. To examine the effect of the deformation caused by crack growth in one of the numerical analyses, the fracture limit was set to a relatively small value so that the formation of the fractured surface was completed immediately, and the effect of the deformation caused by crack growth was excluded. In the other numerical analyses, the fracture limit was set to a relatively large value so that the elements were gradually eliminated as the shearing process progressed. The results of these two numerical analyses were compared with those of the experiments.

Using ABAQUS Explicit [11] (explicit dynamic FEM code), simulations of the shearing test described in Section 2.2, were performed. As shown in Fig. 6, a model assuming a two-dimensional plane strain was created. In this model, the tools were defined as rigid bodies, while the steel plates were defined as elastoplastic bodies. In addition, to prevent the elements from being smashed during the analysis, the edge of the tool was approximated using an arc with a radius of curvature (R_tool) of 0.04 mm. The meshing function of the Arbitrary Lagrangian Eulerian (ALE) method [12] was applied to the elements of the sheet material.

Fig. 6

FEM analysis model simulating shearing.

The steel plate was split into elements with 0.02 mm at the smallest part using the plane strain reduced-integration quadrilateral first-order element CPE4R. The displacement and rotation of the die and holder were restrained, and displacement (explained later) was applied to the punch. Moreover, Coulombic friction was assumed between the tools and steel plates and between the product hole and scrap. The friction coefficient was set to 0.12.

For the work-hardening properties of the steel plate, we used the Swift hardening law, as expressed by eq. (1), to approximate the equivalent stress-plastic strain obtained from the tensile test in the width direction.

where σ_eq (MPa) is the equivalent stress, and ε_eq is the equivalent plastic strain. The von Mises yield criterion was used as the material configuration rule, and isotropic hardening and the normal law were assumed. Previous numerical analyses using the ductile fracture condition equation based on the maximum principal stress indicated that the sheared edge shape is mostly reproducible [13, 14]. Therefore, in this study, the damage value D during shearing was calculated based on the Cockcroft and Latham criteria based on eq. (2) [15].

where σ₁ (MPa) is the maximum principal stress.

First, the deformation state immediately before the onset of the fractured surface formation was analyzed using the above model. Based on the observation results of the sheared edges (Fig. 4), until the intersection points between the punch edge and side reached the boundary between the sheared edge and the fractured surface, a displacement in the negative y direction was applied to the punch. The punch speed was set to 100 mm/s, as in the experiment. This analysis is called the “analysis of the sheared edges”.

The next step was to reproduce the ductile fracture cracks associated with the formation of fracture surfaces. Based on the results shown in Fig. 3, it was assumed that only the element set a located on the line connecting the punch and die edges was fractured (Fig. 7). Subsequently, a limit value was set and a further displacement of 1.2 mm in the negative y direction was applied to the punch. Simultaneously, a correction was applied to the elements whose damage value D exceeded the ductile fracture condition D_crit so that their rigidity became equal to zero. Two analyses were conducted: one in which the ductile fracture condition D_crit was set to zero, and the other in which D_crit was set to 0.34. This analysis is called the “analysis of the fractured surface”. In the latter case, we used the highest damage value D generated on the sheet material when CL/t was 10% in the analysis of sheared edges.

Fig. 7

Element set with ductile fracture limit.

When D_crit was set to zero, the rigidity of Element a between the punch and die edges became zero immediately after the analysis of the fractured surface was initiated, with no deformation caused by the development of cracks, and the formation of the fractured surface was completed. This suggests that the stress remaining on the fractured surface was generated only by the existing stress when the fractured surface began to form.

However, when D_crit was set to 0.34, Element a was subjected to a deformation caused by crack growth. Consequently, damage exceeding D_crit was generated from the crack tip; this caused the rigidity to decrease to zero. Therefore, the residual stresses on the fracture surface can be considered to have been influenced not only by the stresses before the start of the fracture surface formation but also by the deformation that occurs at the crack tip during the fracture surface formation.

The analyzed results at the instant at which the formation of the fractured surface began are shown in Fig. 8. As a similar trend was observed regardless of CL/t, only the results obtained when CL/t was 10% are shown. The stress distribution along the thickness direction is shown in Fig. 8(a). When the fractured surface started forming, compressive stress was generated directly above the die and below the punch in the thickness direction.

Fig. 8

Deformation state of the sheared end face at the start of fracture surface formation (CL/t = 10%); (a) Stress in thickness direction, (b) Damage.

Figure 8(b) depicts the distribution of damage value D. The elements located on the line connecting the punch and die edges, particularly those near the punch edge, have high-damage values. This result suggests that when the fractured surface was formed, a crack developed from the punch to the die edge direction, connecting the two edges.

The results of the residual stress analysis (when the shearing analysis was completed) are shown in Fig. 9. To compare the analyzed results with experimental trends, we focused on the element sets adjacent to Element a which defined the fracture limit. The average value of residual stress in the thickness direction on the element located ±0.25 mm from the thickness center was then determined. Because a dynamic explicit method was used, the stress oscillated immediately after the formation of the fractured surface. However, the amplitude of the stress after the analysis was less than 1% of the average value, thus confirming that this effect was small.

Fig. 9

Analytical results of residual stress on fracture surface; (a) D_crit = 0, (b) D_crit = 0.34.

When D_crit was set to zero, the tensile residual stress values remaining on the sheared edges of the product and scrap were similar, and these values were almost constant, regardless of CL/t (Fig. 9(a)). This result does not agree with the experimental results shown in Fig. 5(a). However, when D_crit was set to 0.34, the tensile residual stress at the sheared edge of the scrap is higher than that at the sheared edge of the product. Moreover, as CL/t increased, the tensile residual stress of the sheared edge of the product increased, whereas the difference between the residual stresses generated on the sheared edges of the scrap and product decreased (Fig. 9(b)). The trend of these analyzed results matches that of the experimental results, as shown in Fig. 5(a).

These results indicate that the residual stress of a sheared edge is not only affected by the stress when the fractured surface starts forming but also by the deformation of the crack tip during the fractured surface formation. In addition, when a higher D_crit value was considered, analytical results were obtained that reproduced the experimental trends more accurately.

As mentioned in Section 4.1, the analyzed results demonstrated that the residual stress on the sheared edges changed considerably according to the deformation caused by crack growth. However, the stress distribution during the shearing process is complex, and it is difficult to interpret only the effect of the deformation generated during crack growth from the analyzed results in Section 4.1. Therefore, in this section, we present an analysis and experiments that extract only the effects of crack growth and analyze the effects of the deformation caused by crack growth on the residual stress on the fractured surface.

Using the two-dimensional model shown in Fig. 10, an analysis was conducted that reproduced the development of cracks caused by shearing in a simplified manner.

Fig. 10

Simple model for crack growth analysis.

For this analysis, we used the explicit dynamic solver ABAQUS Explicit [11]. The central part of the model was divided into elements (size = 0.02 mm) using reduced-integration, quadrilateral, and first-order elements. In addition, by deleting some of the elements of the model in advance, we created precracks and notches (lengths = 0.2 mm). The precracks were one-element-wide, and the notches were 100-element-wide, such that a larger strain was concentrated on the precrack side, and the crack developed in the negative y direction. It was assumed that the tip of the crack caused by ductile fracture had a constant curvature. However, because the precrack was 1-element-wide in this analysis, the shape of the crack tip could not be reproduced accurately. Consequently, the analysis of the crack growth direction is inaccurate. To improve the accuracy, we defined a fracture limit only for element group a so that the crack growth direction could be deliberately controlled, and the analysis did not depend on the accuracy of the crack growth direction.

The ductile fracture condition, D_crit, of element group a, was set to a value of 0.1; at this setting, the elements would not lose their shape. The rigidity of the elements that exceeded D_crit was set to zero.

The analyzed results in Section 4.1 suggest that in the experiment described in Section 2.2, the crack developed from the shear droop side to the burr side of the sheared edge of the product. Therefore, the element group on the right part of the element set a is called the sheared edge of the product, and the element group on the left side is called the sheared edge of the scrap.

As the crack developed from the punch edge to the die edge, the crack growth direction varied according to CL/t. Hence, we analyzed the effect of CL/t by changing the crack growth direction θ. To compare the case in which the crack grows only owing to a load of mode II and the case in which the crack grows owing to loads of mode II (in-plane shear) and mode I (opening), two different analyses were conducted, with θ set to 0° and 10°. From Fig. 3, θ = 10° is equal to the angle of the fractured surface with a CL/t of approximately 15%.

During the shearing process, the material was cut into round or straight shapes. Depending on these cutting shapes, the constraint state in the z-direction in Fig. 10 varies. In this study, analyses using 4-node, reduced-integral continuum plane stress elements (CPS), and reduced-integral continuum plane strain elements (CPE) were respectively conducted for the smallest and largest constraint cases. The constrained state of the spot based on which the residual stress was measured (as described in Section 2.2), was considered close to the state of the analysis using CPE.

When θ was set to 0°, two different analyses using CPS or CPE were conducted to verify the effect of the constraint in the z-direction. In addition, in the analysis using CPE, θ was set to 0° and 10° to verify the effects of crack growth direction.

The analyzed results are shown in Figs. 11 and 12. Figures 11(a) and 11(b) indicate that when θ was 0°, the stress concentrated at the crack tip generated compressive stress on the scrap side and tensile stress on the product side. As shown in Figs. 12(a) and 12(b), as this stress is released after the crack grows, tensile stress remained on the edge of the scrap side, and compressive stress remained on the edge of the product side, thus creating a large residual stress difference between the two edges. The fact that these characteristics were observed when both elements were used suggests that the effect of the constraint state in the z-direction is small. Moreover, as shown in Figs. 11(b) and 11(c), when θ was changed from 0° to 10°, the stress generated at the crack tip changed, and the tensile stress on the product side primarily decreased. As shown in Figs. 12(b) and 12(c), the compressive stress that remained on the product side after the crack growth and the residual stress difference between the two edges decreased.

Fig. 11

Stress distribution in the plate thickness direction during crack growth (CPS: plane stress element, CPE: plane strain element); (a) CPS, θ = 0°, (b) CPE, θ = 0°, (c) CPE, θ = 10°.

Fig. 12

Stress distribution in the plate thickness direction after crack growth (CPS: plane stress element, CPE: plane strain element); (a) CPS, θ = 0°, (b) CPE, θ = 0°, (c) CPE, θ = 10°.

The analysis in Section 4.2 suggests that the residual stress difference between the product and scrap sides was caused by mode II crack growth. Therefore, to validate this analysis, the residual stress on the fractured surface after the crack growth in mode II was experimentally investigated.

Shear deformation in the y-direction was applied to the test piece, which was a rectangular steel plate with notches, as shown in Fig. 13. Assuming that vertically symmetric stress was generated on the test piece, notches of the same shape were made on both edges of the test piece to minimize the effect of the elastic deformation of the test machine. The notches were 0.2 mm wide and 5 mm long, and the tip had a curvature radius equal to 0.1 mm. Furthermore, to limit the development route of the crack, grooves (depth = 0.3 mm) were created on both sides of the test piece using a ball mill with a curvature radius of 3 mm. Thus, the cracks tended to grow along the thinnest part, which made it possible to control the development of the crack route.

Fig. 13

Shape of notched test piece.

The test material was the same steel plate used in the experiment described in Section 2.1. Because the thickness of the specimen in this test was 1.6 mm, the constraint in the z-direction was assumed to be small and close to the plane stress state. However, in the shearing process described in Section 2.2, the constraint in the z-direction was close to the plane strain state. However, the analysis presented in Section 4.2 suggests that this effect is small. On the fracture surface after the test, the residual stress in the crack growth direction (at the central part along the thickness direction) was measured using X-rays at equidistant intervals (0.5 mm apart) within the range shown in Fig. 14. The spot diameter of the X-ray was set to 0.5 mm, and it was irradiated as the angle between the sample and lattice plane direction was varied. The change in the diffraction angle was measured, and the residual stress was calculated from the slope of the 2θ-sin² Ψ graph [10].

Fig. 14

Measurement area of residual stress.

The results of the residual stress measurements are shown in Fig. 15. The residual stress measured on the fracture surface after crack growth was approximately 700 MPa. The residual stress on the edge of the test piece shown on the left side of Fig. 14 is positive, and the residual stress on the edge of the test piece shown on the right side is negative. These results confirm that residual stress remains on the fracture surface formed by the development of the crack caused by the mode II load, and this residual stress may be positive or negative depending on the positional relationship between the crack growth direction and the fractured surface. It was experimentally verified that the tensile residual stress generated on the left side of the test piece was greater than that generated on the right side. Moreover, these results match the trend of the analysis shown in Fig. 12(a), which suggests that the analysis in Section 4.2 successfully reproduces the residual stress generated by the deformation caused by mode II crack growth.

Fig. 15

Residual stress generated on the fracture surface formed by crack growth due to in-plane shear load.

These results suggest that the residual stress generated on the fractured surface was strongly affected by the crack growth direction. If the crack grows from the shear droop side of the sheared edge of the product to the burr side, tensile residual stress is more likely to be generated on the sheared edge of the scrap, primarily because of the components of the crack growth in mode II. Conversely, compressive residual stress is more likely to be generated on the sheared edge of the product, which presumably creates a residual stress difference between the two edges.

When CL/t is large, the crack growth direction deviates from the thickness direction, which increases the load on the components of mode I (opening) and decreases the load on the components of mode II (in-plane shear). Presumably, this reduced the residual stress difference between the two edges. The analyzed residual stress results of the model that only simulated crack growth during shearing (Fig. 12) matched the experimental results (Fig. 5(a)), thus indicating that the residual stress difference between the sheared edges of the product and scrap, as well as the changes in the residual stress on the edge according to CL/t were primarily caused by deformation owing to crack growth.

In this study, analyses were performed to identify the effects of crack growth on the residual stress on a fractured surface formed by shearing. To this end, we investigated the stress that remained on the edges sheared with different punching clearances and on the fractured surface after cracks grew, owing to the load of mode II (in-plane shear), which is dominant in shearing processes. The findings of this study are the following:

• 1)   H.  Hayashi: Current Status and Future of High Strength Steel Sheets in Autobody Manufacturing —Survey on High Strength Steel by the Japan Sheet Metal Forming Research Group—, J. JSTP 58 (2017) 99–104. doi:10.9773/sosei.58.99
• 2)   A.  Uenishi: Development of Advanced High Strength Sheet Steel for NSafe™-AutoConcept, Nippon Seitetsu Giho 412 (2019) 8–13.
• 3)   M.  Takahashi: Current Status and Future Prospects of High-Strength Steel Sheets for Automobiles, J. JSTP 58 (2017) 105–109. doi:10.9773/sosei.58.105
• 4)   K.  Mori,  Y.  Abe and  K.  Sedoguchi: Delayed fracture in cold blanking of ultra-high strength steel sheets, CIRP Ann. 68 (2019) 297–300. doi:10.1016/j.cirp.2019.04.111
• 5)   K.  Mori,  K.  Akita and  Y.  Abe: Springback behaviour in bending of ultra-high-strength steel sheets using CNC servo press, Int. J. Mach. Tools Manuf. 47 (2007) 321–325. doi:10.1016/j.ijmachtools.2006.03.013
• 6)   T.  Matsuno,  Y.  Kuriyama,  S.  Yonezawa,  H.  Murakami and  N.  Ohtake: Mechanism Analysis of Roughness Improvement on Pierced Surface Using Press Working Punch by Finite Element Method, J. JSTP 53 (2012) 836–841. doi:10.9773/sosei.53.836
• 7)   T.  Matsuno,  K.  Sato,  A.  Uenishi,  S.  Higuchi,  T.  Masuda and  T.  Shimizu: Effects of Piercing Punch Coating on Hole-expansion Ratio and Fatigue Properties, J. JSTP 56 (2015) 133–138. doi:10.9773/sosei.56.133
• 8)   K.  Mori,  Y.  Abe,  Y.  Kidoma and  P.  Kadarno: Slight clearance punching of ultra-high strength steel sheets using punch having small round edge, Int. J. Mach. Tools Manuf. 65 (2013) 41–46. doi:10.1016/j.ijmachtools.2012.09.005
• 9)   S.  Aoki,  K.  Kishimoto,  T.  Yoshida and  M.  Sakata: Finite element analysis for ductile fracture near a crack tip under mixed mode conditions, Trans. Jpn. Soc. Mech. Eng. 52 (1986) 2249–2257. doi:10.1299/kikaia.52.2249
• 10)   T.  Goto and  S.  Ohya: The Fundamental Principles and Techniques of X-Ray Stress Measurement and Current Developments in the Field. I: The Fundamental Principles and Techniques of X-Ray Stress Measurement, J. Soc. Mater. Sci., Jpn. 47 (1998) 1188–1194. doi:10.2472/jsms.47.1188
• 11)  ABAQUS Documentation and User Manual, Version 6.14, Simulia, Dassault Systèmes, (2015).
• 12)   S.  Ghosh,  M.  Li and  A.  Khadke: 3D modeling of shear-slitting process for aluminum alloys, J. Mater. Process. Technol. 167 (2005) 91–102. doi:10.1016/j.jmatprotec.2004.08.031
• 13)  M. Takamura, T. Ozaki, Y. Miyoshi, H. Sunaga and S. Takahashi: Proc. 10th Int. Conf. Tech. Plast. (ICTP 2011), (2011) pp. 591–595.
• 14)   T.  Tanaka,  S.  Hagihara,  Y.  Tadano,  T.  Inada,  T.  Mori and  K.  Fuchiwaki: Ductile Fracture Criteria for Cutting Surfaces of Punching Process by Finite Element Method, J. JSTP 52 (2011) 1104–1108. doi:10.9773/sosei.52.1104
• 15)   M.G.  Cockcroft and  D.J.  Latham: Ductility and the Workability of Metals, J. Inst. Met. 96 (1968) 33–39.