Improvement of the Arcan Setup for the Investigation of Thin Sheet Behavior Under Shear Loading

Abstract

Background

Accurate predictions of thin sheet material springback during forming processes are of great interest in the forming industry. However, thin sheets are susceptible to buckling under shear loading.

Objective

The present research aims at improving the so-called Arcan setup for testing thin (1-5 mm) sheet samples with large gauge areas (i.e., width about 21 mm) by introducing anti-buckling devices to mitigate sample buckling.

Method

Three monotonic and one cyclic shear tests were carried out on 1 mm thick C60 high carbon steel.

Results

The use of the proposed anti-buckling device resulted in the suppression of sample buckling. Numerical analyses of the experiment where buckling was eliminated revealed predominant shear stress states in the gauge area (i.e., stress triaxiality = 0), which highlights minor influences of the anti-buckling device on the sample stress state.

Conclusion

To suppress buckling, the use of anti-buckling devices was essential. Moreover, the friction coefficient between the sample and the proposed devices was calibrated ($\mu = 0.33$) in addition to kinematic hardening parameters.

Appendix 1

This appendix gathers stereocorrelation results of tests E1 and E2 that enabled for the improvements utilized in tests E3 and E4.

Test E1

Figure 19 shows out-of-plane displacement fields for different load levels (Fig. 5(a)) and strain values. Positive displacements are oriented away from the reader. Low out-of-plane displacements were measured in the elastic regime of the sample (Fig. 19(a)). Furthermore, the inception of plasticity (Fig. 19(b)) was also characterized by small out-of-plane displacements. However, for the 7.2-kN load level (i.e., the first peak on the load-time plot of Fig. 5a), the out-of-plane displacement amplitudes increased. This growing trend continued while further loading the sample. Furthermore, the out-of-plane displacement distribution was symmetric, which was also observed on the deformed sample in Fig. 5(a). The aforementioned symmetry was observed in the displacement levels (i.e., displacement amplitudes were similar in Fig. 19(d–f)). Even though a stereovision system was employed, these high levels of measured displacement were not considered reliable since the out-of-plane rotation of the ROI caused some parts to be out of focus.

Fig. 19

Measured out-of-plane displacement fields for test E1. The displacements are expressed in mm. F denotes the applied load, and $\epsilon _{xz}$ the average shear strain calculated with the optical gauge

Figure 20 shows measured shear strain fields for different load levels (Fig. 5(a)). The average strain levels in elasticity (Fig. 20(a)) and at the inception of plasticity (Fig. 20(b)) were low as expected. Furthermore, a single strained band developed between the V notches where the strain levels were one order of magnitude higher than on the edges of the ROI (Fig. 20(c)). The rotation of the ROI due to buckling is observed in Fig. 20(d). Further measurements (Fig. 20(e–f)) were deemed unreliable.

Fig. 20

Measured $\epsilon _{xz}$ strain fields for test E1. F denotes the applied load, and $\epsilon _{xz}$ the average shear strain calculated via the virtual sensor. The strained band is outlined by a dashed blue ellipse

Test E2

Figure 21 shows measured out-of-plane displacements for characteristic load levels (Fig. 5(b)) and strain values. As for test E1, the out-of-plane displacements were very small in the elastic regime (Fig. 21(a)) as well as for a large part of the plastic regime (Fig. 21(b–d)). However, clear signs of buckling initiation were observed (Fig. 21(e–f)). The displacements in the center of the sample were negative, whereas on the opposite corners they were positive. This result indicated that wrinkling had started, and was also observed from the shape of the deformed sample in (Fig. 5(b)). The PMMA support fractured due to increased buckling. Thus, stereocorrelation results were no longer deemed reliable beyond this point.

Fig. 21

Measured out-of-plane displacement fields for test E2. The displacements are expressed in mm. F denotes the applied load, and $\epsilon_{xz}$ the average shear strain calculated via the virtual sensor

Figure 22 displays measured shear strain fields. Since buckling of the sample was delayed, the material response (i.e., strain fields) was captured more reliably. Since only elastic strains were present in Figure 22(a–b), they were rather evenly distributed over the ROI, and were at least one order of magnitude higher than the noise floor levels (Table 3). Furthermore, a single strained band developed between the two V notches (Fig. 22(c)) and was observed until the end of the test (Fig. 22(d–e)). Comparing strains between tests E2 and E1, higher levels were achieved due to the more stable material response thanks to the additional supports.

Fig. 22

Measured $\epsilon _{xz}$ strain fields for test E2. The strained band is outlined by dashed blue ellipses. F denotes the applied load, and the $\epsilon_{xz}$ average shear strain calculated via the virtual sensor