Experimental Investigations on Subsequent Yield Surface of Pure Copper by Single-Sample and Multi-Sample Methods under Various Pre-Deformation

Abstract

Using copper thin-walled tubular specimens, the subsequent yield surfaces under pre-tension, pre-torsion and pre-combined tension-torsion are measured, where the single-sample and multi-sample methods are applied respectively to determine the yield stresses at specified offset strain. The rule and characteristics of the evolution of the subsequent yield surface are investigated. Under the conditions of different pre-strains, the influence of test point number, test sequence and specified offset strain on the measurement of subsequent yield surface and the concave phenomenon for measured yield surface are studied. Moreover, the feasibility and validity of the two methods are compared. The main conclusions are drawn as follows: (1) For the single or multi-sample method, the measured subsequent yield surfaces are remarkably different from cylindrical yield surfaces proposed by the classical plasticity theory; (2) there are apparent differences between the test results from the two kinds of methods: the multi-sample method is not influenced by the number of test points, test order and the cumulative effect of residual plastic strain resulting from the other test point, while those are very influential in the single-sample method; and (3) the measured subsequent yield surface may appear concave, which can be transformed to convex for single-sample method by changing the test sequence. However, for the multiple-sample method, the concave phenomenon will disappear when a larger offset strain is specified.

The Anisotropic Distortional Yield Surface Constitutive Model Based on the Chaboche Cyclic Plastic Model

“…It should be pointed out that some combinations of the two cross effect parameters β1,β2 in anisotropic yield model can describe the concave yield surface, which is consistent with the concavity of experimental yield surface under pre-deformation strain of 5% for T2 pure copper [34]. However, it is contrary to the convexity hypothesis of the loading surface deduced by the fundamental Drucker postulate within the classical plastic theory framework, which implies that further study in relation to the concavity of yield surface needs to be performed.…”

“…The subsequent yield surface of T2 pure copper under pretension loading exhibited significant anisotropy [34], as shown in Figure 10. According to the test method described in Section 3, the initial yield surface with the offset strain of 5 × 10 −5 was nearly circular when the material yielded firstly under pretension loading [cf.…”

“…( a ) The experimental yield surfaces with different pretension strains of 1% and 5% [34] versus the results simulated; ( b ) the stress-strain relationship corresponds to the path O-A-B-C.…”

Investigation of Anisotropic Subsequent Yield Behavior for 45 Steel by the Distortional Yield Surface Constitutive Model

“…To investigate the subsequent yield behavior of the materials, the multi-sample method is more proper than the single-sample method [19]. Therefore, the multi-sample method was used to determine the yield stresses along every loading paths in this paper.…”

“…Considering the cross effect of the subsequent yield surfaces by test and mesoscopic simulation [18][19][20], the anisotropic distortional factor d for the distortional yield surface is given by:…”