On the synergy between physical and virtual sheet metal testing: calibration of anisotropic yield functions using a microstructure-based plasticity model

Abstract

This paper scrutinizes in detail the synergy between physical and virtual testing of the mechanical response of sheet metal. In this context, physical testing refers to the usage of physical samples onto which mechanical tests are conducted, while virtual testing refers to multi-scale plasticity simulations onto a model representation of the metallic microstructure derived from microstructural measurement.An extensive experimental campaign was conducted to capture the plastic material response of mild steel sheet in the first quadrant of the biaxial stress space, i.e. for tensile stresses along the Rolling Direction (RD) and Transverse Direction (TD). The experimental data was acquired using state-of-the-art stress-controlled material tests enabling to probe the material up to large

Crystal Plasticity Modeling for Non-ferrous Metals and its Engineering Applications

“…Yamanaka et al 88) conducted a simulation of hydraulic bulging of a 5 000 series Al alloy sheet using the material parameters determined by using a crystal plasticity model and showed that the simulation results were as accurate as those obtained using the parameters determined experimentally. A similar study on a cold-rolled steel sheet was also conducted by Coppieters et al, 83) verifying their ALAMEL model. Roters et al 89) developed the open source software "DAMASK," which contained a variety of crystal plasticity models to describe plasticity of metals and constitutive models.…”

“…However, the simulation results were not in good agreement with the experimental results. Eyckens et al, 82) Coppieters et al 83) and Hama et al 84) reported that for steel sheets the anisotropic hardening of the plastic contour, especially for the equibiaxial tension condition, could not be reproduced regardless of the crystal plasticity model they utilized. One of the reasons for this difficulty in the simulation of bcc metals is that the deformation characteristics at the crystalline level, including the difference in activities of the {110} and {112} slip systems, 31,84) the effect of non-Schmid law, [28][29][30] and the latent-hardening/interaction matrix, 70,71) are not understood and modelled well, as described earlier.…”

The effect of plastic anisotropy on the calibration of an equivalent model for clinched connections

“…Both experiments were adopted to obtain the plastic material behaviour under multi-axial load conditions of the base material used in this paper. Coppieters et al [13] concluded that the shape of the yield locus for this steel remains constant as from Table 1: Swift's hardening law σ = K( 0 + pl eq ) n fitted in a strain range from pl eq = 0.002 up to the maximum uniform strain max . The reported r -values are the measured values at an engineering strain eng =0.10 using gauge marks.…”

“…The test material was assumed to be elastically isotropic (average measured Young's modulus = 233 GPa) and plastically orthotropic. Coppieters et al [13] characterized the plastic anisotropy of the test material. To this end, the material was subjected to 7 linear stress paths in the first quadrant of the stress space using two types of biaxial tensile tests.…”

“…To this end, benchmark experiments (U-shear lap test and H-tension test) were conducted on low carbon steel. Coppieters et al [13] performed extended experiments to characterize the low carbon steel presented in this paper with special attention to the plastic anisotropic of the material. The calibration procedure of the equivalent model is briefly summarized in section 2.…”