Evolution of instantaneous r-values in the post-critical region and its implications on the deformation behavior

Abstract

Abstract The r-value is a key material parameter in sheet metal forming and characterizes the anisotropy of metal sheets. Accurate prediction of extreme deformations, such as in forming or crash events, thus requires accurate knowledge of r over the entire strain range. The methods described in the ASTM E517 and EN ISO 10113 standards, however, account for the region up to necking only and are based on extensometers. Applying the extensometer-based methods to the post-critical region is considered problematic due to the transition from uniform to non-uniform deformation. Researchers have reported the strain-dependence of r but have not revealed the consequences of changing r-values in the post-critical region. This study therefore aims at investigating (i) the suitability of extensometer-based and local strain-based approaches regarding the measurement of instantaneous r up to failure. and (ii) the consequences the neglect of alleged changes of r. Two highly different materials are chosen: the mildly anisotropic dual phase steel DP780 and the highly anisotropic zirconium alloy Zirlo. Strains were measured through digital image correlation (DIC), and results based on two extensometers were compared with results based on local strains in the center of the fracture line. It is shown that soon after the onset of necking, the extensometer approach becomes inappropriate due to an insufficient degree of “localness.” Using the local approach, we find a smooth and approximately linear decrease for both materials. To reveal the implications associated with the consideration/neglect of the strain dependence of r, numerical results were obtained assuming r to be (i) constant and (ii) a function of strain. Anisotropic yield surface evolution was considered through the extended Barlat 89 yield model, anisotropic damage through the generalized damage model MAGD in LS-Dyna, a not yet reported combination offering high flexibility while requiring only limited testing. After MAGD properties were determined by optimization, numerical results for transverse strains in uniaxial tensile specimens were compared with experimental data. Very good agreement was found when assuming r to be strain-dependent whereas the assumption of a constant r resulted in an overestimation after maximum load, which clearly revealed the implications of a changing r upon necking.