Shape Optimization of the Conventional Simple Shear Specimen

Abstract

Shear tests of rectangular sample are widely used by the scientific community for characterizing the material behavior due to large strains obtained. However, for some hard metals, such as the dual-phase steel DP 980, premature rupture occurs in the vicinity of the grips. Due to this fact, the shape of the shear specimen is optimized in this work with the aim of maximizing the deformation achieved in the central part of the specimen without the occurrence of rupture near the grips. As the rupture occurs at the corners of the shear specimen only the boundaries are subjected to shape optimization. A representation with cubic splines is adopted for the definition of the boundaries geometry. The material is defined by Hill’s 1948 yield criterion combined with an isotropic hardening law. Two macroscopic rupture criteria are considered and an objective function approach based on the maximization of the shear strain average value is defined. For this study, a direct search optimization method is used for minimizing the objective function. The optimized geometries obtained for the different rupture criteria and different set of design variables are compared. The use of a larger number of design variables allows to obtain optimized geometries with higher average shear strain. The best specimen geometry shape allows increasing the maximum deformation of DP 980 steel to 1.05 without occurrence of rupture. In addition, the final specimen geometries show a concave shape for the boundaries which means that this kind of shape is the best one to delay the rupture in shear specimens.