Institute of Fundamental Technological Research

Dynamic localization failure of a thin sheet made of AISI 316H steel is considered on the macroscopic and mesoscopic level for proportional and nonproportional stress paths. On the macroscopic level, we propose: (1) the replacement of time as independent variable by a function of plastic dissipation and (2) dependence of the initial equivalent yield stress on stress rate. On the mesoscopic level - the regularized Schmid model for description of the single grain behavior is used and the polycrystalline yield surface generated by the texture development enables to improve the Forming Limit Diagrams for the sheet element.

dynamic localization failure, Forming Limit Diagrams, regularized Schmid law, sheet textures

The rigid-plastic model for the single grain is developed in which the velocity gradient is split into two parts connected with crystallographic slip and micro-shear bands respectively. For crystallographic slip the regularized Schmid law proposed by Gambin is used. For the micro-shear bands the model developed by Pęcherski, which accounts for the contribution of this mechanism in the rate of plastic deformation by means of a function fms is applied. Different constitutive equations for the plastic spin due to two considered mechanisms of plastic deformation are used. The present model is applied to simulate crystallographic texture evolution in the polycrystalline element.

crystallographic texture, modelling of texture, micro-shear bands, regularized Schnid law, plastic spin

Model of evolution of plastic anisotropy due to crystallographic texture development, in metals subjected to large deformation processes, is presented. The model of single grain with the regularized Schmid law proposed by Gambin is used. Evolution of crystallographic texture during drawing, rolling and pure shear is calculated. Phenomenological texture-dependent yield surface for polycrystalline sheets is proposed. Evolution of this yield surface is compared with evolution of phenomenological higher order yield surfaces proposed by Hill and Barlat with Lian for drawing, rolling and pure shear processes. The change of the Hill yield surface and the Barlat–Lian yield surface is obtained by replacing material parameters present in these conditions by texture-dependent functions.

Crystallographic texture, Anisotropic material, Crystal plasticity, Polycrystalline material

A modification of a finite element method by considering large elements is presented. For a given discretization of a system, approximating polynomials of an arbitrary degree are constructed for each element. Such an approach allows an automatic generation of matrices for the resulting systems of equations as well as a straightforward evaluation of unknowns with any desired accuracy. It becomes possible moreover to reproduce exactly shapes of curvilinear elements and to make a numerical analysis of unbounded media. Existing algorithms and programs of the finite element method may be adapted to treat problems within the present formulation.