Numerical analysis of large deformation processes at elevated temperatures

Abstract

The authors describe a theoretical model and kinematic approach suitable for the numerical analysis of problems at large deformation finite strains and rotations. The presented formulations are implemented incrementally with a non-linear and rate-dependent constitutive model, adequate to the simulation of high temperature processes. The large deformation kinematic model is based on the additive decomposition of the transformation gradient and the strain rate tensor in thermoelastic and viscoplastic parts. Stress-strain relations leading to the constitutive equations governing finite deformations are formulated on an unrotated frame of reference. These relations are obtained either by polar decomposition of the transformation gradient or by the rotation increment method. Both approaches and algorithms are thoroughly compared and discussed. The flow rule is a function of the equivalent stress and the deviatoric stress tensor, of the temperature field and of a set of internal state variables. The increments of the state variables are calculated with a forward gradient time integration procedure, based on a numerical estimation of the integral of the strain rate tensor. The model was implemented in a three-dimensional finite element code and tested with a set of tensile and shear tests on aluminium alloy specimens. In order to evaluate the performance of the numerical algorithms with elevated temperature processes, tests were done at temperatures ranging from room temperature to 580 K. Numerical simulation results are compared with experimental results and shown to be in good agreement. Real material behaviour is fairly well predicted and matches the experimental results obtained with different loading conditions at different temperatures.