Comparison of applicability of various thermo-viscoplastic constitutive models in modelling of welding

Consistent tangent moduli for two models of unified theory of viscoplasticity, proposed by Anand and Estrin, and Robinson's potential viscoplasticity are derived in this paper. The tangent moduli for Anand's and Robinson's constitutive models have been re-derived using the new approach which is also applied to Estrin's viscoplasticity for the first derivation of the stiffness matrix. These moduli, which contribute to the global stiffness matrix, are necessary for the implementation of constitutive equations into finite element programs. Also novel is the presentation of finite element simulation results for the same benchmark problem calculated for various constitutive models with material data identified for the same physical material. The benchmark problem for welding is formulated considering moving electric are, latent heat of melting and solidification of welding bath, complexity of cooling after welding, and generation of residual stresses. It is shown that residual stresses and strains are quantitatively different for various constitutive models and they are related not only to the quality of identification of model's parameters but also to the structure of constitutive equations which determines the stiffness matrix appropriate to each constitutive model.