Generalization of the polycrystalline β-model: Finite element assessment and application to softening material behavior

On the basis of the polycrystalline model of Cailletaud and Pilvin [G. Cailletaud, P. Pilvin, Rev. Eur. EF 3 (1994) 515–541], a generalization of the β-scale transition rule from the macroscopic level to the grain level is developed in this paper. The new proposed model is split into several sub-models. It is shown that the classical Pilvin–Cailletaud model describes correctly the overall mechanical behavior of softening materials. However, the local mechanical behavior at the grain level is not well simulated. A polycrystalline aggregate model is then generated and computed by the finite element technique to select the most accurate sub-model in predicting both the overall stress–strain response and the local stress and strain distributions. The material parameters of each sub-model are evaluated using the results of the finite element computations at two levels: (i) the macroscopic level, using the volume average over all Gauss points and (ii) the phase scale, using the volume average over the Gauss points of the elements having the same orientation. The most accurate model is compared with experiments using available monotonic tensile data for Ti–6Al–4V. The selected model appears also to be capable of correctly evaluating the stress–strain behavior at the grain level and reducing the deviation of phase strains with regards to the mean strain.