Elastic-viscoplastic self-consistent modeling for finite deformation of polycrystalline materials

Abstract

Anisotropic 1-site and 2-site self-consistent models are developed to describe the elastic-viscoplastic behavior of polycrystalline materials deformed to finite strains on the basis of rate-dependent crystallographic slip and a generalized Hill-Hutchinson self-consistent approach. The choice of rate-dependent constitutive law at single crystal level implemented in the models is discussed through fitting experimental data and calibrating viscous parameters. It is found that drag-stress type Norton law works well for the 1-site elastic-viscoplastic self-consistent (EVPSC) model while threshold stress type Norton law is suitable for the 2-site EVPSC model to assure that the viscoplastic inter-granular interaction is realistic. Both models have been verified by thoroughly fitting experimental data in literatures. For the 1-site EVPSC model, selected experimental data covers both macroscopic and microscopic mechanical responses of steels during deformation with a large range of strain rate from the quasi-static (10−4s−1) to the dynamic (~104s−1). For the 2-site EVPSC model, in situ neutron diffraction data of nickel-based superalloys with various microstructures was fitted. Both models generally fit the experimental data well. A comparison between the EVPSC and elastic-plastic self-consistent (EPSC) models on the prediction of lattice strains has also been made for both the 1-site and 2-site cases, which verifies the predictability on lattice strains of the newly developed EVPSC models. A validation of the homogenization approach for the EVPSC modeling has been performed, which confirms that the proposed EVPSC models are applicable for cubic structure materials with finite deformations. Our formulation of EVPSC modeling developed in this work shines a spotlight on the way of developing a multi-functional self-consistent model to predict both macroscopic and microscopic deformation behaviors of various polycrystalline materials under different loading rates of 10−4s−1~104s−1.