Abstract
Calibrating and verifying crystal plasticity material models is a significant challenge, particularly for materials with a number of potential slip and twin systems. Here we use digital image correlation on coarse-grained α-uranium during tensile testing in conjunction with crystal plasticity finite element simulations. This approach allows us to determine the critical resolved shear stress, interaction mechanisms and hardening rate of the different slip and twin systems. The constitutive model is based on dislocation densities and twin volume fractions as state variables, and the simulated geometry is constructed from electron backscatter diffraction images that provide shape, size and orientation of the grains, allowing a direct comparison between virtual and real experiments. An optimisation algorithm is used to discriminate between different models for the slip-twin interactions and to find the parameters that reproduce the evolution of the average strain in each grain as the load is increased. A tensile bar, containing four grains aligned with the load direction, is used to calibrate the model with eight unknown parameters. The approach is then independently validated by simulating the strain distribution in a second tensile bar. Different mechanisms for the hardening of the twin systems are evaluated, based on the interaction between coplanar and non-coplanar twins. The latent hardening of the most active twin system turns out to be determined by coplanar twins and slip. The hardening rate of the most active slip system is lower than in fine-grained α-uranium. The method outlined here can be applied to identify the critical resolved shear stress and slip-twin interaction mechanisms of other coarse-grained materials.
Highlights
Hardening in metals is due to interactions within, and between, the slip and twin systems (Kalidindi, 1998)
For a wide range of materials, if they have limited ductility, each of these approaches might be impractical or even impossible to undertake. This is the case for the primary material of interest here - α-uranium (Inouye and Schaffhauser, 1969; Lander et al, 1994) In this paper we demonstrate how the slip-twin interaction mechanisms and the material parameters can be determined from a single uniaxial test on a coarse grained material by comparing the detailed strain and displacement fields within the individual grains determined using digital image correlation (DIC) with crystal plasticity finite element (CPFE) simulations
DIC measurements were made during tensile tests on coarse-grained α-uranium bars containing a small number of grains
Summary
Hardening in metals is due to interactions within, and between, the slip and twin systems (Kalidindi, 1998). Since the seminal research of Asaro (1983), there has been significant effort dedicated towards the development of crystal based models for the inelastic deformation of engineering materials Models of this type can contain a large number of material parameters, if there are a number of different slip and twin systems that can be activated. For a wide range of materials, if they have limited ductility, each of these approaches might be impractical or even impossible to undertake This is the case for the primary material of interest here - α-uranium (Inouye and Schaffhauser, 1969; Lander et al, 1994) In this paper we demonstrate how the slip-twin interaction mechanisms and the material parameters can be determined from a single uniaxial test on a coarse grained material by comparing the detailed strain and displacement fields within the individual grains determined using digital image correlation (DIC) with crystal plasticity finite element (CPFE) simulations
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