Finite element modelling and diffraction measurement of elastic strains during tensile deformation of HCP polycrystals

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Abstract

In this paper a 3D, elastically anisotropic crystal-plasticity based constitutive model is used to describe cyclic deformation and hardening of polycrystalline HCP (hexagonal close-packed) materials. A diffraction post-processor is developed to allow critical assessment of model predictions against XRD data. Model results for titanium alloy Ti-6Al-4V are compared with synchrotron high energy X-ray polycrystalline diffraction data. The significance of elastic anisotropy and three-dimensionality of the model is discussed.

Introduction

Most engineering alloys used in structural applications are polycrystalline. The majority of the material volume is occupied by grains (rather than grain boundary material), unless the grain size is very small (sub-micrometer). Taking this circumstance into consideration, we focus our attention on plastic deformation within grains, which is dominated by crystal slip across grains at low homologous temperatures. In the present study we describe the application of such grain-level crystal plasticity formulation to the analysis of inelastic deformation in polycrystalline aggregates with HCP crystal structure. We concentrate on some issues of general concern, namely: (i) the use of three-dimensional (3D) formulations, as opposed to 2D (plane stress/plane strain) formulations; (ii) the use of a ‘static’ regular mesh, as opposed to a grain-based mesh specific for a particular microstructure; and (iii) the procedure for model calibration by comparison with experimental measurements by high energy X-ray diffraction, which provides a means of assessing mesoscale average values of grain-level elastic strains.

Section snippets

Rate-independent crystal plasticity model: formulation

The present model has been implemented by the authors using the rate-independent formulation described by Manonukul and Dunne [1]. Further developments have been incorporated to include full elastic anisotropy description and to allow 3D analysis. A brief summary of the formulation and the key equations used are given below. The stress rate at a point within a grain during elastic–plastic deformation is given byσ˙=C:D-σtr(D)-Ωσ+σΩ-α=1n(C:Pα+βα)γ˙α,with βα = Wασ  σWα, Wα being the skew part of the

Model calibration against the monotonic stress–strain curve

Crystal elastic stiffness matrix was obtained from the literature [5], and minor scaling modification was applied to improve the agreement over the linear part of the stress–strain curve. Adjusted stiffnesses (in the Voigt notation) were C11 = 160 GPa, C33 = 181 GPa, C44 = 55 GPa, C66 = 55 GPa, C12 = 95 GPa, C13 = 45 GPa. For matching the FE model output with experimental datum points, three groups of plasticity parameters need to be identified for each type of slip system: the initial critical resolved shear

Conclusions

It is apparent from Fig. 11 that the calibrated FE polycrystal elasto-plastic model predicts trends that are in good agreement with the experiment. Although the nominal errors of single diffraction peak fitting are very low (of the order of marker sizes in the Figure), these only reflect the accuracy of determination of the peak centre positions for grains that contribute to diffraction within the gauge volume. In practice this is further affected by other experimental uncertainties. The trends

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