Investigation of Yield Surfaces Evolution for Polycrystalline Aluminum after Pre-Cyclic Loading by Experiment and Crystal Plasticity Simulation.

Damin Lu,Yanjun Chang,Keshi Zhang,Yongting Lan,Guijuan Hu

doi:10.3390/ma13143069

Abstract

This study aims at introducing the back stress of anisotropic strain-hardening into the crystal plasticity theory and demonstrating the rationality of this crystal plasticity model to describe the evolution of the subsequent yield surface of polycrystalline aluminum at the mesoscopic scale under complex pre-cyclic loading paths. By using two different scale finite element models, namely a global finite element model (GFEM) as the same size of the thin-walled tube specimen used in the experiments and a 3D cubic polycrystalline aggregate representative volume element (RVE) model, the evolution of the subsequent yield surface for different unloading cases after 30 pre-cycles is further performed by experiments and numerical simulations within a crystal plasticity finite element (CPFE) frame. Results show that the size and shape of the subsequent yield surfaces are extremely sensitive to the chosen offset strain and the pre-cyclic loading direction, which present pronounced anisotropic hardening through a translation and a distortion of the yield surface characterized by the obvious “sharp corner” in the pre-deformation direction and “flat” in the reverse direction by the definition of small offset strain, while the subsequent yield surface exhibits isotropic hardening reflected by the von Mises circle to be distorted into an ellipse by the definition of large offset strain. In addition, the heterogeneous properties of equivalent plastic strain increment are further discussed under different offset strain conditions. Modeling results from this study show that the heterogeneity of plastic deformation decreases as a law of fraction exponential function with the increasing offset strain. The above analysis indicates that anisotropic hardening of the yield surface is correlated with heterogeneous deformation caused by crystal microstructure and crystal slip. The crystal plasticity model based on the above microscopic mechanism can accurately capture the directional hardening features of the yield surface.

Highlights

Polycrystalline materials often exhibit more complicated plastic anisotropy during the forming and manufacturing processes of metal components [1,2]
We surfaces are close to isotropic expansion in the (σ, 3τ) plane with the increasing offset strains whose observe that the yield surfaces are close to isotropic expansion in the (, 3 ) plane with the shape is smooth convex ellipses with two axes of symmetry: the tensile stress axis σ and the shear increasing√offset strains whose shape is smooth convex ellipses with two axes of symmetry: the stress axis 3τ
The approaches crystal plasticity model considering the back-stress with the finite (GFEM) at different length scales of polycrystalline aggregates is adopted to validate the predictive element models (FEM)

Summary

Introduction

Polycrystalline materials often exhibit more complicated plastic anisotropy during the forming and manufacturing processes of metal components [1,2]. Under the pre-cyclic loading paths, a few studies of the yield surfaces were performed [10,11] and the results showed that cyclic hardening, softening, ratcheting, Bauschinger effect, and cyclic strain amplitude resulted in a complex evolution of subsequent yield surfaces. For these complex subsequent yielding phenomena of materials, the study of yield surface evolution is the key to establish a reasonable constitutive model to describe metal plastic behavior accurately under complex pre-loading paths [10,12].

Objectives

Results

Conclusion