Finite element simulation of ductile fracture in polycrystalline materials using a regularized porous crystal plasticity model

Mikhail Khadyko,Odd Sture Hopperstad,Bjørn Håkon Frodal

doi:10.1007/s10704-020-00503-w

Abstract

In the present study, a hypoelastic–plastic formulation of porous crystal plasticity with a regularized version of Schmid’s law is proposed. The equation describing the effect of the voids on plasticity is modified to allow for an explicit analytical solution for the effective resolved shear stress. The regularized porous crystal plasticity model is implemented as a material model in a finite element code using the cutting plane algorithm. Fracture is described by element erosion at a critical porosity. The proposed model is used for two test cases of two- and three-dimensional polycrystals deformed in tension until full fracture is achieved. The simulations demonstrate the capability of the proposed model to account for the interaction between different modes of strain localization, such as shear bands and necking, and the initiation and propagation of ductile fracture in large scale polycrystal models with detailed grain description and realistic boundary conditions.

Highlights

For many types of Al alloys and steels fracture occurs by ductile fracture mechanisms, namely the nucleation, growth and coalescence of microscopic voids
In the seminal work of Gurson (1977), limit analysis was applied to a spherical void in a von Mises plastic medium to derive the yield function for the porous material
In all these models the sharp vertex is replaced by a smooth one, which means that if the stress is lying exactly in the vertex of the yield locus, producing the same resolved shear stress on adjacent slip systems, it will activate all of these slip systems simultaneously, unlike the rate independent Schmid’s law, where a choice has to be made

Summary

Introduction

For many types of Al alloys and steels fracture occurs by ductile fracture mechanisms, namely the nucleation, growth and coalescence of microscopic voids. Some works try to formulate and implement micromorphic size-dependent porous crystal plasticity (Ling et al 2018) or add a void coalescence criterion (Hure 2019; Siddiq 2019) In these studies, the porous crystal plasticity models were developed and, in some cases, validated using unit cell models. On the other hand fracture in a polycrystal is preceded by a complex stress and strain history with a combination of different types of strain localization (necking and shear banding), crystal orientation evolution and heterogeneous stress fields (Di Gioacchino and da Fonseca 2015; Guery et al 2016; Lim et al 2014) Modelling these processes requires finite element models of the grain structure with a high resolution that are stable for large deformation processes. It is used to simulate the deformation until fracture of polycrystals in plane-strain tension (2D) and uniaxial tension (3D), demonstrating the complex interaction between the heterogeneous grain structure, different modes of strain localization and fracture initiation and propagation in polycrystals with realistic grain structures and boundary conditions

Regularized porous crystal plasticity model

Temporal integration algorithm

Numerical study

Findings

Discussion

Concluding remarks