Phase-field framework with constraints and its applications to ductile fracture in polycrystals and fatigue

Fei Xue,You-Hai Wen,Tian-Le Cheng,Yinkai Lei

doi:10.1038/s41524-022-00700-2

Fei Xue, You-Hai Wen + Show 2 more

Open Access

https://doi.org/10.1038/s41524-022-00700-2

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Abstract

Modeling of ductile fracture in polycrystalline structures is challenging, since it requires integrated modeling of cracks, crystal plasticity, and grains. Here we extend the typical phase-field framework to the situations with constraints on the order parameters, and formulate two types of phase-field models on ductile fracture. The Type-I model incorporates three sets of order parameters, which describe the distributions of cracks, plastic strain, and grains, respectively. Crystal plasticity is employed within grain interiors accommodated by J2 plasticity at grain boundaries. The applications of the Type-I model to single crystals and bicrystals demonstrate the influences of grain orientations and grain boundaries on crack growth. In the Type-II model, J2 plasticity is assumed for the whole system and grain structures are neglected. Taking advantage of the efficiency of the fast Fourier transform, our Type-II model is employed to study low cycle fatigue. Crack closure and striation-like patterning of plastic strain are observed in the simulations. Crack growth rate is analyzed as a function of the J-integral, and the simulated fatigue life as a function of plastic strain agrees with the Coffin–Manson relation without a priori assumption.

Highlights

Modeling of crack initiation and propagation is critical to understand different failure modes of structural materials such as cleavage fracture and fatigue[1]
The Type-I model incorporates three sets of order parameters, which describe the distributions of cracks, plastic strain, and grains, respectively
Based on the variational principle, the equilibrium state of the system corresponds to the situation when the total free energy is at the minimum with respect to local variations in ηiðxÞ, i.e., the npj Computational Materials (2022) 18

Summary

Introduction

Modeling of crack initiation and propagation is critical to understand different failure modes of structural materials such as cleavage fracture and fatigue[1]. Fracture is modeled by treating crack surfaces as sharp interfaces, which often requires remeshing after crack propagation. The phase-field method has emerged as a powerful tool to model crack initiation and propagation[2,3,4,5,6]. In contrast to the sharp interface models, the phase-field model utilizes a diffused interface to describe the transition from intact to fully damaged regions that can conveniently handle the evolution of complex crack patterns with no need for remeshing nor ad hoc criteria for crack propagation[7,8]. Phase-field ductile fracture models were constructed by considering the interaction between plasticity and fracture[4,11,12,13,14], starting from the small strain framework, which successfully capture a variety of anticipated ductile fracture responses at the macroscale. The ductile fracture model has been successfully extended to finite strain regime[15]

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