Phase-Field Fracture Method Based on Eshelby Theory for Heterogeneous PBX

doi:10.19596/j.cnki.1001-246x.8859

Abstract

Abstract:

Taking the advantages of tracking discontinuous material surfaces explicitly within the continuous mechanics framework, the phase field method has been successfully applied to study crack propagation and damage in brittle materials. Considering that the complex micro-structural inclusion-matrix interaction dominates the damage nucleation for heterogeneous PBX, we develop a phase field inclusion model based on the Eshelby's inclusion theory, and carry out the numerical simulation study of damage initiation and evolution. The phase field energy consists of the elastic energy and the inclusion-matrix interaction energy. Combining with the Mori-Tanaka method, the effective elastic moduli of heterogeneous PBXs with different volume fractions are derived. For the proposed phase field inclusion model, the nonlinear debonding effects and damage distribution can be characterized by the phase field order parameter directly. It owns explicity in physical mechanism, and completeness in mathematical theory. We apply this model to compute the high volume fraction heterogeneous PBXs with typical circular and polygonal inclusions, and investigate the influences of loading, inclusion shape, volume fraction and computational parameters on the debonding mechanism. Numerical results indicate that the inclusion-matrix micro-structural evolution promotes interface debonding and the formation of macroscopic material failure, which coincides with experimental observations.

Key words: heterogeneous PBX, inclusion, damage evolution, phase field model, Eshelby theory

CLC Number:

Yun XU, Yao LONG, Meizhen XIANG, Jun CHEN. Phase-Field Fracture Method Based on Eshelby Theory for Heterogeneous PBX[J]. Chinese Journal of Computational Physics, 2024, 41(5): 559-568.

Figures/Tables 11

Fig.1 Debonding of the inclusion phase field model is characterized by Eshelby's eigenstrain (a) debonding region is characterized by eigenstrain; (b) introduce a length scale

Table 1 Computational parameters of heterogeneous PBX

	杨氏模量/GPa	剪切模量/GPa	能量释放率/(J·m^-2)	泊松比
夹杂颗粒	32.45	14.19	3.50	0.143 3
粘结剂	2.40	0.80	1.02	0.499 5
等效模量	7.39	2.47	1.16	0.499 1

Fig.2 Force-displacement loading condition for the computational model with (a) different inclusion volume fractions and (b) different computational parameters in the phase field degradation functions

Fig.3 Damage distribution of model 1 with monodisperse circular inclusions under different loadings

Fig.4 Damage distribution of model 2 with monodisperse circular inclusions under different loadings

Fig.5 Damage distribution of model 3 with bidisperse circular inclusions under different loadings

Fig.6 Damage distribution of model 4 with bidisperse circular inclusions under different loadings

Fig.7 Damage distribution of model 1 with polygonal inclusions under different velocity loadings

Fig.8 Damage distribution of model 2 with polygonal inclusions under different velocity loadings

Fig.9 Damage evolution of model 2 with circular inclusions at different times

Fig.10 Relationship between debonding and energy density and inclusion volume fraction and microstructure (a) critical debonding energy and critical stress; (b) inclusion volume fraction

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