Effective toughness of disordered brittle solids: A homogenization framework

被引:25
作者
Lebihain, Mathias [1 ,2 ]
Ponson, Laurent [2 ]
Kondo, Djimedo [2 ]
Leblond, Jean-Baptiste [2 ]
机构
[1] Univ Gustave Eiffel, Lab Navier ENPC, CNRS, UMR 8205, 6-8 Ave Blaise Pascal, F-77455 Marne La Vallee, France
[2] Sorbonne Univ, Inst Jean le Rond dAlembert, UPMC, CNRS,UMR 7190, 4 Pl Jussieu, F-75005 Paris, France
关键词
Brittle fracture; Homogenization theory; Disordered materials; Effective toughness; Large-scale simulations; Rational design; STRESS INTENSITY FACTORS; FRACTURE-TOUGHNESS; CRACK-PROPAGATION; HETEROGENEOUS MATERIALS; PLANAR CRACK; DEFLECTION; ANISOTROPY; COMPOSITES; PREDICTION; EXPANSION;
D O I
10.1016/j.jmps.2021.104463
中图分类号
T [工业技术];
学科分类号
08 ;
摘要
This paper addresses the question of the homogenization of fracture properties for three-dimensional disordered brittle solids. The effective toughness, identified as the minimum elastic energy release rate required to ensure crack growth, is predicted from a semi-analytical framework inspired by both micromechanics and statistical physics, that encompasses the decisive influences of both the material disorder and the mechanisms of interaction between a crack and heterogeneities. Theoretical predictions are compared to numerical values of the effective toughness that are computed with the fracture-mechanics-based semi-analytical method of Lebihain et al. (2020). Based on a perturbative approach of Linear Elastic Fracture Mechanics, this method allows for the efficient computation of crack propagation under tensile Mode I loading in composite materials containing several millions of inclusions, where the crack interacts with them through two mechanisms : crossing, wherein the crack penetrates the inclusion, and by-pass, wherein the crack wanders out-of-plane and follows the inclusion/matrix interface. We show that our homogenization procedure provides an accurate prediction of the homogenized fracture properties for a broad range of microstructural parameters such as the inclusion toughness, density or shape. This original theoretical framework constitutes a powerful mean to connect the microstructural parameters of materials to their crack growth resistance, beyond the particular cases considered in the simulations performed. As a result, it provides new strategies for the rational design of optimized brittle composites with tailored fracture properties.
引用
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页数:25
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