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
收藏
页数:25
相关论文
共 75 条
  • [41] PINNING IN TYPE-II SUPERCONDUCTORS
    LARKIN, AI
    OVCHINNIKOV, YN
    [J]. JOURNAL OF LOW TEMPERATURE PHYSICS, 1979, 34 (3-4) : 409 - 428
  • [42] Lebihain M, 2019, THESIS SORBONNE U
  • [43] Effective toughness of periodic heterogeneous materials: the effect of out-of-plane excursions of cracks
    Lebihain, Mathias
    Leblond, Jean-Baptiste
    Ponson, Laurent
    [J]. JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS, 2020, 137
  • [44] Crack paths in three-dimensional elastic solids. I: two-term expansion of the stress intensity factors - application to crack path stability in hydraulic fracturing
    Leblond, JB
    [J]. INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, 1999, 36 (01) : 79 - 103
  • [45] Prediction of crack deflection in porous/dense ceramic laminates
    Leguillon, D
    Tariolle, S
    Martin, E
    Chartier, T
    Besson, JL
    [J]. JOURNAL OF THE EUROPEAN CERAMIC SOCIETY, 2006, 26 (03) : 343 - 349
  • [46] Prediction of fracture toughness of ceramic composites as function of microstructure: I. Numerical simulations
    Li, Yan
    Zhou, Min
    [J]. JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS, 2013, 61 (02) : 472 - 488
  • [47] FRACTAL CHARACTER OF FRACTURE SURFACES OF METALS
    MANDELBROT, BB
    PASSOJA, DE
    PAULLAY, AJ
    [J]. NATURE, 1984, 308 (5961) : 721 - 722
  • [48] Milton G.W., 2004, The Theory of Composites
  • [49] Overcoming the brittleness of glass through bio-inspiration and micro-architecture
    Mirkhalaf, M.
    Dastjerdi, A. Khayer
    Barthelat, F.
    [J]. NATURE COMMUNICATIONS, 2014, 5
  • [50] On perturbations of plane cracks
    Movchan, AB
    Gao, H
    Willis, JR
    [J]. INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, 1998, 35 (26-27) : 3419 - 3453