Developing a stochastic model to predict the strength and crack path of random composites

Abstract We characterize fracture and effective stress–strain graphs in 2D random composites subjected to a uniaxial in-plane uniform strain. The fibers are arranged randomly in the matrix. Both fibers and matrix are isotropic and elastic–brittle. We conduct this analysis numerically using a very fine two-dimensional triangular spring network and simulate the crack initiation and propagation by sequentially removing bonds which exceed a local fracture criterion. In particular, we focus on effect of geometric randomness on crack path of random composites. Based on that two stochastic micro-mechanic models are presented that can predict with confidence the failure probability of random matrix–inclusion composites.

[1]  M. Ostoja-Starzewski,et al.  Damage maps of disordered composites: A spring network approach , 1996 .

[2]  J. Mier.  Fracture Processes of Concrete , 1997 .

[3]  Somnath Ghosh,et al.  A two-dimensional automatic mesh generator for finite element analysis for random composites , 1991 .

[4]  W. Weibull.  A statistical theory of the strength of materials , 1939 .

[5]  Somnath Ghosh,et al.  Quantitative characterization and modeling of composite microstructures by voronoi cells , 1997 .

[6]  E. Guyon,et al.  Disorder and fracture , 1990 .

[7]  Somnath Ghosh,et al.  Two scale analysis of heterogeneous elastic-plastic materials with asymptotic homogenization and Voronoi cell finite element model , 1996 .

[8]  Somnath Ghosh,et al.  Multiple scale analysis of heterogeneous elastic structures using homogenization theory and voronoi cell finite element method , 1995 .

[9]  Dan M. Frangopol,et al.  Probabilistic Mechanics & Structural Reliability , 1996 .

[10]  R. Pyrz,et al.  IUTAM Symposium on Microstructure-Property Interactions in Composite Materials : proceedings of the IUTAM symposium held in Aalborg, Denmark, 22-25 August 1994 , 1995 .

[11]  I. Jasiuk,et al.  Damage patterns and constitutive response of random matrix-inclusion composites , 1997 .

[12]  Somnath Ghosh,et al.  Voronoi cell finite elements , 1994 .

[13]  I. Jasiuk,et al.  Fracture of random matrix-inclusion composites: scale effects and statistics , 1998 .

[14]  H. Herrmann,et al.  Statistical models for the fracture of disordered media. North‐Holland, 1990, 353 p., ISBN 0444 88551x (hardbound) US $ 92.25, 0444 885501 (paperback) US $ 41.00 , 1990 .

[15]  P. Radziszewski,et al.  Particle modeling of dynamic fragmentation—II: Fracture in single- and multi-phase materials , 2006 .

[16]  Mohammad Taghi Kazemi,et al.  Size Effect in Fracture of Ceramics and Its Use To Determine Fracture Energy and Effective Process Zone Length , 1990 .

[17]  D. Breysse,et al.  Probabilities and materials : tests, models and applications , 1994 .

[18]  K. Alzebdeh,et al.  Parametric evaluation of progressive damage in polymer concretes: Size effect and statistics. , 2008 .

[19]  D. Breysse.  Probamat, a RILEM/NATO Workshop on Probabilities and Materials: Tests, Models and Applications , 1994 .

[20]  Somnath Ghosh,et al.  Tessellation-based computational methods for the characterization and analysis of heterogeneous microstructures , 1997 .

[21]  Z. Bažant,et al.  Nonlocal damage theory , 1987 .

[22]  A. Chudnovsky,et al.  Statistical fracture mechanics , 1993 .

[23]  Probabilistic fracture mechanics of 2D carbon-carbon composites , 1992 .

[24]  B. Moran,et al.  On the Role of Interphases in the Transverse Failure of Fiber Composites , 1994 .

[25]  M. Ostoja-Starzewski,et al.  Particle modeling of dynamic fragmentation-I: theoretical considerations , 2005 .

[26]  Iwona M Jasiuk,et al.  Crack initiation and propagation in materials with randomly distributed holes , 1997 .

[27]  Martin Ostoja-Starzewski,et al.  Particle modeling of random crack patterns in epoxy plates , 2006 .

[28]  Martin Ostoja-Starzewski.  Micromechanics as a basis of random elastic continuum approximations , 1993 .

[29]  Alexander Chudnovsky,et al.  A probabilistic model of brittle crack formation , 1987 .