Brittle fracture in disordered media: from reservoir rocks to composite solids

We describe and discuss recent discrete models of brittle fracture in disordered media. By comparing the predictions of these models with the experimental data, we argue that such models can provide a rational explanation and quantitative predictions for many fracture properties of disordered media, ranging from reservoir rocks to composite solids such as polymers, metals and ceramics. These models also provide novel predictions that can be used for characterization of fractured media.

[1]  Francisco Guinea,et al.  The Fractal Nature of Fracture , 1987 .

[2]  Amnon Aharony,et al.  Universal critical amplitude ratios for percolation , 1980 .

[3]  D. Srolovitz,et al.  Brittle fracture in materials with random defects. , 1989, Physical review. B, Condensed matter.

[4]  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 .

[5]  William A. Curtin,et al.  Brittle fracture in disordered materials: A spring network model , 1990 .

[6]  Feng,et al.  Behavior of depleted elastic networks: Comparison of effective-medium and numerical calculations. , 1985, Physical review. B, Condensed matter.

[7]  Herrmann,et al.  Electrical breakdown in a fuse network with random, continuously distributed breaking strengths. , 1988, Physical review. B, Condensed matter.

[8]  P. Bak,et al.  Earthquakes as a self‐organized critical phenomenon , 1989 .

[9]  Lucien Benguigui,et al.  Strain and stress at the fracture of percolative media , 1987 .

[10]  De Hosson JT,et al.  Mechanical strength of highly porous ceramics. , 1991, Physical review. B, Condensed matter.

[11]  S. Murrell Fragmentation, form and flow in fractured media. R. Englman and Z. Jaeger, 1986. Volume 8 of Annals of Israel Physical Society. 628 pp. Adam Hilger, Bristol, U.K. Price: £49.50. , 1987 .

[12]  Feng,et al.  Transport properties of continuum systems near the percolation threshold. , 1987, Physical review. B, Condensed matter.

[13]  Li,et al.  Fracture behavior of a solid with random porosity. , 1986, Physical review letters.

[14]  Beale,et al.  Elastic fracture in random materials. , 1988, Physical review. B, Condensed matter.

[15]  Scher,et al.  Analytic model for scaling of breakdown. , 1991, Physical review letters.

[16]  Feng,et al.  Position-space renormalization for elastic percolation networks with bond-bending forces. , 1985, Physical Review B (Condensed Matter).

[17]  Li,et al.  Ductile-brittle transition in random porous Au. , 1992, Physical review letters.

[18]  M. Sahimi,et al.  On three-dimensional elastic percolation networks with bond-bending forces , 1990 .

[19]  L. Sander,et al.  Diffusion-limited aggregation, a kinetic critical phenomenon , 1981 .

[20]  Arbabi,et al.  Elastic properties of three-dimensional percolation networks with stretching and bond-bending forces. , 1988, Physical review. B, Condensed matter.

[21]  A. A. Griffith The Phenomena of Rupture and Flow in Solids , 1921 .

[22]  Didier Sornette,et al.  Self-Organized Criticality and Earthquakes , 1989 .

[23]  Roux,et al.  Scaling laws in fracture. , 1989, Physical review. B, Condensed matter.

[24]  Wang,et al.  Statistical-thermodynamic approach to fracture. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[25]  M. Sahimi,et al.  Stochastic transport in disordered systems , 1983 .

[26]  S. Redner,et al.  A random fuse model for breaking processes , 1985 .

[27]  Arbabi,et al.  Test of universality for three-dimensional models of mechanical breakdown in disordered solids. , 1990, Physical review. B, Condensed matter.

[28]  P. Meakin,et al.  Theoretical study of the influence of strain rate and temperature on the maximum strength of perfectly ordered and oriented polyethylene , 1986 .

[29]  Herrmann,et al.  Scaling and multiscaling laws in random fuse networks. , 1989, Physical review. B, Condensed matter.

[30]  Roux,et al.  Roughness of crack interfaces. , 1991, Physical review letters.

[31]  Zhang,et al.  Dynamic scaling of growing interfaces. , 1986, Physical review letters.

[32]  I. Webman,et al.  Elastic Properties of Random Percolating Systems , 1984 .

[33]  Takayasu Simulation of electric breakdown and resulting variant of percolation fractals. , 1985, Physical review letters.

[34]  W. Brace,et al.  Electrical resistivity changes in saturated rocks during fracture and frictional sliding , 1968 .

[35]  K. Sieradzki,et al.  Brittle behavior of ductile metals during stress-corrosion cracking , 1985 .

[36]  D. Bergman,et al.  Critical Properties of an Elastic Fractal , 1984 .

[37]  Roux,et al.  Experimental measurements of the roughness of brittle cracks. , 1992, Physical review letters.

[38]  H. E. Stanley,et al.  The fractal dimension of the minimum path in two- and three-dimensional percolation , 1988 .

[39]  J. Straley,et al.  Distribution-induced non-universality of the percolation conductivity exponents , 1979 .

[40]  M. Sahimi,et al.  On correction to scaling for two- and three-dimensional scalar and vector percolation , 1991 .

[41]  Arbabi,et al.  Percolation and fracture in disordered solids and granular media: Approach to a fixed point. , 1992, Physical review letters.

[42]  A. Zunger,et al.  Bond lengths around isovalent impurities and in semiconductor solid solutions , 1984 .

[43]  J. G. Zabolitzky,et al.  Precision calculation of elasticity for percolation , 1986 .

[44]  Duxbury,et al.  Breakdown properties of quenched random systems: The random-fuse network. , 1987, Physical review. B, Condensed matter.

[45]  Roux,et al.  Fracture of disordered, elastic lattices in two dimensions. , 1989, Physical review. B, Condensed matter.

[46]  Stephens,et al.  Distribution of fracture strengths in disordered continua. , 1987, Physical review. B, Condensed matter.

[47]  P. Leath,et al.  The failure distribution in percolation models of breakdown , 1987 .

[48]  L. Pietronero,et al.  Fractal Dimension of Dielectric Breakdown , 1984 .

[49]  Goddard,et al.  Elastic percolation models for cohesive mechanical failure in heterogeneous systems. , 1986, Physical review. B, Condensed matter.

[50]  Gang Li,et al.  A simple two-dimensional model for crack propagation , 1989 .

[51]  Ronald L. Biegel,et al.  The kinematics of gouge deformation , 1987 .