Physica A 186 (1992) 160-182
North-Holland ~ ~Z~
Brittle fracture in disordered media:
from reservoir rocks to composite solids*
Muhammad Sahimi
Department of Chemical Engineering, University of Southern California, Los Angeles,
CA 90089-1211, USA
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. Introduction
Fracture processes ranging from brittle fracture, ductile yielding and flow, to
dielectric breakdown, are some of the most poorly understood set of phenom-
ena in science and technology. The range of industrial systems in which failure
phenomena are observed is very broad. Under large stress or strain, a crack
can open up in soils, which grows with time, leading to complex phenomena
such as soil liquefaction and eventually earthquake. Natural or man-made
fractures in oil reservoirs and aquifers are crucial to the flow of oil or
groundwater, especially in rocks that have a very small porosity, e.g., those of
Iran and man other oil fields in the Middle East. Mechanical breakdown of,
and propagation of cracks in, air-plane wings and fuselages can cause an
airliner to crash. It was only three years ago that an Aloha Airlines aircraft
suffered such a phenomenon. An important (and undesirable) property of
many of high T c superconducting materials is their brittleness and mechanical
instability. Polymers, glasses and ceramics often develop microcracks under a
large enough stress or strain, which can lead to their mechanical failure and
eventual fragmentation. The same phenomenon is observed in the grinding of
minerals. Pressurized nuclear reactors can develop cracks in their structure,
which can cause tremendous safety problems. Dielectric breakdown in compo-
* An expanded and more complete version of this paper with applications to many other systems
of practical interest, will appear as a review paper in Int. J. Mod. Phys.
0378-4371/92/$05.00 © 1992-Elsevier Science Publishers B.V. All rights reserved