Elastic fracture in random materials

Journal Article · Thu Mar 31 23:00:00 EST 1988 · Phys. Rev. B: Condens. Matter; (United States)

DOI:https://doi.org/10.1103/PhysRevB.37.5500· OSTI ID:5290482

Beale, P D; Srolovitz, D J

We analyze a simple model of elastic failure in randomly inhomogeneous materials such as minerals and ceramics. We study a two-dimensional triangular lattice with nearest-neighbor harmonic springs. The springs are present with probability p. The springs can only withstand a small strain before they fail completely and irreversibly. The applied breakdown stress in a large, but finite, sample tends to zero as the fraction of springs in the material approaches the rigidity percolation threshold. The average initial breakdown stress, sigma/sub b/, behaves as sigma/sup ..mu..//sub b/approx. =(A(p)+B(p)ln(L))/sup -1/, where L is the linear dimension of the system and the exponent ..mu.. is between 1 and 2. The coefficient B(p) diverges as p approaches the rigidity percolation threshold. The breakdown-stress distribution function F/sub L/(sigma) has the form F/sub L/(sigma)approx. =1-exp(-cL/sup 2/exp(-k/sigma/sup ..mu../)). The parameters c and k are constants characteristic of the microscopic properties of the system. The parameter k tends to zero at the rigidity percolation threshold. These predictions are verified by computer simulations of random lattices. The breakdown process can continue until a macroscopic elastic failure occurs in the system. The failure occurs in two steps. First, a number of springs fail at approximately the strain which causes the initial failure. This results in a system which has zero elastic modulus. Finally, at a considerably larger strain a macroscopic crack forms across the entire sample.

• Research Organization: Department of Physics, University of Colorado at Boulder, Campus Box 390, Boulder, Colorado, 80309-0390
• OSTI ID: 5290482
• Journal Information: Phys. Rev. B: Condens. Matter; (United States), Journal Name: Phys. Rev. B: Condens. Matter; (United States) Vol. 37:10; ISSN PRBMD
• Country of Publication: United States
• Language: English

Related Subjects

656002* -- Condensed Matter Physics-- General Techniques in Condensed Matter-- (1987-)
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
CERAMICS
COMPUTERIZED SIMULATION
CRACKS
ELASTICITY
FAILURES
FRACTURES
MECHANICAL PROPERTIES
MINERALS
RANDOMNESS
SIMULATION
STRESSES
TENSILE PROPERTIES