IJPAM: Volume 72, No. 4 (2011)


Boris Kunin$^1$, Igor Savin$^2$
$^{1,2}$University of Alabama in Huntsville
Huntsville, AL 35899, USA

Abstract. The paper models a particular mode of slow crack growth in brittle composites, namely a sequence of microscopic jumps of random length, each one followed by an arrest of random duration. The jump lengths are modeled by a non-homogeneous Poisson process (with a space coordinate in place of what ordinarily is time), and the arrest durations are modeled by a homogeneous Poisson process whose intensity is related to random energy barriers at the arrest points and, consequently, depends on the crack arrest location. The transition probability for the resulting random process of crack growth is shown to satisfy a hyperbolic PDE. The model predicts scatter, in identical experiments, of critical loads and critical crack lengths. It also captures both scatter and 'scale effect' for macroscopic fracture parameters, including fracture toughness $K_C$ and critical energy release rate $G_C$. There are indications that the model is capable of simulating the Paris law. An illustrative numerical example is considered.

Received: July 4, 2011

AMS Subject Classification: 74R10, 60K35

Key Words and Phrases: brittle fracture, stochastic crack growth, life time scatter, paris law

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2011
Volume: 72
Issue: 4