### STP907: Probabilistic Fracture Kinetics of “Natural” Composites

Krausz, AS

*Professor and associate professor, University of Ottawa, Ottawa, Ont.*

Krausz, K

*Consultant, Ottawa, Ont.*

Necsulescu, DS

*Professor and associate professor, University of Ottawa, Ottawa, Ont.*

Pages: 11 Published: Jan 1986

**Abstract**

The behavior of crack propagation in “natural” composite materials (eutectics) was investigated. It was shown that the conditions of failure should be described by a probabilistic analysis that represents correctly the physical properties, rather than by the usual deterministic approach. It is considered that the method is applicable for the failure analysis of “artificial” composite materials as well.

The environment-enhanced subcritical crack velocity, *v*, is represented by the appropriate kinetics combination of the elementary rate constants, ƙ, as *v* = *f*(ƙ). The rate constants are described explicitly as ƙ=kThexp(−ΔGkT)withCaretΔG=ΔG≠−W(K) where *k* is the Boltzmann constant, *h* is Planck's constant, *T* is the absolute temperature, Δ*G*^{≠} is the appropriate atomic bond energy of the low- and high-strength components encountered, respectively, as the crack tip moves into the corresponding zone, *W* is the mechanical work in the corresponding zone, and *K* is the stress intensity factor.

The physical process is controlled by thermal activation; the consequence of this is that crack growth in a probabilistic process is controlled by the instantaneous state of the load-material-crack system. It is recognized that on the atomic scale, bond breaking as well as healing occurs—the equivalent of the birth-death Markovian processes of probability mathematics. The analysis defines the crack size distribution as a function of time: The expectation value of the probability distribution is the experimentally measurable average; the spread of the probability density function defines the failure time probability of the composite material. It is concluded that the probabilistic physical process leads to a significantly different, and often more dangerous, failure occurrence than what is expected from the usual deterministic analysis.

**Keywords:**

eutectic laminate, subcritical crack propagation, temperature dependence, probabilistic crack size distribution, Markovian process

**Paper ID:** STP19980S

**Committee/Subcommittee:** D30.04

**DOI:** 10.1520/STP19980S

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