# The Effects of Thermal Variation in Fracture Toughness

*by*Robert A. Heller, Virginia Polytechnic Inst and State, Univ, United States,

Hossein Rahemi, Virginia Polytechnic Inst and State, Univ, United States,

**Abstract:**Environmental temperature changes produce cyclic and thermal stresses in cylindrical structures. The probability of failure defined as the chance that a crack, growing under the influence of such stresses exceeds the critical crack length is calculated. Because mechanical properties such as strength, relaxation modulus, and fracture toughness are time and temperature dependent as well as statistically variable quantities, crack growth will be random. To include all these effects, the R.G. Forman crack growth rate relation is used. A hazard function will be defined as the probability of failure during a single cycle after the cylinder has servived N previous cycles. The hazard function will then be integrated to yield the progressively increasing probability of fracture. The stress distribution through the cylindrical wall is not uniform; as a result, a step by step finite element analysis will be carried out to determine stress intensity and critical crack size as the crack travels through the varying stress field. The probability of failure is conditioned on the chance that an initial crack exists.

**Subject Headings:**Cracking | Probability | Stress analysis | Stress distribution | Thermal loads | Failure analysis | Toughness | Temperature effects

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