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Calculations of the stress-strain response of a common tapered disk thermal fatigue specimen are presented. The calculations were made by complete nonlinear finite element solution and by a simpler method employing the elastic strain-invariance principle. The results are used to show the effect of several common test variables on the resulting stress-strain response, to assess the effect of various material behavior and structural analysis assumptions on the stress-strain response, and to explore the application of several high-temperature fatigue damage prediction methods to transient thermal fatigue loading.

Finite element elastic-plastic stress analyses were performed on several notched fatigue specimen geometries used in a test program to determine the room temperature and 550 F fatigue strengths of three low strength steels. Specimen geometries included grooved cylinders and wide notched cantilever bend specimens. The analyses were, with one exception, for reversed loading. The objective in these cases was to predict the steady state response of the specimens by using the cyclic stress-strain relationships. The exceptional case represented an initial effort in analyzing a zero-to-tension cycle with a cyclic loading option in the computer program. The finite element calculated notch root strains were compared with strains measured during the fatigue experiments and with predictions of the commonly used Stowell and Neuber formulae. A good correspondence was found between the experimental strains and those calculated by the finite element method. The Stowell and Neuber formulae were found to overpredict notch root strains at stress levels beyond the initial plastic range. A good correlation of fatigue crack initiation life data for smooth and notched specimens was found using a recently proposed stress-strain function.

Some recent results from investigations in nonlinear fracture mechanics centering about the J-integral are utilized to derive a low-cycle fatigue relationship. The derived relationship has the form of the well-known Coffin-Manson equation, but differs from it in that the controlling variable is predicted to be applied strain energy density rather than plastic strain range. This predicted controlling variable appears to closely parallel several energy-related functions proposed during the past 15 year period.