The Anderson-Bishop Problem—Thermal Ratchetting of a Polycrystalline Metals
The paper readdresses a theory of super-plastic behaviour induced by cyclic temperature for certain classes of polycrystalline metals and composite materials, originally analyses by Anderson and Bishop in the 1950’s for polycrystalline alpha uranium. The background to the original analysis and its subsequent history in the literature is discussed. Two distinct phenomena are involved. The first is ratchetting due to a fluctuating residual stress field and commonly found in structural analysis. The second form of ratchetting is due to the severe kinematic constraint on the deformation of each crystal within a polycrystal. The Anderson Bishop analysis did not take into account the former. Adopting the same kinematic assumptions as these authors, new solutions are discussed for simplified polycrystalline models and an isotropic polycrystal. These new solutions provide functional forms for material behaviour that need to be taken into account in discussions of the phenomena by material scientists.
KeywordsPlastic Strain Strain Growth Residual Stress Field Helical Spring Reverse Plasticity
The first author first became aware of the Anderson and Bishop solutions when working with Roger Anderson on the modelling of a similar phenomena in the irradiation induced swelling of structural steels . In recent years, following an interest in the thermal properties of metal matrix composites it became clear that the solutions have been extensively applied to problems in material science.
The authors wish to thanks Roger Anderson for assistance in this work. The work for this paper was part support by a Leverhulme Emeritus Fellowship to the first named author, which is gratefully acknowledges.
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