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Constitutive laws for radiation-induced deformation are derived based on a phenomenological approach which involves only simple principles of continuum mechanics and avoids detailed mechanistic assumptions. This approach is applied to materials which are initially in an isotropic condition that serves as a reference state. As specific examples of this approach, we consider in detail three forms of constitutive laws. In the first case it is assumed that the deformation rate depends on the current stress as the only tensor variable. For the second case we postulate a dependence on the current stress tensor and the strain tensor as produced during the previous radiation-induced deformation. Finally, the third case deals with a dependence on stress and strain as accumulated during cold-working. In both the latter cases, the material is rendered anisotropic with respect to the reference state. It is shown for the last two cases that the phenomenological approach provides a proper formulation and a clear distinction of such phenomena as stress-affected swelling, irradiation creep, radiation-induced anisotropic growth, and creep-swelling interaction. It also supplies the superposition rules for these phenomena when the material is subject to triaxial stresses which change and redistribute with time.
The constitutive laws as obtained from the continuum approach are not completely suitable for modeling structural materials. Since they are polycrystalline in nature, the constitutive properties may vary from grain to grain, and it becomes necessary to derive a macroscopic constitutive law for the aggregate. This is accomplished by considering an aggregate of many viscoelastic elements linked in parallel. The resulting constitutive law for the aggregate depends on the strain history. Upon sudden load changes, the aggregate exhibits anelastic transient creep. It is shown that the magnitude of the anelastic strain is related to the range of variability for the constitutive properties of the grains.
radiation effects, irradiation creep, swelling, anisotropic growth, swelling-creep coupling, anelastic strains
Associate professor, University of Wisconsin, Madison, Wis.