The elastic-plastic cylinder subjected to radially distributed heat source, lateral pressure and axial force with application to nuclear reactor fuel elements

Abstract

T elastic-plastic deformation of a solid cylinder in the presence of a distributed heat source and subjected to a lateral pressure p and an axial fource F is considered in detail using Tresca's yield function, its associated flow law, and a linear workhardening law. Particular attention is given to the class of problems in which the radial stress, and not the axial stress, is the intermediate principal stress. The general results are applied to the cylindrical nuclear reactor fuel element in the state of plane strain with a radially distributed Gaussian heat source, acting in its fissionable interior. The solution is expressed in closed form in terms of the exponential integral and the incomplete gamma function and is found to exhibit three stages of plastic deformation. In stage I the plastic domain consists of two concentric and adjacent zones with different stress fields and different rates of propagation which expand outward from the centre of the cylinder; in stage II the elastic domain vanishes, while the inner plastic zone continues to propagate; and in stage III a third plastic zone is formed at the outer radius which propagates inward. Throughout the deformation the states of stress are found to exhibit regular progression. A numerical example is included.