Anelastic Behaviour of Materials under Multi-axial Strains

A theory of anelasticity is presented, which involves the relaxation of all the elastic compliances as a function of orientation. It is shown that. in addition to the usual relaxations of Young's and shear moduli. anelastic phenomena related to the relaxation of Poisson's ratio should be considered. Finally, the theory is applied to anelastic data in Zircaloy-4 and AISI-1080 steel. obtained in longitudinal excitations. Introduction The anelastic behaviour of meterlals IS usually described by the standard anelastic solid (SAS) model ( 1). The anelastic properties of such a solid can be expressed by the linear dtfferential equation where is the applied stress. e the strain. JU and JR are the unrelaxed and tM,e relaxed compliances: respectively. and T, is the relaxation time at constant stress. The dot indicates a derivative with respect to the time. The dynamic response of the SAS is very well known and leads to the so called Debye equations for the dynamic modulus and the internal friction ( 1 ) . These equations are generally used to represent the anelastic behaviour of specimens excited under simple situations. like longitudinally or in torsion. In these situatrons. only the relaxat~on of Young's and shear modul~ are measured. Furthermore. for single crystals only the orientation dependence of the relaxation of these two moduli are generally obtained. It is the purpose of this paper to extend the formalism to all the elastic compilances. as a function of orientation, both for cubic and hexagonal symmetries. This will allow the determination of the relaxed and unrelaxed Poisson's ratios. in two orthogonal directions located in the plane perpendicular to the direction of the applied stress. With this information. it is possible ta study the relaxation behaviour in directions perpendicular to the excitation. Finally. some points defect symmetries and particular orientations will be considered. as special situations of the general formalism presented in the paper. Furthermore. the results will be applied to actual experimental data obtained in Zircaloy-4 and AISI-1080 steel.