A Multiaxial Theory of Renewal Inelasticity

A probability-based theory for predicting the inelastic response of materials to a uniaxial loading has been developed by Bagley, et. al. In this theory, predictions of distribution densities result from the postulation of dislocation activations and annihilations. The resulting equations are in the form of renewal equations, asymptotic solutions of which lead to predicted forms of primary and secondary creep responses as functions of chronological time which are in agreement with observation. The introduction of an intrinsic time, obtained by the introduction of a stress-dependent shift factor, then permits the prediction of the response to more general stress-time histories. All parameters and functions required are obtained from a series of creep tests at varying levels of stress. As it is presumed that recovery processes instantaneously erase history effects during secondary creep, the theory is applicable only to metals at higher temperatures. This theory is here extended to multiaxial applications. It is assumed that inelastic deformations are due to shear only, and that the deformation on each plane of maximum shear is independent of the state of stress on the other planes of maximum shear. Thus the deformations on each plane may be found from the one-dimensional theory. These deformations are then used to find strains on all other planes through the appropriate tensor transformation. Although all functions and parameters required by the model are computed from data obtained in tension, the resulting theory enables the prediction of responses to both multiaxial creep and more general multiaxial stress-time histories. Experiments were conducted on a 9 Cr - 1 Mo steel in tension at 600° C to obtain necessary parameters. Further experiments were then conducted in torsion and in states of combined tension and torsion. The deformations to be expected in these tests were computed from the theory, and comparisons made. Finally, two tests were performed in which the orientation of the planes of maximum shear changed significantly during the tests. The theory was found to be satisfactory as a predictive tool for each of these cases.