Relaxation behavior and modeling

Load relaxation tests deliver several orders of magnitude of inelastic strain rate data while elastic strains are converted into inelastic strains see Lemaitre and Chaboche, 1994. (Mechanics of Solid Materials, Oxford University Press, Cambridge p. 264)]. Hart used this test for providing information on the inelastic deformation behavior for modeling purposes. Characteristic relaxation curves were obtained with ductile metals and alloys at room and high temperature showing a scaling relation derived from Hart's theory. Subsequent testing with servo-controlled testing machines and strain measurement on the gage length showed that an increase of prior strain rate also increased the average relaxation rate. For relaxation tests starting in the flow stress region, the relaxation curves can be independent of the stress and strain at the start of the relaxation tests. For the modeling of these newly found relaxation behaviors and other phenomena the viscoplasticity theory based on overstress (VBO) has been introduced. It is shown that VBO admits a long-term (asymptotic) solution that can be used with sufficient accuracy for the flow stress region of the stress–strain diagram. The long-term solution predicts the observed relaxation behaviors and that the relaxation curves coincide when shifted along the stress axis. This behavior is observed for the recently obtained data and is confirmed by two sets of the Hart-type data when they are plotted according to the new method.