A model of the continuous elastoplastic transition in metals
Part 1: The heterogeneous character of a real metal is represented by a model in which the metal is considered to consist of a large number of elements with a variation of individual stress-strain responses. The variation of Poisson's ratio which occurs as a function of strain is used to measure the progress of yielding through the material and hence to calculate the variation in elemental yield strains. By use of data obtained from the completely elastic and fully plastic parts of the stress-strain curve and the yield strain distribution, the elastoplastic transition behaviour can be calculated. Comparisons are presented between computed and experimental stress-strain curves for aluminium, copper, magnesium, nickel, and titanium alloy to demonstrate the validity of the proposed model. Part 2: Sufficient cyclic stressing can change the subsequent stress-strain curve of a steel which normally has a yield point into one with a continuous elastoplastic transition. A model of the elastoplastic transition in metals, developed by the authors in Part 1 to represent the stress-strain behaviour of metals with a continuous elastoplastic transition, is then proposed for representing the stress-strain behaviour of steels in which the yield point has been removed, by stress cycling. Results are presented to show good agreement between the model and the observed stress-strain behaviour of four steels, one of which had no yield point and the other three had their yield points removed by cyclic stressing.