DEVELOPMENT OF STRAIN-RATE GRADIENTS

The development of nonuniformities in tensile deformation and its dependence on material parameters and external conditions have been reanalyzed. It is found that the major influence of strain rate on neck growth is usually through its effect on the rate of strain hardening, rather than on the flow stress itself. In addition, the curvature of the stress-strain curve plays an important role: its usual sign is responsible for the unavoidability of eventual unbounded neck growth. The new analysis uses the state-parameter formulation of constitutive laws, avoiding the integrated strain as a variable. The result is a second-order differential equation describing the development, at each cross section, of the relative gradients of cross-sectional area and of strain rate. Numerical solutions are presented for small strains, analytical ones for slow neck growth. The application of a strain-rate criterion for catastrophic growth leads to a quantitative formula for the maximum tensile ductility, which is in agreement with observations, and provides guidelines for material development. © 1979.