Model of Finite Strain Creep of Metals

Abstract

The finite strain tensile behavior of polycrystalline metal bars at elevated temperatures is investigated. The starting point for the investigation of flow and rupture is a constitutive model which is capable of reproducing, at infinitesimal strain, the basic tensile behavior of elastic, anelastic, and viscous creep response and creep recovery. A finite strain version of the model, together with the governing field equations, is then used to study the response of a perfect cylindrical tensile bar subjected to constant load. Elongation and area histories are obtained, and the governing equations are examined with the purpose of extracting a rupture criterion. In order to study the necking behavior, a linear eigenvalue problem is formulated for both uniform and nonuniform bifurcation modes. The analysis indicates that a uniform mode is possible; however, it depends solely on the structure of the elastic law and formally coincides with rupture or the termination of the flow process. A nonuniform mode is shown, by the approximate method of Galerkin, to be nonexistent.