Viscoplastic Model Development to Account for Strength Differential: Application to Aged Inconel 718 at Elevated Temperature

The magnitude of yield and flow stresses in aged Inconel 718 are observed to be different in tension and compression. This phenomenon, called the Strength differential (SD), contradicts the metal plasticity axiom that the second deviatoric stress invariant alone is sufficient for representing yield and flow. Apparently, at least one of the other two stress invariants is also significant. A unified viscoplastic model was developed that is able to account for the SD effect in aged Inconel 718. Building this model involved both theory and experiments. First, a general threshold function was proposed that depends on all three stress invariants and then the flow and evolution laws were developed using a potential-based thermodynamic framework. Judiciously chosen shear and axial tests were conducted to characterize the material. Shear tests involved monotonic loading, relaxation, and creep tests with different loading rates and load levels. The axial tests were tension and compression tests that resulted in sufficiently large inelastic strains. All tests were performed at 650 C. The viscoplastic material parameters were determined by optimizing the fit to the shear tests, during which the first and the third stress invariants remained zero. The threshold surface parameters were then fit to the tension and compression test data. An experimental procedure was established to quantify the effect of each stress invariant on inelastic deformation. This requires conducting tests with nonproportional three-dimensional load paths. Validation of the model was done using biaxial tests on tubular specimens of aged Inconel 718 using proportional and nonproportional axial-torsion loading. These biaxial tests also helped to determine the most appropriate form of the threshold function; that is, how to combine the stress invariants. Of the set of trial threshold functions, the ones that incorporated the third stress invariant give the best predictions. However, inclusion of the first stress invariant does not significantly improve the model predictions. The model shows excellent predictive capability for nonproportional load paths. Additionally, it reduces to the well-known models of Mises Drucker and Drucker-Prager. The requisite experiments involve reasonably simple load paths in the axial-shear stress plane and hence can be performed on a variety of different materials: be they metallic, geological. polymeric, ceramic or granular. The general form of the threshold function allows representation of inelastic deformation in a range of materials.