Phenomenological modeling of the effect of specimen thickness on the creep response of Ni-based superalloy single crystals

Abstract Isothermal creep tests on single-crystal Ni-based superalloy sheet specimens show a thickness-dependent creep response that is known as the thickness debit effect. A size-dependent creep response at similar length scales has also been observed in a wide variety of other materials. We focus on Ni-based single-crystal superalloys and present a phenomenological nonlinear parallel spring model for uniaxial creep with springs representing the bulk and possible surface damage layers. The nonlinear spring constitutive relations model both material creep and evolving damage. The number of springs and the spring creep and damage parameters are based, as much as possible, on recent experimental observations of the thickness debit effect under two creep test conditions: a low-temperature, high-stress condition, 760 °C/758 MPa, and a high-temperature, low-stress condition, 982 °C/248 MPa. The bulk damage mechanisms accounted for are the nucleation of cleavage-like cracks from pre-existing voids and, at the higher temperature, void nucleation. The surface damage mechanisms modeled at the higher temperature are an oxidation layer, a γ ′-precipitate-free layer and a γ ′-precipitate-reduced layer. Model results for the creep response and for the thickness debit effect are in close quantitative agreement with the experimental results. In addition, the model predicts qualitative features of the failure process that are in good agreement with experimental observations. The simplicity of the model also allows parameter studies to be undertaken to explore the relative roles of bulk and surface damage as well as the relative roles of cleavage-like cracking and void nucleation in the bulk.