Application of a Smooth Approximation of the Schmid's Law to a Single Crystal Gas Turbine Blade

In industrial practice the choice of the most suitable material model does not solely rely on the ability of the model in describing the intended phenomena. Most of the choice is often based on a trade-off between a great variety of factors. Robustness, cost, and time for the minimum testing campaign necessary to identify the model and preexisting standard practices are only a few of them. This is particularly true in the case of nonlinear structural analyses because of their intrinsic difficulties and the higher level of skills needed to carefully exploit their full potential. So, despite the great progress in this field, in certain cases it is desirable to use plasticity models that are rate independent and possess very simple hardening terms. This is for example the case in which long term creep can be an issue or when the designer may want to treat separately different phenomena contributing to inelastic deformation. If the material to be modeled is isotropic, commercial finite element (FE) packages are able to deal with such problems in almost every case. On the contrary for anisotropic materials like Ni-based superalloys cast as single crystals, the choice of the designer is more limited and despite the large amount of research literature on the subject, single crystal constitutive models remain quite difficult to handle, to implement into FE codes, to calibrate, and to validate. Such difficulties, coupled with the unavoidable approximations introduced by any model, often force the practice of using oversimplifications of the material behavior. In what follows this problem is addressed by showing how single crystal plasticity modeling can be reduced to the adoption of an anisotropic elastic behavior with a sort of von Mises yield surface.