A direct method for predicting the high-cycle fatigue regime of shape-memory alloys structures

Abstract

Shape Memory Alloys (SMAs) belong to the class of so-called smart materials that offer promising perspectives in various fields such as aeronautics, robotics, biomedicals or civil engineering. For elastic-plastic materials, there is an established correlation between fatigue and energy dissipation. In particular, high-cycle fatigue occurs when the energy dissipation remains bounded in time. Although the physical mechanisms in SMAs differ from plasticity, the hysteresis that is commonly observed in the stress-strain response of those materials shows that some energy dissipation occurs. It can be reasonably assumed that situations where the energy dissipation remains bounded are the most favorable for fatigue durability. In this contribution, we present a direct method for determining if the energy dissipation in a SMA structure (submitted to a prescribed loading history) is bounded or not. That method is direct in the sense that nonlinear incremental analysis is completely bypassed. The proposed method rests on a suitable extension of the well-known Melan theorem. An application related to biomedical stents is presented to illustrate the method.