We present a phase field-based framework for modelling fatigue damage in Shape Memory Alloys (SMAs). The model combines, for the first time: (i) a generalised phase field description of fracture, incorporating multiple phase field formulations, (ii) a constitutive model for SMAs, based on a Drucker-Prager form of the transformation surface, and (iii) a fatigue degradation function, with damage driven by both elastic and transformation strains. The theoretical framework is numerically implemented, and the resulting linearised system is solved using a robust monolithic scheme, based on quasi-Newton methods. Several paradigmatic boundary value problems are addressed to gain insight into the role of transformation stresses, stress-strain hysteresis and temperature. Namely, we compute Δε−N curves, quantify Paris law parameters and predict fatigue crack growth rates in several geometries. In addition, the potential of the model for solving large-scale problems is demonstrated by simulating the fatigue failure of a 3D lattice structure.
@article{arxiv.2112.08209,
title = {Modelling fatigue crack growth in Shape Memory Alloys},
author = {M. Simoes and C. Braithwaite and A. Makaya and E. Martínez-Pañeda},
journal= {arXiv preprint arXiv:2112.08209},
year = {2021}
}