Modelling fatigue crack growth in Shape Memory Alloys

Abstract

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 ∆ε−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.

Effect of specimen thickness on fatigue crack shape evolution for aluminum alloy

“…In recent years, the evolution of fatigue crack shapes has emerged as a topic of considerable interest. Numerous research studies have been undertaken to investigate crack shapes [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18], and the collective findings suggest that finite thickness specimens exhibit a phenomenon known as the "tunneling effect." Specifically, in specimens with an initially straight crack that eventually penetrates, the central crack front advances ahead of all others as the loading cycles progress.…”