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 generalized 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 linearized 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.

A coupled phase field formulation for modelling fatigue cracking in lithium-ion battery electrode particles

“…By using a scalar phase field d to describe the crack-solid interface, phenomena such as crack deflection, the coalescence of multiple cracks and crack branching become easy to handle in arbitrary geometries and dimensions. Phase field methodologies have been successfully used to model fracture across a wide range of materials and applications, including composites [31,32], functionally graded materials [33,34], shape memory alloys [35,36], rocks [37,38], and piezoelectric materials [39]. Phase field approaches have also been extended to coupled multi-physics problems of chemo-mechanical nature, such as hydrogen assisted fracture [40][41][42][43], corrosion [44,45], cracking of nuclear fuel pellets [46] and particle fracture in Li-Ion batteries [21,23].…”

The role of NiTi shape memory alloys in quality of life improvement through medical advancements: A comprehensive review

“…Numerous models have been developed to describe and predict the functional characteristics of SMAs by researchers such as Auricchio et al, 68 Gu et al, 69 Liu et al, 70 and many more. [71][72][73][74][75][76][77][78][79][80][81][82][83][84][85][86][87][88][89]…”

Computational modelling of hydrogen assisted fracture in polycrystalline materials

“…is used to describe the evolution of the solid-crack interface, taking the value of φ = 0 for the pristine state and of φ = 1 for the fully damaged state. Phase field fracture methods have gained remarkable popularity in recent years and have been successfully used to predict cracking in a wide range of materials and applications, including functionally graded solids [45,46], shape memory alloys [47,48], and fibre-reinforced composites [49,50]. The evolution of the phase field equation is dictated by the energy balance associated with the thermodynamics of fracture, as first presented by Griffith [51] and later extended to elastic-plastic solids by Orowan [52].…”