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. 

Modelling fatigue crack growth in shape memory alloys

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Probabilistic failure mechanisms via Monte Carlo simulations of complex microstructures

Nonlinear thermo-elastic phase-field fracture of thin-walled structures relying on solid shell concepts

https://doi.org/10.1016/j.engfracmech.2022.108693

A stress-based poro-damage phase field model for hydrofracturing of creeping glaciers and ice shelves

A general framework for decomposing the phase field fracture driving force, particularised to a Drucker–Prager failure surface

A generalised phase field model for fatigue crack growth in elastic–plastic solids with an efficient monolithic solver

We present a generalised phase field-based formulation for predicting fatigue crack growth in metals. The theoretical framework aims at covering a wide range of material behaviour. Different fatigue degradation functions are considered and their influence is benchmarked against experiments. The phase field constitutive theory accommodates the so-called AT1, AT2 and phase field-cohesive zone (PF-CZM) models. In regards to material deformation, both non-linear kinematic and isotropic hardening are considered, as well as the combination of the two. Moreover, a monolithic solution scheme based on quasi-Newton algorithms is presented and shown to significantly outperform staggered approaches. The potential of the computational framework is demonstrated by investigating several 2D and 3D boundary value problems of particular interest. Constitutive and numerical choices are compared and insight is gained into their differences and similarities. The framework enables predicting fatigue crack growth in arbitrary geometries and for materials exhibiting complex (cyclic) deformation and damage responses. The finite element code developed is made freely available at www.empaneda.com/codes.

Zeyad Khalil

Papers

A generalised phase field model for fatigue crack growth in elastic–plastic solids with an efficient monolithic solver

A generalised phase field model for fatigue crack growth in elastic-plastic solids with an efficient monolithic solver.