Phase-field modeling of fatigue
Fatigue is responsible for most of the recorded structural failures, yet its design practice is still largely based on empirical laws or the direct testing of structural components. In this project we aimed at developing a novel approach to model the fatigue behavior of brittle materials based on variational phase-field modeling of fracture. We first formulated the model in one dimension to investigate its basic properties, within a collaboration with the external pageUniversità La Sapienza in Rome, and then extended it to two and three dimensions.
The standard phase-field formulation is modified introducing a fatigue degradation function that effectively decreases the fracture toughness of the material accounting for the fatigue loading history through a suitable history variable. Different choices of the degradation function and of the history variables are suggested and their implications discussed.
The numerical results show that the major features of the fatigue behavior known from experiments, including the sequence of crack nucleation, stable and unstable propagation, the Paris law and the Wöhler curves are recovered. Also, the Palmgren–Miner rule and the monotonic fracture behavior are encompassed as special cases.
Funding:
external pageDFG external pageResearch Training Group 2075 “Modelling the constitutive evolution of building materials and structures with respect to aging” (2015-2019)
external pageDFG Priority Program SPP2020 “Cyclic deterioration of High-Performance Concrete in an experimental-virtual lab” (2018-2020)
external pageexternal pageMIUR-external pageDAAD Joint Mobility Program “Variational approach to fatigue phenomena with phase-field models: modeling, numerics and experiments” (2016-2017).