A damage model for predicting the fatigue life of elasto-plastic solids
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The estimation of fatigue life stands as a critical aspect in assessing the service life of many engineering structures, such as offshore wind turbine monopiles, where materials are exposed to low cyclic stress amplitudes. In recent years, variational phase-field models for fracture have emerged as robust mechanistic computational framework for such analyses. One widely adopted approach is based on a fatigue degradation function to reduce the material's toughness [1,2]. This framework has also been extended to ductile fracture [3,4]. Fatigue life is typically represented as a function of the cyclic stress range, in the so-called S-N approach. A pioneering contribution [5] extended the phase-field model proposed in [1,2] to accurately estimate virtual S-N curves in the high cycle fatigue. One of the main assumptions in [5] is the consideration of brittle fracture. However, this assumption becomes less accurate when the material contains internal or surface defects, such as holes, notches or surface roughness. In these cases, plastic deformations induced by stress concentrations are significant, altering the slope of the S-N curve compared to defect-free specimens [5]. In this work, we propose a new phase-field model capable of capturing the effect of plasticity in the fatigue life of elasto-plastic solids. The model has been verified against experimental results. [1] Alessi, R., Vidoli, S., & De Lorenzis, L. (2018). A phenomenological approach to fatigue with a variational phase-field model: The one-dimensional case. Engineering fracture mechanics, 190, 53-73. [2] Carrara, P., Ambati, M., Alessi, R., & De Lorenzis, L. (2020). A framework to model the fatigue behavior of brittle materials based on a variational phase-field approach. Computer Methods in Applied Mechanics and Engineering, 361, 112731. [3] Ambati, M., Gerasimov, T., & De Lorenzis, L. (2015). Phase-field modeling of ductile fracture. Computational Mechanics, 55, 1017-1040. [4] Khalil, Z., Elghazouli, A. Y., & Martinez-Paneda, E. (2022). A generalised phase field model for fatigue crack growth in elastic–plastic solids with an efficient monolithic solver. Computer Methods in Applied Mechanics and Engineering, 388, 114286. [5] Golahmar, A., Niordson, C. F., & Martínez-Pañeda, E. (2023). A phase field model for high-cycle fatigue: Total-life analysis. International Journal of Fatigue, 170, 107558.
