Unified fatigue modeling in a gradient-extended two-surface damage-plasticity framework

Fatigue is one of the primary failure modes of engineering materials, and its modeling and prediction remain challenging, particularly when materials exhibit anisotropic and rate-dependent behavior. In addition to traditional empirical approaches, such as the stress-based S-N curve and Paris’ law, numerical simulations have become a widely used approach for modeling fatigue behavior. Relying on a two-surface gradient-extended damage-plasticity framework, this thesis provides a systematic investigation of fatigue by focusing on three key aspects: tension-compression asymmetry, anisotropic fatigue behavior, and rate-dependent viscous damage-plasticity. First, to capture tension-compression asymmetry (TCA) under cyclic loading, the strain energy is decomposed using three distinct strategies: the volumetric-deviatoric decomposition, the spectral decomposition, and the star-convex decomposition. Subsequently, the plasticity and damage criteria are reformulated after considering the energy decomposition, and the thermodynamically consistent evolution laws for damage and plasticity are derived. The numerical results show that the proposed framework can effectively overcome several limitations of conventional models. In particular, it is capable of capturing the delayed damage nucleation under compressive loading compared with tensile loading. Once the specimen has fully fractured, the model can reproduce the crack-like behavior under compressive loading, such as stress recovery after crack closure. Due to its superior flexibility, the star-convex decomposition is adopted for the subsequent fatigue modeling. Second, an anisotropic low-cycle fatigue model is developed by introducing a novel fatigue degradation function to progressively reduce the threshold for damage initiation. This approach can avoid several issues of existing phase-field fatigue models, where both crack distribution and convergence are influenced by the reduced fracture toughness. Moreover, a second-order structural tensor is incorporated to realize the anisotropic damage evolution, which allows cracks to propagate preferentially along prescribed orientations. By adopting the Drucker-Prager yield criterion and the star-convex decomposition, the model effectively captures the tension–compression asymmetric evolution of plasticity and damage under cyclic loading. Numerical examples demonstrate that damage accumulation under different loading sequences is consistent with the Palmgren-Miner rule, while the predicted fatigue lives are consistent with the Coffin-Manson relation. Furthermore, the introduction of anisotropy not only controls the crack propagation direction but also affects the fracture mode of the specimen. Additionally, the combined effects of the mean load and the proposed fatigue degradation function provide additional flexibility to govern fatigue behavior. Finally, a unified viscous damage-plasticity model is proposed to describe rate-dependent and time-dependent failure mechanisms of ductile materials. Within the two-surface framework, independent plasticity and damage loading functions are adopted. In addition, a Perzyna-type formulation is employed to incorporate viscous effects for both damage and plasticity. Moreover, by integrating the Perzyna and Consistency conditions into a unified onset criterion, the model systematically analyzes their differences under unloading and the subsequent reloading phase. Numerical results show that the model can capture strain-rate effects, as well as the coupled evolution of plasticity and damage in creep and stress relaxation tests. In addition, cyclic loading studies demonstrate the model’s potential for fatigue simulations. The model can accurately account for the influence of loading frequency and dwell time on fatigue behavior, while the viscous parameter provides additional flexibility to regulate fatigue life and crack propagation rates.