断裂相场在循环塑性与疲劳分析中的应用

Metals play an important role in the fields of aerospace, ship, ocean and automobiles.For such materials, cracking and fracture is a common failure mode. Therefore, the study of crack initiation, propagation and structural damage is significant to metal applications. In this paper, a plastic fatigue model is built by extending the phase field approach to fracture to cyclic plasticity with nonlinear isotropic hardening. In this model, the fatigue behavior is described by a fatigue degradation function. This degradation function acts as a fatigue constitutive relation and only takes the fatigue history variable as argument. The ductile fracture analysis on fatigue crack propagation using the proposed model is realized via an in-house MATLAB program, which combines the phase field method with cyclic plasticity and fatigue degradation. The staggered iteration scheme is used to solve the primary unknowns: the displacement field and the phase field. Tension-compression asymmetry is implemented to prevent unphysical cracking due to compression. The plastic constitutive behavior is updated with a return-mapping algorithm. To save computational cost, adaptive load stepping is embedded into the program. With this model, the effects of fatigue degradation function and crack tip geometry on the crack propagation rate are analyzed. Meanwhile, the influences of fatigue history variable and size of notch on crack growth and cyclic plasticity are discussed. First, it is found that the parameters of fatigue degradation are strongly correlated with the crack propagation rate. Then, from the hysteresis loops of the force-displacement curve, it is found that crack propagation gradually decreases the stiffness of structure as expected. Last, the results reveal that under the same loading mode, crack propagates faster with a larger notch radius. It is believed that the model in this work is a useful tool for investigating cyclic plasticity, in that it provides an effective way for studying the crack propagation under various modes of cyclic load and exploring the crack behavior with different plastic models.