An efficient phase-field model for fatigue fracture in viscoelastic solids using cyclic load decomposition and damage superposition

Accurate and efficient evaluations of fatigue fracture is of great importance for the design and evaluation of viscoelastic materials in critical applications subject to cyclic load. In this study, an efficiency-enhanced phase-field model for viscoelastic fatigue fracture is proposed, allowing for fast evaluations of high-cycle fatigue damage. Based on the Boltzmann superposition principle, the cyclic fatigue load is decomposed into a mean load and a zero-mean cyclic load. The response of the mean load is solved numerically, while the response of the zero-mean cyclic load is solved analytically. The phase-field driving force is obtained analytically by combining the responses of the two independent parts, and the phase-field evolution is calculated numerically. In addition, both the dissipated energy and the elastic energy are decomposed using the volumetric-deviatoric decomposition to avoid unrealistic damage under the compression portion of the cyclic load. The proposed efficiency-enhanced model satisfies the energy conservation law as it does not require the fracture toughness degradation or additional fatigue energy treatments. The computational efficiency of the overall fatigue fracture can be greatly improved by leveraging the analytical solution for the response associated with the cyclic load. Numerical investigations are performed, and comparisons with the conventional cycle-by-cycle computation method are made. The results show that the proposed method can reduce the exponential computational demand to a constant or a linear one while achieving an accuracy comparable to that of the conventional method. The effectiveness of the proposed method is further demonstrated using an actual rubber component with testing data.