A unified FFT framework with coupled gradient damage model and phase-field method for the failure analysis of composites

Abstract

A unified FFT framework coupling the Gradient Damage Model (GDM) and the Variational Phase-Field Model (PFM) for failure analysis of composites is proposed. GDM and PFM are used to simulate the failure of the matrix and the interphase, respectively. Based on the similarity of the damage evolution equations (elliptic partial differential equations) of GDM and PFM, a unified iterative solution and numerical implementation based on fast Fourier transform (FFT) are derived, and simultaneously applied to a computational model. In addition, the high computational efficiency of the FFT method is used to solve the mechanical equilibrium problem. The complete form of the PFM is introduced to avoid erroneous damage diffusion at the different phase interfaces of the composites, and a stress decomposition-based PFM is formulated. 2D and 3D computational examples are established to investigate the mesh insensitivity of the damage models used and the erroneous damage diffusion at interfaces. The applicability of the stress decomposition-based PFM at interphase is discussed in the context of single-edge notched specimens under tension and fiber-reinforced composites with interfacial phases under transverse tension. Finally, the performance of the unified computational framework is evaluated using two simple numerical examples, and the mechanical behavior of unidirectional CF/PEEK composites under transverse tensile loading is simulated based on the unified framework. The results are compared with experiments to evaluate the computational accuracy and practical applicability of the proposed framework.