The Analysis Of Cohesive Zone Model And User-defined Subroutine Development In Finite Element Method

Cohesive zone model (CZM) is a computational model based on elastic-plastic fracture mechanics. CZM has been extensively researched and used because the stress singularity at crack tip in linear elastic fracture mechanics can be avoided and both the crack interface stress and fracture energy are taken in calculation. A tiny cohesive zone near the crack tip region has been proposed in CZM. The stress in cohesive zone is a function of the crack opening displacement, and this function is usually called traction-separate law (T-S law). As the research and development of CZM, different T-S laws have been proposed, and have been used in ductile cracking and two-phase material interface cracking.The relationship of stress and displacement is a continuous function and coupling of different dimensionality in exponential cohesive zone model. Considering the exponential CZM in two-dimensional plane model, the complete coupling of normal and shear stress can be achieved only when the parameter q equal to 1. The one-dimensional fracture energy formulation has been proposed in this paper. In the mixed cracking mode, the fracture energy calculating by one-dimensional fracture energy formulation reaches its critical maximum value while the stress reduced to zero first in this dimensional.The cohesive element in finite element software ABAQUS has been studied, and the user-define subroutine which can be applied for CZM has also been analyzed. Based on the research, user-defined material subroutine VUMAT combined with cohesive element has been taken to compile the exponential CZM implemented in ABAQUS. The application of T-S law in VUMAT has been derived. By the analysis of damage and fracture of the linear and nonlinear CZM, the program flow of VUMAT for CZM has been designed respectively.The VUMAT of exponential CZM for the pure cracking mode has been complied. The results calculated by VUMAT subroutine of exponential CZM and bilinear CZM contained in cohesive element have been compared. It has confirmed that the crack initiation and evolution can be accurately simulated by VUMAT subroutine. By the analysis of stress coupling and fracture energy, one-dimensional fracture energy has been taken as the failure criterion of cohesive element in the mixed mode. The VUMAT of exponential CZM for mixed mode has been used to simulate the delamination of composite laminates, and has been compared to the experimental test. The result showed that, the VUMAT can accurately simulated crack initiation and propagation process.The VUMAT subroutine of CZM developed in this paper is applicable for various forms of CZM in finite element analysis, and the convergence problem has been solved in the calculation of VUMAT. The application of exponential CZM for mixed mode has been expanded by one-dimensional fracture energy formulation. By the VUMAT subroutine of exponential CZM, Non-linear CZM can be applied to solve the crack opening simulation in ABAQUS. As a part of National Natural Science Foundation projects (the study of the bonding reliability of anisotropic conductive film and the interface damage), the VUMAT subroutine of exponential CZM and compiling method of VUMAT subroutine combined with cohesive element will be applied in further research of interface model for the study of bonding interface and interface damage.