عنوان مقاله [English]
In this paper, a multi- linear cohesive zone model has been proposed for simulation of mode I delamination in laminated composites. This model considers the fracture process zone (FPZ) effects in the simulation of initiation and
propagation of delamination. This model takes the spring elements with variable spring constants, according to the traction- separation curve of the specimen along the crack growth, to show the residual strength of the material in the FPZ. As a result of the existence of several types of toughening mechanism with different strain energy release rates, it is required to present a procedure which covers all the fracture process zone toughening events. Therefore, in this model, unlike previous ones and commercial codes, all the possible softening behavior of the traction-separation curve is taken into account. For simulation of toughening mechanisms in the FPZ, a finite element method has been chosen as a numerical method. The material outside the FPZ has been modeled with linear elastic behavior. Since the delamination phenomenon takes place between the plies, the crack propagation path is usually known in advance. In order to find the induced loads and relative displacements, a unit load is applied, and the corresponding system of equations has been solved in a step by step procedure. In order to simulate the multi-linearity of the cohesive zone model, several springs have been considered in the crack path and the calculation followed until the last spring in the FPZ shows the final breaking point of the traction-separation curve. At the end of each step, the spring constants will be changed based on the traction-separation curve of the specimen. The results of simulation are presented in the form of load-displacement curves that are in excellent agreement with available experimental results, and correctly show the softening behavior of the material after the failure initiation.