Solutions Of Moving Crack Model With The Restraining Stress Zone

The problem discussed in this work belongs to the dynamic fracture mechanics. Dugdale crack model (i.e., the strip yielding zone crack model) has played an important role for the description of failure and separation mechanisms of materials. The Dugdale static crack model has been generalized to the Dugdale moving crack model by attaching a strip yielding zone to the crack tip. The relative analytical solutions have been obtained. However, the crack opening displacement (COD) is found to be discontinuous when the crack moving speed is equal to the Rayleigh wave speed. Specifically, when the crack moving speed is smaller than the Rayleigh wave speed and reaches to it, COD is the positive infinite. On the other hand, when the crack moving speed is greater than the Rayleigh wave speed and reaches to it, COD becomes the negative infinite. In order to solve this problem, the main work includes the following points.(1) The restraining stress zone differs from the strip yielding zone in physics. The restraining stress zone depends on the material damage degree in the crack tip zone. A restraining stress zone is attached to the crack tip such that a moving crack model with a restraining stress zone is thus established.(2) Assume that the distribution of restraining stresses has a linear distribution. In addition, two speed effect functions are introduced which describe the influences of speed on the remotely applied stresses and restraining stresses. The complex function approach is employed. Obtained are the analytical solutions of stress field, displacement field, stress intensity factor (SIF) and crack opening displacement (COD). The new COD result is continuous at the Rayleigh wave speed and has a finite value. The limitation of the classic result is removed.(3) Based on the analytical solutions of the Dugdale moving crack model and the moving crack model with a restraining stress zone, the numerical calculations are then performed. The influences of crack moving speed and material property on the SIF and COD are analyzed and discussed. Moreover, two results for two different models are compared. Otherwise, the distribution of strain energy density ahead of the moving crack tip is also discussed.