Analytical analysis on the Dugdale model of a finite-width cracked plate by using crack line analysis method

The Dugdale model is one of the most famous achievements in fracture mechanics due to its accurate predication of the size of the plastic zone at the crack tip in comparison with the experimental results. However, the Dugdale model is generally used for the analysis of infinite-width cracked plates, and it has not been successfully extended analytically for the analysis of finite-width cracked plates, which are more commonly seen in engineering structures. In this paper, the Dugdale model of finite-width cracked plates was analytically analyzed based on the crack line analysis method. Solving the plastic zone of the Dugdale model of a finite-width plate with a mode-I center crack was broken down into two problems of finite-width plates, and the analytical solutions of stress intensity factors of the two problems were obtained, respectively. Based on the superposition principle of stress intensity factors, the size of the plastic zone of the Dugdale model of a finite-width plate with a mode-I center crack was obtained. The results are in perfect consistency with the experimental values obtained by Dugdale himself, and the difference between the theoretical curve and the experimental values obtained by Dugdale was eliminated for the first time.