Abstract
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.
Highlights
In the analysis of elastic–plastic fracture mechanics, Dugdale proposed the famous Dugdale model1 based on tensile experiments of steel sheets containing cracks
For an infinite-width plate with a mode-I center crack subjected to uni-directional uniform stress at infinity, the Dugdale model simplified the plastic zone at the crack tip into a wedged band-shaped plastic zone, as shown in Fig. 1(a), and assumed that the material in the plastic zone has ideal plasticity, the yield stress σs is distributed on the interface between the plastic zone and the elastic zone, and the crack and the plastic zone are surrounded by the elastic zone
This study focused on the analysis of the plastic zone of the Dugdale model of a finite-width plate with a center crack subjected to uni-directional uniform stress at infinity by adopting the crack line analysis method proposed by Yi32,33 and obtained the correction coefficient of the Dugdale model of a finite-width plate based on the corresponding infinite-width plate and the expression of the plastic zone length of the Dugdale model of the finitewidth plate, together with the relation curve between the relative length of the plastic zone and the loading ratio
Summary
In the analysis of elastic–plastic fracture mechanics, Dugdale proposed the famous Dugdale model1 based on tensile experiments of steel sheets containing cracks. B. The solving of stress intensity factor KI′′ for a finite-width plate with a mode-I center crack by the crack length of 2c subjected to uniform stress on the crack surface near the crack tip
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