Study on the Fracture Process Zone near the Mode I Dynamic Crack Tip

Evaluation of the shape and size of the fracture process zone near the mode I dynamic crack tip is still a problem unsolved completely at present. The research on the relationship between the fracture process zone and crack velocity near the mode I dynamic crack tip is quite limited, and some researchers have also developed experimental methods or numerical methods. In this research, based on the theory of elastodynamics and the complex stress function method, an approximate method for solving the mode I dynamic crack problem was proposed. The fracture process zone near the mode I dynamic crack tip was analyzed. The results showed that the areas of the fracture process zone determined based on the approximate method are nearly the same as the results obtained based on the well-known stress fields. The approximate method could provide a good reference for determining the fracture process zone near the mode I dynamic crack tip since no analytic methods had been found for evaluating the fracture process zone near the dynamic crack tip to the authors’ knowledge.

Solutions to some classical problems in linear elastostatics

This chapter presents and discusses the solution of several classical problems in linear elastostatics, including thick-walled spheres and cylinders under external and internal pressure; bending and torsion of prismatic bars of arbitrary cross section; and the use of Airy’s stress function method to solve several two-dimensional plane strain and plane stress traction boundary value problems, including a demonstration of the extent of the Saint-Venant effect. The discussion also includes an analysis of the asymptotic stress and deformation fields near the tips of sharp cracks, and a discussion of stress intensity factors which are of importance in linear elastic fracture mechanics.

Dynamic Burst Pressure of Cylindrical Explosion Containment Vessels

Cylindrical explosion containment vessels (ECVs) are widely applied in transportation, nuclear engineering, public security, and scientific research fields to ensure the safety of the staff and equipment. In this paper, a cylindrical ECV model under a nonuniformly explosive load was established. The nonuniformly explosive load is simplified as parabolic pressure acting on the internal wall of the ECV. And then, based on the stress function method and boundary conditions, an analytical solution of the ECV subjected to the parabolic load was obtained. Next, the dynamic burst pressure equation of the ECV under the explosive load was obtained. In the end, the accuracy of the dynamic burst pressure equation was evaluated by comparing with the finite element method (FEM) under different pulse duration. The results demonstrated that the equation can accurately predict the dynamic burst pressure of the ECV. In addition, our researches can provide a benchmark for approximate or numerical solutions. It is rewarding to analyze the failure problem and evaluate the safety and integrity of the pipe and vessels under a nonuniformly explosive load.

Interaction between an edge dislocation near a circular void within the framework of the theory of strain gradient elasticity

The purpose of this paper was to consider an edge dislocation near a circular hole within the isotropic theory of gradient elasticity. The stress field is derived with the help of a stress function method. The gradient stresses possess no singularity at the dislocation line. As a result, the image force exerted on the dislocation due to the presence of the hole remains finite when the dislocation approaches the interface. The gradient solution demonstrates a non-classical size effect.

Surface Stress Analysis of Internally Corroded Pipes Under External Pressure

Corrosion often leads to the failure of transporting pipelines. The surface stresses on the corroded pipes are related to the failure pressure. In this paper, a double circular arc (DCA) model is developed to calculate the surface stress of the internal corroded pipes under external pressure. In addition, a critical corrosion ratio and a critical thickness-to-diameter ratio are presented to determine the location of the maximum stress. Based on the stress function method and bipolar coordinates, an analytical solution of the DCA model was obtained. And then the stress distributions on the internal and external surfaces of the corroded pipes were determined. Next, the equivalent and hoop stresses at several locations in the cross section of the corroded pipes were discussed. The calculated results were validated using finite element method (FEM). Results show that the maximum stresses vary from the internal surface to the external surface with the increase of the corrosion ratio or the thickness-to-diameter ratio. Our research provides a benchmark for approximate solutions to predict the failure pressure and assess the integrity of the corroded pipelines.