The Analysis Of Interface Crack With Arbitrary Crack Tractions

The stability of a crack is influenced by crack tractions. In practical engineering, cracks may appear in some hydraulic concrete structures due to some different reasons like seismic loads, which might affect the stress state of structures. There are stress singularities on the top of the crack. With water entering the crack, it will accelerate crack growth when water entering the crack, which deteriorates structure stability. There are complex stress singularity powers for interface crack. Stresses are more complicated when crack loads exist on the interface. A new numerical method and model are needed.Scaled boundary finite element method (SBFEM) is a good numerical method in solving crack problems, which combines the advantages of finite element method (FEM) with boundary finite method (BFM). The scaled center is chosen at the crack tip. No mesh refinements and special singular elements are needed. The investigated domain boundaries are discretized, which reduces the cost of prepare process. No fundamental solution and singular integration are required, anisotropic materials are handled without additional computational efforts. The scaled boundary finite-element method is extended to analyze the in-plane singular stress fields at cracks and multi-material corners. A complete singularity stress field is represented semi-analytically as a series of matrix power functions of the radial coordinate originating from the singular point. This method is capable of directly evaluating orders of singularity, stress intensity factors, T-stresses, higher order terms and power-logarithmic singularities. In this method, the singular functions are represented analytically.This paper presents an interface crack solving model with arbitrary crack tractions based on scaled boundary finite element method. With the proposed model in this paper, stress and displacement are expressed analytically in the radial direction, and the stress singularity at crack tip is reflected automatically without refined mesh. The arbitrary crack tractions can be first decomposed into one component paralleled to the crack and another one perpendicular to the crack, then both the two components can be expressed as the sum of limited power functions. Each power function is solved analytically. According to the linear superposition principle, the solutions of a structure with arbitrary crack tractions are obtained. Bi-material plates are computed to verify the convergence and accuracy. Interface fracture stress intensity factors are obtained under the condition of different modulus ratio and crack loads. The proposed model in this paper is efficient for both anisotropic and isotropic materials. Numerical examples of plates with crack tractions, in which stress intensity factors and higher order terms of stress are calculated, verify this model. Sensitivity analysis is evaluated about plate geometry and material parameters. Classical examples are calculated to demonstrate the simplicity and efficiency of the model.On the basis of above research, the proposed model is applied to engineering gravity dam. Concrete dam which is built on rock foundation is analyzed its static fracture feature. Interface crack stress intensity factors and higher order singular terms are calculated. The effects of different water pressure distributing in the crack are studied and some useful conclusions are obtained by comparisons. Water pressure in the crack affects I stress intensity factor. When the modulus ratio of concrete dam and rock foundation increases, I stress intensity factor increases obviously and II stress intensity factor decreases in some degree, which means shear component on crack tip increases and appears complex crack. Calculating higher order singular terms means a lot for analyzing plastic zone on crack tip and size effect.