C. W. Woo

Anti-plane shear problem for an edge crack in a finite orthotropic plate

Abstract The problem of an edge crack in a finite orthotropic plate under anti-plane shear is considered. The boundary collocation method is used to calculate the mode III stress intensity factor (SIF). For the case in which the material is isotropic, the present results agree very well with those obtained by using the integral equation method. Furthermore, the method can be extended readily for general cases with arbitrary geometrical and boundary loading conditions and material properties.

The mixed mode problems for the cracks emanating from a circular hole in a finite plate

Abstract The stress intensity factors of two cracks emanating from a hole in a finite plate is analysed by the Muskhelishvili formulation and boundary collocation method. For Mode I case, the present results compared very favorably with the existing solutions. For the mixed mode problems of inclined cracks, the K I and K II values have been obtained for varying crack-length to plate-width ratios, a/b , and different crack angles. It has been demonstrated that the convergence of this method is satisfactory. The proposed stress functions and the calculation procedure may be extended to more complex geometrical and loading cases.

Analysis of an internal crack in a finite anisotropic plate

In this paper the boundary collocation method is presented for computing the stress intensity factors for an internal crack in a finite anisotropic plate. The stress functions are assumed such that they can represent the stress singularity at the crack tips, satisfying not only the governing equations of the anisotropic plate theory in the domain, but also the stress-free conditions on the crack surfaces. Therefore, only the boundary conditions of the plate need to be considered, and they can be satisfied approximately by the Boundary Collocation Method. Numerical examples demonstrated that the proposed method gives satisfactory results compared with the existing solutions.

Boundary collocation method for analyzing perforated plate problems

Abstract The problem of a two-dimensional plate weakened by an array of holes of arbitrary location is analyzed using the Muskhelishvili complex variable formulation and least square boundary collocation method. Several sets of complex stress functions are proposed in this article in solving the perforated plate problem with and without the interaction effect between holes and crack. In addition, the method has been extended to the problem of cracks emanating from one of the holes in a perforated plate. The results in this article compare favorably with the existing solutions.

Statistical analysis of material damage with changing internal structure

Abstract An investigation on the mechanical properties of material with changing internal structure or damage induced by large deformation is carried out. A new experimental procedure has been established for the ductile damage test with a large number of specimens for the purpose of the statistical analysis. The experimental results show that the macroscopic mechanical properties of material both prior to and during the process of the mechanical damage vary in a random manner. The statistical analysis reveals that the scatter of the material properties during the process of damage evolution is larger than that of the original material properties. When the original material properties are treated separately as deterministic and random ones, the obvious statistical discrepancy during the process of the damage evolution is exposed. The results obtained provide much useful information for the prediction of material damage based on the probabilistic formulation.

Stress intensity factors for a circular arc crack by boundary collocation method

Abstract The plane elastic problem for a finite plate with a curved crack is considered. Uniform external tension on the outer boundary is chosen as the applied load. The stress intensity factors at the crack tips are calculated by using the boundary collocation method. The results obtained by this method compare favourably with the existing solutions for the infinite cases. Solutions for the finite plates are given to show the effects of the dimensions.

Fatigue crack propagation in aluminium and PMMA

The applicability of the above fatigue law has subsequently been examined for various materials under different loading conditions. The effective mean stress has since been revealed to be a significant variable influencing the rate of crack propagation [3]~ Forman et al. [3] attributed the sensitivity of mean stress effect on Pariss law to the increased rate of crack propagation as K approached K , the fracture • . . m x ~ c toughness of the materlal. The modlfled ~aris s crack growth zormulation, proposed by Forman, is expressed as

An effective numerical method for an interfacial crack in a finite bi-material plate

In this paper an effective numerical method is presented for analyzing the stress intensity factors associated with the stress field near a partially debonded interface in a finite bi-material plate. The strees functions are assumed such that they can represent the stress singularity at the crack tips, satisfying not only the equilibrium equations in the domain, but also the stress and displacement conditions on the crack surfaces and across the interface. Therefore, only the boundary conditions of the plate need be considered, and they can be satisfied approximately by the Boundary Collocation Method. Numerical examples demonstrated that the proposed method gives satisfactory results and has many advantages compared to other methods.

Analysis of an edge crack in a finite bi-material plate

Abstract The in-plane extension of a finite bi-material plate with an edge crack along the interface is considered. A set of stress functions is assumed such that they satisfy not only the equilibrium equations in the domain, but also the stress and displacement conditions on the crack surfaces and across the interface. Meanwhile, they can also represent the stress singularity at the crack tip. Therefore, only the boundary conditions need to be considered, and they can be satisfied approximately by the boundary collocation method. Numerical examples of stress intensity factor calculation for biaxial and uniaxial loading conditions are given, and it is demonstrated that the proposed method gives satisfactory results.

Composite laminate crack problems using the boundary collocation method

Abstract A comprehensive approach to the solution of various anisotropic composite laminate crack problems is presented. Based upon the complex variable formulation, several sets of stress functions are proposed for the problems of the single edge crack, the double edge crack, cracks emanating from a hole and the interaction between holes and crack. With these functions, the governing equation of anisotropic plate theory, the single valuedness displacement condition and stress-free conditions along the crack can be satisfied automatically, while boundary conditions are approximately satisfied by means of the boundary collocation method in the least square sense. Results obtained here are satisfactory in comparison with existing solutions.