This paper presents the application of weight function method for the calculation of stress intensity factors (K) and T-stress for surface semi-elliptical crack in finite thickness plates subjected to arbitrary two-dimensional stress fields. New general mathematical forms of point load weight functions for K and T have been formulated by taking advantage of the knowledge of a few specific weight functions for two-dimensional planar cracks available in the literature and certain properties of weight function in general. The existence of the generalised forms of the weight functions simplifies the determination of specific weight functions for specific crack configurations. The determination of a specific weight function is reduced to the determination of the parameters of the generalised weight function expression. These unknown parameters can be determined from reference stress intensity factor and T-stress solutions. This method is used to derive the weight functions for both K and T for semi-elliptical surface cracks in finite thickness plates, covering a wide range of crack aspect ratio (a/c) and relative depth (a/t) at any point along the crack front. The derived weight functions are then validated against stress intensity factor and T-stress solutions for several linear and nonlinear two-dimensional stress distributions. These derived weight functions are particularly useful for the development of two-parameter fracture and fatigue models for surface cracks subjected to fluctuating nonlinear stress fields, such as these resulting from surface treatment (shot peening), stress concentration or welding (residual stress).

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Keywords nonlinear stress distributions, stress intensity factor, surface crack, T-stress, three-dimensional analysis, weight function
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Journal Fatigue and Fracture of Engineering Materials and Structures
Jin, Z. (Z.), & Wang, X. (2013). Weight functions for the determination of stress intensity factor and T-stress for semi-elliptical cracks in finite thickness plate. Fatigue and Fracture of Engineering Materials and Structures, 36(10), 1051–1066. doi:10.1111/ffe.12070