Weight functions for the determination of stress intensity factor and T‐stress for semi‐elliptical cracks in finite thickness plate

Abstract

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).

Stress intensity factors calculation for surface crack in cylinders under longitudinal gradient pressure using general point load weight function

“…, and t is the thickness of plates. Jin and Wang used the modified general form of point load WF to determine SIFs and T‐stress of any point along crack front of semi‐elliptical crack in finite thickness plates …”

Weight function, stress intensity factor and crack opening displacement solutions to periodic collinear edge hole cracks

“…Because fatigue cracks usually initiate from stress concentrations, the SIF solutions for crack(s) emanating from a hole or notch were extensively studied by using various methods, [4][5][6][7][8][9][10][11][12][13][14][15][16] for example the mapping function method, 4 boundary collection method 5 and weight function method (WFM). [11][12][13][14][15][16][17] To quantitatively determine the interactions between multiple cracks, the analytical complex stress function method 18 was frequently used to obtain the SIFs for cracks in infinite sheets. 19,20 A simple and accurate approximate method was first proposed by Kachanov 21 and further developed 22,23 to obtain the SIF for arbitrarily arranged cracks in an infinite sheet subjected to remote tension.…”

Analytical and numerical investigation of the stiffness matrix for edge‐cracked circular shafts

“…[1][2][3][4][5][6] The SIFs can be computed by using numerical methods as well as finite element and boundary element methods. Existing methods of approaching fracture mechanics and treating stress concentrations include singular integral equations, 7 weight functions, 8,9 boundary collocation, 10 finite fracture mechanics, 11 finite element method (FEM), 12 strong FEM, 13,14 isogeometric approaches, [14][15][16] numerical cohesive zone modelling, [15][16][17][18] and boundary element approaches. 19 Unfortunately, there is a lack of general solutions that can be applied for many structural configurations.…”