Weight functions and stress intensity factors for pin‐loaded single‐edge notch bend specimen

Abstract

A B S T R A C T A recently developed pin-loaded single-edge notch bend specimen provides an alternative to the single-edge notch tension specimen commonly used for small-crack growth testing. In this paper, weight functions for pin-loaded single-edge notch bend specimen are derived by using two methods, the classical analytical weight function method and the newly developed numerical weight function complex variable Taylor series expansion method. Excellent agreement between the two methods is achieved. Based on these weight functions, accurate stress intensity factors for two load cases, that is, pin-loading and Dugdale loading, which is required for plasticity-induced crack-closure analysis based on the strip-yield model, are determined.Keywords Green's function; pin loading; PSENB specimen; stress intensity factor; weight function. N O M E N C L A T U R Ea = crack length from edge of hole to crack tip B = specimen width E = modulus of elasticity f = non-dimensional stress intensity factor K = stress intensity factor m(a/W, x/W) = weight function M i = coefficients of the numerical WCTSE weight function P = force per unit thickness r = radius of semi-circular edge notch, subscript for reference load case S m = polynomial coefficients of crack line stress u = crack opening displacement V = non-dimensional crack mouth displacement W = characteristic length of crack configuration (W = r in this paper) x = Cartesian coordinate β i = coefficients of the analytical weight function γ i = polynomial coefficients of non-dimensional crack mouth displacement for reference load case ν = Poisson's ratio σ = nominal stress or the Dugdale stress σ(x/W) = crack line stress: stress at the prospective crack site in uncracked body I N T R O D U C T I O NSmall fatigue crack behaviour has been one of the central topics in fatigue crack growth study and small-crack theory based total fatigue life prediction of metallic materials and structures during the past three decades. 1-3 Extensive analytical and experimental investigations on small crack effects have been carried out by many researchers. The most commonly used specimen for small crack growth tests has been the single-edge notch tension specimen (SENT) (Fig. 1a). Recently, a new specimen that has a higher stress concentration factor and can be pin-loaded

Stress intensity factors for surface cracks in single‐edge notch bend specimen by a three‐dimensional weight function method

“…). Closed‐form expressions for m c and m a are given in the Appendix, which are taken from the authors' previous work and from Wu‐Carlsson. These 2D weight functions for the two types of slices were used to determinate 3D SIFs for a surface crack at the semi‐circular notch in SENB specimen covering a wide range of parameters: 1.0 ≤ r / t ≤ 3.0, 0 < a / t < 1.0, 0.2 ≤ a / c ≤ 2.0 and 0 < c / r ≤ 2.0.…”

“…An accurate analytical SIF‐equation by fitting to the WFM and BEM data is given in Zhao et al . . For 3D SIFs, highly accurate SIFs for surface cracks at a semi‐circular notch in SENT specimen were determined by using finite element method (FEM) and WFM, and a curve‐fit SIF equation is available .…”

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

“…One of the most important steps in the fracture and fatigue crack growth analysis of structure with MSD is to determine the fracture parameters, for example, the stress intensity factor (SIF), plastic zone size (PZS) and crack opening displacement (COD). 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, for example the mapping function method, boundary collection method and weight function method (WFM) . To quantitatively determine the interactions between multiple cracks, the analytical complex stress function method was frequently used to obtain the SIFs for cracks in infinite sheets .…”

Stress intensity factors for corner cracks in single‐edge notch bend specimen by a three‐dimensional weight function method

“…Zhao et al . treated this problem by using two weight function methods (WFMs): the classical analytical WFM and the weight function complex variable Taylor series expansion method . The 2D SIFs in Ref.…”

“…It is believed that the systematic 2D and 3D WF analyses in Ref. and in the present paper will provide all the required 2D and 3D SIFs for small crack growth rate correlation and total fatigue life predictions for the new SENB test specimen.…”