PSI - Issue 42

Shiwen Wang et al. / Procedia Structural Integrity 42 (2022) 441–448

442

2

Shiwen Wang, Paul A Shard, Antony M Hurst and Yuebao Lei / Structural Integrity Procedia 00 (2019) 000 – 000

Nomenclature a

depth of crack

c

half length of crack thickness of the plate half length of plate half width of the plate Young’s modulus

t

L

W

E

J

J-integral

J e , J p elastic and plastic J-integral, respectively n strain-hardening exponent of material strain 0 normalised strain for Ramberg-Osgood stress-strain relationship stress 0 normalised stress for Ramberg-Osgood stress-strain relationship applied stress parallel to crack plane FAC Failure Assessment Curve SIF Stress Intensity Factor

1. Introduction The current global limit load solutions in R6 were provided by Goodall and Webster (2001) and Lei (2004a, 2004b and 2004c), which considered plates under tension, bending, and combined tension and bending respectively. Validation of the solutions was provided via systematic detailed non-linear finite element (FE) analyses considering semi-elliptical surface cracks in plates. Limit loads were determined using the reference stress method, such that the FE J values (based on the maximum value along the crack front) were well reproduced. It was then shown that the limit load data obtained in this way could be well predicted by the Goodall and Webster global limit load equation. Global limit load solutions for plate with surface breaking crack were developed by Lei and Budden (2015), to consider biaxial forces and cross-thickness bending. The solutions are for rectangular defects and are based on the concept of net-section plastic collapse and the von Mises yield criterion is adopted. This solution is further developed by Lei (2020) to incorporating more complex loading, such as the bending due to stress parallel to the crack plane on the limit load, to provide a local limit load solution. A reference stress estimation method considering the bending stress parallel to the crack plane has been developed and validated using FE J results via the use of the reference stress J scheme. The results show that the elastic-plastic FE J results are well predicted when the reference stress solution is used in the reference stress J predictions. The predicted values of J were found to be greater than the corresponding FE J values, which indicate that predictions are conservative relative to FE results. This paper aims to provide improved guidance on the limit load solutions for surface-cracked plates subject to complex loading, to include biaxial loading and positive cross-thickness bending (crack opening moment). The J integral data are determined from a series of cracked body finite element analyses (FEA) considering various plate and crack geometries, loading combinations, and elastic and elastic-plastic material assumptions. FEA results have been used to validate the Lei and Budden limit load solutions, principally via R6 Option 3 failure assessment curves (FACs) and comparison with Option 1 and Option 2 FACs. Comparison with other available limit load solutions has also been carried out. 2. Methodology The overall aim of this paper is to validate the limit load solutions for plates containing surface cracks provided by Lei and Budden (2015) based on crack body FE J integral results and the reference stress J scheme. The validation can be carried out via two approaches: 1) The normalized FE J can be compared with the predicted J using the R6