PSI - Issue 42

Shiwen Wang et al. / Procedia Structural Integrity 42 (2022) 441–448 Shiwen Wang, Paul A Shard, Antony M Hurst and Yuebao Lei / Structural Integrity Procedia 00 (2019) 000 – 000

444

4

Assessments have been required to account for different plate/crack geometries, the loading ratios and material models (elastic, elastic and plastic at power n = 5, 10, see below section). The combination of different load ratio are defined as λ = 1 and λ 1 = 0, ±0.5, ±1.0 , which corresponds to biaxial tension and cross thickness bending. The combined end load and bending moment applied in the FE model used a linearly varying distributed pressure at the plate end with maximum value σ m + σ b at the front surface (cracked side) and the minimum value σ m − σ b at the back surface (uncracked side). For deep cracks, part of the crack may be in the compressive region, depending on the value of λ and λ 1 , under which circumstance the crack tip would tend to close. In this paper, the effect of crack face closure has not been considered (allowing crack face overlapping) and J values are extracted only for the crack front locations where the crack tip was open. 2.2. Material properties Both elastic and elastic-plastic material properties are used for FE analyses. For the elastic analyses, the same material properties as Lei (2004a) are used, where Young’s modulus and Poisson’s ratio values are E = 500 MPa and ν = 0.3 respectively. This is an arbitrary E value used for convenience, noting that the stress intensity factor, K , does not depend on E. For the non-linear elastic plastic analyses, the Ramberg – Osgood type stress-strain relationship has been used and can be expressed as following equation, 0 = 0 + ( 0 ) (3) where α and n are a material constant and the strain hardening exponent, respectively, σ 0 is a normalising stress and ε 0 = σ 0 /E . For all elastic-plastic analyses, α = 1, E σ 0 ⁄ = 500 and = 0.3 have been used. Two values of n, n=5 and 10, have been used to examine the higher and lower strain hardening material behaviour, respectively. For convenience of analysis, σ 0 = 1 MPa has been used. For engineering application, yield stress, σ y , is usually defined as the stress at 0.2% plastic strain, inserting this condition into equation (3), then stress ratio, σ y σ 0 ⁄ , is found to be 0 = ( 0. 00 2 0 ) 1 = 1 (4) Therefore, yield stress at 0.2% plastic strain, σ y , is same definition as that of normalising stress σ 0 . 2.3. Validation using FEA solutions and the Reference Stress Method In this paper, the FEA data are used to investigate the global limit loads for surface cracked plate under complex loading using R6 Option 3 failure assessment curves (FACs). The Option 3 FACs is usually generated using the following expression from Section I.6 of R6 (2019): ( ) = ( ) 0.5 (5) = ሺ͸ሻ For N ≠ 0 case, the reference stress, ref , can be expressed as, ref = Φ = √ (2 + √(2 ) 2 + (1 − 1 2 ) 2 ) 2 + 3 4 12 (7) To accentuate the differences between different set of results, the FACs can be presented in the following alternative form: = ( 1 ( ) ) 2 for option 3 (8)