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 3 Option 2 or Option 1 FAC at an L r value which is defined by the selected limit load. In this case, if both are plotted as a function of L r , the predictions using the Option 2 (or Option 1) curve should be located above the curve representing the FE results to declare the limit load solution to be ‘conservative’ ; 2) The L r value which is defined by the selected limit load can be used to define an Option 3 FAC, which can be compared against the Option 2 (or Option 1) curve. In this case, the limit load solution is ‘conservative’ when the Option 3 FAC is located outside the Option 2 (or Option 1) FAC. The details of these approaches, both used within this work for consideration of the Lei and Budden limit load solutions and also other current R6 solutions, are detailed in Section 2.3. 2.1. FE Models and Loadings The FE models include plate containing a semi-elliptical surface crack (Figure 1a) has been used for all analyses. By taking advantage of the two planes of symmetry within the assessment geometry, only a quarter of the plate has been modelled and symmetric boundary conditions have been applied. ABAQUS/Standard (version 6.14-1) 8 node 3 dimensional solid element (C3D8) used with focused mesh around the crack tip (Figure 1b). The mesh contains 10 elements along the half crack front to allow for SIF and J-integral evaluated at 11 crack tip locations along the crack front. Meanwhile, SIF and J evaluation at each crack tip were carried from 15 contours of element rings biased towards the crack tip. An angular parameter, , was introduced to represent locations of the crack front. The mesh was designed to have a constant interval of ∆ =9° and results presented from surface point ( =0°) to the deepest point ( =90°). For each of the modelled plate containing a semi-elliptical surface crack, the model geometry has been set up as: 1) crack half-length, c, is 30mm; 2) plate half width, W=4c; 3) plate half length, L=4W; 4) ratio of crack depth/half length, a/c= 0.2, 0.6 and 1.0; 5) ratio of crack depth/plate thickness, a/t=0.2, 0.5 and 0.8. 443

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Fig. 1. (a) Plate with surface semi-elliptical crack; (b) FE model (a/c=0.6, a/t=0.8) As illustrated in Figure 1a, the cracked plate is subject to a combination of an end load perpendicular to the crack plane, N , a lateral load parallel to the crack plane, N x , and a cross-thickness bending moment, M . For all cases of combined loading, only proportional loading is applied and the possible load ratios, λ and λ 1 , are defined as follows: = = 6 (1) 1 = = (2) where σ m ( = N/2Wt ) is the membrane stress corresponding to the plate end load N, and σ b ( = 3M/Wt 2 ) is the outer fibre bending stress corresponding to the cross-thickness bending moment M. Note that a positive M corresponds to a positive stress. σ x ( = N x /2Lt ) is the membrane stress parallel to crack plane. n xL and n L are normalised limit loads parallel and perpendicular to the crack, respectively.