PSI - Issue 28

Yifan Li et al. / Procedia Structural Integrity 28 (2020) 1140–1147 Author name / Structural Integrity Procedia 00 (2019) 000 – 000 The stress intensity factors and T-stress are functions of the geometry defined by the relative crack length 2 a /W, the hole diameter to plate length ratio D/W and the orientation angle , which can be written as = √ ( 2 W , W D , ) (1) = ∗ ( 2 W , W D , ) (2) where i represents mode I and mode II. Y i and T * are the dimensionless stress intensity factors and dimensionless T stress. And σ is the nominal stress can be calculated by σ =P/B(W － D). 3. Numerical analyses of HCSP specimen The commercial finite element software Abaqus 2017 was used to calculate the dimensionless Y i and T * of HCSP specimen under different mixed mode fractures. The geometry conditions of the model are W = 100 mm, B = 10 mm and the preset hole diameter D, the crack length 2 a , the orientation angle are variable. The Young's modulus and Poisson’s ratio of isotropic sandstone are taken to be E = 20 GPa, v = 0.19 from Wei et al. (2017). The typical mesh pattern for the HCSP specimen model is shown in Fig. 3. In order to produce the singularity of stress/strain field near the crack tip, CPS6 type singular elements with the middle nodes at quarter-point positions were used in the first ring of elements surrounding the crack tip. All other elements are 8-node CPS8 elements. In these simulations, the total numbers of approximately 2500 elements were used for each model. 1143 4

Fig. 3. The typical finite element model of HCSP specimen.

The loading boundary condition is set as that the top and bottom ends of circumference of the preset hole have fixed X displacement and two opposite vertical loads P = 100 N were applied at the circumference ends. The stress intensity factors and T-stress were obtained directly from Abaqus utilizing the contour integral method. Five concentric contours around the crack tip were used to determine the fracture parameters, and then values from outer contour was used to obtain the parameters in order to avoid the effect of domain dependence (Coules et al. 2016). The calculated stress intensity factors and T-stress were then substituted into Eqs. (1) and (2) to obtain the dimensionless parameters Y i and T * as a function of 2 a /W, D/W and . The model used plane stress conditions in this research because the fracture coefficients are independent of the plane stress or plane strain state in 2-D context (Aliha and Saghafi 2013). 4. Results and Discussion Finite element calculations were made for a constant hole diameter to plate length ratio D/W = 0.4 with relative crack lengths 2 a /W varying from 0.5 to 0.8, and for a constant 2 a /W = 0.8 with D/W varying from 0.4 to 0.6. In the finite element models, the crack orientation angle was varied from 0 ° to 65 ° with intervals of 5 ° . Figs. 4 and 5 show