PSI - Issue 5

Behzad V. Farahani et al. / Procedia Structural Integrity 5 (2017) 920–927 Behzad V. Farahani et al./ Structural Integrity Procedia 00 (2017) 000 – 000

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= ∑ ( 2 ) 2 −1 {− [(−1) + 2 ] ( 2 − 1) + ( 2 − 1) ( 2 − 3) } ∞ =1 (5) Since for Mode I the relevant stress is the opening stress , , the algorithm will be applied using this component. So, only Equation (3) of the Williams expansion series is considered in the present study. 2. Experimental Procedure A pre-cracked CT specimen made of Aluminium alloy AA6082-T6 was chosen for this study. It has the dimensions = 40 [ ] and thickness = ⁄20 = 2 [ ] . The material properties were considered as: Young’s modulus = 70 ( ) and Poisson’s ratio = 0.33. A set of DIC cameras was setup to acquire the strain data on the cracked region. DIC cameras were positioned in front of the specimen with a horizontal distance of l = 1000 (mm). Considering ∆ = − , = ∆ ⁄2 , = ( + )⁄2 and = ⁄ , the loading specifications are demonstrated in Table 1. Table 1: Loading conditions. 670 ( ) 67 ( ) 0.1 302 ( ) 380 ( ) 15 ( ) After reaching 170,000 fatigue cycles, the minimum allowable crack size was obtained as ≅ 3.2 , therefore the strain field was captured for seven crack lengths. 3. Numerical Analysis Crack propagation is a significant concept in fracture, fatigue and damage mechanics. Hence, numerical simulations are required to anticipate the failure phenomenon. The computational approaches are applicable to perform the numerical simulation so, the fracture response and the reliability of cracked constructions are determined. The finite element formulation is appropriate for elastic plate problems, nevertheless it is not suitable to handle stress singularities in its conventional formulation (Carpinteri & Paggi 2007). Thus, meanwhile, special elements were developed to tackle the singularities caused by cracks (Byskov 1970). The model was solved through FE and RPIM formulations presented in this section. To obtain a verification of the experimental solution, the model was solved using FEM formulation. It was simulated with an available commercial software, ABAQUS, to evaluate the interesting results such as SIF range, strain field and in particular the strain variation in front of the crack tip. Thus, it is possible to compare the obtained FEM results with the experimental solution. An explicit model was thereby considered in ABAQUS where a 2D plane stress shell was applicable. Moreover, standard 4-node bilinear plane stress quadrilateral elements (CPS4R) were used to form the mesh in which the element size range is between 0.5 and 1 millimeters with a total number of 3927 and 3927 elements and nodes, respectively, see Fig. 2-a. More refined elements were considered in the cracked region where an intended region with a dimension of 7 by 7 millimeters was considered close to the crack tip as shown in a dash-line square in Fig. 2-a. The material and geometric properties were used same as the experimental test and the loading conditions were followed based on Table 1. Besides, two reference points ( 1 and 2 ) were assigned to the model, located in the center of two holes, and they were therefore kinematically coupled with the corresponding holes. They were constrained to the displacement field in x and y directions. Regarding the essential boundary condition, the (4) 1 = √2 3.1. FE Study