PSI - Issue 39

M.R.M. Aliha et al. / Procedia Structural Integrity 39 (2022) 393–402 Author name / Structural Integrity Procedia 00 (2021) 000–000

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Fig. 1. BI-SBB specimen geometry with initial crack used for the numerical model.

Table 1. Material properties of adherents utilized for manufacturing the BI-SBB specimen [7]. Material Properties Alumina Aluminium alloy Elastic modulus E (GPa) 300 70 Poisson’s ratio, ν 0.21 0.33 Fracture toughness K Ic (MPa √m) 3.5 29

Table 2. Material properties of adhesive utilized for manufacturing the BI-SBB specimen [8]. Property Araldite AV138 Young’s modulus, E [GPa] 4.89 Poisson’s ratio, ν 0.35 Tensile failure strength, [MPa] 39.45 Shear failure strength, [MPa] 30.2 Toughness in tension, [N/mm] 0.20 Toughness in shear, [N/mm] 0.38

3. Theoretical investigation of crack growth 3.1. J-integral method The J integral was proposed by Rice [9] in 1968. He demonstrated that the energy release rate can be described as a line integral along any arbitrary contour surrounding the crack. Rice named this quantity the J integral. It is worth noting that the J integral method has been proved to achieve correct results for the fracture parameters of linear elastic materials and epoxy adhesive material [10,11]. In this study, a crack was assumed to be created in the adhesive part, and this part is considered to behave as a linear elastic material. Therefore, by using J integral method, the fracture parameters can be calculated in the ABAQUS software. In ABAQUS software, this parameter is determined by the maximum tangential stress (MTS) criterion, proposed by Erdogan and Sih [12]. Based on the MTS criterion, the stress field in the vicinity of crack tip can be expressed as: = 1 √ 2 2 [ 2 2 − 3 2 ] (1) = 1 √ 2 2 [ + (3 − 1)] (2) where and are the crack tip coordinates found at the crack tip, and and are related to the singular terms of Williams series expansion [13]. The direction of crack propagation can be obtained using either the condition = 0 or = 0 i.e.,