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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2001 (Rao & Rahman 2001). They employed the EFG and FEM to study the material behaviour in the vicinity of the crack and in areas far away from the crack, respectively. Therefore, the SIF was evaluated for the mode I and II loading states for the 2D cracked models. This preliminary work aims to determine the mode I SIF range, ∆ I , the crack propagation and strain fields on the specimen. For this purpose, DIC was used to analyse the experimental data. Besides, the problemwas resolved through two advanced discretisation techniques, FEM and Radial Point Interpolation meshless (RPIM) methods to assess the performance of the numerical approaches. The SIF was therefore calculated from the captured data together with an overdeterministic algorithm. An acceptable agreement amongst all obtained results was accomplished. 2. Analysis A standard CT specimen (as shown in Fig. 1) was used for a cyclic fatigue crack growth test. It is desirable to measure the mode I SIF range, (∆ ), for a variety of crack lengths where the specimen is loaded under tensile state. According to the Standard Test Method for Measurement of Fatigue Crack Growth Rates (ASTM International 2015), the following expression is applicable to calculate ∆ for a fractured CT specimen: ∆ = ∆ √ (1− 2 + ) 3⁄2 (0.886 + 4.64 − 13.32 2 + 14.72 3 − 5.6 4 ) (1)

Fig. 1. A standard CT specimen where W and B are the specimen width and thickness, respectively. In addition, ∆ presents the applied load range and a is the crack length measured in each cyclic fatigue stage. In this case, was measured as = 8.46 ( ) . The presented expression is valid for ⁄ ≥ 0.2 (Newman 1974; Srawley E. 1976). The initial crack size and maximum crack extension is evaluated where the uncracked ligament ( W-a ) is greater than the maximum acceptable SIF. So, ∆ for any crack length derived from Equation (1) was used to verify the experimental and numerical models. In addition, the internal fields obtained from numerical analyses are compared with the experimental DIC one. To compute SIF from experimental DIC data, a numerical algorithm was defined to process the strain field extracted from DIC. This function joins the overdeterministic SIF calculation algorithm and the stress computation based on the principal stresses in the vicinity of a straight front crack under mode I conditions. For the plane problem of a homogeneous isotropic solid, Williams expansion series for plane stress state were used where the significance of is demonstrated in Equation (5), (Williams & Pasadena 1957). = ∑ ( 2 ) 2 −1 {[2 + (−1) + 2 ] ( 2 − 1) − ( 2 − 1) ( 2 − 3) } ∞ =1 (2) = ∑ ( 2 ) 2 −1 {[2 − (−1) − 2 ] ( 2 − 1) + ( 2 − 1) ( 2 − 3) } ∞ =1 (3)