PSI - Issue 60

P.K. Sharma et al. / Procedia Structural Integrity 60 (2024) 335–344 P.K. Sharma/ Structural Integrity Procedia 00 (2023) 000 – 000

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2.2. Evaluation of crack growth using unloading compliance technique

Unloading compliance method is used for determination of crack growth at a particular load-line displacement. In this method, loading and unloading of the specimen is carried out and the slope of elastic unloading curve is noted. This slope gets reduced with increasing crack growth due to reduction in stiffness of specimen. The change in the elastic unloading curve is then used for estimating the crack growth. For each load-line displacement, the unloading compliance values can be calculated using the correlation (Eq. 1) between effective crack lengths to width ratio. = [ 0 + 1 + 2 2 + 3 3 + 4 4 + 5 5 ] (1) where, = √ 1 +1 (2) where, B is width of the specimen, Ci = elastic compliance for specimen and the effective thickness is B e is equal to B − (B − B N )/2B, B N is the net thickness after side- grooving of the specimen, E is Young’s modulus. c 0 -c 5 are the material constant taken from Cravero et al. (2007). The crack growth and load-displacement data of the SENT specimen has been used for evaluating the fracture resistance behavior of the material in the subsequent section. 2.3. Evaluation of crack growth using unloading compliance technique J-integral has been used for evaluating the fracture resistance behavior of the material. The area under load displacement curve and geometric factors (η and γ) have been used for determination of J -integral. For evaluation of fracture resistance, total energy release rate is divided into elastic and plastic parts. The total value of J-integral is expressed as = + (3) where J el = elastic component of J, and J pl = plastic component of J. Here the elastic component of J is calculated as = 2 ′ (4) where ′ is equal to 1− 2 , E is Young’s modulus of elasticity of Alloy 690 material K I denotes the Mode I elastic stress intensity factor for the SENT specimen and it is a function of the a/W ratio. = √ ( ) (5) where ‘P i ’ is the load applied on the SENT specimen at step ‘i‘, ‘B’ is the specimen thickness, and ‘W’ is total width of the specimen. The geometric function for evaluation of elastic stress intensity factor is given in Eq. (6). ( )= ∑ 12 =1 (6) where coefficients are taken from Huang et al. (2014). The plastic part of J-integral is evaluated through the use of η factor and the plastic area (A pl ) obtained through the load-displacement curve as shown in Eq. (7). = [ −1 + −1 −1 ( ( ) − ( −1) )] × [1 − −1 ( − −1 −1 ) ] (7) where is initial uncracked ligament, and value for SENT specimen is taken from Huang et al. (2014).