PSI - Issue 26

Victor Rizov et al. / Procedia Structural Integrity 26 (2020) 97–105 Rizov / Structural Integrity Procedia 00 (2019) 000 – 000

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The partial derivative in the first integral in (11) is determined as: ( ) 1 1 1 1 n z z x u = = −     ,

(22)

1 1 n z are obtained from equations (13) and (14).

where 1  and

The strain energy density, 0 u , is written as

2 1

0 = u

 .

(23)

After substituting of (18) – (23) in (11), the integration is carried-out by the MatLab computer program. The solution to the J -integral in segment, B , of integration contour is found in analogical way. The J -integral value is found by substitution of 1 A J and B J in (12). It should be mentioned that J -integral value obtained y (12) matches exactly the strain energy release rate derived by the compliance method (9). This fact verifies the fracture analysis developed in the present paper. It should also be noted that the solutions to the strain energy release rate and the J -integral derived in the present paper are time dependent since the damage zone depth is function of the time. Parametric study is performed in order to analyze the influence of the damage zone, the material inhomogeneity and crack location along the beam height on the lengthwise fracture behaviour of the beam configuration shown in Fig. 1. For this purpose, the strain energy release rate is calculated by applying the compliance method (9) and the results obtained are presented in non-dimensional form by using the formula ) /( G G E b UL N = . In these calculations, it is assumed that 0.02 = b m, 0.035 = l m, 0.003 = h m and 200 = F N. Also, the crack location is characterized by h h / 2 1 ratio (Fig. 1). Calculations of the strain energy release rate are carried-out at various values of the time in order to analyze the effect of the time on the lengthwise fracture behaviour. The strain energy release rate in non-dimensional form is plotted against the non-dimensional time in Fig. 3 at three h h / 2 1 ratio. The curves in Fig. 3 indicate that the strain energy release rate increases with the time. It can also be observed in Fig. 3 that the strain energy release rate decreases with increasing of h h / 2 1 ratio. 3. Parametric study

/ 2 0.25 1 = h h , curve 2 –

Fig. 3. The strain energy release rate in non-dimensional form plotted against the non-dimensional time (curve 1 – at

at / 2 0.50 1 = h h and curve 3 – at / 2 0.75 1 = h h ).