PSI - Issue 13

J Beswick et al. / Procedia Structural Integrity 13 (2018) 63–68

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Beswick et al. / Structural Integrity Procedia 00 (2018) 000 – 000

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3. Results and discussion

Results from the J-Q analyses of the fracture toughness data are shown in Fig. 2. The experimental data points are shown with marks along the loading lines derived by FE analysis. The failure curves with different probabilities are obtained with parameters  =0.62, k =1.54, calibrated with AR material (left plot). It is remarkable that the same parameters provide a good approximation to the failure points of PS material, when the average toughness of the high-constraint geometry is used in Eq. (2) (right plot). The average toughness of the intermediate-constraint geometry is on the predicted failure locus, with slight over-prediction of the average toughness of the low-constraint geometry. This outcome suggests that if the failure locus of a virgin material is known, i.e. the parameters for constraint-correction via Eq. (2) are available, then making constraint correction of a material with load history would potentially require only a high-constraint test to determine J c . The suggestion clearly requires further support by extensive experimental work, as the limited data points from 10 experiments are not sufficient to determine average toughness and spread with sufficient confidence.

Fig. 2. J-Q failure curves for as-received (left) and pre-strained (right) materials.

The average toughness values measured for AR material were J c ,0.4 =42.0 kJ/m 2 , J c ,0.05 =76.4 kJ/m 2 . The calibration of LA models is performed using the values for the high- and low-constraint geometries. This is based on the so-called constrain correlation plot, Fig. 3, where the relation between predicted average toughness values for different shape and plasticity correction parameters is examined. The parameter  ’ =  1 /  0 denotes the plastic zone region included in the Weibull stress calculation;  ’ =1 means integration points with  1 >  0 are included. Figure 3 (left) displays the constraint correlation for varying values of m . For a curve with fixed m , each point gives a pair of possible toughness values having the same Weibull stress, i.e. each point gives a single probability of failure. This calibration provided m =7.37. Figure 3 (right) illustrates the subsequent calibration of the plastic correction parameter,  in Eq. (5), providing an optimum value  =0.02. With a similar calibration the value of  in Eq. (5) was found to be  =1.5. In all cases the Weibull scale parameter,  u , was found around  2600 MPa. c ,0.2 =47.1 kJ/m 2 , J

Fig. 3. Constrain correlation plot between high- and low-constraint geometries: Calibration of shape parameter (left); Calibration of  in the micro-crack density model (right). Similar is the calibration of  in the exponential model.