PSI - Issue 18

Mehdi Mokhtarishirazabad et al. / Procedia Structural Integrity 18 (2019) 457–471 M. Mokhtarishirazabad / Structural Integrity Procedia 00 (2019) 000–000

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These samples were heat tinted and broken open to measure the final crack length optically (Fig. 10). Crack length measurement was conducted following ASTM 1820 standard, although the requirements for the shape of the crack front was not met. It was observed that significant crack tunnelling had occurred in these samples. A nine-point average procedure based on optical measurement of the crack extension was performed to validate the Δ a UC . The results are reported in Table 3. It was observed that crack extension was significantly underestimated by using the UC method, especially for high constraint samples. It was observed that difference between physical crack extension ( Δ a p ) and Δ a UC was alleviated for shorter cracks and thinner samples which have lower in- and out-of-plane constraint; it appears that the UC method is more accurate in this condition. For example, the error in estimating the Δ a UC for samples with thickness of 5 mm and a/W = 0.2 and the sample with thickness of 20 mm and a/W = 0.5 were 7% and 365%, respectively. To explain the higher accuracy of low constraint samples, one should explore the sources of errors in UC method when a ductile material is tested. Two of these sources are the magnitude of deformation and indentation of rollers in the contact area. As it can be seen from Fig. 9, by decreasing the initial crack length, the maximum CMOD (maximum deformation) for each thickness was almost halved. On the other hand, by decreasing the thickness, the samples went under lower loads. That is, by dividing the maximum load by the thickness of each sample (117 kN, 55 kN, and 26 kN divided by 20, 10 and 5 mm, respectively), it can be seen that the ratio also reduced from 5.85 to 5.2 from thickest to thinnest sample. This means that we applied lower load per unit of thickness in thinner samples, and as a result, lower indentation deformation in contact areas. Both factors (specimen deformation and indentation of the rollers) are perceived as sources of error for underestimating the crack length by UC (Steenkamp 1988). Therefore, reduction of these factors in low constraint samples, can be perceived as the reason for better estimation of the crack extension. The significant underestimation of crack extension can be the reason for unusual fracture behaviour in relation to loss of in- and out-of-plane constraint. Therefore, to evaluate a valid fracture toughness value for the samples being studied, it is essential to have an accurate and reliable estimation of the crack extension. Fig. 11b, shows the R-curves for the 10 mm thick samples. It can be seen that there are two regimes of behaviour: crack tip blunting at low extensions (less than 0.9 mm) and stable ductile crack tearing above 0.9 mm (Paris et al. 1979). However, the aforementioned under-prediction of the crack extension by the UC method has led to evaluating a steeper experimental blunting line for these samples. That is, if a line fits to the low crack extension data, it’s slope will be higher than the slop of the blunting line in R-curve (Eq. 1). With respect to 5 mm thick samples, shown in Fig. 11c, there is good agreement between the experimental and theoretical blunting behaviour. Following the ASTM routine for evaluating J Q , it was observed that by increasing the initial crack length, the estimated value of J Q increases for samples with 10 mm and 5 mm thickness (Fig.12). This suggests that the loss of out-of-plane constraint leads to lower crack growth resistance. It should be mentioned that, to obtain a valid J-R curve for 20 mm thick samples, a detailed FE analysis is required for modifying the compliance calibration function when samples experience considerable deformation. More details about the sources of errors when UC is using for crack length measurement at the presence of high deformation is discussed in the next section. Although there seems to be an agreement between the effect of loss of constraint – in-plane and out-of-plane – on the behaviour of stainless steel 316 at room temperature, any interpretation of such trends should be done after correcting the crack extension. In both cases the resistance curve seems to decrease as the constraint decreases (as depicted in Fig. 12). A possible explanation for this behaviour is that the fracture mechanism of the material at this temperature is judged to be shear – in which the von-Mises stress is the dominant contributor. The loss of constraint lowers the stress triaxiality, therefore increasing the share of von-Mises stress compared to that of hydrostatic stress at any given energy level promoting fracture. Fig. 13 shows how the critical stress intensity factor changes by specimen thickness (Adams, Lai and Ferguson 1986). It can be seen that by decreasing the thickness of a specimen, the contribution of shear fracture increases until a critical thickness in which K C hit a pick. Further thickness reduction results in a drop in K C , where pure slant fracture occurs (Anderson 2017; Adams, Lai and Ferguson 1986). It could be argued that, as the material approaches plastic collapse, it becomes more likely that shear type of fracture becomes the dominant failure mechanism.