PSI - Issue 42

10

Diego F. Mora et. al./ Structural Integrity Procedia 00 (2019) 000 – 000

Diego F. Mora et al. / Procedia Structural Integrity 42 (2022) 224–235

233

(a)

(b)

Fig. 8. Experimental results reported in (Merkert 2002). (a) Fractograph of the crack with crack arrest indicated; (b) Average COD measured.

In order to simulate the crack propagation, the critical stress criterion for the initiation of damage in Eq. (6) was applied. For that, the value of Ic K is substituted by Eq. (1) and the resulting equation is implemented in a UMDGINI subroutine. Thus, the XFEM can be customized in ABAQUS in order to incorporate the temperature dependence of the fracture toughness. In addition, in the case of linear facture mechanics, the energy release rate can be directly related with the fracture toughness as follows:

2

K

(8)

Ic G =

' Ic

E

The propagation criterion is defined as the instant when the energy release rate is larger than the critical energy release rate given in Eq. (8). The simulation was performed for two different cases: Case 1 Constant critical energy release rate for all temperatures Case 2 Temperature dependent critical energy release rate It is also of interest to analyze the effect of the mesh on the crack propagation. Therefore, two meshes were analyzed; Mesh 1 and Mesh 2 with average size 0.5mm and 0.25m, respectively. The numerical solutions for the crack propagation in case 1 for the two refinements are represented in Fig. 9 at the end of the simulated time. Here, only the refined region of the mesh where the initial defect is located is shown. It seems that the crack propagates along the thickness of the cylinder for the two refinements of the mesh considered. The assumption of having a constant critical energy release rate appears to be inappropriate to simulate the propagation since such an approximation pretends a crack grows regardless the local temperature at the crack tip.

(a)

(b)

Fig. 9. Crack propagation of the initial flaw in the test cylinder for case 1 (a) mesh 1; (b) mesh 2.

The simulation is repeated using the meshes in Table 4 but taking the temperature dependent critical energy release (case 2) into account. The results are summarized in Fig. 10, which shows the crack advance for different times on the central region of the cylinder. The crack is presented over the temperature contours at each time. Temperature ranges from 14°C to 250°C as indicated in the color bar on the right. The result for the simulation considering constant