PSI - Issue 33

Domenico Ammendolea et al. / Procedia Structural Integrity 33 (2021) 858–870 Domenico Ammendolea et al./ Structural Integrity Procedia 00 (2019) 000 – 000

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However, the total number of remeshing events between the two mesh arrangements is rather comparable. Such results may be explained because of the local refinement that both the mesh frames have in the region close to the crack tip. As far as the size of the finite elements in the neighbor of the crack tip decreases, remeshing events increase. By comparing the meshes in Fig. 4-b, one observes that the refined zones are rather similar, thus explaining the limited difference in terms of remeshing events. From these results, one can conclude that the proposed strategy requires refined mesh only in the region around the crack tip. This advantage permits performing numerical simulations without spending huge computational resources because the mesh adapts its geometry according to the evolution of the crack trajectory. This case serves as a suitable test to check the ability of the proposed strategy to predict crack propagation mechanisms in an articulate geometry under complex boundary conditions. Specifically, simultaneous mechanical and thermal loadings are considered. Fig. 6-a shows a cruciform plate with square arms of length L=1000 mm, having an initial sloped pre-crack a 0 =0.2L in the bottom-right corner of the core region. The Young’s modulus, Poisson’s ratio, and coefficient of thermal expansion are E=218400 Pa,  =0.3, and  = 1.65e-5 1/°C. The plate is subjected to temperature T=+20°C and T=-20°C on the top and bottom boundaries, respectively. In addition, a uniform traction  =10 Pa acts on AB. The remaining boundaries ( i.e. , H-G, F-E, and C-D) have kinematic constraints that admit sliding translations only. The crack faces are adiabatic. Fig. 6-a depicts the mesh frame used in numerical simulations. Such a frame involves 824 triangular elements arranged finely around the crack tip and coarse in the remaining part of the plate. The short segment that stretches during the simulation is 20 mm length and comprises 4 elements of equal size (see the zoomed view in Fig. 6-b). Fig. 7-a compares the crack trajectories achieved by the proposed strategy and the results developed by Prasad et al. (Prasad et al. (1994)) and Chen et al. (Chen, Wang, Liu, Wang and Sun (2016)), which have used the Boundary Element Method (BEM) and the Singular Edge-based smoothed Finite Element Method (ES-FEM), respectively. The results show that the proposed strategy agrees with the predictions achieved by the other authors. The agreement occurs also in terms of Stress Intensity Factors, as reported in Fig. 7-b. Fig. 8-a and b illustrate the motion of the mesh frame and the evolution of the temperature field during the propagation process. The snapshots correspond to the analysis steps marked in Fig. 8-a by roman numerals. It transpires that the propagation depicted by the proposed approach involves the progressive refinement of the mesh along the crack trajectory, then only where it is necessary. This ability ensures a considerable saving of computational resources. Besides, the results denote the influence of the growing crack on the temperature field. Since the crack faces are adiabatic, the crack advance alters the thermal distribution, as one can see by observing the evolution of the isothermal lines in Fig. 8-b. 4.2 A pre-cracked cruciform plate subjected to thermo-mechanical loadings

Fig. 6. Cruciform plate under mechanical and thermal loadings. (a) A schematic of the geometry. (b) Mesh frame adopted