PSI - Issue 28

6

Domenico Ammendolea et al. / Procedia Structural Integrity 28 (2020) 1981–1991 Author name / Structural Integrity Procedia 00 (2019) 000–000

1986

Fig. 3. A schematic of the propagation process

Simultaneously, crack onset conditions and the angle of crack propagation are determined by a classic fracture criterion ( e.g. the maximum hoop stress, the maximum strain energy release rate, or the minimum strain energy density criteria). When onset conditions are satisfied, the propagation process starts, and the evolution of internal discontinuities are reproduced by the ALE method, according to Eq.s (3)-(6). Additional constraint conditions are implemented in the numerical model to avoid the shape variation of pre-existing cracks, thereby simulating the formation of new crack surfaces exclusively. This condition is ensured by inserting an additional node along the pre existing crack close to the crack tip thus, forming a short segment. This segment is stretched during the propagation process as long as the variation angle is lower than a fixed tolerance value ( toll  ). Once that the tolerance condition is met, a new definition of computational nodes is required and the configuration of the structure achieved during the last step of the propagation process would be used as new geometry for the problem, thus re-starting from the first step of the script. It is worth to note that, during the propagation process, the movement of computational nodes produces mesh distortions, thereby requiring the use of a re-meshing algorithm to form a new regular mesh configuration. Re-meshing events occur when element distortion, assessed through a mesh quality parameter, is lower than a fixed tolerance. This feature reduces the re-meshing process, thus providing relevant computational savings. 4 Results In this section, numerical results are developed aiming to assess reliability and efficiency of the proposed method. Two case of studies are analyzed, in terms of comparisons with experimental and numerical data available from the literature. In both the analyzed cases, geometries are discretized with 6-node triangular elements, and simulations are performed under plane-stress conditions, assuming linear elastic materials. Propagation processes are performed by means of incremental static analyses according to a displacement-based approach, i.e. by evaluating the increment of external loads that produce the prescribed displacement variations of a selected control point. The crack propagation is described by using the ALE approach presented in the previous Section 2.1, whereas the maximum circumferential stress criterion (Erdogan and Sih (1963)) is selected to determine crack initiation conditions and the direction of crack propagation. A double cantilever beam Fig. 4-a illustrates a pre-cracked double cantilever beam of length 300 mm and height 100 mm subjected to two vertical and opposite distributed loads (q) at the free extremity. The pre-crack develops along the half-height of the beam and comprises a straight segment of 138 mm followed by a short branch inclined downwards of 2.6°. The material properties are E=200 GPa (Young’s Modulus) and  =0.3 (Poisson’s ratio). This case has been investigated experimentally by Sumi and Kagohashi (Sumi and Kagohashi (1983)) adopting sample beams made of PMMA. The crack propagation has been reproduced numerically using both mesh-based and meshfree methods. In particular, Ventura et al. (Ventura et al. (2002)) have simulated the crack path using a vector level set approach in the EFG 4.1