PSI - Issue 2_A

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Timothy Crump et al. / Procedia Structural Integrity 2 (2016) 381–388 Crump / Structural Integrity Procedia 409 (2016) 000–000

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With this we can say as long as h min < l c then the cohesive zone can be resolved with typically 2 or more elements in the zone. And if a length between two cohesive surfaces through a cohesive law is such that δ c >> h min then, the crack path can be considered independent of the mesh. The main advantage of XCZM compared to standard FEM methods is that crack propagation is dynamically informed, enabling the capture of changes in crack shape profile due to the extra inertia from reflected waves and dynamic crack initiation. XCZM is implemented via an algorithm in Code_Aster, Ferté (2014). While considering Fig.3, the procedure for this is as follows: given a potential crack surface, the equilibrium state is computed with the quasi-explicit approach (b), the crack front is then updated based on the computed cohesive state (c), an angle of propagation is then determined along the crack front (d), the potential crack surface is then updated accordingly (e) and then the cohesive internal variables are corrected (a).

Fig. 3. XCZM propagation algorithm, Ferté (2014).

3. Results The experiment modelled had a DCB with an initial low constraint blunt notch, exposed to a loading and the subsequent fracture patterns observed, as in Fig.4(a), Kobayashi (1985). The initial material properties for this were known to be: Young’s modulus E = 32GPa, Poissons ratio υ = 0.2, mass density of ρ = 2450 kg/m 3 and also an applied loading in the material’s y-axis direction of σ y = 1 MPa, as in Fig.4(b). The initial rigid cohesive zone parameters used in line with Song (2008) were σ c = 28MPa and G c = 3Jm -2 . It was noted in the experiment that after a period of self-similar growth the macro-crack branched into two symmetrical crack paths with a bifurcation angle of 8 o with a calculated branching stress intensity factor K Ib = 3.2 MPa√m for the single edge notched specimen, Kobayashi (1985).

(b)

(a)

Fig. 4. (a) Experimental result for Homolite-100; (b) DCB schematic with initial blunt crack used for the XCZM model.