PSI - Issue 18

Roberta Massabò et al. / Procedia Structural Integrity 18 (2019) 484–489 Author name / Structural Integrity Procedia 00 (2019) 000–000

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The energy release rate for the propagation of the delaminations is calculated using different techniques: the J integral and the compliance method. For homogeneous edge-cracked layers and bi-material beams with a single delamination, the J-integral can be expressed in closed form in terms of the sub-resultants acting at the cross sections of the different beam arms and the solution coincides with predictions made using classical discrete layer models. More details on the model and applications to a number of relevant problems are in (Massabò and Darban, 2019).

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Fig. 1. (a) Multiply delaminated layered beam and homogenized description. (b) Interfacial traction law to reproduce perfectly brittle fracture.

3. Single and multiple, mode II dominant delamination fracture of layered beams Some applications of the homogenized model to simply supported and cantilever bend beams, shown in Fig. 2, are presented in this section to highlight the capability of the model to analyze single and multiple mode II dominant delamination fracture. The results confirms that the model, which uses only three displacement variables as a classical single layer theory, is able to describe the discrete event of brittle delamination fracture, reproduce interaction effects of multiple delaminations and follow unstable delamination growth.

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Fig. 2. (a) Three-point bend-beam and homogenized model used for the comparison with the experimental results in Fig. 3. (b) Cantilever beam with two delaminations and homogenized model, used to study the interaction of multiple delaminations in Fig. 4.

Fig. 3 shows the macro-structural response of a unidirectionally reinforced End-Notched Flexural specimen, shown in Fig. 2a with (2) (1) h h h   and materials #1 = #2 through the critical load for crack propagation versus load-point deflection. The critical load has been obtained using the fracture criterion II IIC  G G , with II G the energy release rate. The dimensionless critical load per unit width is given by   2 / 4 / 3 / cr IIC P hE h a  G and coincides with that obtained using classical structural mechanics approaches. The 2D solution of the problem, ,2 cr D P , has additional terms, which