PSI - Issue 47

Francesco Ascione et al. / Procedia Structural Integrity 47 (2023) 826–841 Author name / Structural Integrity Procedia 00 (2019) 000–000

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� � 1

� � �

(3)

The damage variable D assumes the following expression: �� � � � � � � � � � � (4) where is the current sliding. From Eqn. (4), it is easy to verify that if � � , the damage variable is equal to zero; while, if � � , the damage variable is equal to 1 (corresponding to complete separation between adherents, which are no more connected by adhesive layer). The latter condition (D =1) corresponds to satisfying the following linear fracture criterion here adopted: �� �� , � � � 1 (4) The symbol �� represents the work done by the traction (shear stress) and its conjugate relative displacement (sliding). 3.3 Load-bearing capacity and governing parameters To faithfully reproduce the ENF experimental procedure, used to evaluate the fracture energy in mode II of the two resins under investigation, the numerical analyses were carried out using displacement control. In order to build the typical load vs displacement curve of a ENF test, the following governing parameters were fixed: the adhesive fracture energy, �� , � � , and the shear limit stress, � , as material parameters for the adhesive layer and the longitudinal Young modulus of the adherents, � , as the material parameter for the pultruded members. Preliminary, a parametric study on the influence of each parameter on the load-bearing capacity of the ENF joint was conducted. Based on adhesives commonly used for civil engineering applications, the following ranges of values for the fracture energy, the ultimate shear stress and the Young modulus along fiber direction were adopted: 0.5 � �� , � � � 10.0 (5a) 5.0 � � � � 50.0 � (5b) 10000.0 � � � � 30000.0 � (5c) In Figure 9, the maximum load ( ��� ) vs limit shear stress ( � ) curves are reported as the fracture energy increased. For low values of the fracture energies (0.5-1.5 N/mm), no significant differences in terms of load ��� are recorded when varying the shear strength. On the contrary, for high values of the fracture energy, significant differences in terms of load ��� , are recorded. Similar trends were found in [Xu et al 2012]. Furthermore, in order to verify that the fracture energy in mode I had no effects on the results obtained, the graph of Figure 9 was replaced twice obtaining the same result: � , � � was assumed equal to 1 N/mm and 100 N/mm.