Issue 50

B. Benamar et alii, Frattura ed Integrità Strutturale, 50 (2019) 112-125; DOI: 10.3221/IGF-ESIS.50.11 114 subsequently selected in the common plane between the plates, introducing the parameters of rupture of the adhesive. During loading, plate separation occurs when the failure conditions are satisfied. The cohesive law initially contains a linear regime up to a stress threshold that initiates a softening as the surfaces move away from each other until a separation translated by a null rigidity [22]. The stiffness parameter inputs (K nn , K ss and K tt ) required by ABAQUS® are the module of the cohesive (E, G) material divided by its thickness [23]. When K nn = Young’s modulus / thickness of adhesive layer in normal direction; K ss = Shear’s modulus / thickness of adhesive layer in tangential direction 1; K tt = Shear’s modulus / thickness of adhesive layer in tangential direction 2. A linear constitutive relationship between stresses (σ) and relative displacements (δ) is established (Fig. 1). Figure 1 : The linear softening law for mixed-mode cohesive damage models. The model requires the knowledge of the local strengths (σ u,i , i = I, II, III) and of the critical strain energy release rates (G IC ). Damage onset is predicted using the following quadratic stress criterion: 2 2 2 1 1 1 if 0 = 0 if 0 I II III uI uII uIII                                (1) Where σ i (i = I, II) represent the stresses at a given integration point of the interface finite element in each mode. Mode I represents the local opening mode and mode II, III the shear mode at the interface. Crack propagation was simulated by the linear energetic criterion. 1 I II III IC IIC IIIC G G G G G G                      (2) The area under the minor triangle of Fig.1 represents the energy released in each mode, while the bigger triangle area corresponds to the respective critical fracture energy. When Eqn. (2) is satisfied damage propagation occurs and stresses are completely released, with the exception of normal compressive ones [24]. This energy is based on the cohesive damage evolution and it is defined using the Benzeggagh–Kenane criterion [25], with a linear softening law. Fracture energies of G I = 0.3N/mm and G II = 0.6N/mm are used for normal (Mode I) and shear (Mode II and Mode III) cohesive failures respectively as used by Campilho et al. [26]. The introduced parameters in the calculation code Abaqus are: ** MATERIALS ** *Material, name=Cohesive *Damage Initiation, criterion=QUADS