Issue 48

J.P.S.M.B. Ribeiro et alii, Frattura ed Integrità Strutturale, 48 (2019) 332-347; DOI: 10.3221/IGF-ESIS.48.32 339 were applied at the opposite edge. In the following Section, the triangular CZM formulation, applied in all models and incorporated in Abaqus ® , is presented. Figure 5: Mesh detail for the L O =25 mm double-lap joint (CZM failure analysis). Mixed-mode triangular model CZM are based on a relationship between stresses and relative displacements (in tension or shear) connecting paired nodes of cohesive elements (Fig. 6), to simulate the elastic behaviour up to t n 0 in tension or t s 0 in shear and subsequent softening, to model the degradation of material properties up to failure. The shape of the softening region can also be adjusted to conform to the behaviour of different materials or interfaces [35]. The areas under the traction-separation laws in tension or shear are equalled to G IC or G IIC , by the respective order. Under pure loading, damage grows at a specific integration point when stresses are released in the respective damage law. Under a combined loading, stress and energetic criteria are often used to combine tension and shear [36]. The triangular law (Fig. 6) assumes an initial linear elastic behaviour followed by linear degradation. Elasticity is defined by a constitutive matrix ( K ) containing the stiffness parameters and relating stresses ( t ) and strains (  ) across the interface [37] n nn ns n s ns ss s . t K K t K K                         K t  (4) t n and t s are the current tensile and shear tractions, respectively, and  n and  s the corresponding strains. A suitable approximation for thin adhesive layers is provided with K nn = E , K ss = G xy and K ns =0 [25]. Damage initiation can be specified by different criteria. In this work, the quadratic nominal stress criterion was considered for the initiation of damage, already shown to give accurate results [25] and expressed as [37] n s n s 2 2 0 0 1. t t t t               (5) are the Macaulay brackets, emphasizing that a purely compressive stress state does not initiate damage. After the mixed- mode cohesive strength is attained ( t m 0 in Fig. 6) by the fulfilment of Eqn. (5), the material stiffness is degraded. Complete separation is normally predicted by a linear power law form of the required energies for failure in the pure modes by considering the power law exponent  =1 [37] I II IC IIC 1. G G G G                 (6) R ESULTS Fracture envelopes of the adhesives he present Section aims at estimating the most suitable propagation criterion exponent using the fracture envelope analysis. With this purpose, the pure-mode toughnesses ( G IC and G IIC ) and mixed-mode toughnesses ( G I and G II ) are first required. T