PSI - Issue 47

J.E.S.M. Silva et al. / Procedia Structural Integrity 47 (2023) 70–79 Silva et al. / Structural Integrity Procedia 00 (2019) 000 – 000

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Fig. 3. Boundary conditions applied to the model and details of partitions in the bond-line to aid the meshing.

3.2. CZM description In the adhesive joints’ case, the triangular cohesive law has been found suitable to model the behaviour of structural adhesives (Campilho et al. 2013). Moreover, the number of parameters required to establish a triangular cohesive law is the lowest in comparison with the other cohesive law shapes. A triangular cohesive law is depicted in Fig. 4. Under pure mode loading, the cohesive traction ( t n ) increases linearly until reaching a maximum value, t n 0 corresponding to  n 0 that is the onset displacement. Once t n 0 is reached, the stiffness decreases linearly until t n =0, corresponding to the maximum displacement  n f . Although this description corresponds to the traction case, the shear case is similar, being the terms t s 0 ,  s 0  and  s f .

Fig. 4. Triangular cohesive law.

The area beneath the t n -  n curve, coloured in grey in Fig. 4, corresponds to the energy dissipated in the process or G IC (Alfano 2006). Under pure mode II, G IIC should be considered instead. Under mixed mode, each individual mode contributes to material degradation until fracture. Therefore, the stiffness in mixed mode corresponds to a matrix, K COH , which relates to the stiffnesses in pure mode, as follows.

n s       =    t t

nn K K K K ns

n        s  

n       s  

1

sn

, with

,

(1)

=



T

ss

o

where T o is the original thickness of the cohesive element. This formulation is described in detail in the references (de Sousa et al. 2017). Then, a quadratic stress criterion is employed to combine traction and shear stresses, which combination leads to damage initiation. However, the criterion assumes that compression does not contribute to