PSI - Issue 41

P.M.D. Carvalho et al. / Procedia Structural Integrity 41 (2022) 24–35 Carvalho et al. / Structural Integrity Procedia 00 (2019) 000 – 000

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2.5. Triangular CZM Although cohesive formulations can represent pure or mixed modes, the latter is present in most of the applications of adhesive joints. Although several cohesive laws exist, the triangular law provides a good representation of the actual behavior of adhesives in bonded joints (Campilho et al. 2013). In addition, the triangular law requires fewer parameters than other cohesive laws, easing the experimental work necessary to determine those parameters, and consequently its application within computational software (Campilho et al. 2013). Under pure mode, the triangular cohesive law relates the maximum force in traction ( t n 0 ) or shear ( t s 0 ) that the material sustains and the displacements at that instant ( d n 0 or d s 0 ). This first segment is linear with stiffness K . Then, a second line connecting that point to the corresponding failure displacement ( d n f , d s f ) represents the material degradation until fracture. The area beneath the whole curve is the respective toughness, i.e., G IC and G IIC (de Sousa et al. 2017). In mixed mode, both mode I (traction) and mode II (shear) contribute to material degradation until fracture; in this case, the stiffness ( K COH ) is a matrix relating the stiffness in traction ( E ) and shear ( G ) moduli with the strains in the respective directions (traction and shear). Finally, damage initiation is defined by a quadratic criterion combining the proportions of traction and shear stresses within an elliptic envelope, noting that compression does not contribute to damage initiation, and damage propagation is assessed by a linear power-law expression relating G I and G II with the respective limit values. This formulation is described with more detail in the literature (Rocha and Campilho 2018). 3. Results 3.1. Validation with experimental data A CZM validation is initially performed using the same geometry and loading presented in Section 2.2, and the same adherends and adhesives described in Section 2.1, but in single-adhesive conditions. Thus, the tested geometry is that presented in Fig. 1. The geometry, loading and boundary conditions are thus identical to those used in the numerical dual-adhesive study, and a positive validation of the numerical approach will enable its further application to different adhesive combinations. After fabrication and testing, the experimental data was treated and analyzed to provide the average P m and respective standard deviation, whose results were promptly compared to the numerical output for each t P2 . Fig. 5 depicts the experimental average/deviation of P m and respective CZM predictions for the SAJ with the 2015 and 7752.

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P m [kN]

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t P2 [mm]

Exp 2015

Num 2015

Exp 7752

Num 7752

Fig. 5 – Experimental and CZM comparison as a function of t P2 for the SAJ.

All failures initiated by cracking at x / L O =0 and subsequent growth towards the other edge. After specimen testing, the fracture surfaces were visually inspected, showing cohesive failures for all adhesives and t P2 . The fracture surfaces for both 2015 and 7752 were smooth, indicative of ductile fractures, with clear evidence of cohesive failures. Moreover, the L-component plasticized in the joints with the 2015 and t P2 =1 mm, and with the 7752 and t P2 =1 and 2 mm, although for this last joint it was below 0.1%. Independently of the adhesive, there is a marked P m increasing tendency with t P2 . The 2015 shows an increasing growth rate for higher t P2 , while P m for the 7752 grows linearly with