PSI - Issue 33

A.F.M.V. Silva et al. / Procedia Structural Integrity 33 (2021) 138–148 Silva et al. / Structural Integrity Procedia 00 (2019) 000–000

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2.4. CZM description Relationships among stresses and relative displacements linking similar nodes of cohesive elements are the fundament of the CZM. Additionally, those relations (often entitled CZM laws) may be established in pure and mixed mode and make possible to capture the material’s behavior up to failure (Luo et al. 2016). This study relies on triangular pure and mixed-mode laws to model the adhesive layer (Fig. 4).

Fig. 4. Mixed-mode triangular CZM law used in Abaqus ® (Abaqus® 2013)

Under pure-mode loading, damage initiation occurs when the cohesive strength in tension or shear ( t n 0 or t s 0 , respectively) is attained, i.e., the material’s elastic behavior is cancelled and degradation starts (Sane et al. 2018). Furthermore, the crack propagates up to the adjacent pair of nodes when the values of current tensile or shear cohesive stresses ( t n or t s , respectively) become null. Under mixed-mode loading, stress and/or energetic criteria are often used to combine the pure-mode laws, and damage begins when the mixed mode cohesive strength ( t m 0 ) is reached (Dimitri et al. 2015). Several criteria are available for damage initiation and growth when the analysis encompass mixed-mode loadings. Nevertheless, this study focused on the quadratic nominal stress criterion and a linear power law form for the damage initiation and growth, respectively. This model is described in detail in the work of Rocha and Campilho (2017). The adhesives’ properties used in Abaqus ® are depicted in Table 1 and Table 2, considering t n 0 and t s 0 as the values of  f and  f described in Section 2.1, respectively. 3. Results 3.1. Experimental validation To validate the numerical model used for tubular joint analysis, validation with experiments was undertaken considering a SLJ geometry, using the same adhesive and DIN 55 Si7 steel adherends. Numerical modelling was undertaken similarly to the description of Section 2.3, except for the consideration of 2D models using CPE4 solid elements for the adherends and COH2D4 cohesive elements for the adhesive. For further details on the experimental and numerical parts of the validation study, reference (Valente et al. 2019) can be consulted. Aiming to validate the CZM technique, P m and the displacement at P m (  P m ) were compared with the reference experimental values. Fig. 5 shows the P -  curve (a) and P m and  P m (b) comparison between the experimental tests and CZM validation. The P -  curves of Fig. 5 (a) reveal a marked difference between both results. Data collected from the experimental procedure showed a marked increase in the failure displacement (567.8% compared to the numerical curve). That result is, however, influenced by the technique implemented by the impact test equipment. Actually,  is obtained from integration of accelerometer data, which can lead to an offset by excess of the experimental  . The experimental P m is lower than that obtained from the numerical model. This difference is however attributed to the perfect bonding assumption in the numerical simulations, uniform bond thickness and absence of flaws. Manufacturing variability is also not accounted with numerical models. Fig. 5 (b) quantifies the observed differences, and shows that the numerical P m result is 15.8% higher than the experimental value. The differences between the experimental and numerical P m results can be explained by the fact that it is complicated to experimentally reproduce the numerical conditions. Some