PSI - Issue 28

M.Z. Sadeghi et al. / Procedia Structural Integrity 28 (2020) 1601–1620 M.Z. Sadeghi et al./ Structural Integ ity P ocedia 00 ( 019) 0 0–0 0

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Fig. 18. SDEG variable in cohesive elements with a bondline thickness (left) t a = 0.20 mm and (right) t a = 0.90 mm at onset of damage.

In the case presented above, over prediction of G C leads to over prediction of P m as a function of bondline thickness t a . This is evident from Fig. 18, the distribution of SDEG (Scalar stiffness deformation variable) is more uniform in case of bondline thickness t a equal 0.20 mm. The difference between the experimental and the predicted FE results can be attributed to different reasons which are discussed below:  One possibility this divergence could be attributed to the effect of viscoelastic dissipation present in the adhesive involved in the estimation of J-integral, especially with the increase of mode-II component. Also, the effect of loading rate between the traction values considered in (Campilho et al., 2011b) and the current experiments has to be considered to obtain an accurate depiction of fracture load (P m ) since as the loading rate increases, the value of fracture toughness G c decreases (Blackman et al., 2009; Cho et al., 2010).  In the current study, G IIC was obtained through extrapolation of mixed-mode data based on B.K law. Direct determination of G IIC using ENF or any other pure mode II tests could result in lower values and combination with other mixed-mode ratios could produce a lower value of B-K law index. Such considerations might influence the FE prediction of fracture load (P m ).  Another reason could be attributed to applicability the B-K law, describing the interaction between the determined G C for different mixed-mode ratios over predicts the failure load. Other parameters (such as t n and t s ) also should be investigated for the adhesive to get a better understanding about the corresponding traction values for different mixed-mode ratios and the shape of the CZM model (as in the current model bi-linear CZM was used). In terms of the accuracy of the results, the selection of the data reduction method would not impact fracture toughness - G IC . Estimation of G IIC is impacted by the data reduction methods. This is further substantiated from a study where six different data reduction methods were used and a good degree of accuracy was obtained (Santos and Campilho, 2017). To investigate the applicability of determined G IC and G IIC for particular adhesive thickness, in a SLJ with different adhesive layer thickness, two different models namely Model I (t a = 0.35 mm) and Modell II (t a =1.0mm) were considered. In other words, the determined values of G IC and G IIC for t a of 0.35 mm and 1.0 mm were considered for SLJ based on t a of 0.2 and 0.9 mm respectively. FE load-displacement (P-  ) curves for the SLJs with adhesive thickness of 0.2 and 0.9 mm thickness are shown in Fig. 19. For the SLJ with ta of 0.2 mm, the implementation of determined fracture properties of Model I and Model II in both cohesive element and surface-based cohesive approaches gave similar results in comparison to that of representative experimental result. For the SLJ with an adhesive thickness of 0.9 mm, the results are a bit different. Both model I and II resulted in the same predicted fracture load for the joint in the surface-based cohesive approach (nearly 7400 N). The predicted load displacement curve shows smaller stiffness with respect to the experimental curve. For the cohesive elements, Model I and II predicted the failure load about 7965 N and 7600 N respectively (i.e. 12 and 7% increase in comparison to the experimental result).