PSI - Issue 57

Cristian Bagni et al. / Procedia Structural Integrity 57 (2024) 598–610 Author name / Structural Integrity Procedia 00 (2019) 000 – 000 specimens, due to their geometry, tends to decrease from the beginning of the test. In this case, 0 is chosen as close as possible to the beginning of the test and ensuring that the first condition is met. In summary, the following steps can be performed: • The stiffness ( ) , calculated from the raw load and displacement data recorded during the test according to Eq. 1, is filtered by applying a rolling median (cyan points in Fig. 7); • The resulting stiffness dataset is normalised according to Eq. 4; • The normalised ( ) is approximated using a least squares polynomial fit (blue line in Fig. 7); • The number of cycles corresponding to the required value of stiffness drop is extracted. 607 10

Fig. 7. Example of normalised stiffness vs cycles plot: filtered datapoints (cyan) and polynomial fit (blue).

The stiffness drop failure criterion is more flexible compared to the other two options, since it allows the definition of failure to be tailored to the needs/requirements of each company and/or application, that are not necessarily always the same. For example, it is possible to correlate a given stiffness drop to the appearance of the first visible crack on the surface of the adhesive or select a value of stiffness drop that guarantees a minimum allowable residual fatigue life. Once the most appropriate failure criterion is chosen, it is possible to determine a series of load-life (LN) datapoints from the testing of adhesively bonded specimens as representative as possible of the production parts and processes of interest. The LN datapoints can then be reverse-engineered into stress-life (SN) datapoints by calculating the peel stress range, ∆σ peel , through linear superposition as follows: ∆ peel = peel_max_unit load ∙ ∆ = peel_max_unit load ∙ max ∙ (1− ) (5) where peel_max_unit load is the maximum peel stress, obtained from the FE model (with a unit load applied), at the centroid of the membrane shell elements wrapped around the solid elements modelling the adhesive (the element experiencing the highest peel stress is likely to corresponds to the location where failure should initiate). max is the maximum of the applied sinusoidal load for each test, and = min max ⁄ is the load ratio. Finally, through statistical analysis of the SN datapoints it is possible to derive mean (50% certainty of survival, 50% confidence interval) and design (e.g. 97.7% certainty of survival, 95% confidence interval) SN curves and corresponding parameters. At the time of writing a series of tests in collaboration with an electric vehicle manufacturer, NIO Performance Engineering Ltd, involving both lap shear and coach peel adhesive joint specimens, is underway at Hottinger Brüel & Kjær’s ‘Advanced Materials Characterisation & Testing’ laboratory in the United Kingdom . To illustrate the