PSI - Issue 52

Ruben I. Erives et al. / Procedia Structural Integrity 52 (2024) 600–610 Ruben Erives et al./ Structural Integrity Procedia 00 (2019) 000–000

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formed a two-channel linear array with a spacing of 250 mm and a waveform velocity of 3500 mm/s. The AE win set-up file for the tests specified a detection threshold of 45 dB and a hit data set including rise time, counts, MARSE energy, duration, amplitude, and average carrier frequency. The data acquisition frequency is 20 Hz. 3. Data analysis The combined end- opening, δ, is simply the norm of the tangential and normal end-opening displacements, while φ represents the phase angle between them as shown in Equation 2. = � 2 + 2 , (1) = −1 � � . (2) The fracture resistance of the interface is calculated from an analytic solution of the J-integral for a DCB-UBM specimen (Sørensen 2009). = 21 ( 12 + 22 ) −6 1 2 4 2 3 1′ , (3) where M 1 and M 2 are the applied moments, B is the width of the specimen, H is the height of the specimen, and E' 1 is the young’s modulus under plain strain. Note that the subscript “0” is used to refer to initiation conditions, e.g., 0 denotes fracture resistance at crack initiation. 3.1. Determination of delamination onset from acoustic emission signals The AE measurements are used to determine the onset time of delamination, 0 , which is then correlated to the end-opening displacement and load measurements (and thus to the onset of fracture resistance). Each of the installed AE sensors outputs six different time dependent features namely rise time, hit count, energy (in attoJ), duration (in μs), amplitude (in db or V), and average frequency (in kHz). The signals from the two sensors are also triangulated to provide the localization of the acoustic emission source, e.g., delamination crack. Each of the six measured AE features evolve differently, however, they typically exhibit two characteristic regions; a region with slow initial progression where acoustic emission is low, and a region with a rapid increase of acoustic emission. The transition from the slow to the fast increase of acoustic emission indicates that the crack is now propagating. In a cumulative plot of any of the measured AE features, this rapid transition can often be easily identified visually as shown in Fig. 2a. This method has been used in previous studies e.g., (Erives et al. 2023) where the knee observed in the cumulative plot of the hit counts was used to identify the crack initiation. 3.2. Definition and determination of deviation from linearity Typically, the load-displacement curve from a fracture mechanics test remains (close to) linear up until a crack starts propagating. This observation can be used to determine initiation by defining a criterion value based on such a deviation from linearity. The deviation from linearity, ∆ℓ , can be used as an alternative or complementary criterion for determining the initiation of delamination. To calculate, ∆ℓ , the following steps can be followed. First, a linear fit of the initial part of the moment against opening curve needs to be carried out. Since the curve starts to deviate before crack initiation it is important to determine an upper bound limit. Based on observations a limit of 80% of the moment at crack initiation, 0 , was chosen for the linear fit. A lower bound limit of 10% 0 was also used since