PSI - Issue 28

Mor Mega et al. / Procedia Structural Integrity 28 (2020) 917–924 M. Mega and L. Banks-Sills / Structural Integrity Procedia 00 (2019) 000–000

920

4

In eq. (3), B is the specimen width, and F and N are correction factors which account for large displacements and the loading blocks, respectively. It is important to note that with this method, the delamination length, which is known to be di ffi cult to measure for mode II testing [8, 9, 14], is used. Moreover, for the critical initiation interface energy release rate, the small number of visual data points which may be used to obtain a precise value of m may be problematic. The second method used here is based on BT, as described in [15]. This solution takes into account the di ff erent thicknesses of each arm. For a C-ELS specimen with upper and lower arm thicknesses of h 1 and h 2 , respectively, where h 1 h 2 , G Ic and G IIc may be calculated as G Ic = 1 64 P 2 a 2 BE f I (1 − γ ) 2 (1 + γ )(1 − ξ ) G IIc = 3 16 P 2 a 2 BE f I (1 − ξ ) ξ 2 (1 + γ ) (4) where E f is the flexural modulus of the specimen, The third method makes use of FEAs. For each specimen, a two-dimensional analysis was carried out using the program Abaqus [21]. The value of G ic was found by means of an area J -integral. The phase angle ˆ ψ , given by ˆ ψ = arctan ( ˆ K 2 ˆ K 1 ) (6) was also determined. The stress intensity factors ˆ K 1 and ˆ K 2 were obtained by means of DE [16] and VCCT [22]. Note that, ˆ K = ˆ K 1 + i ˆ K 2 = K ˆ L i ε (7) where K = K 1 + iK 2 , i = √ − 1, ε is the oscillatory parameter and ˆ L is a length scale. I = Bh 3 12 h = h 1 + h 2 2 ξ = h 1 2 h γ = ( 1 − ξ ξ ) 3 . (5) It may be noted that G Ic is zero for a UD laminate. It may also be pointed out that both the ECM and BT methods described here do not take into consideration that the delamination is between two dissimilar plies. Load-displacement curves for all six C-ELS NPC specimens tested are presented in Fig. 2. The NL, visual, and 5% o ff set or maximum initiation load P are indicated on each curve in the figure. Note that the specimens are labeled with the identifiers CELS which represents the test type; a number that denotes the batch; followed by a number which represents the specimen in the tested series. It may be observed that specimens CELS-2-4 and CELS-2-5 are less sti ff than the other specimens. Since the investigated material was manufactured by means of a wet-layup process, such di ff erences in the compliance may occur. Values of these loads are given in the second, sixth and tenth columns of Table 1. These were used to calculate G ic from the film insert, for ∆ a = 0 by means of the methods described in Section 2.2. For the ECMmethod, the delamination length ∆ a was measured visually from test images captured by the LaVision system when initiation and propagation occurred using ImageJ software [23]. For each value of ∆ a , the load P and actuator displacement d , measured by the Instron, appear on the corresponding images. The NPC stage is performed in order to create a natural crack with propagation between 2 and 5 mm at which point unloading is performed. As a result, only three to five data points were obtained visually from the test and used to fit a curve to determine the parameters m and C 0 for the relation in eq. (1). The small number of data points resulted in inaccurate values of the fitting parameter m which caused unrealistically small values of G ic of between 100 N / m and 500 N / m. From these results it may be concluded that ECM is not suitable for C-ELS NPC tests. For the BT method, the energy release rates G Ic and G IIc for all C-ELS NPC specimens were calculated by means of eqs. (4). The flexural modulus E 1 f was obtained by means of a calibration procedure described in [4], and found to be E 1 f = 31 . 3 GPa. The values of P at initiation in Table 1 are used in the calculation and a is taken as the initial 3. Test and analyses results