The near tip stress field in the equivalent plate will have a structure given by Eq. 18.3 [16]. σij ¼X N n¼0 Anrð n 1=2Þf nðθÞþX M m¼0 Bmr mgmðθÞ X N n¼0 Cnrð n 1=2ÞhnðθÞ X M m¼0 Dmr mkmðθÞ (18.3) Where r and θ denote the polar coordinate of a point with respect to the crack tip and fn(θ), gm(θ), hn(θ), and km(θ) are trigonometric functions, explicit form of which are available in [16]. In Eq. 18.3, constants An, Bm, Cn and Dm can be evaluated from isochromatic fringe data using the least square over deterministic method described in [16]. The opening mode SIF KI and sliding mode SIF KII are related to the coefficients, A0 and C0 as shown in Eq. 18.4. KI ¼ ffiffiffiffiffi 2π p A0; KII ¼ ffiffiffiffiffi 2π p C0 (18.4) Mode mixity (Θ), which shows the strength of mode-II stress field relative to mode I field, is defined as Θ¼tan 1 KII KI (18.5) The SIF thus obtained is the thickness averaged SIF or equivalent SIF (Keq) for the equivalent homogenous plate. The SIF in each individual layer is given by Ke ¼ Ee Eeq Keq; Kp ¼ Ep Eeq Keq (18.6) where, subscripts e and p refer to Epoxy and PMMA respectively. To extract the SIF and other constants (Eq. 18.3) from isochromatics, the fringe order at a select set of points around the crack-tip was sampled. To check the accuracy of solution, fringes are regenerated using the extracted coefficients and compared with the fringes obtained experimentally. Crack propagation angle is calculated using the experimentally determined SIFs in maximum tangential stress (MTS) criterion and in the minimum strain energy density (SED) criterion [17]. The actual crack propagation angle has been compared with those predicted by MTS and minimum SED criteria. The criticality condition for crack initiation is also calculated using the MTS and SED criteria for the Epoxy layer. 18.4 Results 18.4.1 Static Test The results of the AFPB test will be discussed in this section. The load–displacement record of the layered plate subjected to AFPB loading (s ¼6 mm) is shown in Fig. 18.4. The isochromatics corresponding to the selected loads (a, b, c in Fig. 18.4) are shown in Fig. 18.5. As Epoxy is less tough compared to PMMA, the initiation of the crack growth was first observed in Fig. 18.3 Contour plots of in Epoxy and PMMA layers for AFPB with s ¼6 mm (a) opening strain (ε11) (b) normal strain (ε22) (c) shear strain (ε12) 150 A.J. Jacob et al.
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