Geometry, Materials and Boundary Conditions
The core and facing materials are exactly the same as the test specimen (Table 1) discussed in the last section and the cross-section of the member investigated is also the same (h = 50mm, t = 3.6mm). The total length of the column investigated is 420mm and it is considered clamped at either end. Because of symmetry involved – barring the unlikely scenario of sudden interference of antisymmetric modes of bifurcation – only half the column length of 210mm included between the line of symmetry on the left and the clamped end on the right is considered (Fig. 10). A rigid surface incapable of rotation and lateral translation is created to model the clamped end. A symmetrically located initial delamination of total length 102mm is deemed to exist between bottom facing sheet and the core. Fig. 10 shows the configuration and other pertinent details.
Fig. 10. Configuration of case I
Details of the Analysis
Finite Element mesh configuration is the same as in Fig. 3 though the length of the column and the cohesive layer elements are different. The size of the elements is 0.25mm in the longitudinal direction and plane strain elements (CPE4R) with reduced integration were employed in the analysis as before. Unlike the previous example, the column is treated as having unit width (1mm) and the loads are reported as per unit width. The load is inducted by prescribing the end-shortening (relative to the plane of symmetry). The critical value of SERR in the opening mode is once again taken as 1.27N/mm. The value of maximum stress, Omax is taken as 10MPa and 8o is taken as before equal to 0.01mm.
The model was perturbed slightly by incorporating imperfections in order to keep the delamination open and prompt the structure towards delamination buckling and growth. To this end, a linear stability analysis without the cohesive layer was conducted and the buckling loads and modes were obtained. The first three buckling loads were found to be 562N, 2079N and 3466N respectively. Of these the first (Fig. 11(a)) and the second (Fig. 11(b)) pertain to delamination buckling – the former keeps the delamination fully open and the latter partially closed. The last one (Fig. 11(c)) is an overall buckling mode. It is clear that the first alone is critical and therefore an imperfection in the form of this mode is incorporated in the model with a maximum deflection of 0.5mm at the center. Given the stoutness of the member (relative to the length, L/d =7.3) and the magnitude of the overall buckling load, it is clear that overall bending of the column plays a relatively minor role in the problem.
Fig. 11. The first three buckling modes