# Buckling and Delamination

The column is compressed in a quasi-static manner, so that end-shortening increases from zero to a value at which the facings undergo an average strain of 1.5%. Nonlinearity sets in as soon as the delamination tends to buckle outward and at a load of 650N/mm (a longitudinal stress of 116MPa in the facing sheets) delamination begins to grow (Fig. 12). At first this is rather rapid and occurs with little increase in load (points A, B and C in Fig. 12), but soon settles down to a relatively modest rate and delamination occurs under increasing load thereafter. Finally at load of 1380N/mm (average stress of 246MPa), a limit point is reached and thereafter delamination growth is accompanied by shedding of the load by the member. At a load of 1294N/mm the delamination length recorded is 152.25 (the end-shortening = 3.15mm). Compressed to an end-shortening of say 3.5mm, almost complete delamination of the bottom facing occurs, but this would necessarily be accompanied by other forms of failure not considered here. Fig. 12 shows the variation of the load with end-shortening. The observed behavior is in very good agreement to that obtained by EL-Sayed, S., 2002 (not shown) though their model tends to be slightly stiffer at the more advanced delamination range. Also indicated in the figure are the delamination growths recorded at certain significant points in the history – in

particular the values corresponding to end – shortening magnitudes of 0.8mm, 1.0mm and 1.2mm respectively. Fig. 13 shows the deformed shape when end shortening is 2mm.

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 Fig. 13. Static response for case I: Deformed shape at an end shortening of 2mm

Case II

We next consider a sandwich column (Fig. 14) which is significantly slender in comparison to that presented in Case I. The column is clamped at its ends as before, the total length (L) now is 300mm and the total depth, d is 20mm. Thus the L/d is twice that in Case I. Further the thickness of the facing sheets, t is only 0.5mm each and thus d/t = 40 – again about thrice as much as in Case I. The motivation for studying such a case is to examine the influence of overall bending and wrinkling on the delamination growth. (The geometry is the same as that studied by El-Sayed, S., 2002). An initial delamination of the top facing sheet of 10mm at the center was considered (5mm on either side of symmetry).

Both the core and facing sheets are assumed to be isotropic, for simplicity with: Ef = 26900MPa, vf = 0.3 and Ec = 269MPa, Vc = 0.3, where E and V stand respectively for Young’s modulus and Poisson ratio and the subscripts f and c stand for the facings and the core respectively. Two values of Gic are considered, viz. 1.270N/mm2 and 0.635N/mm2, with Omax = 6MPa and 8o = 0.01mm.

Finite Element Modeling

In view of the relatively small thickness of the facing sheets, modeling it with solid elements was not considered viable as the aspect ratio of the four noded elements needs to be maintained around unity. Therefore it was decided to use 2-noded shear-deformable beam elements to model the facing sheets. The core was modeled using 4-noded plane stress elements (CPS4R) with reduced integration.

The reference nodes of the beam elements of the top sheet were placed at the bottom of the beam section and those of the bottom sheet at the top of the section in order to ensure deformation compatibility with core elements. The element size along the longitudinal direction was maintained at 0.25mm and thus there were 600 elements in each layer of elements. The aspect ratios of the core elements were kept around unity. The width of the column was taken as 1mm as before.