Non-linear temperature-curvature relationships for unsymmetric graphite-epoxy laminates

A geometrically non-linear theory is used to study the relationship between temperature and curvature of unsymmetric elevated temperature cure graphite-epoxy laminates. Numerical and experimental results are obtained for square (04/904)T laminates of various sizes. It is shown that over a certain temperature range the temperature-curvature relationship of unsymmetric laminates can bifurcate and be triple valued. The triple-valued relationship indicates that more than one laminate shape is possible at a given temperature. Two shapes are cylindrical and the third is a saddle shape. The temperature range over which the relationship is multivalued depends on the size of the laminate. A stability analysis shows that when a multivalued relationship exists, the saddle shape is an unstable equilibrium configuration. When the single-valued saddle shape solution exists, it is a stable equilibrium configuration. Experiments are described which were used to obtain data to compare with the predictions of the theory. Comparisons with experiments arc quite good. As might be expected, the sharpness of the theoretical temperature-curvature relationship near the bifurcation points is not realized in the experiments. It is shown how imperfections in the laminate can be included in the theory to account for the more realistic behavior.