Bending of long cross-ply composite circular cylinders

Abstract

The response of long, thin-walled, cross-ply composite tubes subjected to pure bending was studied analytically. The formulation includes three parts: pre-buckling response, material failure and bifurcation buckling. The pre-buckling response is analyzed using nonlinear kinematics to accommodate the ovalization of the cross-section. The formulation is based on the principle of virtual work and is used to generate a numerical solution procedure. The Tsai-Wu failure criterion is used to detect material failure in the pre-buckling response. The maximum stress criterion was also considered for comparison. Finally, the buckling analysis considers the possibility of bifurcation into modes containing periodic displacements along the axis of the tube. The tubes are assumed to be geometrically perfect and free of residual stress. Three materials-AS3501 graphite-epoxy, Kevlar 49-epoxy, and E-glass-epoxy-and three diameter-to-thickness ratios-50, 100 and 400-are considered. The moment-curvature response of the tubes is non-linear due to the ovalization of the cross-section (Brazier effect) which induces a limit moment instability. Either material failure or bifurcation buckling always occurs prior to the limit moment in the cases considered. Little difference was observed between the failure loads predicted by the Tsai-Wu and the maximum stress criteria. Tubes with plies of circumferentially oriented fibers in the outermost and innermost positions in the wall proved superior in strength compared with the other cases considered.