Quasi-Static and Dynamic Buckling of Thin Cylindrical Shape-Memory Shells

To investigate the buckling behavior of thin and relatively thick cylindrical shape-memory shells, uniaxial compression tests are performed at a $295K$ initial temperature, using the CEAM/UCSD’s modified split Hopkinson bar systems and an Instron hydraulic testing machine. The quasi-static buckling response of the shells is directly observed and recorded using a digital camera with a close-up lens and two back mirrors. To document the dynamic buckling modes, a high-speed Imacon 200 framing camera is used. The shape-memory shells with an austenite-finish temperature of $Af=281K$⁠, buckle gradually and gracefully in quasi-static loading, and fully recover upon unloading, showing a superelastic property, whereas when suitably annealed, the shells do not recover spontaneously upon unloading, but they do so once heated, showing a shape-memory effect. The thin shells had a common thickness of $0.125mm$ a common outer radius of $2.25mm$ (i.e., a common radius, $R$⁠, to thickness, $t$⁠, ratio, $R∕t$⁠, of 18). A shell with the ratio of length, $L$⁠, to diameter, $D$$(L∕D)$ of 1.5 buckled under a quasi-static load by forming a nonsymmetric chessboard pattern, while with a $L∕D$ of 1.95 the buckling started with the formation of symmetrical rings which then changed into a nonsymmetric chessboard pattern. A similar buckling mode is also observed under a dynamic loading condition for a shell with $L∕D$ of 2. However, thicker shells, with $0.5mm$ thickness and radius $4mm(R∕t=8)$⁠, buckled under a dynamic loading condition by the formation of a symmetrical ring pattern. For comparison, we have also tested shells of similar geometry but made of steel and aluminum. In the case of the steel shells with constrained end conditions, the buckling, which consists of nonsymmetric (no rings) folds (chessboard patterns), is sudden and catastrophic, and involves no recovery upon unloading. The gradual buckling of the shape-memory shells is associated with the stress-induced martensite formation and seems to have a profound effect on the unstable deformations of thin structures made from shape-memory alloys.