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TECHNICAL PAPERS

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

[+] Author and Article Information
Sia Nemat-Nasser

Center of Excellence for Advanced Materials, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0416sia@ucsd.edu

Jeom Yong Choi, Jon B. Isaacs, David W. Lischer

Center of Excellence for Advanced Materials, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0416

J. Appl. Mech 73(5), 825-833 (Nov 22, 2005) (9 pages) doi:10.1115/1.2165241 History: Received February 03, 2005; Revised November 22, 2005

## Abstract

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.

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## Figures

Figure 1

Photograph of the buckling-test setup, showing the upper and lower platens made of maraging steel, an aluminum sample, and an extensometer

Figure 2

Schematic diagram of photographic setup, showing two back mirrors, a focusing lens, and the recording camera

Figure 3

Photograph of the fixed-end bucking-test setup, showing the sample and its reflections in the back mirrors

Figure 4

Photograph of the grip parts and the specimen

Figure 5

Schematic diagram of the dynamic-test setup, showing the Hopkinson bar, a PC-based digital oscilloscope, a trigger delay generator, an Imacon 200 framing camera, and an image processing computer displaying a set of actual images

Figure 6

Schematic diagram of constraining platens used in the mini-Hopkinson bar tests

Figure 7

Photograph of platens used in the (a) mini-Hopkinson bar with displacement limiting pin, and (b) the 1∕2in. Hopkinson bar

Figure 8

Photographs of NiTi tube (R∕t=18) buckling in uniaxial compression, showing the tube at its (a) initial stage, (b) the maximum displacement, and (c) the unloaded stage

Figure 9

Photograph of the buckled maraging steel tube (R∕t=18)

Figure 10

The load-displacement relation for the NiTi tube (R∕t=18) shown in Fig. 1, obtained under a displacement-controlled loading with a cross-head speed of 6.99×10−3mm∕s (nominal strain rate ≈10−3∕s)

Figure 11

Photographs of NiTi tube (R∕t=18) buckling in uniaxial compression under a displacement-controlled loading with a cross-head speed of 6.99×10−3mm∕s (nominal strain rate ≈10−3∕s); numbers correspond to the load-displacement states of Fig. 1

Figure 12

Variation of load with displacement for a NiTi tube, obtained under a displacement-controlled loading with a cross-head speed of 6.78×10−3mm∕s (nominal strain rate ≈10−3∕s); the tube (R∕t=18) is annealed at 773K for 150min, resulting in an Af temperature higher than 295K

Figure 13

Photographs of NiTi tube (R∕t=18) buckling in uniaxial compression under a displacement-controlled loading with a cross-head speed of 6.78×10−3mm∕s (nominal strain rate ≈10−3∕s); numbers indicate the load state in Fig. 1, and the tube is annealed at 773K for 150min, resulting in an Af temperature higher than 295K

Figure 14

Photographs of the recovery by heating of the buckled NiTi tube, showing a shape-memory effect

Figure 15

Variation of load with displacement for a NiTi tube (R∕t=18) with unconstrained ends, obtained under a displacement-controlled loading with a cross-head speed of 8.76×10−3mm∕s (nominal strain rate ≈10−3∕s); the tube is annealed at 773K for 150min, resulting in an Af temperature higher than 295K

Figure 16

Photographs of NiTi tube with unconstrained ends, buckling in uniaxial compression under a displacement-controlled loading with a cross-head speed of 8.76×10−3mm∕s (nominal strain rate ≈10−3∕s); numbers correspond to the load stages in Fig. 1, and the tube is annealed at 773K for 150min, resulting in an Af temperature higher than 295K

Figure 17

Photographs of the recovery by heating of the buckled NiTi tube, showing a shape-memory effect

Figure 18

Variation of load with displacement for an aluminum tube (R∕t=18) with unconstrained ends, obtained under a displacement-controlled loading with a cross-head speed of 6.71×10−3mm∕s (nominal strain rate ≈0.57×10−3∕s)

Figure 19

Photographs of aluminum tube (R∕t=18) with unconstrained ends, buckling in uniaxial compression under a displacement-controlled loading with a cross-head speed of 6.71×10−3mm∕s (nominal strain rate ≈0.57×10−3∕s); numbers correspond to the load stages in Fig. 1

Figure 20

Figure 21

Variation of stress with nominal strain, obtained using mini-Hopkinson bar; L∕D is 2.5

Figure 22

Photographs of the dynamic buckling of a thin NiTi tube (R∕t=18), obtained using mini-Hopkinson bar; L∕D is 2.5, and the term “strain” refers to the axial shortening divided by L

Figure 23

Variation of stress with nominal strain, obtained using stress-reversal 1∕2in. Hopkinson bar; R∕t is 8 and L∕D is 2

Figure 24

Photographs of the dynamic buckling of a thick NiTi tube (R∕t=8), obtained using stress-reversal 1∕2in. Hopkinson bar; L∕D is 2, and the term “strain” refers to the axial shortening divided by L

Figure 25

Variation of stress with nominal strain, obtained using stress-reversal 1∕2in. Hopkinson bar; R∕t is 8 and L∕D is 0.85

Figure 26

Photographs of the dynamic buckling of a thick NiTi tube (R∕t=8), obtained using stress-reversal 1∕2in. Hopkinson bar; L∕D is 0.85, and the term “strain” refers to the axial shortening divided by L

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