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Research Papers

# Wrinkling of Tubes by Axial Cycling

[+] Author and Article Information
Rong Jiao, Stelios Kyriakides

Research Center for Mechanics of Solids, Structures and Materials, WRW 110, C0600, The University of Texas at Austin, Austin, TX 78712

J. Appl. Mech 77(3), 031012 (Feb 23, 2010) (11 pages) doi:10.1115/1.4000431 History: Received April 28, 2009; Revised August 05, 2009; Published February 23, 2010; Online February 23, 2010

## Abstract

Circular tubes compressed into the plastic range first buckle into axisymmetric wrinkling. Initially, the wrinkle amplitude grows with increasing load, but induces a gradual reduction in axial rigidity that eventually leads to a limit load instability and collapse. For lower $D/t$ tubes, the two instabilities can be separated by strain levels of a few percent. Persistent stress-controlled cycling can cause accumulation of deformation by ratcheting. Here, the interaction of ratcheting and wrinkling is investigated. In particular, it is asked if compressive ratcheting can first initiate wrinkling and then grow it to amplitudes associated with collapse. Experiments on SAF2507 super-duplex steel tubes with $D/t$ of 28.5 have shown that a geometrically intact tube cycled under stress control initially deforms uniformly due to material ratcheting. However, in the neighborhood of the critical wrinkling strain under monotonic loading, small amplitude axisymmetric wrinkles develop. This happens despite the fact that the maximum stress of the cycles can be smaller than the critical stress under monotonic loading. In other words, wrinkling appears to be strain rather than stress driven, as is conventionally understood. Once the wrinkles are formed, their amplitude grows with continued cycling, and as a critical value of amplitude is approached, wrinkling localizes, the rate of ratcheting grows exponentially, and the tube collapses. Interestingly, collapse was also found to occur when the accumulated average strain reaches the value at which the tube localizes under monotonic compression. A custom shell model with small initial axisymmetric imperfections, coupled to a cyclic plasticity model, is used to simulate these cyclic phenomena successfully.

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## Figures

Figure 5

Cyclic stress history applied in the experiments

Figure 6

Figure 7

Radial displacement axial profiles after different numbers of cycles showing the growth and localization of wrinkles for CWR19

Figure 8

Peak axial displacement per cycle versus N and corresponding maximum radial displacement in wrinkles for CWR19

Figure 1

Scaled schematic of the experimental setup used

Figure 2

Typical stress-shortening response from a monotonic compression test of an inelastic circular cylindrical shell. Marked are the onset of wrinkling (↓) and the limit load (̂), followed by localization and collapse.

Figure 3

(a) Radial displacement axial profiles recorded at different average strain levels during the monotonic compression test in Fig. 2 that show the evolution of the wrinkles. (b) Axial scans showing the evolution of wrinkles and their localization at higher strain levels.

Figure 4

Critical wrinkling strains (εC) and average limit strains (ε¯L) versus D/t from 15 experiments of Bardi and Kyriakides (8) and several new experiments with D/t≅28.5

Figure 9

Peak displacement per cycle versus N from three experiments with slightly different initial prestraining

Figure 10

Calculated axial stress-shortening response for CWR19

Figure 11

Comparison of measured and calculated peak axial displacement and maximum radial displacement versus N

Figure 12

(a) Calculated radial displacement axial profiles after different numbers of cycles showing the growth and localization of wrinkles for CWR19. (b) The initial and three tube deformed configurations during the cyclic history.

Figure 13

Comparison of measured and calculated peak displacements per cycle versus N from three experiments with slightly different initial prestraining

Figure 14

Effect of imperfection parameters on calculated δxp−N ratcheting response

Figure 15

Effect of relaxation coefficient Cr on calculated δxp−N ratcheting response

Figure 16

Yield and bounding surfaces and associated variables of the Dafalias–Popov model

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