Wrinkling of Circular Tubes Under Axial Compression: Effect of Anisotropy

Relatively thin-walled tubes bent into the plastic range buckle by axial wrinkling. The wrinkles initially grow stably but eventually localize and cause catastrophic failure in the form of sharp local kinking. The onset of axial wrinkling was previously established by bifurcation analyses that use instantaneous deformation theory moduli. The curvatures at bifurcation were predicted accurately, but the wrinkle wavelengths were consistently longer than measured values. The subject is revisited with the aim of resolving this discrepancy. A set of new bending experiments is conducted on aluminum alloy tubes. The results are shown to be in line with previous ones. However, the tubes used were found to exhibit plastic anisotropy, which was measured and characterized through Hill's quadratic anisotropic yield function. The anisotropy was incorporated in the flow theory used for prebuckling and postbuckling calculations as well as in the deformation theory used for bifurcation checks. With the anisotropy accounted for, calculated tube responses are found to be in excellent agreement with the measured ones while the predicted bifurcation curvatures and wrinkle wavelengths fall in line with the measurements also. The postbuckling response is established using a finite element model of a tube assigned an initial axisymmetric imperfection with the calculated wavelength. The response develops a limit moment that is followed by a sharp kink that grows while the overall moment drops. The curvature at the limit moment agrees well with the experimental onset of failure. From parametric studies of the various instabilities it is concluded that, for optimum predictions, anisotropy must be incorporated in both bifurcation buckling as well as in postbuckling calculations.

Section: Parametric Studycontrasting

confidence: 55%

“…Despite the scatter, the measurements clearly show that k exp are significantly lower than the values predicted for all D/t's considered. Motivated by the recent findings of Kyriakides et al (2005), we will investigate if inelastic anisotropy played a role in this discrepancy.…”

Section: Introductionmentioning

confidence: 97%

Yield anisotropy effects on buckling of circular tubes under bending

Corona

Lee

Kyriakides

2006

“…The results demonstrate the growth and eventual localization of wrinkles. The number of scans performed was not sufficient to pinpoint the onset of bifurcation as was done in Kyriakides et al (2005) and . Instead, predictions of the critical bifurcation stress and strain values (r C ,e C ) = (102.5 ksi, 1.48%) developed using the mechanical properties given in Table 3 are listed in Table 1.…”

Section: Experimental Set-up and Proceduresmentioning

confidence: 99%

“…where 2k is the wavelength of the axisymmetric buckling mode evaluated as discussed in Kyriakides et al (2005). The end at x = Nk is radially free and symmetry about the specimen mid-span (x = 0) is assumed.…”

Section: Wþ: ð1cþmentioning

confidence: 99%

Ratcheting, wrinkling and collapse of tubes under axial cycling

Jiao

Kyriakides

2009

a b s t r a c t Circular tubes compressed into the plastic range first buckle into axisymmetric wrinkling modes. Initially the wrinkle amplitude grows with increasing load. The wrinkles gradually induce a reduction in axial rigidity eventually leading to a limit load instability followed by collapse. The two instabilities can be separated by strain levels of a few percent. This work investigates whether a tube that develops small amplitude wrinkles can be subsequently collapsed by persistent cycling. The problem is first investigated experimentally using SAF 2507 super-duplex steel tubes with D/t of 28.5. The tubes are first compressed to strain levels high enough for mild wrinkles to form; they are then cycled axially under stress control about a compressive mean stress. This type of cycling usually results in material ratcheting or accumulation of compressive strain; here it is accompanied by accumulation of structural damage due to the growth of the amplitude of the initial wrinkles. The tube average strain initially grows nearly linearly with the number of cycles, but as a critical value of wrinkle amplitude is approached, wrinkling localizes, the rate of ratcheting grows exponentially and the tube collapses. The rate of ratcheting and the number of cycles to failure depend on the initial compressive pre-strain and on the amplitude of the stress cycles. However, collapse was found to occur when the accumulated average strain reaches the value at which the tube localizes under monotonic compression. A custom shell model of the tube with initial axisymmetric imperfections, coupled to a cyclic plasticity model, are presented and used to simulate the series of experiments performed successfully. A sensitivity study of the formulation to the imperfections and to key constitutive model parameters is then performed.

“…Comparisons between the predictions of both flow and deformation theories and experimental results were then performed in Kyriakides et al (2005), and , in the case of axially loaded cylindrical shells, including the effect of anisotropy with the use of the Hill's yield criterion. The flow theory significantly overpredicts both the critical stresses and strains, whereas the deformation theory gives rise to predictions much closer to the experimental values.…”

Section: Introductionmentioning

confidence: 99%

Elastoplastic bifurcation and collapse of axially loaded cylindrical shells

Grognec

van²

2008

International audienceIn this paper, a shell finite element is designed within the total Lagrangian formulation framework to deal with the plastic buckling and post-buckling of thin structures, such as cylindrical shells. First, the numerical formulation is validated using available analytical results. Then it is shown to be able to provide the bifurcation modes-possibly the secondary ones-and describe the complex advanced post-critical state of a cylinder under axial compression, where the theory is no longer operative