Edmundo Corona

On the performance of kinematic hardening rules in predicting a class of biaxial ratcheting histories

It is well known that strain-symmetric axial cycling of thin-walled metal tubes in the presence of pressure results in a progressive accumulation (ratcheting) of circumferential strain. It was previously demonstrated that the prediction of the rate of ratcheting under constant internal pressure, by nonlinear kinematic hardening models, is very sensitive to the hardening rule adopted. It was shown that the Armstrong-Frederick hardening suitably calibrated and used in a class of models can yield reasonably good predictions of the rate of ratcheting for a range of cycle parameters. In this paper, the subject is revisited in the light of further experimental results involving simultaneous cycling of the internal pressure and the axial strain. Experiments and analyses were performed for a family of five such biaxial loading histories. A similar sensitivity to the kinematic hardening rule used in the models was observed in all the new loading histories. Furthermore the hardening rule calibrated in the constant pressure experiments was found to yield accurate predictions for three of the loading histories considered and poor predictions for the other two. The reasons for this varied performance are analyzed and some recommendations for implementation of such models in structural applications are made.

Buckling of elastic—plastic square tubes under bending

Abstract This paper addresses the response, buckling and collapse of long, thin-walled, seamless steel square tubes under pure bending using a combined experimental and analytical approach. All tubes tested had nominal cross-sections with height equal to 1 in. (25.4 mm) and ranged in height-to-thickness ratios (h/t) from 15.4 to 28.6. The experiments were conducted under curvature control. It was found that the deformation of the cross-section that accompanied bending was uniform along the tubes for low values of curvature. At higher values, periodic ripples with wavelengths approximately equal to the width of the cross-section appeared on the compression flange. These ripples increased in amplitude with further bending. For tubes with higher h∼ the increase was more pronounced. Tubes with lower h/t showed more moderate increases in ripple amplitude but developed regions spanning several ripples in which the cross-section deformation was more pronounced. In all cases, collapse occurred when a kink formed on the compression flange of the tube. Rayleigh—Ritz type formulations based on the principle of virtual work were developed to predict the response and buckling of the tubes. Results include predictions of the response considering the effect of uniform cross-section deformation and predictions of the critical curvature at which the ripples appear. The numerical results are in good agreement with experimental observations.

On bend-stretch forming of aluminum extruded tubes — II: analysis

Part II describes a two-dimensional model of the bend-stretch-pressure forming process, which assumes that the tube shape and all applied loads are uniform along the length. This simplification results in a significant improvement in computational time over corresponding three-dimensional models. The model is validated through comparisons with experimental results discussed in Part I and its application to the design process is illustrated. The model is then used to study the current manufacturing process and to evaluate some possible alternative loading histories. The effect of tension and pressure on the cross-sectional distortion, springback and net elongation are discussed in light of the predictions. Additionally, the merits of changing the tension and pressure after forming are discussed. The simulations and corresponding experiments are used as the basis for a design methodology for selecting the order and magnitude of the loads applied during the forming process.

Degradation and collapse of square tubes under cyclic bending

Abstract This paper presents the results of an experimental investigation of the elastic–plastic degradation and collapse of steel tubes with square cross-section under cyclic pure bending in a curvature symmetric fashion. The results indicate that the structural performance of the tubes degrades due to the growth of periodic, transverse deflections in their flanges. The wavelength of these deflections is equal to the wavelength of the buckling mode of the tubes under monotonic pure bending. Persistent cycling induces localization of the amplitude of these deflections and leads to the formation of a kink in one of the flanges. This causes collapse of the tube.

Effect of yield surface evolution on bending induced cross sectional deformation of thin-walled sections

Abstract Bend–stretch forming is commonly used to shape extruded tubular aluminum parts for automotive and other applications. The tubes are pre-stretched, pressurized and bent over rigid curved dies. Tension prevents buckling of the compressed side and helps reduce springback. An unwanted byproduct of the process is distortion of the cross section. Small amounts of pressure applied during forming can reduce this distortion. The problem was studied through a combination of experiment and analysis. In numerical models of the process the inelastic behavior of the aluminum alloy was modeled through isotropically hardening plasticity. With the limitations imposed by this model, use of a J 2 -type yield surface resulted in uniform underprediction of cross sectional deformation. The predictions matched the measurements when a non-quadratic yield function appropriately “calibrated,” was used instead. The change in yield function shape alters the instantaneous normals to the yield surface which, in turn, affect the calculated strain increments. This paper demonstrates how suitably calibrated nonlinear kinematic hardening models can have the same corrective effect. The calibration involves selection of a suitable kinematic hardening rule. Changes in the hardening direction alter the instantaneous normals and therefore alter the plastic strain increments resulting in approximately the same net effect as the switch from the von Mises to the non-quadratic yield function.

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.

Buckling of steel bars with Lüders bands

Abstract Experiments and simulations are presented for the study of interaction between material and structural instabilities that occur in mild steel bars under axial compression. The material instability consists of Luders bands that nucleate and propagate along the specimens. The structural instability involves lateral deflections of the bar leading to collapse. The study includes an investigation of bars of several different lengths. The mechanical response in the experiments were monitored through measurements of axial load, axial and midspan lateral displacements, and full field imaging of a brittle coating showing the Luders deformation. Interesting interactions exist between the localized deformation due to the material-level instabilities and the global collapse of the bars. Finite element simulations, using a constitutive model with a nonmonotonic stress–strain behavior, showed good agreement with the experiments and helped to explain the variety of collapse modes seen in the experiments. The symmetry of imperfections and/or loading misalignments have dramatic effects on the evolution of Luders deformation and the eventual collapse mode. Certain imperfections lead to deformation modes that delay structural collapse.

Buckling of T-beams under cyclic bending

This paper presents the results of an experimental study of the response and stability of elastic-plastic T-beams under cyclic pure bending, with emphasis on local buckling. The objectives of the study were to determine the evolution of instabilities and to find parameters useful to determine the degree of damage incurred during cycling. All specimens were subjected to a quasi-static curvature symmetric loading history of constant amplitude. The results indicate that, in the range of curvature amplitudes considered, structural degradation was mainly due to progressive growth of a ripple in the lateral deflection of the web. The unstable growth of one of the features of this ripple led to the formation of a local buckle, which caused a marked reduction in the moment capacity of the specimens. Further cycling resulted in fracture of the web at the local buckle. The best indicator of degradation was a measure of the amplitude of the ripple in the lateral deflection of the web. This measure could be used to generate a criterion for assessing the current state of the specimens in relation to their useful life under cyclic bending.

Plastic Buckling and Collapse of Tubes Under Bending and Internal Pressure

This paper presents results from a recent combined experimental-analytical study of the inelastic response and the sequence of events that lead to collapse of pipes bent under internal pressure. Experimental results from stainless steel 321 seamless tubes with D/t of 52 are reported. The tubes were loaded by pure bending at fixed values of pressure ranging from zero to a value that corresponds to 0.75 times the yield pressure. The moment-curvature response is governed by the inelastic characteristics of the material. Bending induces some ovalization to the tube cross section while, simultaneously, the internal pressure causes the circumference to grow. Following some inelastic deformation, small amplitude axial wrinkles appear on the compressed side of the tube, and their amplitude grows stably as bending progresses. Eventually, wrinkling localizes, causing catastrophic failure in the form of an outward bulge. Pressure increases the wavelength of the wrinkles as well as the curvature at collapse. The onset of wrinkling is established by a custom bifurcation buckling formulation. The evolution of wrinkling and its eventual localization are simulated using a FE shell model. The material is represented as an anisotropic elastic-plastic solid using the flow theory, while the models are assigned initial geometric imperfections that correspond to the wrinkling bifurcation mode. It will be shown that all aspects of the observed behavior including the failure by localized bulging can be successful reproduced by the models developed.Copyright

Wall Curl in Bending of Laminated Steel

Laminated steel sheets consist of thin visco‐elastic polymer layers sandwiched between sheets of steel and are used primarily in products where sound and vibration need to be damped. Although laminated steel products have been successfully manufactured by stamping, these parts are relatively flat. Problems arise, however, when using the material in bending operations. The main problem is the fact that the sheets develop curl after bending. This has prevented the use of laminated steel in mass‐production settings. This investigation concentrates on the study of the bending characteristics of laminated steel in a wiping die configuration. Experiments have been conducted in a specially designed wiping set‐up to assess the curl and springback characteristics of the laminated sheet. In addition, a finite element model has been developed to simulate the experiments. The predicted bent shapes of the specimens are very close to the experimental results. The numerical model has also been used to conduct parametric studies of the dependence of the final shape of laminated steel on geometric and material parameters. Both experimental and numerical results indicate that wall curling is characteristic of laminated steel and depends on the thickness of the sheet and the properties of the polymer layer.