Plastic Torsion Research Articles

Plastic Torsion Analysis of Monosymmetric and Point-Symmetric Beams

This paper extends a simple method of analyzing the plastic torsion collapse of compact equal flange I-section beams to monosymmetric and point-symmetric beams. The method can be used manually, is much easier than elastic analysis, and is no more difficult than the plastic collapse analysis of beams in bending. The use of plastic torsion analysis avoids the conservatism of first yield analysis and design because it accounts for the spread of plasticity through the cross section and the redistribution of torque that occurs in redundant members after the first hinge forms. Designs based on plastic analyses of torsion will lead to significant economies over the first yield designs based on elastic analysis. Equations are developed in this paper for the uniform torsion plastic torques and for the plastic bimoments of monosymmetric I-sections, lipped and unlipped channels, and equal flange lipped angles, and of point-symmetric lipped and unlipped Z-sections. A worked example of the plastic torsion collapse and design of a lipped channel is present.

Plastic Torsion and Related Problems

A simple algorithm to calculate the maximum torsional load for a cylindrical shaft is presented. The algorithm is based on the notion of viscosity solutions to the eikonal equation, and is not restricted to simply-connected cross-sections. Applications to other, related problems, such as ferromagnetic thin films, and elastic buckling of thin film blisters are also discussed.

Formation of metastable states in nanostructured Al- and Ti-based alloys by the SPTS technique

Nanostructured Al and Ti-based alloys have been processed by severe plastic torsion straining (SPTS). It is shown that SPTS under high pressure of these quenched alloys results in refinement of their microstructures to grain sizes of 70–100nm and leads to formation of supersaturated solid solutions. Structural changes during heating of the obtained nanostructured alloys are investigated.

Torsion of Nonlinear Viscous Shafts

In this study, we reconsider the torsion of nonlinear viscous shafts. Attention is paid to the analytical solution of the nonlinear partial differential equation arising in the problem's formulation, and it is concluded that the stresses τxy, τxz, and the torque T(t) can be found in terms of the partial derivatives of the warping function ϕ. Theoretical results are given for circular cross sections, and it is shown that the present method gives the same results as those for elastic (m= 0) and perfectly plastic torsion (m→∞). It is further proved that it is not possible to give analytical solutions for nonregular boundaries, such as rectangular and triangular cross sections.

Fatigue and ratcheting interactions

A review of experimental data from cyclic plasticity investigation performed on two structural steels was carried out to determine the influence of ratchet strain accumulation on fatigue life. Thin-walled tubular specimens, manufactured from a low-carbon steel (En3) and a low alloy steel (En19), were subjected to a range of constant twist amplitude cyclic plastic torsion, in combination with a range of constant axial loads. The results show that the En19 steel accumulates plastic axial strain at a much lower rate than the En3 steel. For both steels, the effect of increasing axial load is to reduce the fatigue life, with the fatigue lives for the En19 steel being higher than those for the En3 steel. Additionally, the slope of the Manson-Coffin plot remains virtually constant irrespective of the axial load in the case of the En19 steel. In the case of the En3 steel, however, for any given axial load, the Manson-Coffin plots show a change in slope, leading to shorter than expected fatigue lives at low plastic shear strain amplitudes.

Three—Dimensional Elastic-Plastic FEM Analysis on Torsion of Square-Section Bars

Summary This paper deals with FEM analysis on the torsion of solid bars. Using EM program MARC, three—dimensional elastic—plastic torsion problem, which have not to date been solved, were analysed. Thus, the longitudinal strain during twisting is calculated for the first time. The decreasing ratio of axial length becomes smaller with the increase of strain -hardening ratio. Furthermore, the decreasing ratio of axial length of the square—section bar was larger than that of the circular—section bar. The same tendency has been observed in previous experiments.

A duality theorem for plastic torsion

Limit analysis of prismatic torsion bars was the earliest attempt to apply plasticity theory to a continuum. The simplicity of the problem made it feasible to use the two-dimensional Prandtl stress function, defined for the elastic torsion problems, for the plastic stress distributions as well. The gradient of the stress functions for plastic torsion has a constant magnitude, and hence a function of this type assumes the profile of a sand hill. This sand hill analogy of Nadai (1950, The Theory of Flow and Fracture of Solids. McGraw-Hill, U.K.) gave a visual sense of possible nonsmoothness of such stress functions and thus discontinuous stress fields. Many stress functions of plastic torsion for relatively simple cross-sections have been constructed graphically. However, collapse modes in terms of warping functions were much less reported. In this paper, we shall establish a duality theorem which relates the correct stress function to the correct warping function, thus providing the means to obtain complete static and kinematic solutions. This dual variational principle leads naturally to a general numerical algorithm which guarantees convergence and accuracy. In this paper, we shall only present three exact solutions to verify the theorem, to demonstrate the possible non-smooth feature of the solutions and to reiterate this effective dual variational approach to limit analysis in general.

Laws governing the axial deformation of metals subjected to plastic torsion

The laws governing the axial deformation of aluminum alloy D16, steel St. 3, and commercially pure copper under plastic torsion are investigated. It is demonstrated that strain accumulation in the direction of elongation occurs in these metals, irrespective of the loading regime. It is established that their behavior depends on the temperature and strain amplitude, as well as on the number of torsion cycles.

Analytical Solutions for Circular Bars Subjected to Large Strain Plastic Torsion

The inelastic behavior of solid circular bars twisted to arbitrarily large strains is considered. Various phenomenological constitutive laws currently employed to model finite strain inelastic behavior are shown to lead to closed-form analytical solutions for torsion. These include rate-independent elastic-plastic isotropic hardening J2 flow theory of plasticity, various kinematic hardening models of flow theory, and both hypoelastic and hyperelastic formulations of J2 deformation theory. Certain rate-dependent inelastic laws, including creep and strain-rate sensitivity models, also permit the development of closed-form solutions. The derivation of these solutions is presented as well as numerous applications to a wide variety of time-independent and rate-dependent plastic constitutive laws.

Comments on “A closed form solution for the limit moment in the plastic torsion of an elliptical cylinder, by D. J. Unger”

Comments on “A closed form solution for the limit moment in the plastic torsion of an elliptical cylinder, by D. J. Unger”

Multi‐grid solutions to the elastic plastic torsion problem in multiply connected domains

AbstractThe elastic plastic torsion problem for an elastic, perfectly plastic cylinder with multiply connected cross section twisted around its longitudinal axis is formulated as an obstacle problem for an associated stress potential, the obstacle being defined in terms of a generalized distance function. Based upon the reformulation of the obstacle problem as an equivalent linear complementarity problem, the latter is discretized by means of finite difference techniques, and a monotonically convergent iterative scheme for its numerical solution is developed. At each step of the iteration the solution of a reduced system of discrete Poisson equations is required which is done by applying multi‐grid techniques with respect to a hierarchy of grid‐point sets. Combined with a suitably chosen nested iteration process this results in a computationally very efficient algorithm for the approximate solution of the elastic plastic torsion problem.

Plastic torsion of prismatic metal bars—mainly in respect of length changes: A review

The plastic torsion of circular and non-circular prismatic bars is reviewed. Primarily, the torsion test is conducted to provide shear-stress data, but investigation shows many poorly explained or explored phenomena associated therewith, particularly the nature of length changes with increasing strain and the effects of the discontinuous yielding of steel in torsion. Some of such phenomena as the latter are very pertinent to an understanding of suchmetal processing operations as include twisting, hot as well as cold, and fast as well as slow.

The experimental verification of the evolution of kinematic and isotropic hardening in cyclic plasticity

S imple plastic shear, plastic torsion, cyclic plastic shear, cyclic plastic tension-compression and out of phase tests of 18G2A and 21CrMoV57 steel were performed. The specimens were loaded monotonically and cyclically with constant effective strain rate under controlled amplitude of plastic strains at room temperature. Using the technique of successive unloadings, the standard physical quantities and the stress jumps corresponding to opposite directions of plastic straining were measured. For the Huber-Mises yield surface such results enable the evolution of kinematic and isotropic hardening for such programs to be followed. The results obtained show new effects concerning the influence of strain history on cyclic plasticity and can be useful for verification of existing theoretical approaches and stimulation of new theoretical ideas.

Nature of the ?yield tooth? under torsion in plastic-deformed whiskers

The plastic torsion of whiskers with high Peierls barriers has been studied. As the samples for the studies we chose p-type germanium whiskers with growth axis. The diameter of the whisker was (5–60)·10−6 m and the gauge length was (1–4)·10−3 m. The whiskers were dislocation-free in the initial state. Within the framework of the continuum model developed by us for the plastic deformation of whiskers under torsion, we analyze the anomalies of the torsional stress-strain diagram under different testing conditions and with preliminary deformation. The “flow tooth” during the torsion of a whisker is attributable to the nonuniform distribution of dislocations over the cross section of the whisker and high barriers to the dislocation motion.

A closed form solution for the limit moment in the plastic torsion of an elliptical cylinder

A compact, closed form solution is obtained for the limiting torque of a perfectly plastic elliptical cylinder.

The exact moment for the plastic torsion of a cylindrical bar of elliptical cross section

An exact expression for the limiting moment of the torsion of an isotropic, perfectly plastic elliptical bar has not been previously derived. In this note, the solution of this classical problem is reduced in form to a single quadrature. It is shown by comparison that an approximation due to Sokolovsky is inaccurate for large aspect ratios of semiaxes. Through a transformation of coordinates, the exact solution is also applicable to the plastic torsion of an orthotropic circular cylinder with generators perpendicular to a principal axis. It follows that for highly orthotropic materials an approximate solution derived by Hill may also prove inaccurate.

Springback analysis in torsion of rectangular strips

A theoretical analysis of the springback of narrow rectangular strips under torsional loading is presented. The theoretical analysis is supported by experimental results for different materials, different thicknesses and different lengths, keeping the width of the strips constant. Finally an analytical generalized expression relating angle of twist and twisting moment and residual angle of twist per unit length for rectangular bars under plastic torsion is obtained in non-dimensionalized form.

An anisotropic plasticity model for inelastic multi-axial cyclic deformation

The nature of the axial plastic strains resulting from cyclic plastic torsion of tubes with a steady axial load are examined. An anisotropic yield surface model is used to predict the axial plastic strains within a cycle of shear strain. The steady state cyclic shear stress-strain curve is used as material data to predict the cumulative axial strains over a number of cycles. The proposed yield surface model predicts the cumulative strains quite well for a wide range of cyclic strains and end loads and for cyclic strain hardening and softening materials.

Behaviour with Plastic Torsion of Solid Bar : 1st Report, Axial Extension and Surface Roughness with Torsion)

塑性ねじりとそのひずみ履歴による金属材料の挙動にについて実験を行い,引張りひずみ材のねじりによって軸方向に縮みを生じることを定量的に各種金属について検討した.またひずみ履歴による軸方向変位とともに,表面粗さについても調査し,ねじりもどしによる回復を各種金属の比較のもとに実験を行い,回復において材料となる特有な挙動を有することが明らかとなった.

ANISOTROPIC YIELD SURFACES IN CYCLIC PLASTICITY

Abstract— An anisotropic form of the Von Mises yield criteria is presented which includes linear terms and therefore enables Bauschinger effects to be considered when constructing yield or loading surfaces.The coefficients representing the state of anisotropy are expressed in terms of the uni‐axial and shear yield stress of the material. It is suggested that this form of the yield or loading surface can be used to determine the plastic strains for a range of multi‐axial and cyclic plasticity problems and results are presented for the particular case of a tube subjected to cyclic plastic torsion with an axial stress.