Characterizing Torsional Properties of Microwires Using an Automated Torsion Balance

In order to characterize the torsional behavior of microwires, an automated torsion tester is established based on the principle of torsion balance. The main challenges in developing a torsion tester at small scales are addressed. An in-situ torsional vibration method for precisely calibrating the torque meter is developed. The torsion tester permits the measurement of torque to nN m, as a function of surface shear strain to a sensitivity of sub-microstrain. Using this technique, we performed (monotonic and/or cyclic) torsion tests on polycrystalline copper and gold wires. It is found that (i) a size effect appears in both the initial yielding and the plastic flow of torsional response; (ii) a reverse plasticity occurs upon unloading in cyclic torsion response; and (iii) the Hall-Petch effect and the strain gradient effect are synergistic. We also performed cyclic torsion tests on human hairs and spider silk which are natural protein fibers with a different morphological structure to metallic wires. It is shown that the single hair exhibits torsional recovery, and that the spider silk displays torsionally superelastic behavior whereby it is able to withstand great shear strain.     

Buckling of cylindrical shells under combined torsion and hydrostatic pressure

Results are given for a series of tests conducted to determine the elastic buckling behavior of circular cylindrical shells under hydrostatic pressure and torsion, both for individual and for combined loads. Nondimensional interaction curves are presented in terms of the geometric parameters of the cylinders and, in general, follow the parabolaP+T ²=1, whereP andT are the nondimensional critical hydrostatic and torsional loads, respectively.     

A combined analytical,numerical, and experimental study of shape-memory-alloy helical springs

In this paper, the pseudoelastic response of shape memory alloy (SMA) helical springs under axial force is studied both analytically and numerically. In the analytical solution two different approximations are considered. In the first approximation, both the curvature and pitch effects are assumed to be negligible. This is the case for helical springs with large ratios of mean coil radius to the cross sectional radius (spring index) and small pitch angles. Using this assumption, analysis of the helical spring is reduced to that of the pure torsion of a straight bar with circular cross section. A three-dimensional phenomenological macroscopic constitutive model for polycrystalline SMAs is reduced to the one-dimensional pure shear case and a closed-form solution for torsional response of SMA bars in loading and unloading is obtained. In the next step, the curvature effect is included and the SMA helical spring is analyzed using the exact solution presented for torsion of curved SMA bars. In this refined solution, the effect of the direct shear force is also considered. In the numerical analyses, the three-dimensional constitutive equations are implemented in a finite element method and using solid elements the loading–unloading of an SMA helical spring is simulated. Analytical and numerical results are compared and it is shown that the solution based on the SMA curved bar torsion gives an accurate stress analysis in the cross section of the helical SMA spring in addition to the global load–deflection response. All the results are compared with experimental data for a Nitinol helical spring. Several case studies are presented using the proposed analytical and numerical solutions and the effect of changing different parameters such as the material properties and temperature on the loading–unloading hysteretic response of SMA helical springs is studied. Finally, some practical recommendations are given for improving the performance of SMA helical springs used as energy dissipating devices, for example for seismic applications.     

A model of dilute polymer solutions with hydrodynamic interaction and finite extensibility. II. Shear flows

The results from numerical calculations for steady shear, the start-up and cessation of steady shear, and the stress relaxation after a step shear stain are discussed in detail for a bead-spring chain model with consistently averaged hydrodynamic interaction between the beads and consistently averaged finite extensible springs. Calculations are made for a large range of spring stiffnesses 10 ⩽ b ⩽ ∞ and a hydrodynamic interaction strength h^* = 0.15 a value which has been estimated from experimental results. This model is found to satisfy the Hassager-Bird and the Lodge-Meissner relations.     

Free-edge stresses and progressive cracking in surface coatings of circular torsion bars

This paper considers the explicit solutions of free-edge stresses near circumferential cracks in surface coatings of circular torsion bars and their application in determining the progressive cracking density in the coating layers. The problem was formulated within the framework of linear elastic fracture mechanics (LEFM). The free-edge stresses near crack tip and the shear stresses in the cross-section of the torsion bar were approached in explicit forms based on the variational principle of complementary strain energy. Criterion for progressive cracking in the coating layer was established in sense of strain energy conservation, and the crack density is thereby estimated. Effects of external torque, aspect ratio, and elastic properties on the density of progressive cracking were examined numerically. The present study shows that, in the sense of inducing a given crack density, compliant coating layer with lower modulus has much higher critical torque than that of a stiffer one with the same geometries and substrate material, i.e., compliant coating layer has greater cracking tolerance. Meanwhile, the study also indicates that thicker surface coating layer is more pliant to cracking than the thinner ones. The present model can be used for analyzing the damage mechanism and cracking tolerance of surface coatings of torsion shafts and for data reduction of torsional fracture test of brittle surface coatings, etc.     

Torsion of composite laminated bars with a large number of layers

I.IntroductionInmodernengineeringstructures,compositelaminatememberswiththickcross-sectionhavebeenextensivelyusedforundergoinghighload/presurcandanti-detonating.Duetotheinherentinbomogencousandanisotropicofmaterialsand3-Dconstructionalfeatures,classicallaminatetheoriesincludinghighorderplatetheory)areinadequate.Therefore,anewchallengetodevelopthicklaminatetheoriesisraised.ItisextremelydifficultandexDensiveforelementsdiscretizationinanalysisofstressesbyFEMI'j,becausethicklaminatesconsistofhu…     

An experimental study on the static and impact torsional buckling of cylindrical shells

In this paper, experimental studies are carried out on the buckling of circular cylindrical thin shells under impact torque. Experiments of impact buckling are made on a Hopkinson torsional bar. The torsional bar gives a step torque on the shells. Through an analysis of the strain-time curve obtained in experiment, the dynamic buckling critical torqueM _er and buckling waves numbern of the shell with different geometric data and some qualitative results are obtained. The buckling behavior of circular cylindrical thin shells under static and impact torque is compared.     

Eringen’s length scale coefficient for buckling of nonlocal rectangular plates from microstructured beam-grid model

Based on a microstructured beam-grid model, closed form solutions for Eringen’s length scale coefficient are derived for the buckling of nonlocal rectangular plates under compressive uniaxial load. The microstructured beam-grid model comprises rigid beam elements connected by rotational springs and torsional springs. Stiffness of the rotational springs and torsional springs are expressed in terms of the plate flexural and torsional rigidities, respectively. Exact buckling solutions are obtained for the microstructured beam-grid model. By interpreting the rigid element length as the internal characteristic length, the Eringen’s length scale coefficient $e_0$ may be determined by comparing the buckling load from the microstructured beam-grid model and the nonlocal rectangular plate model. The small length scale coefficient is shown to be dependent on the buckling mode, the aspect ratio of plate and boundary conditions.     

An inversion method for identification of elastoplastic properties of a beam from torsional experiment

A new method of determining elastoplastic properties of a beam from an experimentally given value T?T(φ) of torque (or torsional rigidity), during the quasistatic process of torsion, given by the angle of twist φ∈[φ_*,φ^*], is proposed. The mathematical model leads to the inverse problem of determining the unknown coefficient g=g(ξ²), ξ?|∇u|, of the non-linear differential equation −∇(g(|∇u|²)∇u)=2φ, x∈Ω⊂R². The inversion method is based on the parametrization of the unknown coefficient, according to the discrete values of the gradient ξ?|∇u|. Within the range of J₂-deformation theory, it is shown that the considered inverse coefficient problem is an ill-conditioned one. A numerical reconstruction algorithm based on parametrization of the unknown coefficient g=g(ξ²), with optimal selection of the experimentally given data T_m?T(φ_m), is proposed as a new regularization scheme for the considered inverse problem. Numerical results with noise free and noisy data illustrate applicability and high accuracy of the proposed method.     

The application of graph theory to the limit analysis for torsion of thin-walled bars with complex cross-sections

Graph theory is employed in this paper as a means to establish the topological model of complex thin-walled cross-sections. On this basis, the upper and lower bound theorems of the plastic limit analysis are applied to the analysis of the plastic limit shear flows on the cross-section of thin-walled bars under St. Venant torsion. Corresponding mathematical programming problems are formulated and their duality is shown. After solving the linear programming problem corresponding to the lower bound theorem, the limit torsional moment of a thin-walled cross-section can be calculated according to the shear stress distribution in the limit state. The formula for calculating the limit torsional moment is given. Furthermore, the limit state of thin-walled cross-sections under St. Venant torsion is also discussed and the concept of the limit tree is introduced. A computer program has been developed by the author. Results calculated by the program for typical complex cross-sections are given.     

开口厚壁截面短构件的约束扭转1）

为了分析开口厚壁截面短构件的约束扭转问题,采用统一分析梁模型与有限节线法,对T形和L形厚壁截面短构件约束扭转时横截面的翘曲和应力分布情况等问题进行了分析研究.算例计算结果表明：开口厚壁截面短构件存在与其横截面形心位置不一致的扭转（弯曲）中心,构件在不过扭转中心的外力作用下会产生弯扭耦合变形,其横截面将产生不均匀翘曲,横截面上的翘曲正应力和扭转剪应力均呈非线性分布.     

波形钢腹板PC组合箱梁纯扭作用下抗扭承载力计算模型

以扭转理论和固定角软化桁架模型为基础,推导了纯扭作用下波形钢腹板PC组合箱梁的抗扭承载力计算模型.该模型针对组合箱梁极限状态时,波形钢腹板处于屈服和未屈服状态两种情况,分别建立了剪应交连续与剪力流连续方程,模型同时考虑了不同位置预应力筋对抗扭承载力的不同作用.通过四根试验梁抗扭承载力理论计算结果与试验数据的对比分析,结果表明本文提出的计算模型不仅能够有效的计算抗扭承载力,还能计算出混凝土开裂后的扭矩-扭率曲线.     

Torsin of Functionally Graded Isotropic Linearly Elastic Bars

The purpose of this research is to investigate the effects of material inhomogeneity on the torsional response of linearly elastic isotropic bars. The work is motivated by the recent research activity on functionally graded materials (FGMs), i.e. materials with spatially varying properties tailored to satisfy particular engineering applications. The classic approach to the torsion problem for a homogenous isotropic bar of arbitrary simply-connected cross-section in terms of the Prandtl stress function is generalized to the inhomogeneous case. The special case of a circular rod with shear modulus depending on the radial coordinate only is examined. It is shown that the maximum shear stress does not, in general, occur on the boundary of the rod, in contrast to the situation for the homogeneous problem. It is shown that the material inhomogeneity may increase or decrease the torsional rigidity compared to that for the homogeneous rod. Optimal upper and lower bounds for the torsional rigidity for nonhomogeneous bars of arbitrary cross-section are established. A new formulation of the basic boundary-value problem is given. The results are illustrated using specific material models used in the literature on functionally graded elastic materials. This revised version was published online in August 2006 with corrections to the Cover Date.     

Delayed presetting of helical springs

Abstract

This article establishes the calculation of remaining deformation and residual stress for helical springs after long-lasting presetting process. The article extends the model for the immediate presetting process accounting the creep deformation of the spring. The method is based on plasticity theory for the instant flow overexposed by the relaxation over the long-term presetting. In this article, the following method is used. The plastic deformation of the helical spring with the circular cross section occurs instantly. If the shortening of the spring in the tool holder persists, the relaxation of stresses occurs and the force of the spring reduces. As the consequence, after the elastic unloading of the long-time presetting, the residual stresses spring reduce gradually with the squeezing time as well. The final length of the springs considerably shortens with the increasing preset duration. The advantage of the discovered closed form solutions is the calculation without the necessity of complex finite-element simulation of spring length loss and residual stresses after presetting process. The analytical expressions are proposed and the exact calibration applied for evaluation of factors for presetting processes.     

Quasi-Static Torsion Characterization of Micro-diameter Copper Wires

A method to measure very small torques that subject micro-diameter copper wires to plasticity is developed for quasi-static torsion experiment. Following the concept in the work by Fleck et al. (Acta Metall. Mater. 42:2, 1994), we employed a glass fiber filament as the torque cell. To calculate the small torques applied on the micro-diameter copper wires, an additional rotation sensor is required to measure the rotation of the glass fiber torque cell. The rotation sensor system is attached between the glass fiber and the copper wire specimen. It uses a laser extensometer to gauge the distance between a helical and a horizontal reflection tapes on a foam cylinder, which is calibrated with the angle of rotation. A new set of torsional experimental data for the copper wires with four different diameters, from 16–180 μm, are presented. All copper wires exhibit a typical elastic-plastic response. The torsional properties of these copper wires were not found to be significantly different. The uncertainties of the measurement and analysis are discussed.     

The effect of temperature on the viscoelastic behavior of linear low-density polyethylene

Summary Observations are reported on linear low-density polyethylene in isothermal torsional oscillation and relaxation tests at various temperatures ranging from room temperature to 110 C. Constitutive equations are derived for the viscoelastic response of a semicrystalline polymer at small strains. The polymer is treated as an equivalent network of strands bridged by junctions (entanglements, physical cross-links on the surfaces of crystallites and lamellar blocks). The network is thought of as an ensemble of meso-regions with various potential energies for rearrangement of strands. Two types of meso-domains are introduced: active, where strands separate from temporary junctions as they are excited by thermal fluctuations, and passive, where detachment of strands is prevented by the surrounding macromolecules. The time-dependent behavior of the ensemble reflects separation of active strands from their junctions and merging of dangling strands with the network. Stress–strain relations are developed by using the laws of thermodynamics. The governing equations involve six material constants that are found by fitting the experimental data. The study focuses on the effects of (i) temperature, (ii) the deformation mode (torsion versus bending), and (iii) the loading program (oscillations versus relaxation) on the adjustable parameters.This work was partially supported by the West Virginia Research Challenge Grant Program     

Stochastic torsional stability of an oil drill-string

The aim of this paper is to investigate the influence of uncertainties on the torsional vibration of drill-strings, in order to find out which uncertainty affects most significantly the torsional stability. The unstable torsional behavior is commonly associated to polycrystalline diamond compact bits, and manifests itself in the form of stick-slip oscillations. The stick-slip is a severe type of self-excited vibration characterized by large fluctuations in the rotation of the bit. It not only increases the bit wear, but also can cause drill-string failures. The analysis were done using a mathematical model of the drill-string based on classical torsion theory discretized by means of the finite element method. The bit-rock torque was included in the model as a nonlinear boundary condition at the bottom end of the drill-string. The values of the model parameters are typical values of a real drilling situation, which are subject to a high degree of uncertainty, what justifies a stochastic analysis. We have built probability distributions for the uncertain parameters and used Monte Carlo method to obtain the stochastic stability maps.     

Low frequency vibrations of elastic bars

The method of expansion of three-dimensional displacements in a double power series of the transverse coordinates is employed to find one-dimensional equations applicable to low frequency vibrations of uniform, elastic, isotropic and anisotropic bars. The axial displacements accompanying torsion are chosen specially for each cross-sectional shape of bar—resulting in the correct, or nearly correct, torsional rigidity. Applications are to bars of elliptic, triangular and rectangular sections, illustrating various independent and coupled extensional, flexural and torsional modes of motion.     

Correspondence Between One- and Two-Equation Models for Solute Transport in Two-Region Heterogeneous Porous Media

In this work, we study the transient behavior of homogenized models for solute transport in two-region porous media. We focus on the following three models: (1) a time non-local, two-equation model (2eq-nlt). This model does not rely on time constraints and, therefore, is particularly useful in the short-time regime, when the timescale of interest (t) is smaller than the characteristic time (?? ₁) for the relaxation of the effective macroscale parameters (i.e., when t?????? ₁); (2) a time local, two-equation model (2eq). This model can be adopted when (t) is significantly larger than (?? ₁) (i.e., when ${t\gg\tau_{1}}$ ); and (3) a one-equation, time-asymptotic formulation (1eq ^??). This model can be adopted when (t) is significantly larger than the timescale (?? ₂) associated with exchange processes between the two regions (i.e., when ${t\gg\tau_{2}}$ ). In order to obtain insight into this transient behavior, we combine a theoretical approach based on the analysis of spatial moments with numerical and analytical results in several simple cases. The main result of this paper is to show that there is only a weak asymptotic convergence of the solution of (2eq) towards the solution of (1eq ^??) in terms of standardized moments but, interestingly, not in terms of centered moments. The physical interpretation of this result is that deviations from the Fickian situation persist in the limit of long times but that the spreading of the solute is eventually dominating these higher order effects.