Characterization of the Torsional Behavior of Photosensitive Polymer Obtained by Stereolithography

An experimental and numerical mixed method based on the torsion test with and without warping of cross sections has been developed in order to characterize the shear behavior of a polymer material obtained layer by layer from a photosensitive resin (CiBA SL5170) polymerized by laser beam by the stereolithography technique. In this article, first the stereolithography technique is briefly presented, as well as the torsion device with and without warping of cross sections. Experimental and numerical results in static torsion of the polymer SL5170 are presented: shear modulus and strength of the material. From test results, a modeling of the superposition ratio of tensile and torsion stresses is proposed. It shows that the torsion of beams is complex. Torsion stresses and the tensile stress owed to the warping of section are superposed. In small-deformations state, material behavior behaves in a linear elastic way; experimental and numerical results are quantitatively and qualitatively coherent and conform to predictions of the elastic torsion theory. From experimental analysis of fatigue and elastoplastic damage behavior of the polymer, a phenomenological approach of the isotropic damage model is proposed. Based on the thermodynamics of irreversible processes, this local approach starts from a variant of the Chaboche-Lemaître model coupling plasticity and damage. This formulation is justified by the necessity to take into account the real stress state produced in the polymer during the torsion test.     

Certain characteristics of the straining of curved rods

The solution of the boundary-value problem for the region of the transverse cross section of a curved rod is investigated in relation to the function characterizing the warping of cross sections in elastic torsion. Analytical solutions are given for two problems involving the stressed-strained state of a rod whose axis is curved along a circular arc due to bending by a transverse force and torsion concentrated torque. It is shown that the deflection perpendicular to the plane of the initial curvature of the rod axis is accompanied by elastic rotation of the transverse cross sections. It is found that an additional stress system develops during the torsion of a curvilinear rod (in comparison with a straight rod). Some other characteristics of the stressed-strained state of curved rods are described.Translated from Problemy Prochnosti, No. 7, pp. 75–80, July, 1991.     

一维杆状结构声子晶体扭转振动带隙研究

从椭圆杆的扭转振动方程出发，利用平面波展开法，给出了无限周期结构的一维声子晶体杆的扭转振动能带结构。发现一维声子晶体具有扭转振动带隙，并且分析了椭圆形状对带隙频率的影响。利用有限元方法计算了有限周期结构的椭圆杆的扭转振动频率响应，在带隙频率范围内频率响应具有明显的衰减。扭转振动是噪声及振动控制领域研究的主要对象之一，周期结构杆中存在扭转振动带隙为减振理论与应用提供了一种新的思路。     

Use of the superelements method to solve problems involving a longitudinal shear crack

The method of superelements is used to solve problems in fracture mechanics. A study is made of the torsion of a rod containing longitudinal cracks. It is shown that a square is a convenient form of superelement for the tip of a type-III crack. The stiffness matrix of the superelement is calculated and a numerical example is presented.Translated from Problemy Prochnosti, No. 3, pp. 73–77, March, 1995.     

Numerical studies on the identification of the material parameters of Rivlin's hyperelasticity using tension-torsion tests

Summary This paper deals with the identification of material parameters of elasticity relations based on Rivlin's hyperelasticity for incompressible material response, where the free energy evolves as a polynomial in the first and second invariant of the right Cauchy-Green tensor. This elasticity relation has the advantage of incorporating the material parameters linearily. The numerical studies are applied to tension, torsion and combined tension-torsion tests with cylindrical carbon black-filled rubber specimens represented in Haupt and Sedlan [1] and [2]. In the identification process the analytical solution of the resulting boundary value problem leads to a linear least square solution. In this article attention is focused on the numerical solution of several models proposed in the literature and their behavior for both a large and a small number of test data.     

Fracture of Laser-Hardened Cylindrical Rods Caused by Torsion and Tension

We study the influence of the direction of motion of a laser beam over the surface of a cylindrical rod in the process of hardening on its strength and character of fracture caused by torsion. The process of hardening of specimens made of 45 steel performed in the tangential direction along a spiral and in the longitudinal direction along the generatrix with different degrees of overlapping of laser tracks results in the formation of an anisotropic structure, which strongly affects the investigated characteristics. The best results are obtained in the case where the direction of deformation of the rods coincides with the direction of screwing of a nut on a right-hand screw and the material of hardened tracks works in compression. In the case of torsion in the opposite direction, the material of hardened tracks works in tension and the strength of the specimens slightly increases. At the same time, their plasticity abruptly decreases.     

Stability and bifurcation of helical equilibrium of a thin elastic rod

Summary. The helical equilibrium and its stability of a thin elastic rod with noncircular cross section and intrinsic curvature and twist under application of force and torque are discussed in this paper. A stability condition of the helical equilibrium in the general case is derived in first approximation. The helical equilibrium of a rod without intrinsic curvature and twist is stable when the bending stiffness of the rod about the binormal axis is larger than the bending stiffness about the normal axis, and is always stable for a rod with circular section. The same condition is valid for a rod with intrinsic twist under pure torsion, or a planar ring with intrinsic twist, too. Greenhills formula as stability condition of a stretched and twisted straight rod with circular cross section applies also when the rod has intrinsic twist, and the influence of the asymmetry of the cross section on the stability diagram of a straight rod with noncircular cross section is demonstrated. In case of a rod with noncircular cross section under pure torsion each helical equilibrium corresponds to a singular point of Euler angles, and a static bifurcation of the number and stability of possible helical equilibriums with the change of intrinsic twist is presented.     

Elastic-plastic torsion of a Cosserat-type rod

Summary Elastic-plastic torsion of a Cosserat-type rod of a solid circular cross-section is considered. The governing equations are linearised using a small parameter which is equal to the relative grain rize. The linearized problem is subjected to asymptotic analysis based on the singular perturbation technique. Qualitative features of the elastic-plastic state of the rod are discussed. Apparently, this is the first explicit asymptotic solution for the elastic-plastic Cosserat continuum.     

Comparison of boundary element and finite element methods in the inelastic torsion of prismatic shafts

The accuracy and computational efficiency of the boundary element and the finite element methods are compared in this paper for problems of time-dependent inelastic torsion of prismatic shafts. Several cross-sections and two types of twisting history are considered in the numerical examples. The shaft material is assumed to obey an elastic-time hardening creep constitutive model.     

拉杆疲劳裂纹导致的组合转子性能退化研究

 组合转子作为燃气轮机等的核心部件,其性能退化机理并不明确,揭示其性能退化机理并有效地进行性能退化评估对燃气轮机等长期安全运行具有重要意义.为此,从结构损伤导致性能退化的角度出发,分析拉杆裂纹引起的组合转子性能退化特性.分别建立了组合转子有限元模型和弯曲、扭转刚度模型,利用有限元模型对拉杆上含初始裂纹的组合转子进行裂纹扩展分析,得到拉杆裂纹扩展速率;利用弯曲和扭转刚度模型分析了不同深度的裂纹对组合转子振动的影响,得到组合转子固有频率随裂纹尺寸的变化规律;并提出了衡量由微裂纹导致的组合转子性能退化的度量指标,实现了拉杆裂纹引起的组合转子性能退化的定量评估.研究表明：随着拉杆裂纹尺寸的增大,裂纹的扩展速率变快;拉杆裂纹的存在对组合转子的弯振影响较大,对扭振影响相对较小.     

The torsion of a tube (or a rod): General cylindrical kinematics and some axial deformation and ratchet measurements

Summary It is shown that the Murnaghan's displacement field is the more general form for a cylindrical tube (or rod) of isotropic material submitted to a load having the same symmetries. The use of this field enables us to analyse correctly the data furnished by strain gages. This is particularly useful in the case of torsion: the influence of a small misorientation, which actually always exists, can then be explained and taken into account.A series of experimental results of cyclic torsion tests with no axial force, obtained with stainless steel tubes, clearly indicates the existence of an axial ratchet, which is an elongation; this sign is confirmed by two other tests with a superalloy and an engineering steel. The amount of ratchet per cycle seems material dependent, is greatly influenced by a small axial force and is sensitive to the loading history.With 9 Figures     

Theoretical modeling of a diode-pumped Nd:YAG laser with a solid nonfocusing pump light collector

We report theoretical modeling for a diode-side-pumped Nd:YAG laser in which the laser rod is fixed in a solid nonfocusing (prismatic) light collector. The geometry provides for pumping the rod from four sides, which gives a relatively uniform gain profile across the transverse section of the rod and enables a high tolerance of the laser output to resonator and pump diode misalignment. The numerical model is developed to illustrate how the pumping uniformity and the transfer efficiency are affected when changes in the collector and lasing materials are made. We use small-signal gain measurements to test the predictions of the model and to examine the extent to which surface scattering from the rough rod barrel further spatially averages the deposited pump energy. The effects of the different refractive indices of the rod, collector, and fixant and the absorption properties of the laser material on optical transfer efficiencies are discussed.     

A computational study of the relations between material properties of long-rod penetrators and their ballistic performance

The paper summarizes a series of two-dimensional numerical simulations which were performed to study the effects of material properties on the terminal ballistics of long-rod penetrators. Our focus was on the properties of the rod material, unlike recent works which concentrated on a target’s properties. We varied almost all the relevant parameters within a large range of values in order to study the separate effects of each one. These parameters included: compressive and tensile strengths, elastic moduli, melting temperatures and the maximum equivalent plastic strain (failure strain) of the rod material. Most of the simulations were performed for an actual experiment with 300 mm tungsten-alloy long-rod, impacting a semi-infinite steel target. The simulations show that the mechanical and thermal softening mechanisms are the most dominant, as far as the depth of penetration is concerned. In contrast, the elastic moduli and spall strength have a negligible effect as far as penetration depth is concerned.     

结构参数影响聚能杆式弹丸成型的数值模拟

应用LS-DYNA3D软件对聚能杆式弹丸的形成过程进行数值模拟,研究了药型罩外曲率半径、壳体厚度、外层炸药等因素对聚能杆式弹丸成型的影响规律,得出形成理想聚能杆式侵彻体的各参数之间的关系;并对比分析了钢壳和铝壳形成理想聚能杆式弹丸的条件差异;模拟结果可应用于轻型壳体的聚能杆式战斗部结构设计。     

Erprobungsmethodik für zyklisch überelastisch beanspruchte Bauteile unter Torsion – Bauschinger‐Kenngrößen für 54SiCr6

Power transmission contains several torsion‐stressed parts. Especially shafts and springs are numerous considered. Helical springs as a special type of springs are mainly stressed by torsion load. During operation the spring's load is basically elastic. In some cases, like overload or machine disaster, the load exceeds the spring's yield stress. For a single event the deformations can be calculated easily by using flow charts. However in other cases the spring will be stressed several times with alternating plastic load. Therefore the calculation will not be as easy as in the single load case. Especially the hardening and softening mechanisms have major influence on material behavior. For high strength steel this material behavior is not fully investigated right now. Present article shows a way how to investigate several important Bauschinger parameters based on plastic torsion load for the high strength steel 54SiCr6. Finally it can be shown that 54SiCr6 is influenced by the Bauschinger effect. On the other hand the needed material characteristic can be investigated by the shown methodology. Based on the identified data, analytical and numerical calculation of alternating plastic torsion load can be done.     

Strengthening RC beams with composite fiber cement plate reinforced by prestressed FRP rods: Experimental and numerical analysis

This paper deals with the development of a new strengthening system for reinforced concrete beams with externally-bonded plate made of composite fiber cement reinforced by rebars made of fiber-reinforced plastic (FRP) [1]. The proposed strengthening material involves the preloading of FRP rod before mortar casting. The paper presents experimental and numerical analysis carried out on many large-scale beams strengthened by well-known reinforcement techniques, such as externally bonded Carbon Fiber-Reinforced Plastic (CFRP) plate and the Near Surface Mounted (NSM) technique, which are compared to the proposed new strengthening material through four-point bending tests. Results are analyzed with regard to the load-displacement curve, bending stiffness, cracking load, yield strength and failure load. The developed numerical model is in agreement with the experimental results. It clearly shows the effects of prestressed FRP rod on cracking mechanisms and internal strength distribution in the analyzed beams.     

Small torsional vibration superposed on finitely deformed state of a circular cylindrical rod of transversely isotropic elastic material

Starting with a class of small deformations superposed on a finitely deformed state of a transversely isotropic elastic solid, we study a problem of small torsional vibration superposed on homogeneous finitely deformed state of a circular cylindrical rod made of transversely isotropic elastic material. It has been found that free vibration is possible and, due to anisotropy, the speed of propagation of waves of torsion along the cylinder is increased or decreased according as the initial stressed state is under tension or compression.     

Damage evolution in nickel-base alloy torsion specimens and its influence on subsequent tensile deformability

The massive forming process can consist of consecutive deformation steps. Voids, initiated in preceding forming steps or present from the material production process, can reduce the deformability in the subsequent forming processes.Therefore, this work evaluates the influence of initiated voids on the deformability in a two step forming process. In the first step voids were initiated in a nickel-base alloy by torsion deformation of a rod. Tension specimens were machined from this predamaged rod and deformed until failure at a test temperature of 1000 °C. The tensile elongation leads to failure as a result of the growth and coalescence of the inherent voids. A constant void volume fraction at fracture was obtained for the specific material and test conditions, whereas the reduction in area - or fracture strain - varies significantly.     

Torsion of carbon fiber composite pyramidal core sandwich plates

A combined theoretical, experimental and numerical investigation of carbon fiber composite pyramidal core sandwich plates subjected to torsion loading is conducted. Pyramidal core sandwich plates are made from carbon fiber composite material by a hot compression molding method. Based on the Classical Laminate Plate Theory and Shear Deformation Theory, the equivalent mechanical properties of laminated face-sheet are obtained; based on a homogenization concept combined with a mechanical of materials approach, the equivalent in-plane and out-of-plane shear moduli of pyramidal core are obtained. A torsion solution is derived with Prandtl stress function and can be used in the sandwich plate with orthotropic face-sheets and orthotropic core. The influences of material properties and geometrical parameters on the equivalent torsional stiffness are explored. In order to verify the accuracy of the analytical torsion solution, experimental tests of sandwich plate samples with different face-sheet thicknesses are conducted and two types of finite element models are developed. Good agreements among analytical predictions, finite element simulations and experimental evaluations are achieved, which prove the validity of the present derivation and simulation. The proposed method could also be applied in design applications and optimization of the pyramidal core sandwich structures.     

Some results of a study of the problem of the tension-torsion of naturally twisted rods with a straight axis

General relations are presented for the components of the stress and strain tensors in the case of a naturally twisted rod in a moving orthogonal coordinate system. An algorithm is described for calculating the stress-strain state of the rod under the influence of external static loads. The boundary-value problem is replaced by a variational problem and solved as a three-dimensional problem of the linear theory of elasticity by the Ritz method. The algorithm is programmed in the language PL/1 for an ES-series computer. A discussion is presented of the results of the solution of two problems — the tension of the rod by a concentrated axial force and its torsion by a distributed moment. An analysis is made of the degree and character of the effect of two different factors on the stress-strain state: constraint of plane displacement of the cross sections and natural twisting of the rod. The results of the computer calculations are compared with experimental data and closed analytical solutions.Translated from Problemy Prochnosti, No. 12, pp. 59–64, December, 1990.