管件无模拉伸成形力能参数数学模型研究

对不锈钢管件无模拉伸变形速度场及力能参数进行了理论及实验研究.分析了不锈钢管件无模拉伸的变形模型、速度场以及力能参数的影响因素及影响规律,采用上限法确定了不锈钢管件无模拉伸速度场及力能参数物理模型,填补了国内外关于不锈钢管件无模拉伸变形及力能参数物理模型研究的空白.为不锈钢管件无模拉伸工艺工业化应用奠定基础.     

线材无模拉拔成形力数学模型研究

采用上限法确定了钨合金线材无模拉拔成形速度场及力能参数物理模型.分析了钨合金线材无模拉拔成形的变形模型、速度场以及力能参数的影响因素及影响规律,无模成形力能参数的影响因素主要有冷热源间距、断面减缩率、变形温度、拉伸速度、冷热源移动速度以及材料种类等,为无模拉拔成形工艺工业化应用奠定基础.     

Application of inverse finite element method in tube hydroforming modeling

In tube hydroforming, the inverse finite element method (IFEM) has been used for estimating the initial length of tube, axial feeding and fluid pressure. The already developed IFEM algorithm used in this work is based on the total deformation theory of plasticity. Although the nature of tube hydroforming is three-dimensional deformation, in this paper a modeling technique has been used to perform the computations in two-dimensional space. Therefore, compared with conventional forward finite element methods, the present computations are quite fast with no trial and error process. In addition, the solution provides all the components of strain. Using the forming limit diagram (FLD), the components of strain can lead us to measure the potentials for failures or wrinkles during the deformation. The results of analysis for free bulging and square bulging have been compared with some published experimental data and the results obtained by conventional commercial software.     

管材无模扩径壁厚变化数学模型研究

对管材无模扩径变形速度场及壁厚变化规律进行了理论及实验研究.分析了管材无模扩径的变形模型、速度场以及壁厚变化的影响因素及影响规律,采用上限法确定了管材无模扩径速度场及壁厚变化数学模型.     

Design and analysis of planar shape deformation

Shape deformation refers to the continuous change of one geometric object to another. We develop a software tool for planning, analyzing and visualizing deformations between two shapes in . The deformation is generated automatically without any user intervention or specification of feature correspondences. A unique property of the tool is the explicit availability of a two-dimensional shape space, which can be used for designing the deformation either automatically by following constraints and objectives or manually by drawing deformation paths.     

Effect of monoaxial stretching on molecular motion in Kapron

The effect of cold drawing on molecular motion in Kapron has been studied by the mechanical-loss method at a frequency of 1 Hz. A specially adopted procedure for carrying out experiments made it possible to evaluate the contribution to losses from amorphous bands and crystallites selectively. The decrease (recovery) of logarithmic decrement with time in freshly deformed Kapron samples has been observed — a phenomenon analogous to the known Köster effect, which is characteristic of low-molecular-weight crystalline solids. It has been shown that just as in conventional crystalline substances, the time dependence of damping in Kapron can be explained within the framework of the Granato-Hikata-Lücke theory, in conformity with which the recovery is caused by gripping of dislocations by point defects induced by the deformation. The dependence of the rate of recovery on the degree of deformation and the conditions of deformation (in the loaded or relieved state of the sample) is discussed.S. Ordzhonikidze Siberian Metallurgical Institute, Novosibirsk. Translated from Mekhanika Polimerov, No. 2, pp. 202–208, March–April, 1972.     

Mechanical properties of blends of liquid crystalline copolyesters with polyprophylene

Conclusions A significant effect of the addition of LCP on the mechanical properties and their anisotropy has been established. Already, if one considers the shape of curves of the stress-strain relationship it can be seen that curves typical for semicrystalline polymers (pure polypropylene) with clearly visible yield point and significant cold drawing leading to an anisotropic stiffening are changing into curves without yielding and with a brittle failure (LC-rich blends). Generally, the tensile elasticity modulus increases with increasing LCP content for both MD and TD. The maximum value of anisotropy of elastic properties was noted for a rather low content of LCP (c = 5%). On the contrary, the stress at yield decreases with increasing LCP content. The same was observed for the strain at yield but in both cases an important increase of anisotropy has taken place. Consequently, the total elongation during drawing (strain at break) showed a drastic decrease for blends with higher LCP content (about 60–80 times). The addition of the LCP to polypropylene has led to a stiffness increase (higher elasticity modulus) but simultaneously to a considerable plasticity decrease. As a confirmation of these observations, there served also the creep test where a decrease of the creep compliance (by two times) for LC-rich blends as compared with pure PP was noted.It also should be emphasized that, generally, a smaller effect of LCP content on the elastic deformation was noted than that on the time dependent effects (nonelastic creep deformation).Published in Mekhanika Kompozitnykh Materialov, Vol. 30, No. 4, pp. 442–450, July–August, 1994.     

Two-fluid Casson model for pulsatile blood flow through stenosed arteries: A theoretical model

Pulsatile flow of blood through mild stenosed narrow arteries is analyzed by treating the blood in the core region as a Casson fluid and the plasma in the peripheral layer as a Newtonian fluid. Perturbation method is used to solve the coupled implicit system of non-linear differential equations. The expressions for velocity, wall shear stress, plug core radius, flow rate and resistance to flow are obtained. The effects of pulsatility, stenosis, peripheral layer and non-Newtonian behavior of blood on these flow quantities are discussed. It is found that the pressure drop, plug core radius, wall shear stress and resistance to flow increase with the increase of the yield stress or stenosis size while all other parameters held constant. The percentage of increase in the resistance to flow over the uniform diameter tube is considerably very low for the present two-fluid model compared with those of the single-fluid model.     

FEM-Simulation of “Die-Less Hydroforming”

The following contribution focuses on the FEM-simulation of “Die-Less-Hydroforming” using LS-DYNA. That specific forming technology is used to create structures by inflating initial seal-welded flat 2D blanks as well as 3D hollow bodies without using any die, mould or punch in contrast to conventional hydroforming (e.g. tube hydroforming or hydromechanical deep drawing). (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Application of a viscoplastic material model on a combined quasi-static-electromagnetic forming process

The prediction and simulation of material behavior by finite element methods has become indispensable. Furthermore, various phenomena in forming processes lead to highly differing results. In this work, we have investigated the process chain on a cross-shaped cup in cooperation between the Institute of Applied Mechanics (IFAM) of the RWTH Aachen and the Institute of Forming Technology and Lightweight Construction (IUL) of the TU Dortmund. A viscoplastic material model based on the multiplicative decomposition of the deformation gradient in the context of hyperelasticity has been used [1,2]. The finite strain constitutive model combines nonlinear kinematic and isotropic hardening and is derived in a thermodynamically consistent setting. This anisotropic viscoplastic model is based on the multiplicative decomposition of the deformation gradient in the context of hyperelasticity. The kinematic hardening component represents a continuum extension of the classical rheological model of Armstrong-Frederick kinematic hardening. The constitutive equations of the material model are integrated in an explicit manner and implemented as a user material subroutine in the commercial finite element package LS-DYNA with the electromagnetical module. The aim of the work is to show the increasing formability of the sheet by combining quasi-static deep drawing processes with high speed electromagnetic forming. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Plastic mechanical analysis of drawing force based on a twin elliptical die

According to the stream function requirement, a twin elliptical die for rod or wire drawing is designed, and the subsequent plastic mechanical analysis is carried out. In terms of the volume constant condition, a kinematically admissible velocity field describing the drawing process is constructed. Based on the velocity field, the analytical expression of internal plastic deformation energy rate accounting for the non-zero shear strain rate is obtained by using the mean value theorem of integral. Then, the analytical expression of friction energy rate is also derived by the mean value theorem of integral. Ultimately, the analytical expression of the drawing force is obtained based on the upper bound method. It is found that there exists the optimal die semi-angle which depends on the relative reduction and friction factor. The analytical drawing force based on the twin elliptical die is validated by the corresponding simulated results, and a very agreement is found since the relative errors between them are less than 9.2%.     

On the two-dimensional orthogonal drawing of series-parallel graphs

It has been known that every planar 4-graph has a 2-bend 2-D orthogonal drawing, with the only exception being the octahedron, every planar 3-graph has a 1-bend 2-D orthogonal drawing with the only exception being K₄, and every outerplanar 3-graph with no triangles has a 0-bend 2-D orthogonal drawing. We show in this paper that every series-parallel 4-graph has a 1-bend 2-D orthogonal drawing.     

Stresses in elastic conical tubes of transversely isotropic materials with spherical anisotropies under temperature and force loadings

Analytic solutions are proposed for a number of new problems on determining the state of stress of a transversely-isotropic hollow cone with spherical anisotropy. An exact solution of the problem of the axisymmetric deformation of a long conical tube (or continuous cone) from an elastic transversely-isotropic material with spherical anisotropy subjected to an axial force is obtained in a spherical coordinate system R, , θ, the material axis of symmetry is directed along the spherical radius R. A rigorous solution is given of the problem of the uniform heating of a conical tube of transversely-isotropic material with spherical anisotropy for particular values of Poisson's ratios; the material axis of symmetry is directed along the θ-axis. For arbitrary Poisson's ratios an asymptotic solution is found for the temperature problem for a tube with small conicity.     

Deformation induced martensite transformation in a cold-worked forming process of austenitic stainless steel

Within the last years the goal of industrial manufacturing processes – such as tube forming – has shifted towards an optimization of technological as well as mechanical properties of the manufactured structures. For example, during the forming procedure of sheets made of austenitic stainless steel X5CrNi18-10, the content of strain-induced martensite needs to be controlled. In order to achieve optimal structural properties of the manufactured tube with respect to very high-cycle fatigue (VHCF), a martensite ratio of approximately 25% needs to be obtained [1]. On the basis of experimental investigations this contribution deals with the numerical simulation of the tube-forming process with special consideration of the martensite ratio c as a function of temperature and deformation field. For this purpose we extend an existing martensite model on polyaxial states of stress and compare experimental results and numerical simulations for the modified model. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

How to draw a clustered tree

The visualization of clustered graphs is a classical algorithmic topic that has several practical applications and is attracting increasing research interest. In this paper we deal with the visualization of clustered trees, a problem that is somehow foundational with respect to the one of visualizing a general clustered graph. We show many, in our opinion, surprising results that put in evidence how drawing clustered trees has many sharp differences with respect to drawing “plain” trees. We study a wide class of drawing standards, giving both negative and positive results. Namely, we show that there are clustered trees that do not have any drawing in certain standards and others that require exponential area. On the contrary, for many drawing conventions there are efficient algorithms that allow to draw clustered trees with polynomial asymptotically-optimal area.     

Some problems of the theory of plasticity for metals with strength differential

Within the framework of the problem of describing the plastic deformation of polycrystalline metals with strength differential, we consider problems of selection of universal constants and functions of the material that control the influence of the first and third invariants of the stress tensor. The possibility of using different types of experiments for the determination of these constants and verification of the theory is analyzed. It is shown that the traditionally used combined tension–torsion experiments on a thin-walled tube do not enable one to distinguish the influence of hydrostatic pressure and the Lode angle. The expedience of using biaxial tension and other experiments on simple and complex loading of a thin-walled tube by an axial force and internal pressure is justified.     

Thermal buckling and post-buckling analysis of geometrically imperfect FGM clamped tubes on nonlinear elastic foundation

Present research deals with the thermal buckling and post-buckling analysis of the geometrically imperfect functionally graded tubes on nonlinear elastic foundation. Imperfect FGM tube with immovable clamped–clamped end conditions is subjected to thermal environments. Tube under different types of thermal loads, such as heat conduction, linear temperature change, and uniform temperature rise is analyzed. Material properties of the FGM tube are assumed to be temperature dependent and are distributed through the radial direction. Displacement field satisfies the tangential traction free boundary conditions on the inner and outer surfaces of the FGM tube. The nonlinear governing equations of the FGM tube are obtained by means of the virtual displacement principle. The equilibrium equations are based on the nonlinear von Kármán assumption and higher order shear deformation circular tube theory. These coupled differential equations are solved using the two-step perturbation method. Approximate solutions are provided to estimate the thermal post-buckling response of the perfect/imperfect FGM tube as explicit functions of the various thermal loads. Numerical results are provided to explore the effects of different geometrical parameters of the FGM tube subjected to different types of thermal loads. The effects of power law index, springs stiffness of elastic foundation, and geometrical imperfection parameter of tube are also included.     

静脉壁的力学特性及负压失稳问题

应用一类超弹性应变能函数,通过非线性弹性理论,研究了静脉壁在跨壁压及轴向拉伸联合作用下的变形和应力分布等力学特性,并分析了静脉壁的负压失稳问题．首先利用超弹性材料薄壁圆筒模型,得到了静脉壁在跨壁压及轴向拉伸联合作用下的变形方程,给出了正常静脉压下静脉壁的变形曲线和应力分布曲线,讨论了静脉壁的变形和应力分布规律．然后给出了负跨壁压下静脉壁的变形曲线,并由能量比较讨论了静脉壁的负压失稳问题．     

Dynamic responses of shear flows over a deformable porous surface layer in a cylindrical tube

This paper investigates dynamic responses of a viscous fluid flow introduced under a time dependent pressure gradient in a rigid cylindrical tube that is lined with a deformable porous surface layer. With the Darcy’s law and a linear elasticity assumption, we have solved the coupling effect of the fluid movement and the deformation of the porous medium in the Laplace transform space. Governing equations are deduced for the solid displacement and the fluid velocity in the porous layer. Analytical solutions in the transformed domain are derived and the time dependent variables are inverted numerically using Durbin’s algorithm. Interaction between the solid and the fluid phases in the porous layer and its effects on fluid flow in tube are investigated under steady and unsteady flow conditions when the solid phase is either rigid or deformable. Examples are presented for flows driven by a Heaviside or a sinusoid pressure gradient. Significant effects of the porous surface layer on the flow in the tube are observed. The analytical solutions can be used to test more complicated numerical schemes.     

Forward and reverse creep of a physically nonlinear polymer material

From tension and torsion experiments under constant load, the authors determine the parameters of a material with physically nonlinear creep. They examine the applicability of these parameters to represent the deformation properties of materials under other loading systems. They give a method of drawing the reverse creep curve (in integral form) with parameters different from those of active creep.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 5, pp. 786–795, September–October, 1973.