Solution of problems on the stress state of rotating anisotropic hollow cylinders that are nonuniform in the circumferential direction

A new approach is proposed to determining the stress-strain state of a rotating cylinder with elastic characteristics that vary in the radial and circumferential directions. Problems of this type are solved by expanding the stresses and the displacements into Fourier series, leading to a resolvent system of ordinary differential equations of a high order. The loads in these equations are given with allowance for the radial displacements. The problems are solved numerically by the method of discrete orthogonalization. As an illustration, specific problems are solved for several variants of nonuniformity of the elastic properties in the circumferential direction. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 35, No. 12, pp. 56–62, December, 1999.     

Experimental analysis of dynamic mechanical properties for artificially frozen clay by the split Hopkinson pressure bar

A device for impact compression experiments is the split Hopkinson pressure bar with a refrigerating attemperator. Data for incident and reflected waves are obtained by the measuring technique with strain gauges, and data for transmitted waves are obtained by the measuring technique with semiconductor gauges. Static compression tests of frozen clay are conducted at an identical temperature and different strain rates of 0.001 and 0.01 sec ⁻¹ . Dynamic stress-strain curves are obtained at strain rates of 360–1470 sec ⁻¹ . The low and high temperatures correspond to high and low strain rates, respectively. It is shown that both the temperature and strain rate affect the frozen soil deformation process. Different dynamic stress-strain curves obtained at the same temperature but different strain rates are found to converge. The test results indicate that frozen soil has both temperature-brittleness and impact-brittleness.     

碳布叠层/碳复合材料动态压缩性能测试研究

利用带有波形整形器的Split Hopkinson Pressure Bar(SHPB)技术测试了碳布叠层/碳复合材料在应变率为500、1 500 s-1时的动态压缩性能。研究结果表明:利用轧制紫铜作为整形器材料不仅可以有效地实现对碳布叠层/碳复合材料的常应变率压缩加载，而且有助于改善试样两端的应力平衡，从而保证测试数据的可靠性；此外，与准静态压缩相比较，在动态压缩载荷下，碳布叠层/碳复合材料的压缩强度有较强的应变率效应，且复合材料压缩强度的动态增加函数可以用Cowper-Symonds幂函数的形式来表示。     

Quadratically Nonlinear Cylindrical Hyperelastic Waves: Derivation of Wave Equations for Plane-Strain State

A method is proposed for deriving nonlinear wave equations that describe the propagation and interaction of hyperelastic cylindrical waves. The method is based on a rigorous approach of nonlinear continuum mechanics. Nonlinearity is introduced by means of metric coefficients, Cauchy-Green strain tensor, and Murnaghan potential and corresponds to the quadratic nonlinearity of all basic relationships. For a configuration (state) dependent on the radial and angle coordinates and independent of the axial coordinate, quadratically nonlinear wave equations for stresses are derived and stress-strain relationships are established. Four ways of introducing physical and geometrical nonlinearities to the wave equations are analyzed. For one of the ways, the nonlinear wave equations are written explicitly__________Translated from Prikladnaya Mekhanika,Vol. 41, No. 5, pp. 40–51, May 2005.     

膨胀环受力历史对应力应变关系的影响

利用两类实验装置开展了无氧铜TU1膨胀环实验研究,发现:电磁膨胀环在加载阶段,样品受体力作用,满足均匀变形的假定;而爆炸膨胀环在加载阶段,样品内壁受面力冲击作用,不满足均匀变形的假定。针对这个差异,发展了一种考虑冲击阶段变形不均匀性的新方法,利用回收样品几何变形,将冲击阶段试样环内轴向塑性应变、径向塑性应变纳入等效塑性应变的计算中,通过修正后的方法更准确地获得了材料的应力应变关系。     

The effect of strain softening in the matrix material during void growth

A Finite element analysis has been employed to investigate the growth of an initially spherical void embedded in a cylinder of elastic-plastic material. The boundary displacement of this cylindrical cell is regulated by the value of a parameter α which controls the radial shrinkage of the cell as it elongates. A large strain analysis was used and results for both strain hardening and strain softening (after an appropriate amount of hardening has taken place) have been obtained. The effects of different mean tensile stresses, equivalent strains and initial void volume fractions have also been included. The numerical work shows relationships between the mechanical and geometrical variables that may favour ductile fracture by void coalescence or by shear decohesion.     

Analysis of dynamic stress intensity factors of thick-walled cylinder under internal impulsive pressure

Dynamic stress intensity factors are evaluated for thick-walled cylinder with a radial edge crack under internal impulsive pressure. Firstly, the equation for stress intensity factors under static uniform pressure is used as the reference case, and then the weight function for a thick-walled cylinder containing a radial edge crack can be worked out. Secondly, the dynamic stresses in uncracked thick-walled cylinders are solved under internal impulsive pressure by using mode shape function method. The solution consists of a quasi-static solution satisfying inhomogeneous boundary conditions and a dynamic solution satisfying homogeneous boundary condi- tions, and the history and distribution of dynamic stresses in thick-walled cylinders are derived in terms of Fourier-Bessel series. Finally, the dynamic stress intensity factor equations for thick-walled cylinder containing a radial edge crack sub- jected to internal impulsive pressure are given by dynamic weight function method. The finite element method is utilized to verify the results of numerical examples, showing the validity and feasibility of the proposed method.     

Dynamic stress intensity factors of two collinear cracks in orthotropic medium subjected to time-harmonic disturbance

Dynamic stresses are obtained for an infinite orthotropic medium weakened by two collinear cracks. Time-harmonic elastic waves are interrupted at normal incidence by the line cracks. Fourier transform is applied reducing the problem to solving a pair of dual integral equations. Solution method involves expanding the crack surface displacement in a series of functions that vanish along a collinear line outside the cracks. The unknown coefficients in the series are evaluated by using the Schmidt method. Dynamic stress intensity factors are computed and displayed graphically for an orthotropic medium that corresponds to the elastic properties of boron-epoxy composite.     

Inelastic deformations of stainless steel leaf springs-experiment and nonlinear analysis

A stainless steel leaf spring is designed and constructed followed by its performance evaluation by experiment and non-linear analysis so that an insight into the optimum use of material can be made. Cantilever beams of uniform strength, popularly termed as leaf springs, undergo much larger deflections in comparison to a beam of constant cross-section; that needs inclusions of geometric non-linearity for rigorous analysis. This study deals with such a cantilever beam, but takes into account the material non-linearity as well. Experiments were conducted for such a cantilever beam, with highly non-linear stress-strain curves. In addition to the experiment, a computer code in ‘C’ has been developed using the Runge-Kutta technique for the purpose of simulation. Effective modulus-curvature relations are obtained from the non-linear stress-strain relations for different sections of the beam and used for the analysis. It is seen that non-linear stress-strain curve governs the bending of the beam. Importantly, non-linear analysis shows the stresses are not so high as predicted by the linear theory without end-shortening. Moreover, the tensile and compressive stresses are different in magnitude and both decrease along the span. Experimental load-deflection curves are found to be initially concave upward but, non-linear and convex upward at a high load. Comparison of the numerical results with the available experimental results from another research group and theory shows excellent agreement verifying the soundness of the entire numerical simulation scheme.     

Radial expansion of a granular medium in spherical and cylindrical layers

An exact solution that describes the fields of displacements and stresses in an expanding spherical layer is constructed within the framework of the theory of small strains of a granular medium with rigid particles. For finite strains, the problem reduces to a nonlinear system of ordinary differential equations, which is solved by numerical methods. Similar solutions are found in the problem for a cylindrical layer. Based on these solutions, the effect of the dilatancy of the granular medium on the stress-strain state near expanding cavities is found. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 3, pp. 190–196, May–June, 2009.     

应用云纹干涉法测量冷挤压孔周残余应力分布

本文就冷挤压加工后紧固孔周的残余应力测量问题进行了研究。文中提出了径向切割法以释放欲求剖面的周向残余应力;采用高灵敏度的云纹干涉法测量残余应力释放后引起的附加变形;用载波错位法获得高反差的应变条纹图。     

较低应变率大应变条件下聚氨脂泡沫材料的态力学性能实验

利用加长型分离式霍普金森压杆(入射杆长6000mm、子弹长800mm)研究聚氨脂泡沫材料在较 低应变率大应变条件一维应力状态下的动态力学性能,获得了约550s的长加载脉冲,得到了该材料在应变 率520s-1、应变0.15条件下的应力应变曲线,对较低应变率条件下,应变率与动态应力平衡之间的关联进行 了讨论。     

爆轰波对碰驱动下金属圆管膨胀变形特性研究

采用高速分幅摄影和激光速度干涉仪（velocity interferometer system for any reflector, VISAR）联合测试技术,对HR-2钢管在爆轰波对碰驱动下的膨胀变形特性进行了研究。实验得到了圆管膨胀变形的过程图像以及圆管特定部位径向膨胀的位移-时间曲线和速度-时间曲线。采用LSDYNA-3D程序对HR-2钢管的膨胀变形过程进行了数值模拟,计算结果与实验结果吻合较好。     

Dynamic axisymmetric problem of the direct piezoeffect for a radially polarized anisotropic piezoceramic cylinder

An unsteady problem of electroelasticity for a long radially polarized anisotropic piezoceramic cylinder with normal stresses that are arbitrary functions of time applied to the radial surfaces is considered. A closed solution is constructed by the method of expansion with respect to eigen vector-functions. This solution allows determining the frequencies of natural oscillations, the stress-strain state of the element, and the potential and intensity of the induced electric field.     

The alignment error of the hole-drilling method

The hole-drilling method is one technique for measuring residual stresses. All the existing equations for the calculation of residual stresses are based on the assumption that the hole is located at the rosette center. In this paper, the stress-strain relationship for the eccentric hole case has been derived and expressed in terms of the off-center distance and the polar angle. The alignment error is studied and demonstrated by two examples, namely, a uniaxial-stress field and a hydrostatic-stress field. The error analysis yielded the following typical result: ten percent of hole radius off-center will yield about five-percent measurement error for the standard rosette (EA-09-062-RE-120).     

应变率历史对应力应变曲线的影响

利用普通SHPB实验系统、双试件SHPB实验系统，对一特种钢材进行了不同应变率历史的动态压缩实验，获得了不同应变率历史所对应的应力应变曲线。通过量化平均应变率相同的情况下不同应变率历史所对应的应力应变曲线的差别，以及量化应变率历史的恒定程度，初步分析了应变率历史对应力应变曲线的影响。研究结果表明:特别是在较高平均应变率下，应变率历史对试件材料的应力应变曲线有明显的影响，在材料动态本构关系研究中应当考虑应变率历史的影响。     

Rheological properties of fresh and cryopreserved human arteries tested in vitro

Cryopreservation is widely used to preserve blood vessels for a while but is controversially suspected to affect the mechanical behavior of these allografts. The aim of this study was to determine whether differences in the three-dimensional mechanical behavior exist or not between fresh and cryopreserved arteries. Using a previously developed experimental system, in vitro inflation tests were performed on twenty segments of human fresh and cryopreserved arteries, in static conditions. Opening angles were also measured from images of rings in zero-stress state. The initial reference state was chosen as the unloaded state and tests were performed on specimens stretched at natural “in vivo” length. Mechanical measures calculated are “natural” (Hencky) strains (finite deformations), “true” (Cauchy) stresses in radial, circumferential, and longitudinal directions as well as strain energy per unit volume. Tangent moduli are derived from radial and circumferential stress-strain characteristics using non-linear curve fitting. Values of incremental and pressure-strain elastic parameters, wall stiffness, and compliance per unit length are also calculated. Results are presented in terms of characteristics of stresses and strains in the three directions, axial force, tangent moduli vs strains or stresses, and energy per unit volume, for both types of artery, with reference to transmural pressure. Detailed numerical results are given at mean transmural pressure or in the physiological range. Significant differences are indicated by statistic Student T-tests. Results obtained show that significant differences exist between rheological properties of fresh and cryopreserved segments of human artery. Strains, stresses, axial force, strain energy, and wall stiffness values highlight those differences whereas elastic parameters, compliance, and opening angle do not. The usefulness of some parameters to compare the mechanical behavior existing between fresh and cryopreserved arteries is therefore underlined. Received: 3 January 2000 Revision received: 12 April 2000 Accepted: 8 May 2000     

Measurement of Applied Stresses and Residual Stresses on a Residual Stress Model by Applying Two Different Loads

Applied stresses on a residual stress model have previously been obtained by measuring the residual stresses and the resultant stresses generated by applying a load. The present paper reports that the applied stresses and the residual stresses on the residual stress model can be obtained by measuring two resultant stresses generated by applying loads of two different magnitudes. In the proposed method, the residual stresses need not be obtained from the residual stress model before applying a load. The residual stress model used to test the proposed method is a circular disk with frozen stresses that is subjected to a diametral compressive load at a certain angle. The applied stresses and the residual stresses on a residual stress model were experimentally and precisely obtained by digital photoelasticity using linearly polarized light.     

Analysis of axially symmetrical residual stresses in bars and tubes

A new method has been developed for the determination of residual stresses in a cylinder. Boring out or removing layers from outside induces changes in the length and diameter of the remaining bar. The initial distributions of the stresses are derived from measurements of the length change only. Details of equations required for the calculations are described. The method rests on an assumption that the radial displacement just below a surface is equal to the radial displacement at a new surface after removal of the surface layer of material. This assumption leads to relations between the three residual-stress components. The numerical calculations of these relations agree well with the experimental data for quenched cylinders obtained by using the Sachs method in other investigations. A brief general discussion is given on the equilibrium conditions of the residual stresses determined.     

Numerical-Analytic Solution of Boundary-Value Stress-Strain Problems for Rotating Anisotropic Cylinders

A numerical-analytical approach is proposed to solve boundary-value stress-strain problems for hollow inhomogeneous cylinders under centrifugal loading. Their elastic characteristics vary in both radial and circumferential directions. The governing system of ordinary differential equations is derived using Fourier series for stresses and displacements. It is solved by the discrete-orthogonalization method. Solutions to specific problems are exemplified __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 8, pp. 82–87, August 2005.