The dependence of yield stress on strain rate as determined from ball-indentation tests

A ball-indentation experiment was conducted to explore the possibility of using this test for the investigation of strain-rate dependence of yield properties of materials. The initial velocities of indentation used were between 0.0002 and 3 ips. Force and depth of penetration were measured continuously during a test. Using these and the results given in a previous report, the dependence of yield pressure of the indentation test on penetration velocity is shown for a range of velocities from 0.0002 to 300 ips. Results are presented for annealed C1018 steel, annealed 1100 F and annealed 6061-T6 aluminums. For all materials tested, the dependence of yield stress on strain rate seems to be derivable from the ball-indentation results by using Tabor's empirical formulas and an equation relating strain rate and velocity of penetration. The increase of yield pressure over the range of indentation velocities is 100 percent for steel, 30 percent for 1100 aluminum and 20 percent for 6061 aluminum.     

Uniformly moving screw dislocation interacting with interface cracks in anisotropic bimaterials

This paper attempts to investigate the problem for the interaction between a uniformly subsonic moving screw dislocation and interface cracks in two dissimilar anisotropic materials. Using Riemann–Schwarz’s symmetry principle integrated with the analysis singularity of complex functions, we present the general elastic solutions of this problem and the closed form solutions for interface containing one and two cracks. The expressions of stress intensity factors at the crack tips and image force acting on moving dislocation are derived explicitly. The results show that the stress intensity factors at the crack tips decrease with increasing velocity of dislocation, and larger dislocation velocity leads to the equilibrium position of dislocation leaving from crack tips. The presented solutions contain previously known results as the special cases.     

A moving screw dislocation near interfacial rigid lines in two dissimilar anisotropic media

This paper attempts to investigate the problem for the interaction between a uniformly moving screw dislocation and interface rigid lines in two dissimilar.anisotropic. materials. Integrating Riemann-Schwarz＇s symmetry principle with the analysis singularity of complex functions, we present the general elastic solutions of this problem and the closed form solutions for interfaces containing one and two rigid lines. The expressions of stress intensity factors, at the rigid line tips and image force acting on moving dislocation are derived explicitly. The results show that dislocation velocity has an antishielding effect on the rigid line tip and a larger dislocation velocity leads to the equilibrium position of dislocation closing with the rigid line. The presented solutions contain previously known results as the special cases.     

多孔材料吸能行为对相对密度和冲击速度的依赖性

多孔材料是一种优异的吸能缓冲材料,但由于其变形模式的非单一性以及动态应力应变曲线的难获取性,其吸能行为对相对密度和冲击速度的依赖性关系还并不完全明朗。本文基于不需要提前作本构假定的波传播法,开展了多孔材料的吸能行为研究。采用多孔材料的细观有限元模型进行Taylor冲击虚拟实验,获取全场质点速度时程曲线,结合Lagrange分析法得到多孔材料的局部应力应变信息,进而探讨了动态吸能性能对材料相对密度和冲击速度的依赖性。研究结果表明多孔材料的吸能行为可依据变形模式分为三个阶段。在冲击模式下,多孔材料单位体积吸能与相对密度成线性增加关系,此时惯性起主导作用;在过渡模式下,惯性的主导作用减弱,单位体积吸能量的增加速率随相对密度的增加而减弱;在准静态模式下,多孔材料只能发生微小的变形,其吸能很少。本文进一步获得了区别于多孔材料准静态应力-应变曲线的动态应力-应变状态曲线,并考察了其与相对密度之间的关系。结果表明：随着相对密度的增加,多孔材料的动态压实应变将变小,而动态塑性平台应力将提高。     

Normal perforation of a thin infinite plate by a flat-headed cylindrical projectile

Analytical formulae for calculating the stress acting on the contact surface between projectile and target and for calculating the moving velocity of this contact surface under impact are both suggested in this paper. These formulae can be thought of as a generalization of the well-known Hopkins and Kolsky’s theory in plastic domain. And then, an analytical formula for calculating ballistic limit is also suggested. It is also proved in this paper that the shear stress acting on the cylindrical surface of the plug is distributed uniformly.     

A model of bubbles rising in a fluidized bed

A model for a single fully developed bubble moving in an unbounded fluidized bed is presented. The model allows bubble growth or shrinkage during the rise inside the bed, as well as dependence of the rise velocity upon specified bed parameters. Limiting cases of nearly spherical bubbles and of sufficiently large bubbles whose form resembles that of a spherical segment are considered in more detail. The form of bubbles rising in either fluidized beds or one-phase liquids, and its dependence on the effective “surface tension” acting on the bubble boundary are discussed.     

侵彻条件下两类靶体材料静阻力的探讨

以空腔膨胀理论为主要理论工具，通过比较侵彻近区塑性材料和脆性材料动力学行为的差异，对两类不同材料静阻力（R_t）的本质进行探讨，并对脆性材料侵彻的若干应用问题提出建议。研究表明:（1）R_t是靶体介质以固体特性抵抗局部扩孔、具有时间平均特性的弹体横截面平均应力，其具体取值随着材料的物理力学特性、侵彻模型、撞击速度等因素而变化，因此不是材料的固有特性。（2）对于塑性靶体的非变形侵彻问题，静态空腔膨胀理论的结果能够对R_t作出比较合理的预测；对于拟流体侵彻问题，一般需要对静态空腔膨胀理论的结果加以修正。（3）脆性材料的R_t主要取决于破碎后介质的力学特性而与完整材料的力学特性关系不大，且与单轴抗压强度之间不满足纯粹的单调关系；当侵彻速度较低时，应考虑侵彻速度对侵彻阻力的强化作用，这种强化作用的本质是内摩擦；当侵彻速度足够高时，脆性材料体现出恒定不变的“动力硬度”，其反映了材料的本征阻力特性。（4）提高脆性材料的侵彻阻力的关键在于减小应力波峰值后环向拉应力的幅值、抑制材料的破碎速度和程度，具体措施包括主动或被动地增加外围压、对基质中添加增韧增强纤维等；为了实现对脆性材料侵彻问题更高精度的数值模拟，建议更加重视对破碎介质动力学特性的研究。     

Thermoelasticity of bodies with microstructure and microtemperatures

This paper is concerned with a linear theory of thermodynamics for elastic materials with microstructure, whose microelements possess microtemperatures. It is shown that there exists the coupling of microrotation vector field with the microtemperatures even for isotropic bodies. Uniqueness and continuous dependence results are presented. The theory is used to establish the solution corresponding to a concentrated heat source acting in an unbounded continuum.     

Plane stress state problems for notched bodies whose plastic properties depend on the form of the stress state

We consider one possible approach to the problem of describing the dependence of material plastic strain characteristics on the stress hydrostatic component arising in many porous, fractured, and other inhomogeneous materials. The plastic strain of the media under study is investigated under the plasticity assumption in the corresponding generalized form with the use of the form parameter of the stress state. The plasticity constitutive relations are stated on the basis of the plastic flow law associated with the accepted plasticity condition. For the conditions of plane stress state in the framework of the material rigid-plastic model, a system of partial differential equations is obtained and conditions for its hyperbolicity are determined. The relations for determining the stress fields and velocity fields in plastic domains are obtained, and their properties are investigated. The problem of tension of a strip with symmetric angular notches is solved, where the stress fields are determined and the continuous displacement rate field is constructed. The problem of uniform symmetric tension of a plane with a circular hole is considered. The stress fields in a strip with symmetric circular notches are examined. A comparison with solutions for plastically incompressible media whose properties are invariant with respect to the form of the stress state is performed.     

Interrelation of creep and relaxation for nonlinearly viscoelastic materials: application to ligament and metal

Creep and stress relaxation are known to be interrelated in linearly viscoelastic materials by an exact analytical expression. In this article, analytical interrelations are derived for nonlinearly viscoelastic materials which obey a single integral nonlinear superposition constitutive equation. The kernel is not assumed to be separable as a product of strain and time dependent parts. Superposition is fully taken into account within the single integral formulation used. Specific formulations based on power law time dependence and truncated expansions are developed. These are appropriate for weak stress and strain dependence. The interrelated constitutive formulation is applied to ligaments, in which stiffness increases with strain, stress relaxation proceeds faster than creep, and rate of creep is a function of stress and rate of relaxation is a function of strain. An interrelation was also constructed for a commercial die-cast aluminum alloy currently used in small engine applications.     

Analytical investigation of the fluid flow in the interface region between a porous medium and a clear fluid in channels partially filled with a porous medium

In this paper analytical solutions for the steady fully developed laminar fluid flow in the parallel-plate and cylindrical channels partially filled with a porous medium and partially with a clear fluid are presented. The Brinkman-extended Darcy equation is utilized to model the flow in a porous region. The solutions account for the boundary effects and for the stress jump boundary condition at the interface recently suggested by Ochoa-Tapia and Whitaker. The dependence of the velocity on the Darcy number and on the adjustable coefficient in the stress jump boundary condition is investigated. It is shown that accounting for a jump in the shear stress at the interface essentially influences velocity profiles.     

On the force acting on a heated spherical drop moving in a gaseous medium

The flow around a heated spherical drop in a viscous non-isothermal gaseous medium with uniformly distributed constant-power heat sources (sinks) acting inside is theoretically described in the Stokes approximation. It is assumed that the mean temperature of the drop surface can differ substantially from the temperature of the ambient gaseous medium. An analytical expression for the drag force and drift velocity in the gravity field is derived by solving hydrodynamic equations with allowance for the temperature dependence of viscosity, thermal conductivity, and density of the gaseous medium.     

A device for measuring the velocity of ultrasonic waves: An application to stress analysis

In this paper we present a device for the practical application of an ultrasonic critical-angle refractometry (UCRfr) technique. UCRfr is a technique for measuring the velocity of longitudinal, shear and Rayleight waves, developed to improve the traditional ultrasonic methods for measuring the stress level in materials by means of acousto-elasticity. The technique consists of relating the variations in wave propagation velocity to variations in the angle of refraction at the interface with a second medium. Variations in the angle of refraction are determined on the basis of delay in receiving of the same wave at two different points. The study deals with the measurements of velocity changes of longitudinal wave due to uniaxial stress. In the present work the effects of stress on aluminum and steel specimens have been studied. Experimentation has show the potential of the technique for stress measurement; on the other hand, when the applied stress is known, it allows the measurement of the acoustoelastic constants of longitudinal waves. As regards measuring variations in velocity induced by stress, using this method it is possible, with a suitable choice of the material the device is made of, to isolate the effects of stress on velocity from the possible effects of temperature.     

Torsional surface waves in heterogeneous anisotropic half-space under initial stress

The present paper is concerned with the propagation of torsional surface waves in a heterogeneous anisotropic half-space under the initial compressive stress. The heterogeneity in the half-space is caused by the linear variation in rigidity, initial compressive stress and density. The solution part of the problem involves the use of Whittaker function. The dispersion equation has been obtained in a closed form, which shows the variation of phase velocity with corresponding wave number. Effects of anisotropy and initial stress have been shown by the means of graphs for different anisotropic materials. It has found that the phase velocity of torsional waves decreases with increment in initial stress and inhomogeneity. Obtained phase velocity of torsional surface wave is found to be less than the shear wave velocity, which agrees with the standard result.     

Mechanism of shear attenuation near the interface under combined compression and shear impact loading

We investigate the compressional/shear coupling plastic wave propagation characteristics analytically for ideal elastic–plastic materials in both stress and particle velocity spaces, focusing on the shear wave attenuation near the interface occurring in pressure–shear plate impact experiments. The results show that the shear attenuation is strongly associated with the wave propagation characteristics of the coupling waves. In the stress space, as the shear stress increases, an adjustment of the stress components is observed and the final stress state along the wave path is a combined pure shear- and hydrostatic pressure-state. In the particle velocity space, the wave structures with different loading and maximal transverse particle velocity are obtained. The maximal transverse particle velocity varies with the longitudinal velocity and forms a boundary line. Once the loading transverse velocity exceeds this line, a transverse particle velocity discontinuity occurs at the impact interface. If the bonding strength is sufficiently high, there will be a shear band in the target in the extreme vicinity of the interface.     

Fracture of a body with a periodic set of coaxial cracks under forces directed along them: an axisymmetric problem

Linearized solid mechanics is used to solve an axisymmetric problem for an infinite body with a periodic set of coaxial cracks. Two nonclassical fracture mechanisms are considered: fracture of a body with initial stresses acting in parallel to crack planes and fracture of materials compressed along cracks. Numerical results are obtained for highly elastic materials described by the Bartenev–Khazanovich, Treloar, and harmonic elastic potentials. The dependence of the fracture parameters on the loading conditions, the physical and mechanical characteristics of the material, and the geometrical parameters is analyzed Translated from Prikladnaya Mekhanika, Vol. 45, No. 2, pp. 3–18, February 2009.     

Angular Dependence of Rayleigh-Wave Velocity in Prestressed Polycrystalline Media with Monoclinic Texture

This article is concerned with Rayleigh waves propagating along the free surface of a macroscopically homogeneous, prestressed half-space. In the meso-scale, the half-space in question is taken to be a textured polycrystalline aggregate of cubic crystallites, which has the normal to its free surface being a 2-fold axis of monoclinic sample symmetry. Under the theoretical framework of linear elasticity with initial stress, an angular dependence formula, which shows explicitly how the phase velocity of Rayleigh waves depends on the propagation direction, the prestress, and the crystallographic texture, is derived from a constitutive equation motivated by Hartig's law. This velocity formula includes terms which describe the effects of texture on acoustoelastic coefficients, and it is correct to within terms linear in the initial stress and in the anisotropic part of the incremental elasticity tensor. Since its derivation makes no presumption on the origin of the initial stress, this velocity formula is meant to be applicable when the prestress is induced by plastic deformations such as those incurred during the surface enhancement treatment of low plasticity burnishing. The angular dependence formula assumes a simpler form when the texture of the prestressed half-space is orthorhombic. This revised version was published online in July 2006 with corrections to the Cover Date.     

Boundary layers in highly anisotropic plane elasticity

The boundary layer method proposed by Everstine and Pipkin for the analysis of highly anisotropic materials, such as fibre-reinforced materials, in elastic plane strain is developed and extended also to include plane stress. It is applied to problems of point forces acting on half-planes, and to two crack problems. The boundary layer solutions are compared with known exact solutions in anisotropic elasticity, and it is found that the boundary layer theory gives good results for elastic constants typical of a carbon fibre reinforced resin.     

Transport Processes in Nonequilibrium Spherically-Symmetric Gas Outflow into a Vacuum

The transport processes in the nonequilibrium outflow of a monatomic gas into a vacuum are investigated using direct numerical statistical simulation. The quantitative dependence of the macroscopic parameters, such as the density, velocity, temperature, stress, and heat flux, on the distance from the source is determined. In the case of a gasdynamic source the dependence of the stress and the heat flux on the strain rate tensor components and the temperature gradient is established. The applicability range of the well-known hypersonic approximation is determined.     

Why traction-free? Piezoelectric crack and Coulombic traction

The non-zero traction condition is introduced in piezoelectric crack problems with the unknown Coulombic traction acting on the crack surfaces. An analytical solution under this condition is obtained by means of the generalized Stroh formalism and by accounting for the permittivity of medium inside the crack gap. As the crack in such materials can be thought of as a low-capacitance medium carrying a potential drop, the Coulombic traction always pulls the two opposite surfaces of the crack together. It is proved that under relatively larger mechanical loading and relatively smaller electrical field, the Coulombic traction may be negligible and the previous investigations under the traction-free crack condition may be accepted in a tolerant way, otherwise the Coulombic traction may lead to some erroneous results with over 10% relative errors. It is also shown that, unlike the traction-free crack condition, the applied electric field does change the Mode I stress intensity factor (SIF) for a central crack in an infinite plane piezoelectric material, and in this way may significantly influence piezoelectric fracture. It is also concluded that the variable tendencies of the normalized SIF and the ERR against the applied electric field depend on the mechanical loading levels. This load-dependence feature may lead to a transformation of the normalized SIF and the ERR from an even functional dependence to an odd functional dependence on the applied electric field.