Motion of a rigid punch at a low velocity along the boundary of a viscoelastic half-plane

The contact problem of the interaction of a rigid punch with a viscoelastic half-plane is considered. The dependence of the displacement of the boundary of half-plane on the normal load applied to it is determined, and the integral equation for determining the contact pressure is derived and solved by the method of “small λ”. Distributions of contact pressures under the punch are graphically represented.     

The axisymmetric viscoelastic contact problem with rotational friction

The boundary value problem that arises when a mechanically rough rigid punch of arbitrary axisymmetric profile is pressed against the surface of a linear aging viscoelastic half space and is also made to rotate about its axis, so that there is total slip between the contacting surfaces is analysed and solved. The moment required to make the punch rotate, on the assumption that the coefficient of friction obeys a power law or is a constant, and the total normal pressure acting on the punch may each be evaluated in terms of the history of the radius of the contact area. Application is made to the special cases where the punch has the form of (i) a cone, (ii) a paraboloid of revolution and (iii) a flat ended cylinder. Apart from case (iii) where the contract area is constant we can only find an explicit expression for the moment in terms of total pressure so long as the contact area is increasing. The case of constant total pressure and Maxwell viscoelastic material is examined in more detail.     

On indentation of a pair of rigid punches connected by an elastic beam into an elastic half-plane with regard to the friction and adhesion forces in the contact region

The contact problem of indentation of a pair of rigid punches with plane bases connected by an elastic beam into the boundary of an elastic half-plane is considered under the conditions of plane strain state. The external load is generated by lumped forces applied to the punches and a uniformly distributed normal load acting on the beam.It is assumed that the contact between the punch and the elastic half-plane can be described by L. A. Galin’s statement, i.e., it is assumed that the adhesion acts in the interior part of each of the contact regions and the tangential stresses obeying the Coulomb law act on their boundaries.With the symmetry taken into account, the problem is stated only for a single punch, and solving this problem is reduced to a system of four singular integral equations for the tangential and normal stresses in the adhesion region and the contact pressure in the sliding zones. The solution of the constitutive system together with three conditions of equilibrium of the system of punches connected by a beam is constructed by direct numerical integration by the method of mechanical quadratures.As a result of the numerical analysis, the contact stress distribution functions were constructed and the values of the sliding zones and the punch rotation angle were determined for various values of the geometric, elastic, and force characteristics.     

刚性圆形压头作用下热电材料半平面的无摩擦接触问题

热电材料可以将热能转化为电能,反之亦然,这一优良的性质将有助于研发更具成本效益的设备和器件。本文研究了刚性圆形压头作用在热电材料半平面的无摩擦接触问题。假定压头为电导体、热导体,且压头压入深度及与材料的接触区域宽度未知。首先求解电场和温度场,利用傅里叶变换得到了电势函数、温度、电流密度和能量通量的解析表达式。然后求解弹性场,利用积分变换和边界条件,将该热弹性接触问题转化为第一类奇异积分方程并数值求解。数值结果讨论了压头半径和热电载荷对法向接触应力、电流强度因子和能量通量强度因子的影响。结果表明,对于圆压头,热电材料的法向电流密度、法向能量通量在接触边缘表现出奇异性,而表面法向接触应力在接触边缘为零。本文建立的研究模型有助于更深层次的了解热电材料的接触行为。     

A Piezoelectric Technique for Evaluation of Crack Closure

The ability of the piezoelectric materials to work as sensors and actuators was employed in a technique for monitoring the degree of crack closure and to detect the crack opening load. The technique is demonstrated through experiments with a cracked beam. It consists in exciting the specimen with a piezoelectric actuator and recording the electromechanical response of piezoelectric sensors placed near the crack mouth, while applying a bending moment to open the crack. The sensors in the neighborhood of the crack present a reduction in the amplitude response signal due to the progressive decrease of the dynamic strains near the crack, as the bending load causes the crack to open, reducing the contact between the surfaces of the fatigue crack and the load transmission through the contact area. The results show that the method has a high sensitivity to the state of crack closure, allowing for the direct determination of the crack opening load.     

磁电弹复合材料和刚性导电导磁圆柱压头的二维微动接触分析

本文求解平面应变状态下磁电弹复合材料半平面和刚性导电导磁圆柱压头的二维微动接触问题。假设压头具有良好的导电导磁性,且表面电势和磁势是常数。微动接触依赖载荷的加载历史,所以首先求解单独的法向加载问题,然后在法向加载问题的基础上求解循环变化的切向加载问题。整个接触区可以分为内部的中心粘着区和两个外部的滑移区,其中滑移区满足Coulomb摩擦法则。利用Fourier积分变换,磁电弹半平面的微动接触问题将简化为耦合的Cauchy奇异积分方程组,然后数值离散为线性代数方程组,利用迭代法求解未知的粘着/滑移区尺寸、电荷分布、磁感应强度、法向接触压力和切向接触力。数值算例给出了摩擦系数、总电荷和总磁感应强度对各加载阶段的表面接触应力、电位移和磁感应强度的影响。     

New Methodologies for Fracture Detection of Automotive Steels in Tight Radius Bending: Application to the VDA 238–100 V-Bend Test

Background

The VDA 238–100 tight radius V-bend test can be used to efficiently characterize the bendability and fracture limits of sheet metals in severe plane strain bending. Material performance in plane strain bending is critical for the selection of advanced high strength steels for energy absorbing structural components.

Objective

The detection of failure based upon a reduction in the punch force can lead to erroneous predictions of failure for ductile or thin gage alloys in the VDA 238–100 test. New failure criteria were proposed and evaluated across a range of automotive steels.

Methods

Four detection methods in the V-bend test were evaluated based upon the load drop, bending moment, novel stress metric and the strain rate for seven steels with strength levels from 270 to 1500 MPa. The appropriate failure threshold was identified from visual inspection of the surface during bending.

Results

The vertical punch force will decrease as a consequence of the mechanics in the V-bend test at intermediate bend angles even without fracture. The novel stress-based metric accounts for sheet thinning and could successfully identify “false positives” and punch lift-off when considering the strain-rate evolution.

Conclusions

Failure detection using the VDA load threshold method may significantly under-report the bend performance of alloys with intermediate-to-high bendability or thin gauges. The proposed stress-based metric can reliably detect fracture for bend angles in excess of 160° and be readily calculated using the existing data. The VDA load threshold for failure can work well for materials that exhibit significant cracking.

     

Non-slipping adhesive contact of a rigid cylinder on an elastic power-law graded half-space

In this paper, adhesive contact of a rigid cylinder on an elastic power-law graded half-space is studied analytically with the theory of weakly singular integral equation and orthogonal polynomial method. Emphasis is placed on the coupling effect between tangential and normal directions which was often neglected in previous works. Our analysis shows that the coupling effect tends to reduce the contact area in the compressive regime. The effect of bending moment on the adhesion behavior is also examined. Like a pull-off force, there also exists a critical bending moment at which the cylinder can be bended apart from the substrate. However, unlike pull-off force, the critical bending moment is insensitive to the gradient exponent of the graded material.     

Torsion of rough elastic half-space by rigid punch

Torsion of an elastic half-space by a rigid punch is investigated. The boundary of the half-space is assumed to be rough. Two geometries of the punch-parabolic and flat end are considered. It is shown that the contact area consists of stick and slip zones. This fact, which is well-known in the classical torsional contact of the elastic half-space with the smooth surface and the parabolic punch, also holds true for the flat-ended punch if the boundary roughness is involved. The partial slip problems are reduced to the integral equations, which are solved numerically. The presented results show the effects of boundary roughness on the shear stresses, size of the stick area and the relation between the twisting moment and the angle of twist.     

The size-dependent elastohydrodynamic lubrication contact of a coated half-plane with non-Newtonian fluid

Based on the couple-stress theory, the elastohydrodynamic lubrication(EHL)contact is analyzed with a consideration of the size effect. The lubricant between the contact surface of a homogeneous coated half-plane and a rigid punch is supposed to be the non-Newtonian fluid. The density and viscosity of the lubricant are dependent on fluid pressure. Distributions of film thickness, in-plane stress, and fluid pressure are calculated by solving the nonlinear fluid-solid coupled equations with an iterative method. The effects of the punch radius, size parameter, coating thickness, slide/roll ratio, entraining velocity, resultant normal load, and stiffness ratio on lubricant film thickness, in-plane stress, and fluid pressure are investigated. The results demonstrate that fluid pressure and film thickness are obviously dependent on the size parameter, stiffness ratio, and coating thickness.     

Electro-mechanical frictionless contact behavior of a functionally graded piezoelectric layered half-plane under a rigid punch

The frictionless contact problem of a functionally graded piezoelectric layered half-plane in-plane strain state under the action of a rigid flat or cylindrical punch is investigated in this paper. It is assumed that the punch is a perfect electrical conductor with a constant potential. The electro-elastic properties of the functionally graded piezoelectric materials (FGPMs) vary exponentially along the thickness direction. The problem is reduced to a pair of coupled Cauchy singular integral equations by using the Fourier integral transform technique and then is numerically solved to determine the contact pressure, surface electric charge distribution, normal stress and electric displacement fields. For a flat punch, the normal stress intensity factor and electric displacement intensity factor are also given to quantitatively characterize the singularity behavior at the punch ends. Numerical results show that both material property gradient of the FGPM layer and punch geometry have a significant influence on the contact performance of the FGPM layered half-plane.     

A four-part boundary value problem in elasticity — indentation by a discontinuously concave punch

A solution is given for the frictionless indentation of an elastic half-space by a flat-ended cylindrical punch with a central circular recess, when the load is large enough to establish a circular region of contact in the recess. The problem is reduced to two simultaneous Fredholm equations using the method of complex potentials due to Green and Collins. Results are presented for the relationship between load, contact radius and penetration for various punch geometries.     

海底管道离地点的接触条件探讨

海底管道的铺设分析和提升分析都用到管道和海床之间的接触条件，这个同时含有挠度、转角和弯矩的接触条件，在一般的力学模型中是很难理解的．考虑海床变形，通过海床和管道的变形分析，给出这种接触条件的真实背景和使用条件．     

考虑畸变影响的箱梁横向弯矩计算方法

为研究偏心垂向荷载作用下梯形截面单室箱梁的横向弯矩,对框架分析法计算箱梁横向弯矩的方程进行优化,并在刚性支承法的基础上提出一种更加简单的横向弯矩计算方法;与框架分析法不同,横向弯矩可采用能量变分法求解,建立以箱梁顶板剪力差为未知量的四阶控制微分方程,采用比拟的弹性地基梁解法解出剪力差,得出梯形截面单室箱梁横向弯矩的能量变分法解。对几种箱梁横向弯矩计算方法用两个算例进行验证,结果表明,能量变分法解将箱梁底板上的弯矩误差绝对值由15.41%降到了9.68%;本文方法得出的横向弯矩结果和有限元结果吻合较好,弯矩误差绝对值最大不超过6.01%;本文方法和能量变分法可有效降低箱梁底板上的弯矩误差,计算精度得到提高。     

Effect of closure of collinear cracks on the stress-strain state and the limiting equilibrium of bent shallow shells

The problem of closure of collinear cracks during bending of a shallow shell is considered within the framework of the Kirchhoff theory. Crack closure is described using the model of contact along a line on one of the shell faces. Strain and moment intensity factors and fracture load are studied as functions of shell curvature and defect location, and the distribution of contact forces along the cracks is investigated.     

Uniform motion of a plane punch on the boundary of an elastic half-plane

The dynamic contact problem of a plane punch motion on the boundary of an elastic half-plane is considered. The punch velocity is constant and does not exceed the Rayleigh wave velocity. The moving punch deforms the elastic half-plane penetrating into it so that the punch base remains parallel to itself at all times. The contact problem is reduced to solving a two-dimensional integral equation for the contact stresses whose two-dimensional kernel depends on the difference of arguments in each variable. A special approximation to the kernel is used to obtain effective solutions of the integral equation. All basic characteristics of the problem including the force of the punch elastic action on the elastic half-plane and the moment stabilizing the punch in the horizontal position in the process of penetration are obtained. A similar problem was considered in [1] and earlier in the “mode of steady-state motions” in [2, 3] and in other publications.     

具有内核伸出段的套管构件在线接触阶段的受力性能研究

针对具有内核伸出段的轴压套管构件,建立了线接触阶段的力学模型;利用小挠度理论推导出了内核和套筒的剪力、弯矩、挠度、分布接触力、集中接触力等物理量的计算公式。通过与无内核伸出段套管构件的对比算例验证了本文相关物理量推导的正确性,分析了内核与套管在不同刚度比下相关物理量的变化情况。结果表明:由于内核伸出段的影响,点接触会提前向线接触变化,使套管构件的轴向承载力显著下降,端部的接触反力及内核的剪力、弯矩有显著的增加。对具有内核伸出段的套管构件进行了力学性能分析,结果表明:内核与套筒的间隙对线接触长度没有影响,内核的弯矩、剪力随着间隙的增加而增大;随着内核伸出段长度的增加,线接触长度及内核的弯矩、剪力增大。     

The evolution of the process zone when a complete contact is subject to cyclically varying loads

A rigid punch pressed against an incompressible half-plane by a constant normal load is subject to both a cyclically varying shearing force, and a synchronously varying underlying bulk tension. The evolution of the slip/stick distribution along the contact interface is found during a loading cycle. An asymptotic approach is subsequently used to determine the order of singularity, and hence spatial distribution of the local stress state. A generalised stress intensity factor is then defined to scale the corresponding asymptotic solution, and hence map out the evolution of the process zone. The analysis shows that there is a smooth transition in the form of the asymptotic solution in moving from an ‘adhered’ contact edge to a ‘slipping’ contact edge, and vice versa. The implications of the results to fretting fatigue are discussed.     

Frictionless contact of a functionally graded magneto-electro-elastic layered half-plane under a conducting punch

This paper investigates the two-dimensional frictionless contact problem of a functionally graded magneto-electro-elastic materials (FGMEEMs) layered half-plane under a rigid flat or a cylindrical punch. It is assumed that the punch is a perfect electro-magnetic conductor with a constant electric potential and a constant magnetic potential. The magneto-electro-elastic (MEE) properties of the FGMEEM layer vary exponentially along the thickness direction. Using the Fourier transform technique, the contact problem can be reduced to Cauchy singular integral equations, which are then solved numerically to determine the normal contact stress, electric displacement and magnetic induction on the contact surface. Numerical results show that the gradient index, punch geometry and magneto-electro-mechanical loads have a significant effect on the contact behavior of FGMEEMs.     

复合材料结构力学分析CAE软件现状

复合材料结构分析软件是用以分析、设计复合材料结构的重要工具,常用的复合材料结构分析软件包括基于CAD软件发展而来的复合材料分析工具、通用有限元软件自带复合材料分析工具和以Digimat等为代表的专业化复合材料结构分析软件。本文对常用的复合材料分析软件进行了综述,介绍其主要功能,从学术、应用等多方面探讨相关产品的优点及不足;论述了专业化复合材料结构分析软件的特点及功能;分析了复合材料结构分析软件的现状和发展趋势;探讨了复合材料结构力学分析CAE软件在国产化方面所需进一步解决的问题。