Quasistatic indentation of a rubber-covered roll by a rigid roll

The nonlinear elastic problem involving the indentation of a slightly compressible rubber-like layer bonded to a rigid cylinder and indented by another rigid cylinder is analysed by the finite element method. Both the geometric and material nonlinearities are accounted for. The finite element formulation of the problem is based upon a variational principle recently proposed by Cescotto and Fonder, and is valid for both slightly compressible and incompressible materials. The results computed and presented graphically include the shape of the indented surface, the pressure distribution over the contact surface, and the stress distribution at the bond surface. For the same contact width, the results for the compressible material are found to differ significantly from those for the case when the rubber-like layer is assumed to be incompressible.     

The elasto-plastic indentation of a half-space by a rigid sphere

Using the finite element method, a detailed study of the deformations and stresses produced in an elastic-perfectly plastic half-space indented by a rigid sphere was done. The analysis covers the transition region from the maximum elastic contact load to a state where this load has been increased one hundredfold. Experimental results available in the literature are in good agreement with the analysis. In solving repeatedly the large number of linear equations involved in the solution of the problem, it was found profitable, in order to save computer time, to modify the direct elimination method. This technique is described in some details in the paper.     

Applications of conservation integral to indentation with a rigid punch

When a substrate of the brittle material is indented by a relatively rigid, square-ended punch, a singular stress field and K-dominant region will arise at the near-surface adjacent to the punch corners. The singularity of this stress field is identical with the mode I crack. The stress intensity factor in this case represents the intensification of the stress fields induced by indentation. In present article, a new method to determine the stress intensity factors of the indentation problems is developed based on the conservation law. The physical meanings of the proposed method and some numerical analysis have been investigated.     

Dynamic rigid indentation induced by sliding frictionless contact

Dynamic rigid indentation induced by sliding frictionless contact is studied by considering a rigid smooth half-wedge which simultaneously translates tangentially and normally at constant speeds with respect to the surface of an elastic half-space. A more general problem is treated by homogeneous function techniques and the solutions are then applied. Among other results, it is found that if no tangential speed is imposed, the half-wedge must approach a flat punch configuration and a maximum normal force must be applied. The normal half-space surface displacements are also plotted.     

地震作用下刚体滑动位移的计算与比较——基于Coulomb摩擦模型

首先对滑动干摩擦模型的研究现状进行了系统的论述。推导了基于Coulomb摩擦模型时刚体在简谐地面运动时滑动位移的解析方程;讨论了滑动状态与粘结状态过渡时刻的求解精度对刚体与地面相对位移的影响;对基于摩擦力－位移模型和基于Coulomb摩擦模型下刚体在简谐地面运动作用下滑动位移的差异进行了对比。然后采用Newmark线性加速度法推导了基于Coulomb摩擦模型刚体在任一地震加速度作用下滑动位移的数值求解方法;对比了基于摩擦力－位移模型和基于Coulomb摩擦模型下刚体在任一地面运动作用下滑动位移的差异。     

The dynamic indentation of an elastic-viscoplastic work-hardening slab by a rigid punch

A unified theory for elastic-viscoplastic work-hardening materials, which requires neither a yield criterion nor loading or unloading conditions, is implemented to solve two-dimensional dynamic problems. Specifically, the theory is applied to the dynamic indentation by a rigid indenter of a slab made of an elastic-viscoplastic material. The contact area between the indenter and the slab at any time is not known in advance but should be determined from the process of the solution. An iterative numerical procedure is proposed by which the complete solution is determined from the dynamic elastic-viscoplastic equations, the moving mixed boundary conditions, the requirement that the contact normal stresses are compressive and that no interpenetration occurs outside the contact area. The method is applied to the indentation problem of a viscoplastic slab by a long rigid circular cylinder, and by a wedge-shaped die. Comparisons with the corresponding perfectly elastic problems are given.     

摩擦力和样品厚度对压痕法测量生物试样弹性的影响

生物试样的弹性测量可为生物体疾病的早期诊断和治疗提供依据。利用压痕法对生物试样的弹性进行了测量,并用有限元软件对压痕过程进行了模拟。研究发现,试样厚度对弹性测量存在影响,试样厚度越大,测量结果越接近试样真实的杨氏模量。当试样厚度为压痕深度的75倍时,测量误差仅为0.74%。又研究了压头速度对弹性测量结果的影响。研究发现,当压头速度较大时,由于摩擦力的作用,测量结果与试样弹性的真实值之间存在一定的差异。在模拟过程中添加摩擦力可准确反演试样的弹性,误差在5%以下。     

The indentation of an elastic layer by a rigid stamp under conditions of complete adhesion

Summary In this paper the indentation of an elastic layer by a rigid stamp is treated under conditions of complete adhesion beneath the stamp, where the ratio of the half-width of the contact region and the thickness of the layer is assumed to be small. The cases of a flat stamp and a polynomial one are considered successively and two applications are treated.

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Die Einprägung einer elastischen Schicht von einem starren Stempel bei vollständiger Befestingung under conditions of complete adhesion

Zusammenfassung Die vorliegende Arbeit befaßt sich mit dem Eindringen eines starren Stempels in eine elastische Schicht für den Fall, daß die Unterseite des Stempels auf der Schicht befestigt ist.Dabei wird angenommen, daß die halbe Breite des Berührungsgebietes klein ist gegenüber der Dicke der Schicht.Zwei Sonderfälle werden näher untersucht: der flache Stempel und der polynomförmige Stempel. Zwei Anwendungen werden behandelt.

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With 6 Figures     

A system of rigid bodies with dry friction

The mechanical system we propose to deal with is a finite set of perfectly rigid bodies submitted to: (a) usual constraints, meaning holonomous, bilateral, frictionless constraints, depending or not on time; (b) forces, they are functions of time, velocity, and the generalized variables of the system; (c) punctual contacts with dry friction between some bodies of the system or between bodies of the system and some extraneous rigid bodies, the motion of which is explicitly given as a function of time. In the first part, the general equations of the problem are introduced, existence theorems are given, and comments are made about the mechanical significance of both the assumptions and the foregoing results. The equations are set in the second part, which is thus essentially concerned with mechanics and may be read independently. The proofs of the theorems are to be found in the third part.     

刚体面内位移激光散斑测量研究

运用散斑统计理论,结合数字图像处理技术,设计了一套激光散斑测量刚体面内微小位移的实验系统,再利用刚体位移前后的散斑图像的互相关性,实现了刚体面内的位移测量.测量结果表明,针对刚体面内小于300μm的微小位移,x轴和y轴的绝对位移误差为±14μm,相对误差为±6.25%左右.     

Thermal and slip mechanism effects in rapid indentation by a flat punch

Summary The rapid indentation of a fully-coupled thermoelastic body by a flat, smooth rigid punch is studied in a 2D dynamic analysis. A semi-infinite punch width is assumed to be a valid short-time model, and a zone of slip mechanisms is assumed to form under the punch edge, and to relax the stresses there. The mathematical problem is reduced by superposition and transform methods to a Wiener-Hopf equation which, despite the dependence of poles and branch points on the time transform parameter, can be solved exactly. Imposition of the stress relaxation property of the zone then removes the singularity in punch edge stresses, thereby giving a relation for the contact region temperature change. Because a thermoelastic characteristic length of 0(10^–4)m is the scale factor, this transform can be inverted for so-called long times without invalidating the short-time nature of the model. The inversion shows that, despite the absence of actual plasticity and contact friction, nominal but not negligible temperature increases can occur in the contact region.     

Frictionless indentation by a rigid wedge: The effect of tangential displacements in the contact zone

Recent dynamic analyses of frictionless rigid indentation on linearly elastic half-planes assume that the tangential displacement of half-plane points in contact with the indentor is negligible. This assumption is used as a justification for denning the contact zone size, although not known in advance, on the undeformed half-plane, and for uncoupling the tangential and normal displacements in the contact zone. This article examines the validity of this assumption for the symmetric wedge with a constant indentation speed and a contact zone which, as denned on the undeformed half-plane, extends at a constant subcritical rate. Both the coupled and uncoupled solutions are obtained analytically and compared. The difference between the half-plane size defined on the undeformed half-plane and its size on the deformed half-plane may actually be greater for the uncoupled solution. Moreover, the coupled solution does not exhibit the wedge apex stress singularities found for the uncoupled solution.     

Sliding friction and wear of structural ceramics

Further analysis has been performed on SiC and partially stabilized ZrO₂ specimens employed in a previous study of sliding friction and wear. Wear volumes have been measured, wear debris has been studied by X-ray diffraction and transmission electron microscopy, and comparative X-ray diffraction studies have been performed on worn and unworn surfaces. There is no correlation between the wear during running-in and the steady-state coefficient of friction established by this process. ZrO₂-ZrO₂ friction couples wear much faster than SiC-SiC couples, which in turn wear faster than ZrO₂-SiC couples. In these last couples wear occurs mostly on the ZrO₂ member, but does not measurably promote the tetragonal to monoclinic phase transformation. Adding graphite to SiC reduces the wear of SiC-SiC couples somewhat, but improving their initial surface finish has the opposite effect. All wear debris exhibited a bimodal particle-size distribution, which observation can be rationalized with the wear surface topographies reported previously.     

Sliding friction and wear of structural ceramics

A study has been made of the unlubricated sliding friction and wear behaviour of various like and unlike combinations of four materials -sintered-SiC, graphitized SiC, siliconized SiC and a Y₂O₃-stabilized ZrO₂ — in air at room temperature under dynamic conditions approximating the motion of a piston in the cylinder of an idling automotive engine. The steady state friction coefficient _f is largely independent of the initial surface finish, but is in all cases unacceptably high (0.25 _f 0.50) for engine applications. When the running-in process involves smoothing of the wear surfaces, the coefficient of friction decreases asymptotically towards its steady state value; and when running-in involves roughening, this coefficient usually increases asymptotically as the wear surfaces develop their steady state topographies. Friction couples containing siliconized SiC were the only exceptions to this pattern of behaviour. In every case the high steady state friction is accompanied by considerable wear. The results suggest that ceramic components will not be used unlubricated in reciprocating situations.     

Effect of friction and cavity depth on the elastic indentation of a cylindrical rod

Using finite element analysis, the elastic displacement of a rigid cylindrical rod pushed by an axial load into an existing cavity of the same diameter as the rod located in the surface of a half space was studied. It was found that such displacement is proportional to the applied load and decreases with increasing depth of the cavity. It is the largest for the slip condition over all the contact surfaces and the smallest for the stick condition over the same surfaces. Also for the same load, the maximum von Mises stress under the punch decreases with increasing depth of the cavity. If not glued to the punch, both the bottom and the lateral surfaces of the cavity are in contact with the punch during deformation.     

The contact problem of a rigid stamp with friction on a functionally graded magneto-electro-elastic half-plane

We consider in this study the frictional sliding contact problem between a functionally graded magneto-electro-elastic material and a perfectly conducting rigid punch subjected to magneto-electro-mechanical loads. The problem is formulated under plane strain conditions. Using Fourier transform, the resulting plane magneto-electro-elasticity equations are converted analytically into three coupled singular integral equations in which the unknowns are the normal contact stress, the electric displacement and the magnetic induction. These integral equations are then solved numerically to obtain the distributions of the normal contact stress, electric displacement and magnetic induction at the surface of the graded medium. The main objective of this paper is to study the effect of the non-homogeneity parameter, the friction coefficient and the elastic, electric and magnetic coefficients on the surface contact pressure, electric displacement and magnetic induction distributions for the case of flat and circular punch profiles.     

Pressure with friction of a perfectly rigid die upon an elastic half space with cracks

We study the interaction of a rigid die with a base of any shape and the surface of an elastic half space containing cracks in the presence of friction in the contact zone. The solution of the plane contact problem of the theory of elasticity is obtained by the method of singular integral equations. The detailed analysis of the problem is performed for the case where the base of the die is parabolic and a crack is rectilinear and appears on the surface of half space. We also investigate the effects of the friction coefficient, crack length, its orientation, and location on stress intensity factors KI and KII at the crack tip and the distribution of contact stresses under the die.     

Restitution and friction laws in rigid body collisions

This paper presents an alternative approach of restitution and friction laws in rigid body collisions. The present method does not include the use of the rigid body kinematics during impact, in writing the balance equations as well as in formulating the relevant constitutive laws. That is accomplished by introducing initial and final impulses, these semi-global quantities being connected by friction and restitution coefficients. Several examples, from existing literature, are presented to show the ability of the present theory to solve impact problems involving main motion scenarios.