MD simulation of the effect of contact area and tip radius on nanoindentation

Molecular dynamics simulations of nanoindentation are performed on monocrystal copper. A new "contact atoms" method is presented for calculating the contact area. Compared with conventional methods, this method can provide the contact area more accurately not only for sink-in but also for pile-up situation. The effect of tip radius on indentation is investigated too. The results indicate that the measured hardness of the material will become higher as the tip radius increases.

Nonlinear dynamics of atomic force microscopy with intermittent contact

When the atomic force microscopy (AFM) in tapping mode is in intermittent contact with a soft substrate, the contact time can be a significant portion of a cycle, resulting in invalidity of the impact oscillator model, where the contact time is assumed to be infinitely small. Furthermore, we demonstrate that the AFM intermittent contact with soft substrate can induce the motion of higher modes in the AFM dynamic response. Traditional ways of modeling AFM (one degree of freedom (DOF) system or single mode analysis) are shown to have serious mistakes when applied to this kind of problem. A more reasonable displacement criterion on contact is proposed, where the contact time is a function of the mechanical properties of AFM and substrate, driving frequencies/amplitude, initial conditions, etc. Multi-modal analysis is presented and mode coupling is also shown. (c) 2006 Published by Elsevier Ltd.

Simple phenomenological determination of contact stiffness and elastic modulus of Ce-based bulk metallic glasses through nanoindentation

The viscoelastic deformation of Ce-based bulk metallic glasses (BMGs) with low glass transition temperature is investigated at room temperature. Contact stiffness and elastic modulus of Ce-based BMGs cannot be derived using the conventional Oliver-Pharr method [W. C. Oliver and G. M. Pharr, J. Mater. Res. 7, 1564 (1992)]. The present work shows that the time dependent displacement of unloading segments can be described well by a generalized Kelvin model. Thus, a modified Oliver-Pharr method is proposed to evaluate the contact stiffness and elastic modulus, which does, in fact, reproduce the values obtained via uniaxial compression tests. (c) 2007 American Institute of Physics.

Reflection of shock-wave in pur foam from rigid wall

Keller proposed that a building, a mechanical installation or a body wrapped bya layer of foam plastics may be an efficient means for protection from damage ofblast wave. However, the practical effect was beyond expectation. For example, agunner wearing the foam plastics-padded waistcoat was injured more seriously by theblast wave from a muzzle. Monti took the foam plastics as homogeneous two-phasemedium and analyzed it with the theory of dusty flow. The obtained results showthat the peak pressure behind the reflected shock wave from rigid wall with foamcoat exceeds obviously that without foam coat under the same condition. Gel'fand,Patz and Weaver made experimental observations by means of shock tubes and veri-

Stress-distribution at the rigid circular-arc inclusion end

The elastic plane problem of a rigid co-circular arc inclusion under arbitrary loads is dealt with. Applying Schwarz's reflection principle integrated with the analysis of the singularity of complex stress functions, the general solution of the problem is found and several closed-form solutions to some problems of practical importance are given. Finally, the stress distribution at the arc inclusion end is examined and a comparison is made with that of the rigid line inclusion end to show the effect of curvature.

Stress-distribution around a rigid line in dissimilar media

The elastic plane problem of a rigid line inclusion between two dissimilar media was considered. By solving the Riemann-Hilbert problem, the closed-form solution was obtained and the stress distribution around the rigid line was investigated. It was found that the modulus of the singular behavior of the stress remains proportional to the inverse square root of the distance from the rigid line end, but the stresses possess a pronounced oscillatory character as in the case of an interfacial crack tip.

Effects of contact resistance on thermal-conductivity of composite media with a periodic structure

The thermal conductivity of periodic composite media with spherical or cylindrical inclusions embedded in a homogeneous matrix is discussed. Using Green functions, we show that the Rayleigh identity can be generalized to deal with thermal properties ot these systems. A new calculating method for effective conductivity of composite media is proposed. Useful formulae for effective thermal conductivity are derived, and meanings of contact resistance in engineering problems are explained.

The plane problem of collinear rigid lines under arbitrary loads

The elastic plane problem of collinear rigid lines under arbitrary loads is dealt with. Applying the Riemann-Schwarz symmetry principle integrated with the analysis of the singularity of complex stress functions, the general formulation is presented, and the closed-form solutions to several problems of practical importance are given, which include some published results as the special cases. Lastly the stress distribution in the immediate vicinity of the rigid line end is examined.

Slightly slanting impact on an elastic cantilever column-an experimental study

Experiments concerning slightly slanting impact between a flat-ended rigid body and a flat-ended elastic cantilever column with a rectangular cross-section have been performed. The experimental results are compared with the theoretical ones. The small angle of incidence was measured by using an optical method. The impact process was studied by using a split disc for the rigid body, with the two halves bonded together and electrically insulated from each other. The disc and the column were parts of an electric circuit. Different contact states could be distinguished according to different voltage levels. Reasonably good agreement between theory and experiment was found. Thus, the impact duration has its minimum under perfectly axial impact as predicted by the theory. Also, the predicted process of alternating line and surface contact was observed. Furthermore, the existence of a small critical angle of incidence was verified. This critical angle of incidence divides the impact processes into two categories: (1) The rigid body and the column end come into surface contact before separation. (2) They separate without surface contact. Comparison of axial strains between theory and experiment shows good agreement.

Methods of Obtaining Instantaneous Modulus of Viscoelastic Solids Using Displacement-Controlled Instrumented Indentation with Axisymmetric Indenters of Arbitrary Smooth Profiles

We derive a relationship between the initial unloading slope, contact depth, and the instantaneous relaxation modulus for displacement-controlled indentation in linear viscoelastic solids by a rigid indenter with an arbitrary axisymmetric smooth profile. While the same expression is well known for indentation in elastic and in elastic-plastic solids, we show that it is also true for indentation in linear viscoelastic solids, provided that the unloading rate is sufficiently fast. When the unloading rate is slow, a "hold" period between loading and unloading can be used to provide a correction term for the initial unloading slope equation. Finite element calculations are used to illustrate the methods of fast unloading and "hold-at-the-maximum-indenter-displacement" for determining the instantaneous modulus using spherical indenters.

Relationships between Initial Unloading Slope, Contact Depth, and Mechanical Properties for Spherical Indentation in Linear Viscoelastic Solids

Using analytical and finite element modeling, we examine the relationships between initial unloading slope, contact depth, and mechanical properties for spherical indentation in viscoelastic solids with either displacement or load as the independent variable. We then investigate whether the Oliver-Pharr method for determining the contact depth and contact radius, originally proposed for indentation in elastic and elastic-plastic solids, is applicable to spherical indentation in viscoelastic solids. Finally, the analytical and numerical results are used to answer questions raised in recent literature about measuring viscoelastic properties from instrumented spherical indentation experiments.

Experimental Study on Flow Induced Vibration of a Cylinder with Two Degrees of Freedom Near a Rigid Wall

The flow-induced vibration of a cylinder with two degrees of freedom near a rigid wall under the action of steady flow is investigated experimentally. The vibration amplitude and frequency of the cylinder and the vortex shedding frequency at the wake flow region of the cylinder are measured. The influence of gap-to-diameter ratio upon the amplitude response is analyzed. The experimental results indicate that when the reduced velocity (Vr) is in the range of 1.2 < Vr < 2.6, only streamwise vibration with small amplitude occurs, whose frequency is quite close to its natural frequency in the still water. When the reduced velocity Vr > 3.4, both the streamwise and transverse vibrations of the cylinder occur. In this range, the amplitudes of transverse vibration are much larger than those of streamwise vibrations, and the amplitudes of the streamwise vibration also get larger than those at the range of 1.2 < Vr < 2.6. At the range of Vr > 3.4, the frequency of streamwise vibration undergoes a jump at certain values of Vr, at which the streamwise vibrating frequency is twice as much as the transverse one. However, when the streamwise vibration does not experience a jump, its frequency is the same as that of the transverse vibration. The maximum values of second streamwise and transverse vibration amplitudes increase with increasing gap-to-diameter ratios.

Contact pressure of porous Al2O3 probed by nanoindentations

Contact pressure of porous Al2O3 probed by nanoindentation was investigated by dimensional analysis with special attention paid to scaling effects in the mechanical behavior. It was found that, for sample containing small grains and interconnected pores, the contact pressure is manifest dominated by bonding strength of the porous alumina. Whereas the samples with coarse grain and various porous structures exhibit higher contact pressures and smaller residual deformations, which can be attributed to the mechanical response of the solid-phase under current limited peak loads.

Adhesive behavior of two-dimensional power-law graded materials

In this paper, we investigate the adhesive contact between a rigid cylinder of radius R and a graded elastic half-space with a Young's modulus varying with depth according to a power-law, E = E-0(y/c(0))(k) (0 < k < 1), while the Poisson's ratio v remains constant. The results show that, for a given value of ratio R/C-0, a critical value of k exists at which the pull-off force attains a maximum; for a fixed value of k, the larger the ratio R/c(0), the larger the pull-off force is. For Gibson materials (i.e., k = 1 and v = 0.5), closed-form analytical solutions can be obtained for the critical contact half-width at pull-off and pull-off force. We further discuss the perfect stick case with both externally normal and tangential loads.

An extension of the two dimensional JKR theory to the case with a large contact width

In the Hertz and JKR theories, parabolic assumptions for the rounded profiles of the sphere or cylinder are adopted under the condition that the contact radius (width) should be very small compared to the radius of the sphere or cylinder. However, a large contact radius (width) is often found in experiments even under a zero external loading. We aim at extending the plane strain JKR theory to the case with a large contact width. The relation between the external loading and the contact width is given. Solutions for the Hertz, JKR and rounded-profile cases are compared and analyzed. It is found that when the ratio of a/R is approximately larger than about 0.4, the parabolic assumptions in the Hertz and JKR theories are no longer valid and the exact rounded profile function should be used.