In this chapter, the applications of nanoindentation techniques were performed on several calibration materials. Based on the experimental results, quantification of mechanical properties was conducted in terms of relevant basic analyses. Meanwhile, finite element method was employed to verify some assumptions. The following conclusions can be made in this chapter:
(1) The determined Young’s moduli of copper and fused silica approximate their typical counterparts, but the case for hardness is different. For fused silica, the deviation of hardness is probably ascribed to pile-up phenomenon, whilst for copper, the offset may
0 20 40 60 80 100 120 1.11 1.12 1.13 1.14 1.15 1.16 1.17x 10 4 time (s) in d e n ta ti o n d e p th (n m ) Experiemtnal data
Three element model
E1= 76.37 MPa, E2= 7.39 MPa = 969.15 MPa*s, R-square = 0.9986
also be attributed to indentation size effect and pile-up, where the former dominates the latter.
(2) Creep phenomenon was observed in copper and fused silica by nanoindentation, and thus it can be seen that nominally elastic materials may more or less consist of viscous properties.
(3) By finite element simulation, it is indicated that the empirical relation between hardness and yield stress may not be a good description to account for plastic properties and work hardening.
(4) Silicon wafer is a typical brittle material. Both pop-in and pop-out events were observed during nanoindentation on silicon wafer. Radial and lateral cracks occur in the residual impression in microscope, and the latter causes chipping of the silicon surface. The fracture toughness of silicon wafer estimated by Lawn’s method approaches its typical value.
(5) The three element model proves a good characterization for viscoelastic constitutive relationship of polystyrene. By fitting with the experimental data, both elastic moduli and viscosity coincide with the typical values in order of magnitude.
5
Effects of adhesion on shakedown behavior of
microcontacting bodies
5.1 Introduction
Theoretical analysis, numerical simulation and experiments are referred to as three basic means of scientific research. In this chapter, studies are conducted mainly by the second method. Nanoindentation belongs to microcontact, and it is appropriate to consider surface effects on microcontact where adhesion forces dominate bulk forces due to high ratio of surface area to volume. In this chapter, nanoindentation is viewed as microcontact in general. Chapter 3 introduces several classic contact models taking surface adhesion into consideration. Nevertheless, adhesion-induced deformation is assumed to be purely elastic in these models, while in practice, a high adhesion force can induce plastic deformation, even without externally applied load. On the other hand, the interfacial forces used in these models are approximation to their real counterpart, and there are substantial differences. Owing to these two aspects, it is still impossible to obtain analytical solution for most real adhesive contact problems where interfacial forces and the surface profile are mutually dependent, and the constitutive relation exhibits elastic-plastic property. In this regard, computational simulation proves to be an efficient means to solve such self-consistent adhesive contact problems.
The investigation of adhesion effects on microcontact is of guiding significance for the studying the durability of miniaturized systems subjected to cyclic loading. Obviously contact fatigue and wear due to surface adhesion forces exert adverse effect on the lifetime of
miniaturized systems subjected to cyclic loading, e.g. microelectromechanical (MEMS) system[139][140], nanoelectromechanical (NEMS) system, and head/disk interface (HDI)[141]. By
means of finite element simulation, a number of analyses interpret the above issues by the model of nanoindentation, i.e. microcontact subjected to cyclic loading, and they suggest that adhesion forces play a significant role in affecting the mechanical behavior of contacting bodies.
Fig 5.1 Schematic of stress-strain curve for (a) pure elastic (b) elastic shakedown (c) plastic
shakedown and (d) ratchetting[142].
Generally speaking, the mechanical response of engineering structures to cyclic loading is dependent on its mechanical properties (e.g. elastic modulus, initial yield stress and work hardening rules) and features of the cyclic load (e.g. its maximum and minimum values). When the effective stress is below elastic limit, only elastic deformation occurs as shown by Fig 5.1 (a). If the stress is slightly higher that the elastic limit, plastic deformation will emerge in the first cycle, which causes residual stress such that only elastic deformation occur in subsequent cycles. Since the initial elastic-plastic response of the structure shakes down to wholly elastic behavior, this phenomenon is known aselastic shakedown, as illustrated in Fig 5.1 (b). Once the stress exceeds elastic shakedown limit, the structure may exhibit reverse or
alternating plasticity over each cycle known as plastic shakedown as shown by Fig 5.1 (c). Structures undergoing plastic shakedown will fail after a finite number of load cycles due to low-cycle fatigue. Alternatively the structure may provide net increments of plastic strain within each cycle as illustrated by Fig 5.1 (d), and the strain will accumulate until gross plastic deformation and eventually incremental plastic collapse occurs. This response is called asratchetting.
For microcontact, not only elastic shakedown limit, but also the surface forces are crucial to
understanding failure of microcontact subjected to cyclic loading. Kadin[99] used finite
element method and Lennard-Jones potential to model repetitive adhesive contact between a rigid surface and an elastoplastic sphere. By specifying the sphere with a kinematic strain hardening manner, they investigated the effect of surface adhesion on the shakedown behaviors of the inenter-substrate system. Song and Komvopoulos[143]used the same means to
simulate repetitive adhesive contact between a rigid sphere and an elastic-perfect plastic half-space, and their results showed that plastic shakedown can also occur even for a small maximum normal displacement due to the low yield strength of the material. Nevertheless, there are rare studies on the shakedown behavior of isotropic hardening materials subjected to repetitive adhesive contact.
The main goal of this chapter is to investigate the effect of adhesion forces on shakedown behavior of spherical microcontact subjected to cyclic loading. To accomplish this objective, an elastoplastic half-space is modeled to be indented by a rigid sphere subjected to cyclic loading-unloading. To provide a thorough investigation, the work hardening rule of indented material takes two basic forms, i.e. isotropic hardening and kinematic hardening, to account
for potential plastic shakedown. The interaction force between the rigid spherical indenter and the substrate obeys a more accurate law, i.e. Lennard-Jones potential. Finite element method is employed to solve the self-consistent adhesive contact problem due to mutual dependence of interaction forces and the surface profile.