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We improve the analysis of indentation by employing a model of the expansion of a spherical cavity in which a generalization of the velocity field proposed by Avitzur for metal extrusion is considered; its components vary with the distance to the indenter apex r as 1 /r s , with s a free parameter. By neglecting the material displacement we apply this model to conical indentation (apical angle 2θ) of an elastic solid (Young's modulus E ), a rigid–perfectly plastic (RPP) solid (yield stress σ 0 ) and elastic–perfectly plastic (EPP) solids with indentation index X   =  ( E*/ σ 0 ) cot θ and estimate the hardness H and the shape ratio c p   =   h c / h , where h and h c are the penetration depth and the contact depth respectively. s is determined by minimizing the total work (elastic case) and the plastic power (RPP and EPP cases). The results of the model are in agreement with the available exact results (elastic case) and numerical results (RPP and EPP cases). [ABSTRACT FROM AUTHOR]

In depth-sensing nanoindentation, the load–depth curve F ( h ) is acquired, from which a single value for hardness H and a second for the indentation modulus E ind are inferred. This is a very poor outcome since F ( h ) is a source of much more information. This paper describes a technique to extract the hardness H ( h ) as a continuous depth-dependent function from the load–depth-curve. This was accomplished by assigning each depth h a corresponding contact depth h C   =   h C ( h ) that can be calculated using an iteration algorithm. The hardness is then simply H ( h )  =   F ( h )/ A C ( h C ( h )). For very simple area functions A C , an analytical solution h C ( h ;   F ) can even be found. Furthermore, the differential hardness H d is introduced as an additional hardness quantity, which is obtained when dividing the load increment Δ F by the resulting increase in contact area Δ A C . It turns out that H and H d are identical quantities for a material of constant hardness only. When the hardness is depth- and, therefore, size-dependent, H d differs from H in a definite way, which depends on the hardness evolution with depth, i.e. on the indentation size effect of the material under investigation. The differential hardness proves particularly useful for inhomogeneous samples and situations where the hardness is time-dependent. [ABSTRACT FROM AUTHOR]

This study investigates the incipient plasticity during a nanoindentation test with a spherical indenter in magnesium oxide single crystals. The load–displacement curves show multiple pop-ins, interspaced by elastic deformation, and reveal the transition from an initial elastic deformation regime to a continuous elastoplastic one. Nanoindentations have been stopped after the first pop-in and the dislocation structures have been three-dimensionally characterized by AFM observations of the surface deformation and by nanoetching. The dislocation pattern shows two activated slip systems. The resolved shear stress has been calculated just before the pop-in, for all of the activated slip systems. The final positions of the dislocations generated during the first pop-in reveal that they were all nucleated at the point of maximum resolved shear stress. [ABSTRACT FROM AUTHOR]

Based on load–depth data, as measured by nanoindentation with a Berkovich tip, stress–strain curves of metal films (Al, Cu and Ti) with thickness of 1 to 4  µm were determined. This so-called inverse analysis was carried out using a neural network approach. The method uses hardness and stiffness data from indentation into the film/substrate composite with a depth range of 10 to 200% of the film thickness, and yields the material parameters describing a nonlinear elastic–plastic stress–strain curve of the Armstrong–Frederick type. It is shown that the method can only be applied if a sufficient difference in film and substrate hardness is present. For all films investigated, a significant dependence of the film strength on its microstructure, as characterized by focused ion beam microscopy, has been found. [ABSTRACT FROM AUTHOR]

Indentation contact mechanics of coating/substrate composites is addressed in elastic and viscoelastic regimes. An analytical solution for the elastic Boussinesq problems is examined first using an appropriate contact pressure distribution. The analytical expression for the elastic modulus E eff of layered composites is then converted to the corresponding stress relaxation modulus Y eff   ( t ) using the correspondence principle of linear elastic and linear viscoelastic deformations. Several numerical simulations for the stress relaxation behaviour of layered composites, i.e., a viscoelastic coating on an elastic substrate, an elastic coating on a viscoelastic substrate, etc., are demonstrated to obtain rheological insights into the contact behaviour of coating/substrate composites for flat-ended cylindrical indentation. The assumptions and approximations included in the theoretical considerations are carefully addressed. The viscous squeezing flow, in a thin coating film, out of the geometrically constrained space beneath the indenter is also examined. [ABSTRACT FROM AUTHOR]

There is increasing interest in using sharp cube-corner indenters in nanoindentation experiments to study plastic properties. In combination with finite element methods, it is, for example, possible to extract stress–strain curves from load–displacement curves measured with differently shaped pyramidal indenters. Another example is the fracture toughness of coatings, which can be studied using cracks produced during indentation with cube-corner tips. We have carried out indentation experiments with Berkovich and cube-corner indenters on eight different materials with different mechanical properties. To gain information about the formation of pile-up and cracks, indentation experiments with cube-corner indenter were performed inside a scanning electron microscope (SEM) using a custom-built SEM-microindenter. The results show that reliable hardness and modulus values can be measured using cube-corner indenters. However, the fit range of the unloading curve has a much bigger influence on the results for the cube-corner than for the Berkovich tip. The unloading curves of a cube-corner measurement should, therefore, be carefully inspected to determine the region of smooth curvature, and the unloading fit range chosen warily. Comparison of the modulus results shows that there is no significant difference between cube-corner and Berkovich measurements. Also for hardness, no fundamental difference is observed for most of the investigated materials. Exceptions are materials, such as silicon nitride, cemented carbide or glassy carbon, where a clear difference to the hardness reference value has been observed although the modulus difference is not pronounced. [ABSTRACT FROM AUTHOR]

Since the presentation of the complete elastic field of an extended Hertzian approach [J. Phys. D 37 2761 (2004).] (treating the problem of mechanical contact of two bodies with shape functions of symmetry of revolution of the type z ( r )  = r 2 / d 0   +   r 4 / d 2   +   r 6 / d 4   +   r 8 / d 6   +  ···), a number of publications have appeared showing useful applications of the new theory. They are mainly dedicated to the problem of parameter identification in nanoindentation experiments. In this paper, these new analysis techniques are summarized and further applications concerning indentation testing are proposed. Thus, the main topics of the paper are: (1) purely elastic indentation experiments: (a) two spheres in contact  → revised (with the new theoretical results, the limits of the classical Hertzian approach are investigated), (b) arbitrarily shaped indenters of symmetry of revolution and their resulting elastic field at each point within the either monolithic or layered sample material, and (c) the determination of the surface pressure distribution in the case of layered materials. (2) Elasto-plastic indentation experiments: (a) the concept of the effectively shaped indenter, (b) identification of Young's modulus, hardness and yield strength for monolithic and layered materials, (c) about the determination of intrinsic stresses via indentation experiments  →  an in principle feasibility study, and (d) about pile-up and sink-in (does the new mathematical tool also help in analyzing and detecting indents where pile-up or sink-in has occurred?). The new techniques are in parts demonstrated on real nanoindentation data. The results are discussed and, wherever possible, compared with the outcome of other analyzing procedures. [ABSTRACT FROM AUTHOR]

A novel test system/analysis is proposed for determining the in situ true contact area during indentation loading/unloading by the use of an optically transparent indenter. A sapphire planoconvex lens as a spherical indenter or a diamond tetrahedral pyramid indenter is optically coupled with a microscope system equipped with a CCD video camera. This indentation microscope enables us to directly view the in situ contact impression, along with the measurement of the hysteresis curve of the indentation load-penetration depth relation. The in situ contact area can be readily determined from each frame of the video movie using an image analyzer that is synchronized with the indentation load. Accordingly, the mechanical properties including the true indentation stress–strain curve can be evaluated directly from these observable parameters without using any assumptions that have always been required for estimating the contact area in the conventional depth-sensing indentation apparatus. [ABSTRACT FROM AUTHOR]

Correct interpretation of sharp indentation experiments requires a fundamental understanding of the mechanics involved in the process. Such an understanding can only be achieved if an appropriate mechanical model is used to describe the problem. These models can, in rare cases, be purely analytical, but nowadays numerical modelling is a vital part of the mechanical approach. Furthermore, with the development of new materials and nanoindentation devices, material (constitutive) modelling has becomes very important. The aim of the present paper is to present an overview of the modelling of sharp indentation experiments. Indentation of classical Mises elastoplastic behaviour, in particular, will be considered, in addition to indentation modelling of other types of materials. In addition, some fundamental issues in indentation modelling will be discussed. These issues include (1) the influence from large deformations, (2) differences and similarities between cone and pyramid indentation results, (3) the influence of residual stresses, (4) the effective elastic modulus at indentation and (5) the differences and similarities between indentation and scratch results. Most of these results have been published previously in international journals but their implications, in the author's opinion, have not been fully appreciated by the indentation community or, at least, not debated sufficiently. [ABSTRACT FROM AUTHOR]

An original instrumented microindenter capable of testing materials up to 1000°C in an inert atmosphere has been developed. After describing the principle and its characteristics, the possibilities of the technique is illustrated with tests on NiAl(Pt) materials representative of the bondcoats of thermal barrier coatings. A modelling approach based on FEM calculations has been developed, which enables, by solving the inverse problem, to identify the variables of the constitutive law of the materials tested. Comparison of results thus obtained with published data when available shows a satisfactory agreement. This experimental technique, combined with the modelling approach, opens up a new way to determine the constitutive behaviour law of materials at a local scale and in a large temperature range. [ABSTRACT FROM AUTHOR]

Size effects in plasticity at small length scales have been widely reported in a variety of loading situations. The hardness size effect has often been cited as an archetypal example. The indentation size effect was clearly demonstrated by Lim and Chaudhri [Phil. Mag. A 79 2979 (1999)] in spherical indentation experiments on copper and, subsequently, in experiments on iridium by Swadener et al . [J. Mech. Phys. Solids 50 681 (2002)]. They showed that large radius indenters produced an indentation stress–strain curve independent of indenter radius with a hardening coefficient equivalent to that in uniaxial tests on the same materials. For smaller indenters, the indentation stress–strain curves appeared at progressively higher pressures for smaller radius indenters. Here, we present similar experimental data for nickel. We simulate these experiments by inputting the uniaxial stress–strain data into a finite element model, which has no intrinsic length scale dependence (essentially using the von Mises criterion for yield). We show that a simple increase in the initial yield stress of the uniaxial stress–strain curve input to the model, allows the indentation behaviour of the smaller radius indenters to be simulated. The increase in yield stress with decreasing indenter radius is shown to follow a single relation for all the metals studied – Al, Cu, Ni and Ir. We show that the indentation size effect is a geometrical effect – consistent with critical thickness theory for the initiation of yielding over a finite volume. The magnitude of the size effect depends only on indenter radius, providing a predictive method for the yield strength in spherical nanoindentation of bulk materials. [ABSTRACT FROM AUTHOR]

Indentation of linearly viscoelastic materials is explored using elastic–viscoelastic correspondence analysis for both conical-pyramidal and spherical indentation. Boltzmann hereditary integrals are used to generate displacement–time solutions for loading at constant rate and creep following ramp loading. Experimental data for triangle- and trapezoidal-loading are examined for commercially-available polymers and compared with analytical solutions. Emphasis is given to the use of multiple experiments to test the fidelity and predictive capability of the obtained material creep function. Plastic deformation occurs in sharp indentation of glassy polymers and is found to complicate the viscoelastic analysis. A new method is proposed for estimating a material time-constant from peak displacement or hardness data obtained in pyramidal indentation tests performed at different loading rates. [ABSTRACT FROM AUTHOR]