J. S. Field

A simple predictive model for spherical indentation

A simple model is described with which the entire force versus penetration behavior of indentation with a sphere, during loading and unloading, may be simulated from knowledge of the four test material parameters, Youngs modulus, Poissons ratio, flow stress at the onset of full plastic flow and strain hardening index, and the elastic properties of the indenter. The underlying mechanisms are discussed and the predictions of the model are compared with data produced by an ultra low load, penetration measuring instrument.

Determining the mechanical properties of small volumes of material from submicrometer spherical indentations

The stress/strain behavior of bulk material is usually investigated in uniaxial tension or compression; however, these methods are not generally available for very small volumes of material. Submicrometer indentation using a spherical indenter has the potential for filling this gap with, possibly, access to hardness and elastic modulus profiles, representative stress/strain curves, and the strain hardening index. The proposed techniques are based on principles well established in hardness testing using spherical indenters, but not previously applied to depth-sensing instruments capable of measurements on a submicrometer scale. These approaches are now adapted to the analysis of data obtained by stepwise indentation with partial unloading, a technique that facilitates separation of the elastic and plastic components of indentation at each step and is able to take account of the usually ignored phenomena of “piling up” and “sinking in”.

Determination of fracture toughness from the extra penetration produced by indentation-induced pop-in

The fracture toughness of small volumes of brittle materials may be investigated by using pyramidal indenters to initiate radial cracks. The length of these cracks, together with indenting load and the hardness to modulus ratio of the material, were combined to calculate the critical stress intensity factor K c pertinent to fracture toughness. Modulus and hardness may be obtained from the literature or may be measured using nanoindentation techniques. If the material volume is very small, such as single grains in a conglomerate, a reduction of scale may be obtained by reducing the internal face angles of the indenter. This encourages crack initiation at lower loads, but cracks produced at very low loads are short and difficult to measure. Experiments on fused silica and glassy carbon suggested that radial cracks are initiated during loading and that when indenters with sufficiently small angles are used these cracks immediately pop-in, to become fully developed median/radial crack systems. Following pop-in, the rate of penetration of the indenter increases and at higher loads there is an extra increment of penetration over that which would otherwise have occurred. In this study a method is described whereby this extra penetration may be determined. Then for two dissimilar brittle materials, crack length is shown to be correlated with extra penetration leading to a relationship that may possibly avoid the necessity for crack-length measurement.

Elasto-plastic deformation of glass-like carbons heat-treated at different temperatures

Nano-indentation of glass-like carbons (GCs) heat-treated at different temperatures was carried out with a 3 μm radius spherical tipped indenter. The effect of crystal structure and micro-texture on elastic and elasto-plastic deformation resulting from the indentation was observed. The elastic modulus and yield stress of GCs was found to reduce with elevation of heat treatment temperature (HTT). The power law fitting constant k for the elasto-plastic deformation of the loading stress–strain curves by the indentation and the indentation elasticity index k/E* reduced with development of the graphitic structure of GC, so that ‘elasticity’ of GC decreased with the elevation of HTT of GCs. Hysteresis loops were observed on the indentation force–displacement curve during the loading–unloading cycle. Hysteresis energy loss, which corresponds to the area of the hysteresis loops, increased with the elevation of HTT for the same terminal load. The indentation ductility index D, the ratio of hysteresis energy loss to total indentation energy, was linearly dependent on indentation elasto-plastic deformation strain eep. The indentation elasto-plastic modulus m, which is obtained from the slope of the plots of D versus eep, reduced with the elevation of HTT of GCs. From the reduction of m, it was concluded that ‘plasticity’ (or ‘ductility’) of GC increased with the elevation of HTT of GCs.

An experimental investigation of the use of random squeezing to determine the complex modulus of viscoelastic fluids

Abstract A method for determining the complex modulus of viscoelastic fluids, based on small amplitude random squeezing between parallel plates, is experimentally examined. In a single brief test, this previously unused method is shown to produce the complex modulus spectrum of small volumes of fluid with wide ranging viscosities, over more than two decades of frequency. The apparatus and fluid sample are treated as a dynamic system and transfer functions, simply related to complex modulus, are calculated from measurements of relative plate motion and the variation of the associated normal force.

Indentation hysteresis of glassy carbon materials

Abstract Indentation hysteresis during both pointed and spherical indentation is a common feature of the observed force-displacement response of glassy carbon materials. Field and Swain proposed a method of analysis of this behaviour with spherical indenters in the form of classic indentation stress-strain curves. They also proposed that the response resulted from limited reversible slip of the graphite-like nanocrystalline structure of these so-called glassy carbon materials. The present work extends the previous study by investigating the influence of the nanocrystalline grain size and the hysteretic response with indenters of sharper apical angle. It is found that the extent of the hysteresis is dependent upon the grain size as is the contact stress for the initiation of yielding. The critical strain for the onset of non-recoverable hysteretic response is clearly identified with sharper-apical-angle indenters. This irreversibility of the hysteretic response is discussed in terms of an analysis proposed by Brown whereby the critical limit for the strain for reversible hysteretic behaviour was related to the percolation limit for plastic shear strain sites within a material.

Micro-Fourier rheometer : Inertial effects

The inertial effects in a random squeezing rheometer are examined, both theoretically and experimentally. The rheometer is based on small amplitude random squeezing between two parallel plates, where the upper plate is driven by a random displacement with a broad band spectrum. A fast Fourier transform is used to deliver the complex modulus (or viscosity) of the fluid in a single brief test, over more than two decades of frequency. The inertia of the fluid is shown to produce an error factor, which is also a function of the frequency. The correction factor can be well approximated by a first-order correction in the Reynolds number, for a very large range of Reynolds number, making the inertial correction a very simple procedure for light fluids.

Investigation of the mechanical properties of two glassy carbon materials using pointed indenters

Abstract Precision force–displacement measurements have been made of the continuous indentation of two glassy carbon materials using three pyramidal indenters with different apical face angles. The data for all three indenters shows hysteresis with almost complete recovery on unloading despite contact pressures reaching a considerable fraction of the elastic modulus. The extent of hysteresis on unloading was found to depend upon the apical angle of the pointed indenters. The data are analysed following a procedure developed by Oliver and Pharr. It is found that the hardness decreases with increasing apical angle of the indenter whereas the modulus is almost independent of the indenter angle except for the sharpest indenter upon the initiation of radial cracks about the impression during loading.

Elasto-Plastic Behavior of Glassy Carbon and Silica Glass by Nano-Indentation with Spherical Tipped Indenter

Glassy carbons (GCs), obtained by pyrolysis and heat treatment of thermosetting resins above 1000°C, are hard and brittle materials that fail suddenly when loaded in tension or compression.1, 2, 3 In commercially available GCs, the mean grain diameter, evaluated from micrographs under a field-emission electron gun type scanning electron microscopy, and the crystallite sizes, calculated from X-ray powder diffraction profiles, both slightly increased with the elevation of heat treatment temperature (HTT) from 1000°C to 3000°C.4.