Indenter Diameter Research Articles

Theory and application of microindentation in studies of glide and cracking in single crystals of elemental and compound semiconductors

The microhardness of Si (MP 1688 K), GaP (1623 K), GaAs (1510 K) and InP (1327 K) single crystals was determined by indentation (Vicker's hardness, VHN) of low-index facets at loads of 5–100g at 296–673 K, complementing earlier work on Ge and InSb. In the brittle range, extending up to about 0.35 Tmelt (K), cracking occurred preferentially along the diagonals of the indentations, and was observed at all loads, with the possible exception of the lowest (5 g) in the case of InP at 289 K. At higher temperatures the relative orientations of crack and slip traces on the crystal surface, as observed by SEM, suggested that cracks nucleated preferentially at the slip-band intersection, as was also noted by Hirsch et al. (Phil. Mag.3 (1985) 759) in GaAs above 600 K. As earlier in Ge, the VHN was found to depend on the load, L, as Lp, and on the indentation diameter, d, as dn, with p = 1/2 and n = 2, as required by the model of indentation plasticity of Banerjee and Feltham [4, 5], but higher p and n values were found if chipping at the indentation edges was evident. The effect was related to the resulting decrease in indentation diameter due to the work lost, through chipping, by the indenter. Above about 0.35 Tmelt (K), relaxation of the dislocation structures entails a decrease of p and n; both parameters tend to zero as T → Tmelt. Shear and tensile stresses seem to co-operate in the process of plastic deformation, the role of normal stresses, acting across slip planes, predominating in the ‘brittle’ range.

Sea‐Ice Indentation in Creeping Mode

A finite element method of analysis is developed and applied to the study of global and local pressures generated on a cylindrical indenter during sea‐ice deformations in the creeping mode. Numerical simulations are performed under plane stress conditions to assess the influence of interface adfreeze and friction, material constants for a multiaxial power‐law creep model, indenter diameter, and ice‐sheet velocity on predicted pressures. The results are compared with those based on approximate methods of analysis. Stress, strain rate, and strain contours are obtained in addition to the distribution of interface pressures.

Hardness test of porous metals by a spherical indenter.

The relationship between the Brinell hardness HB and the flow stress σε of sintered porous metals is examined considering the ratio d/D ; the diameter of indentation to that of the indenter. When d/D=0.4, at which the Brinell hardness test is usually done, the ratio c=HB/σε varies from 2 to 3 with a relative density ρ of 0.70 to 0.97. However, when d/D=0.7 to 0.9, the ratio c is almost constant at 2.5 to 2.8 without influence of the relative density. Therefore, the flow stress of porous metals can be estimated from the Brinell hardness test at a ratio d/D of 0.7 to 0.9.

Development of vibrotactile measurement techniques for assessing mechanoreceptor performance at the fingertip

In recent years knowledge of the basic physiology of mechanoreceptors has advanced considerably. The translation of this knowledge into psychophysical threshold measurement techniques for assessing mechanoreceptor performance at the fingertip will be described. The sensitivity of three types of mechanoreceptors, the Pacinian corpuscles, Meissner corpuscles, and Merkel disks, is obtained from threshold measurements with sinusoidal vibratory stimuli at various frequencies across the band from 2–400 Hz. Parameters affecting the coupling of the vibrating probe to the finger, namely, static force, skin indentation, and probe diameter, have a significant and different effect on the thresholds for the different receptors. The role of background vibration of physiological origin (physiological noise) on the perception thresholds will be discussed.

Skin blood flow changes and tissue deformations produced by cylindrical indentors.

Since skin blood flow as a function of applied pressure depends on many factors, one may find different curves within each group of subjects, making separation of groups difficult. A dimensional analysis has been out which indicates that the percent decrease in skin blood flow associated with external loading is primarily a function of only three variables: the ratios of bone depth and bone diameter to indentor diameter, and percent compression of the tissue overlying the bone. The load itself is found to be unimportant. It is concluded that measurement of bone depth, bone diameter, and tissue deformation are more important than pressure measurements. Measurements of skin displacement and average indentor pressure for four male subjects indicate that tissue stiffness increases with age, regardless of disability, so that higher pressures are required to produce the same displacement in older subjects.

Indentation fracture transitions in polymethylmethacrylate

The temperature transition associated with fracture initiation by ball indentation of polymethylmethacrylate (PMMA) has been studied, and the results compared with the predictions of an energy scaling analysis. It is found that in accordance with the theory (i) the transition temperature, though subject to statistical variability, is a strong function of the size of geometrically similar indentations, (ii) there are two transitions corresponding to (a) the radial fraction of deep plastic-elastic indentations and (b) ring cracking under the quasi-Hertzian stress fields of shallow indentations, (iii) the criterion for fracture is approximately ac= alpha E Gamma /Y2 where ac is the critical indentation diameter, E is Young's modulus, Y is yield stress in uniaxial testing and Gamma is the fracture surface work, alpha is about 50 for radial fracture and 140 for ring crack initiation. Certain anomalies in the temperature range -10 degrees C to +10 degrees C are attributed to variation in craze length. There are marked changes in the mode of indentation fracture at low temperatures, where the polymer behaves like an inorganic glass; the transition temperature is also affected by the condition of the specimen surface and the presence at the interface of water and graphite.

Relation of Load to Radial Crack Length for Spherical Indentations in Hot-Pressed ZnS

Hot-pressed ZnS was indented by spherical indenters of various radii. The relation of the load (P) and radial crack length (cr) was better modeled by Pαicr½, where di is the indentation diameter, than by Pαcr3/2.

Indentation loading studies of acoustic emission from temper and hydrogen embrittled A533B steel

Isothermal tempering at 500 °C (within the region rendering low alloy steels susceptible to reversible temper embrittlement) induced acoustic emission activity in A533B steel during indentation loading. Samples, when sectioned, were found to contain small (∼10 μm long) MnS inclusions, some of which had debonded from the matrix material when they were near the indentations. Hydrogen charging prior to testing greatly enhanced the acoustic emission activity. It also resulted in the formation of small (∼20 to 200 μm) microcracks in samples tempered at 500 °C. These microcracks, when examined by optical metallography, appear to have propagated along prior austenite grain boundaries, consistent with fractographic observations of temper embrittlement in other low alloy steels. Many were nucleated by MnS inclusion debonding and all were confined to within a few hundred micrometers of the sample surface and within two or three indenter diameters from the indent. It is proposed that trace impurities (P, As, Sb, Sn) diffuse during the 500 °C temper to both the MnS inclusion interfaces and the prior austenite grain boundaries, reducing local cohesive strength. The tensile field created by the indenter debonds inclusions to form crack nuclei. Moderate acoustic emission results. In the absence of hydrogen these void nuclei may grow but do not coalesce to form observable cracks. The prior austenite grain boundaries, which in contrast to the dispersed inclusions can provide continuous crack paths, are not sufficiently temper embrittled to fracture without the assistance of hydrogen at these stresses. Hydrogen charging induces a high hydrogen concentration in a surface layer of the sample. This reduces further the grain boundary cohesion, and cracks initiated at inclusions are able to propagate along continuous grain boundary paths, generating additional energetic acoustic emission signals. This process can continue after unloading the indenter due to hydrogen diffusion to the residual stress field.

Indentation processes in poly(methyl methacrylate). I. Ball indentation

The indentation of PMMA is shown to be highly dependent on indenter-PMMA friction and a correction for this effect is proposed. For penetrations greater than half a radius the pressure varies with penetration rate and ball size as predicted by the expanding cavity model of Puttick et al. (1977) provided the indentation diameter is determined under load and the friction correction is applied. This allows assignment of a value to the parameter plastic-zone radius/cavity radius, c/a. Observations of the growth and position of the region of anomalous refractive index beneath the indenter and the fracture surfaces shows the creation of a core of material beneath the indenter which can be identified with the cavity of the plastic-elastic model. This allows an alternative estimate of c/a and both methods give a value of 1.9.

Time-dependent flow properties from indentation tests

An effort was undertaken to investigate the possibility of using indentation tests to extract time-dependent flow property information from small, cylindrical specimens. Lead specimens were tested by conventional creep, indentation creep, conventional stress relaxation, and indentation load relaxation techniques. Indentation creep and indentation load relaxation results were found to fit the conventional creep and the stress relaxation results, respectively, by defining an effective stress σ eff = P m /5.33 and an effective strain rate ε eff = h D , where P is the indentation pressure, D is the indentor diameter, and h the indentation rate. Of the two indentation tests, the indentation load relaxation test should be the easier to scale down to smaller specimens.

Characterization of silicon nitride single crystals and polycrystalline reaction sintered silicon nitride by microhardness measurements

Identification of α- and β-phases of Si3N4 single crystals grown from Si melt could be made with the help of Vickers microhardness measurements. The effect of chemical additives, e.g. metallic Fe and BaF2, on the microhardness of Si3N4 was also determined. Different constants involved in the empirical Meyer relationship between load and indentation diameters could be correlated with the porosity and microhardness of Si3N4 single crystals and polycrystalline, reaction sintered Si3N4.

The hardness of cubic single crystals by spherical indentation

Spherical indenters have been used to study the effect of indentation diameter on the hardnesses of variously oriented surfaces of ductile and semi-brittle cubic single crystals. The results are discussed in terms of the elastic recovery, the initial yield, the strain hardening and the crack nucleation processes occurring around and beneath the indenter.

Stress-strain curve for aluminium from a continuous indentation test

Continuous indentation tests using a 6.35 mm diameter steel ball were carried out on polycrystalline aluminium (99.995%) at forces up to 942 N (96 kg) and a total displacement of 65μm. On loading the results were observed to follow the classical Hertz equation until the elastic limit was reached at 4.6±0.2 N (0.47 kg), 1.02±0.05μm. The unloading results after plastic indentation were found to fit the Hertz solution for an indenter in a spherical hole. Using the Hertz theory it was possible from the unloading results to determine the mean stress and strain under the ball, together with the indentation diameter, plastic strain, Meyer stress and ratio of elastic to total strain, enabling a stress-strain curve for hardness to be drawn. The elastic limit of aluminium occurred at a stress of 4.7±0.2×108Pa (46kg mm−2) and a strain of 1.27±.05%. At a total strain of 11.25% the stress was 11.7±0.2×108Pa (115 kg mm−2).

Mn-Znフェライトの摩擦と変形(第1報)

Measurements were made on the indentation and friction of diamond hemispheres with various radii on Mn-Zn ferrite single crystals at a room temperature. Vickers and Knoop indenters were used in the indentation experiments. In the indentation and friction of ferrite, a plastic deformation occurs in ferrite, although the deformation is accompanied with the formation of cracks at higher contact loads. The relationship between diameter of indentation and load is expressed by the empirical formula, known as Meyer's law, where Meyer index takes a value of 2.2-2.0. A similar formula also holds in the case of sliding of hemisphere on ferrite, the index taking a value of 2.3-1.9. The critical load at which cracks are produced in the indentation or frictional track on ferrite is directly proportional to the radius of the diamond hemisphere. The critical loads on the sliding decrease to below half of those on the case of static indentation with same radius of hemisphere. The anisotropy of hardness of ferrite single crystal is fairly small. A little anisotropy of friction is also observed. Although the sliding on (100) plane exhibits a maximum anisotropy with sliding direction, the ratio of the friction in the [011] sliding to that in the [001] sliding is only a value of 1.2. The friction is slightly independent upon the crystallographic planes. It is concluded that the adhesion theory of friction is generally applicable to the frictional mechanism of ferrite single crystal. The relationship between frictional force F and contact load W can be expressed by the equation, F=αWc, where α and c are the constants. The value of index c approaches to unity with the increase of the radius of hemisphere.

Investigation of the relation between the depth of penetration and indentation diameter in polymer hardness measurements

It has been experimentally demonstrated that for polymeric materials the area of the indentation should not be calculated from the depth of penetration of the spherical indenter, since this gives hardness values that are too low. It is shown that when the surface of a polymeric specimen is indented by a rigid ball, the effect of the spherical stress tensor on the yield point is important; the average stress on the contact area at the beginning for forced high-elastic deformation is close to the compressive yield stress of the polymeric material and considerably higher than its tensile yield stress.

Bearing strength of lunar soil

Bearing load vs penetration curves have been measured on a 1.3 g sample of lunar soil from the scoop of the Surveyor 3 soil mechanics surface sampler, using a circular indentor 2 mm in diameter. Measurements were made in an Earth laboratory, in air. This sample provided a unique opportunity to evaluate earlier, remotely controlled, in-situ measurements of lunar surface bearing properties. Bearing capacity, measured at a penetration equal to the indentor diameter, varied from 0.02–0.04 N cm−2 at bulk densities of 1.15 g cm−3 to 30-100 N cm−2 at 1.9 g cm−3. Deformation was by compression directly below the indentor at bulk densities below 1.61 g cm−3, by outward displacement at bulk densities over 1.62 g cm−3. Preliminary comparison of in-situ remote measurements with those on returned material indicates good agreement if the lunar regolith at Surveyor 3 has a bulk density of 1.6 g cm−3 at 2.5 cm. depth; definitive comparison awaits both better data on bulk density of the undisturbed lunar soil and additional mechanical-property measurements on returned material.

On the Plastic Flow Beneath a Blunt Axisymmetric Indenter

A new approach to large strain plasticity problems in which the material is considered to behave in a plastic-elastic fashion, instead of as a plastic-rigid body, is applied to the axisymmetric blunt indenter. The ratio of the mean stress on the punch face to the uniaxial flow stress of the material (constraint factor C) is found to be 2.82 for an extensive specimen. However, it is shown that a small part of the punch face is elastically loaded, and if the loaded punch area is assumed equal to the size of the plastic impression, then the constraint factor to be used is 3.00 instead of 2.82. This is the value to be used in interpreting the ordinary brinell test. Hardness values are shown to be independent of the degree of friction on the face of a blunt indenter and of the elasticity of the indenter. The amount of material required beneath an axisymmetric indenter in order that there be no upward flow is found to be about 2.6 times the diameter of the impression for steel. However, the exact value depends on Young’s modulus of elasticity, Poisson’s ratio, material hardness, and the depth of the impression relative to the diameter of the indenting sphere. When two opposing axisymmetric indenters are employed, the influence of one on the other will be less than one percent when their spacing is approximately 11.5 times the indentation diameter. A blunt indenter may be defined as one which gives no upward flow in a hardness test. Upward flow should be avoided in hardness testing since it causes the mean stress on the punch face to produce a given impression to be sensitive to friction and the tendency of the metal to strain harden. Upward flow may be prevented by use of an extensive specimen relative to the depth of the impression, large indenter angle (160–180 deg), and high indenter friction (rough surface and no lubricant). The flow stress measured by a blunt indenter is that corresponding to the onset of plastic flow. When upward flow is permitted, the flow stress measured by an indentation hardness test will correspond to an appreciable plastic strain which increases as the included angle of the indenter decreases. The quantity measured by an indenter that performs with upward flow is, therefore, quite ambiguous when the material tested strain hardens.

Deformation of amalgam by indenters.

Using steel spherical indenters, the relationship between indentation diameter and load was determined for a mature amalgam. The form of this relationship allowed the regions of elastic and plastic deformation to be identified; hence, Young's modulus and yield point could be calculated. Local contact stresses in the mouth also were estimated.

Instrument for evaluating the diameter and depth of an indentation under the load of an imbedded ball

Instrument for evaluating the diameter and depth of an indentation under the load of an imbedded ball

Dynamic Indentation Using Rigid Slow Speed Conical Indenters

Rigid conical indenters of various weight, of half angle 30, 45, 60, and 75 deg were made to impinge normally on blocks of duralumin, copper, and lead at various speeds. Among other things the resulting indentation diameter is shown to be related to the velocity at impact raised to approximately the power 2/3. The experimental results here reported confirm those of previous workers but interpretation of them is different.