Indent recovery

Thompson JB, Kindt JH, Drake B, Hansma HG, Morse DE, Hansma PK. Bone indentation recovery time correlates with bond reforming time. Nature (Lond) 2001 414 773-776. 

Hardness is a measure of a material s resistance to deformation. In this article hardness is taken to be the measure of a material s resistance to indentation by a tool or indenter harder than itself This seems a relatively simple concept until mathematical analysis is attempted the elastic, plastic, and elastic recovery properties of a material are involved, making the relationship quite complex. Further complications are introduced by variations in elastic modulus and frictional coefficients. 

Bar, G., Delineau, L., Hafele, A. and Whangbo, M.H., Investigation of the stiffness change in, the indentation force and the hydrophobic recovery of plasma-oxidized polydimethyl-siloxane surfaces by tapping mode atomic force microscopy. Polymer, 42(8), 3627-3632 (2001). 

It has been shown that the anisotropy depends on the orientation of the diagonals of indentation relative to the axial direction 14). At least two well defined hardness values for draw ratios A. > 8 emerge. One value (maximum) can be derived from the indentation diagonal parallel to the fibre axis. The second one (minimum) is deduced from the diagonal perpendicular to it. The former value is, in fact, not a physical measure of hardness but responds to an instant elastic recovery of the fibrous network in the draw direction. The latter value defines the plastic component of the oriented material. 

From the foregoing it is clear that indentation anisotropy is a consequence of high molecular orientation within highly oriented fibrils and microfibrils coupled with a preferential local elastic recovery of these rigid structures. We wish to show next that the influence of crystal thickness on AMH is negligible. The latter quantity is independent on 1 and is only correlated to the number of tie molecules and inter-crystalline bridges of the oriented molecular network. 

As an alternative purification procedure, the checkers have esterified the crude acid by refluxing it for 2 hours with three times its weight of methanol and 2 ml. of 98% sulfuric acid. The solution is poured into 10 volumes of water and extracted with the minimum amount of chloroform required to give a clean separation of layers. The chloroform solution is washed with water, dried over calcium chloride, and distilled from a Claisen flask with an indented neck. Methyl 1-adamantanecarboxylate is collected at 77-79° (1 mm.) m.p. 38-39°. Hydrolysis of the ester with the calculated amount of 1A potassium hydroxide followed by acidification yields 1-adamantanecarboxylic acid m.p. 175-176.5° 90% overall recovery. 

Hardness is essentially a measure of stiffness and in principle can be related to modulus. For plastics, the term hardness refers to resistance to indentation but depending on the test method the measurement is made either with the indentation load applied or after its removal when elastic recovery has taken place. The standard methods are given in ISO 868 (Shore) [6] and ISO 2039 (Ball indentation and Rockwell) [7]. However, Vickers microhardness is more satisfactory for monitoring degradation of rigid materials. 

Observations of the specificity of indentations, excluding measurement of the magnitude of Vickers pyramid penetration, enable a description of the properties of minerals, ceramic materials, or other brittle bodies (Vigdo-rovich and Yelenskaya, 1967 A. Szymanski et al., 1969). The action of elastic-recovery forces after removal of the pressure often causes perturbation in the structure of the test surface, around the site subjected to loading (Fig. 6.3.1). This is described in Section 6.2. 

The Micromet M-ll hardness tester supplied by A. J. Buehler Inc. of the United States is fitted out with two types of Vickers and Knoop indenters, an automatic load feeder and a light signalling device, allowing measurement to be made only after elastic recovery of the sample (Fig. 4.3.25). 

The microhardness of the SiC compact measured under a 19.6 N load increases by incorporating SiC-coated MWCNTs, as shown in Table 10.7. The hardness reaches 30.6 GPa for the content of 5 vol% SiC-coated MWCNTs. This high hardness is considered as an apparent value due to the elastic recovery of the indentation after loading. This interesting phenomenon is discussed later. On the other hand, the increment of hardness by incorporating uncoated MWCNTs is very low compared with the increment by incorporating SiC-coated MWCNTs. This behavior may be due to the poor adhesion with the matrix. 

The amorphous phase appearing above 20 GPa at room temperature (see above) has also recently been studied by X-ray diffraction [135] and Raman scattering [132,133]. Serebryanaya et al. [135] identify the structure as a three-dimensionally polymerized Immm orthorhombic lattice, but find that compression above 40 GPa gives a truly amorphous structure. In contrast to the orthorhombic three-dimensional polymer structure discussed in the last section, the best fit here is found for (2+2) cycloaddition in two directions, with (3+3) cycloaddition in the third, and thus some relationship to the tetragonal phase. From the in situ X-ray data a bulk modulus of 530 GPa is deduced, about 20% higher than for diamond. Talyzin et al. [132, 133] find that this phase depolymerizes on decompression into linear polymer chains, unless the sample is heated to above 575 K under pressure. A strong interaction with the diamond substrate is also noted, such that only films with a thickness of several hundred nm are able to polymerize fully [ 132]. Hardness tests were also carried out on the polymerized films, which were found to be almost as hard as diamond and to show an extreme superelastic response with a 90% elastic recovery after indentation [133]. 

The problem of recovery leads to the question of hardness. Hard substances have a high number of strongly directed, covalent chemical bonds per unit volume. Soft substances generally have fewer bonds per unit volume or bonds that are weak or weakly directed, such as ionic or dipole attractive forces. Bond energy per unit volume has the same dimensions as pressure (force per unit area), and a plot of hardness measured by the Knoop indenter versus the bond energy per molar volume for various substances is essentially linear, provided that one chooses substances for which the bonding is predominantly of one type (i.e., not mixed, as in graphite or talc). 

The mechanism of the indentation process has been clearly defined by Tabor (1947). When a ball presses on a metal surface, the material deforms elastically. As the load increases, the stresses soon exceed the elastic limit and plastic flow starts. By increasing the load still further the material directly beneath the penetrator becomes completely plastic. On release of the load there is an amount of elastic recovery. 

By measuring the initial distance of indentation and the distance of recovery the modulus E can be determined. 

Baer et al (1961) later considered the indentation process in which large loads are placed on a spherical penetrator and the material beneath the indenter becomes permanently displaced. In addition, he defined the recovery process which occurs immediately after the load is released analysing it in terms of the elastic concepts developed by Hertz (Love, 1927). 

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