Indent shape

When it is desired to evaluate the specific surfaces of a set of closely related samples of solid, however, only one of the samples needs to be calibrated against nitrogen (or argon), provided that all the isotherms of the alternative adsorptive can be shown to have indentical shape. A simple device for testing this identity, by use of the a,-plot, is described in Section 2.13 by means of the a,-plot it is also possible to proceed directly to calculation of the specific surface without having to assign a value to or to evaluate the BET monolayer capacity, of the alternative adsorptive. 

Vickers Hardness. The Vickers or diamond pyramid hardness (DPH) developed in 1924 was an improvement over the Brinell test. The Vickers test used a pyramidal diamond as the indenter. This permitted the hardness testing of much harder materials, and the constant 136° angle of the indenter eliminated the problem of variable indentation shape encountered using spherical indenters (1). 

Sakhalinskii — Russian Federation origin. White tubers, with spherical and indented shape. Maintained by Institut National de la Recherches Agronomique (INRA), UMR-DGPC, Montpellier, France (INRA MPHE001493) limited immediate availability. 

Use in routine industrial testing, which requires improved automation so that the monitoring of changes in indenter shape, for example, is more reliably performed. 

Diamond is the hardest material known, with a value of 10 on the Mohs scale, which is a scratch hardness test or, on the Knoop scale, which is an indentation test dependent on the load, indenter shape and the crystal face, giving a value of 5,700-10,400 kgmm . The hardness is attributed to the strength of bonding of the atoms in conjunction with the uniformity. There is, however, a possibility that there are new materials, sueh as carbon nitride (C3N4) and compressed Ceo that may eventually be shown to be harder than diamond. 

The indenters and their indentation shapes vary widely, leaving different impressions. The appropriate dimensions of these impressions on the surfaces are measured to obtain interesting research data. Conversion charts, from hardness to other properties of interest, appear in the literature. Basically, glass and ceramic hardness tests are carried out using static methods, usually by means of a diamond indenter and low test loads, because brittle materials tend to propagate cracks. 

Hardness H defines the resistance to local deformation of a material when indented, drilled, sawed, or abraded. It involves a complex combination of properties (elastic modulus, yield strength, strain-hardening capacity). The prevailing deformation mechanism depends upon the material and the type of tester. Hardness is either measured by (1) static penetration of the specimen with a standard inden-ter at a known force, (2) dynamic reboimd of a standard indenter of known mass dropped from a standard height, or (3) scratching with a standard pointed tool under a load. The hardness tester, indenter shape, and force employed strongly influence the hardness numbers (1). 

Figure 2.9. Influence of surface siope on indent shape.

These then are a number of equations and observations that have resulted from using glass to study the processes that generate indentation shapes and cracks around such indents. 

Because it is sometimes advantageous to have an indenter that more closely reflects the symmetry of the plane being indented, a triangular-based pyramidal indenter was developed during the late 1950 s it is the Berkovich indenter. This indenter has an angle of 65° between the vertical axis and each of its three faces which penetrate the surface. Equation (1.8) allows hardness values to be calculated when Qb is measured as the perpendicular distance from an apex to the opposite base of the triangular indent shape produced on the surface. 

This yield criterion would need to be used in any extended calculation of Hx or indentation shape, which explains why empirical and semiqualitative work is the order of the day in this field and approximate constraint factors are used. 

Figure 1.6. Schematic representation of indent shapes for materials with different constraint factors, (a) Mises material with Tabor constraint, (b) Mises material with Hill constraint or Mises-Coulomb material with o = —0.2, H 0.2E. (c) Mises-Coulomb material with no stress hardening but about 45% densification, typical of glass, (d) Little densification but large values oUi.

Results obtained with different-shaped indenters cannot be compared directly the curves relating hardness and crack length for each indenter shape are unique. 

Indentation hardness data can also give the yield stress via analysis of the stresses in the coating due to the indenter. For an elastic-perfectly plastic coating response, plastic flow occurs at the indentation pressure corresponding to the hardness as defined in Eq. 7, so that an elastic analysis of the stresses below the indentation at these conditions, in conjunction with an appropriate yield criterion results in the relationship between hardness and yield stress. The resulting relationship is a function of the indenter shape. For example, for the dynamic indentation of a urethane coating on an epoxy primed aluminium substrate by a spherical indenter, the authors applied an approximate elastic theory [34] in... 

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