Indentation hardness

A hardness indentation causes both elastic and plastic deformations which activate certain strengthening mechanisms in metals. Dislocations created by the deformation result in strain hardening of metals. Thus the indentation hardness test, which is a measure of resistance to deformation, is affected by the rate of strain hardening. 

As well as being a good way of measuring the yield strengths of materials like ceramics, as we mentioned above, the hardness test is also a very simple and cheap nondestructive test for (Ty. There is no need to go to the expense of making tensile specimens, and the hardness indenter is so small that it scarcely damages the material. So it can be used for routine batch tests on materials to see if they are up to specification on without damaging them. 

A good example is the problem of the hardness indenter that we referred to in the hardness test in Chapter 8. Then, we stated that the hardness... 

Fig. 11.4. The plastic (low of material under a hardness indenter - a simplified two-dimensional visualisation.

Slides Slab and sheet metal rolling extrusion, etc., of polymers tensile-testing machines hardness-testing machines hardness indentations. 

Two pieces of work-hardened 5000 series aluminium alloy plate were butt welded together by arc welding. After the weld had cooled to room temperature, a series of hardness measurements was made on the surface of the fabrication. Sketch the variation in hardness as the position of the hardness indenter passes across the weld from one plate to the other. Account for the form of the hardness profile, and indicate its practical consequences. 

Mechanics of hardness indentation 137 Meso-4,5-dimethyloctane 75 Mesogenic groups 50, 52 Mesophase 149... 

Figure 1.2 Shapes of various hardness indenters (adapted from Shaw, 1973).

The theory just presented shows how the behavior of electrons leads to bonding in the ground state of a molecule. When dislocations move to produce plastic deformation and hardness indentations, they disrupt such bonds in covalently bonded crystals. Thus bonds become anti-bonds (excited states). This requires that the idea of a hierarchy of states that is observed for atoms be extended to molecules. 

Hardness indentations are a result of plastic, rather than elastic, deformation, so some discussion of the mechanisms by which this occurs is in order, especially since the traditional literature of the subject is confused about its fundamental nature. This confusion seems to have arisen because it was considered to be a continuous process for a great many years, and because some metals behave plastically on the macroscopic scale in a nearly time-independent fashion. During the twentieth century, it became well established that plastic deformation is fundamentally discontinuous (quantized), and a time-dependent flow process. 

In textbooks, plastic deformation is often described as a two-dimensional process. However, it is intrinsically three-dimensional, and cannot be adequately described in terms of two-dimensions. Hardness indentation is a case in point. For many years this process was described in terms of two-dimensional slip-line fields (Tabor, 1951). This approach, developed by Hill (1950) and others, indicated that the hardness number should be about three times the yield stress. Various shortcomings of this theory were discussed by Shaw (1973). He showed that the experimental flow pattern under a spherical indenter bears little resemblance to the prediction of slip-line theory. He attributes this discrepancy to the neglect of elastic strains in slip-line theory. However, the cause of the discrepancy has a different source as will be discussed here. Slip-lines arise from deformation-softening which is related to the principal mechanism of dislocation multiplication a three-dimensional process. The plastic zone determined by Shaw, and his colleagues is determined by strain-hardening. This is a good example of the confusion that results from inadequate understanding of the physics of a process such as plasticity. 

Glide bands are observed around hardness indentations in lysozyme so dislocations (with large displacements) are associated with its deformation. 

ISO 2039-1 2001 Plastics - Determination of hardness - Part 1 Ball indentation method ISO 2039-2 1987 Plastics - Determination of hardness - Part 2 Rockwell hardness ISO 2439 1997 Flexible cellular polymeric materials - Determination of hardness (indentation technique)... 

In the case of potassium nitrate the Vickers hardness indentations have not a quadratic shape. This is due to a direction dependent hardness in the crystal lattice of this material. The direction dependency can be explained with an anisotropic effect in the lat-... 

An unfortunate aspect of hardness is that it is difficult to quantify in an absolute manner. Most hardness scales are relative and fairly qualitative, and there is a proliferation of different hardness scales. Some of the more common scales are shown in Figure 5.19. In a typical hardness test, a hard indenter of a standard shape is pressed into the surface of a material under a specified load, causing first elastic and then plastic deformation. The resulting area of the indentation or depth of indentation is measured and assigned a numerical value. The value depends upon the apparatus and scale used. 

Tate D. R., 1945, A comparison of micro-hardness indentation tests, Trans. Am. Soc. Metals, 35, 374-389. 

There are two main techniques used to measure the fracture toughness of ceramics fracture stress and hardness indentation. The former measures the load to fracture of a pre-cracked specimen using a single edge notched beam (SENB) or a chevron notched beam (CNB) sample. The main drawback of this technique is ensuring that the crack tip is atomically sharp. The second method uses the crack formed at the corners of the indentation produced during a Vickers indentation hardness test. This technique is rapid and relatively inexpensive. However, the toughness values measured are those of the surface, unlike the values obtained by fracture of the pre-cracked beams which are a measure of the bulk material properties. 

Indentation hardness is a very common determination in materials testing. In this test a very hard indenter (a hard steel sphere in the Brinell test, a diamond pyramid in the Vickers test) is pressed under a load into the surface of the material. 

Hardness measurements usually fall into three main categories scratch hardness, indentation hardness and rebound or dynamic hardness. 

ISO 2439-80 Polymeric Materials, Cellular Flexible —Determination of Hardness (Indentation Method), 4 pp... 

In the first procedure (3), a Vickers hardness indenter is used to place a controlled flaw into the polished surface of the ceramic. The size of the cracks emanating from the hardness impression are measured on the surface for a particular indentation load, P. KIC is given by the expression ... 

An alternative method of determining the plasticity and elasticity of a material is indentation hardness testing. The principle of indentation hardness testing is that a hard indenter of specified geometry, either a sphere or square-based pyramid, is pressed onto the surface of the test... 

Durometer Hardness - Indentation hardness of a material as determined by either the depth of an indentation made with an indentor under specified load or the indentor load required to produce a specified indentation depth. The tool used to measure indentation hardness of polymeric ma-... 

Shore Hardness - Indentation hardness of a material as determined by the depth of an indentation made with an indentor of the Shore-t5 e durometer. The scale reading on this durometer is from 0, corresponding to 0.100" depth, to 100 for zero depth. The Shore A indenter has a sharp point, is spring-loaded to 822 gf, and is used for softer plastics. The Shore D indenter has a blunt point, is spring-loaded to 10 Ibf, and is used for harder plastics. Also called Shore A, Shore D.. 

There are several techniques by which K f. can be measured. The two most common methods entail measuring the fracture stress for a given geometry and known initial crack length and measuring the lengths of cracks emanating from hardness indentations. 

Due to its simplicity, its nondestructive nature, and the fact that minimal machining is required to prepare the sample, the use of the Vickers hardness indentations to measure Ki. has become quite popular. In this method, a diamond indenter is applied to the surface of the specimen to be tested. Upon removal, the sizes of the cracks that emanate (sometimes) from the edges of the indent are measured, and the Vickers hardness H in GPa of the material is calculated. A number of empirical and semiempirical relationships have been proposed relating Ki., c, Y, and //, and in general the expressions take the form... 

To measure hardness more precisely a known load is applied slowly to a hard indenter that is placed onto the smooth surface to be tested. The surface is deformed plastically, and the indent size or depth after the indenter is removed is taken as the measure of the indentation hardness of the material. The hardness is often recorded as an empirical hardness number, related to the size of the indentation. 

Figure 10.23 Hardness indenters (a) Brinell steel or tungsten carbide sphere (b) Rockwell A, C, D diamond cone (c) Rockwell B, F, G steel sphere (d) Vickers diamond pyramid and (e) Knoop diamond pyramid...

ISO 2439. Polymeric materials, cellular flexible—Determination of hardness (indentation technique). 1980. 

When we walk on the ground, our steps can densify soil, break up agglomerates, and leave footprints. In a similar way, any hard object can leave imprints on a material surface. The harder the counterbody material, the stronger its influence is on the material surface. In particular, when a hard indenter (e.g., diamond) touches the surface of another hard material (ceramic or semiconductor), very high pressures can be achieved under the indenter (Fig. 1) because there is no or minimal stress relaxation due to the plastic flow of the material. 

At this point, it is important to define what we mean by hardness. Hardness is the resistance of a material to penetration of a hard indenter. The softer the material, the deeper the indenter will penetrate its surface. The definition of hardness as resistance to plastic deformation, which can be found in many textbooks, does not reflect the complexity of processes that occur in materials upon interaction... 

In the following sections we will describe the phase transformations and amor-phization that occur in many ceramics and semiconductors under contact loading, including that of indentation with hard indenters or scratching, grinding, milling, etc. 

Extensive TEM studies by Page et al. [65] delivered all previous low-temperature electron microscopy results to the consistent view that (i) silicon becomes amorphous in response to the high contact stresses under a hardness indenter and (ii) limited dislocation arrays are generated around the deformed volume at contact loads exceeding some threshold value. The authors also argued that the dislocation arrays might occur as a means of accommodating the displacements from the densification transformation, rather than as a primary response to the indenter intrusion. 

Fig. 28. Raman spectra taken from hardness indentations in germanium, (a) Pristine material outside the contact area, (b, c) Indentation area, slow unloading, (d, e) Indentation area, fast unloading. Data from Reference [134].

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