Berkovich Indentations

Fig. 29—Scanning elecron micrograph of a smaii nanoindentation made with a Berkovich indenter in a 500 nm aiuminum fiim deposited on giass (from Ref. [64]).

Flowever, in order to probe the fracture toughness of thin films or small volumes using ultra low load indentation, it is necessary to use special indenters with cracking thresholds lower than those observed with the Vickers or Berkovich indenters (for Vickers and Berkovich indenters, cracking... 

The dimensional ratios of indentations obtained with the first three, most common, indenters, taking indentation depth to be 1, are for the measured parameters 7—with the Vickers indenter 30.5—with the Knoop indenter 7.4—with the Berkovich indenter. 

The mechanical behavior of coatings under point loading conditions was studied by nanoindentation using Berkovich indenter on Nano Indenter-II (MTS Systems Corporation, Oak Ridge, TN, USA). The nanohardness of chromium and molybdenum coatings was determined by the Oliver and Pharr analysis. 

The standard methods to determine the coating microhardness by indentation of a pyramid-shaped diamond indenter are described in ASTM E384-07 (2007). Depending on the shape of the indenter, Knoop- and Vickers-type diamonds as well as Berkovich indenters can be distinguished. The reported hardness number expressed in N mm-2 (MPa) is the force exerted on the specimen surface by the diamond indenter used to produce the impression. In principle, the technique is less affected by porosity than the scratch tests based on measuring the indenter travel caused by a specific increase in load. Microhardness tests are usually made... 

Similar extrusions were revealed by TEM in the Berkovich indentations made in (100) Si at ultralow loadings ( 10 mN) [16]. Although isolated diffraction patterns were not obtained from the extruded material due to the presence of underlying crystal, the amorphous nature of this material was inferred from the absence of any crystalline diffraction and tilting experiments. Further, at these experimental conditions (below the cracking threshold), no evidence of dislocation activity or other mechanisms of plastic deformation operating outside the clearly demar-... 

In situ conductivity measurements by Clarke et al. [6] (Vickers and Knoop indenters) and by Pharr et al. [8] (Berkovich indenter) showed a drop in Ge resistance during indentation with sharp tips and thus provided the first experimental support to the notion of indentation-induced metallization in germanium. The TEM analysis of the indented Ge samples by Clarke et al. [6] revealed amor-phized material within the indentations, similar to the results obtained on silicon. 

The SEM images of the Berkovich indentations in the (111) surface of B4.3C reveal the presence of discrete deformation bands within the indentation contact area, which apparently follow the sample crystallography (Fig. 44). Similar features have been observed previously in TiB2 and AI2O3 [213] and discussed in detail in connection with the indentation size effect by Bull et al. [214]. It was proposed [214] that the yielding beneath the indenter occurs nonuniformly in some hard materials and the discrete dislocation slip-steps are generated to re-... 

Figure 6.2 Schematic diagram of a nanoindentation test (a) and commonly used indenter type (b) Vickers indenter (c) elongated diamond-shaped indent formed on the sample by Knoop indenter (d) spherical indenter and (e) Berkovich indenter.

Pyramid Indenters. The most common pyramid indenters are the Vickers, Knoop, and Berkovich indenters. The Vickers indenter consists of a square-based diamond pyramid with included angles (a) of 136° between nonadjacent faces. The Knoop test uses a rhombic-based diamond with included angles of 172° and 130° between opposite edges. The Berkovich indenter is a diamond trigonal pyramid whose facets form an angle of 65.3° with respect to the normal to the base. 

The Vickers indenter penetrates the surface about twice as far as the Knoop indenter for a given load. The latter is very sensitive to material anisotropy because of the twofold S5unmetry of the indentation. The Berkovich indenter is preferred to the four-side pyramids when extremely small indentations are produced. 

Berg Method. See diver method. Berkeley Clay. A plastic, refractory kaolin from S. Carolina P.C.E.34. Berkovich Indenter. A 3-faced diamond pyramid for indentation hardness tests. 

Figure 3.17. Berkovich indentations on (lit) plane of CaFj which has an 001 slip system. Scale bar 10 /tm. From reference (29).

Henshall and Brookes have derived an equation for the Berkovich indenter starting from equation (5.41) and using a constraint factor of 2.57 ... 

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. 

For the reasons developed in Chapters 2 and 5, we would not usually recommend the use of spherical or conical indenters for hardness measurements in materials with a marked tendency to brittle behavior because of the circumferential tensile stress, or where a significant amount of pile-up, controlled by discrete slip planes, may cause distorted indentations. Consequently, in this part of Chapter 3, we shall be concerned only with pyramidal indenters such as the Knoop, Vickers, and Berkovich indenters as well as the pentagonal indenter, which was designed with the advantages of the pyramidal indenters in mind but so as to offset the intrinsic anisotropy of crystals. Here we shall identify the orientation of a given indenter with respect to its facets, as sketched in Figures 2.3 and 2.5, rather than its diagonals. 

A simple estimate for kc is that it relates the depth to the radius of an equivalent cone with the same volume as the impression. Thus, for a Berkovich indentation... 

---