Richard C. Bradt

The microhardness indentation load/size effect in rutile and cassiterite single crystals

AbstractThe microhardness indentation load/size effect (ISE) on the Knoop microhardness of single crystals of TiO2 and SnO2 has been investigated. Experimental results have been analysed using the classical power law approach and from an effective indentation test load viewpoint. The Hays/Kendall concept of a critical applied test load for the initiation of plastic deformation was considered, but rejected to explain the ISE. A proportional specimen resistance (PSR) model has been proposed that consists of the elastic resistance of the test specimen and frictional effects at the indentor facet/specimen interface during microindentation. The microhardness test load, P, and the resulting indentation size, d, have been found to follow the relationship n

Single crystal cleavage of brittle materials

P = a_1 d + a_2 d^2 = a_1 d + (P_c /d_0^2 ) d^2

Knoop microhardness anisotropy of single-crystal LaB6

nnThe ISE is a consequence of the indentation-size proportional resistance of the test specimen as described by a1. a2 is found to be related to the load-independent indentation hardness. It consists of the critical indentation load, Pc, and the characteristic indentation size, do.

Single‐crystal elastic constants of fluorapatite, Ca5F (PO4)3

The indentation load/size effect (ISE) for the Knoop microhardness measurement of vitreous silica is considered for indentation in different test environments. Analysis was through the application of Meyers Law, the Hays/Kendall approach of a critical load for the initiation of flow and the proportional specimen resistance (PSR) model proposed by Li and Bradt. The PSR model in combination with a normalized form of Meyers Law was found to describe consistently the measurements and to yield a load-independent Knoop microhardness for fused silica of 540 kg/mm2. The model also explains the effects of different indentation test environments, suggesting the effect is a result of their lubricating effects at the indenter facet/specimen interface.

The indentation size effect and the hardness of single crystal diamond on the (001) 〈110〉

Cleavage of brittle single crystals is reviewed and the historical criteria for the phenomenon are critically examined. Previously proposed criteria, including those based on crystal structure (crystal growth planes, the planes bounding the unit cell, and planar atomic packing) and crystal properties (ionic charge of possible cleavage planes, bond density, elastic modulus, and surface free energy), are found to be applicable only to particular crystals or to isostructural groups, but each lacks universal application. It is concluded that the fracture toughness (KIc) of the crystallographic planes is the most appropriate criterion. Measurements reveal that the ‘cleavage toughnesses’ of brittle single crystals are usually about 1 MPa m1/2 or less.Measurements of the fracture toughnesses of brittle polycrystalline aggregates are then compared to the single crystal cleavage values in those instances where reliable results are available for the same crystal structures. Polycrystalline toughnesses are consistently higher, in part because of the lack of continuity of cleavage cracks through the polycrystalline aggregates. However, the increment of toughness increase is only 1–2 MPa m1/2. The role of grain texture or preferred crystal orientation is also addressed. It is concluded that polycrystalline aggregate toughnesses are often highly anisotropic and that the values for intensely oriented microstructures may approach those for single crystal cleavage.

Microhardness anisotropy of single crystals of calcite, dolomite and magnesite on their cleavage planes

The Knoop microhardness of single crystal sulphur was measured as a function of crystallographic orientation and applied test load on the (110) and (111) planes. Microhardnesses were determined to be in the range of 25–35 kg mm−2. Anisotropy of the microhardness and a normal indentation size effect (ISE) were observed. The ISE was addressed by the application of the traditional power law and the proportional specimen resistance model (PSR) of Li and Bradt. The load-independent hardness was determined, from which it was concluded that the (111) plane is harder than the (110) plane and also that the (111) plane is more anisotropic in microhardness.

Cascadating fracture in a laminated tempered safety glass panel

Abstract Knoop microhardness profiles were determined for lanthanum hexaboride (LaB 6 ) on the (100), (110) and (111) planes for indentation test loads from 50 to 300 gf. These profiles were analyzed with respect to possible slip systems to explain the Knoop microhardness anisotropy by applying the effective resolved shear stress concept advanced by Brookes and coworkers. As the results of this study, the predicted slip systems for LaB 6 are {100}〈011〉,{110}〈111〉 and {111}〈110〉. The load dependence of the microhardness was initially addressed in terms of the classical Meyers law P = Ad n for which the two parameters A and n were observed to be related. The peculiar dimensionality of the classical Meyers law coefficient A was addressed by applying the concepts of a load-independent “true” microhardness, critical indentation load and characteristic indentation size. Subsequently the development of a normalized Meyers law was directly demonstrated, yielding P= 2P c n d d 0 ∗ η where P c is a critical test load indicative of the region where hardness is independent of the indentation test load and d 0 ∗ is a characteristic indentation dimension, below which the indentation size effect is significant. It is suggested that this normalized Meyers law may have universal applicability to different hardness tests and materials.

Microhardness anisotropy on the (010) cleavage plane of single crystals of Bi2S3 and Sb2S3

The single‐crystal elastic stiffnesses of fluorapatite, Ca5F(PO4)3, have been measured by an ultrasonic technique. The values are: C11=152.0, C12=49.99, C13=63.11, C33=185.7, and C44=42.75 GPa. These results are compared with previously published values to resolve anisotropy contradictions and differences in magnitude. The apatite crystal structure is not very elastically anisotropic. It suggests that the elastic anisotropy of bone derives primarily from the hierarchical microstructure of that biocomposite and not from the anisotropy contribution of the apatite mineral component.