Fracture toughness hardness equations

The development of indentation fracture mechanics has also allowed fracture toughness to be determined using indentation cracks. Indeed, the ease with which these cracks can be introduced and the simple specimen preparation involved has popularized this approach. Moreover, it has allowed crack behavior to be studied for cracks in a size range that is close to that found in practice. There are two main approaches for determining fracture toughness from indentation cracks. In the first approach, the size of the radial cracks that emanate from the hardness impression are measured. It is recognized that the parameter x depends on the elastic properties of the indented material. It has been proposed that x=P E H), where )8 is a constant that depends only on the indenter geometry and H is hardness. Equation (8.64) can, therefore, be written as... 

As it is well-known, the ultimate objective in the development of ceramic and glass matrix composites is to increase the fracture toughness of the brittle matrix. In order to analyse the toughening achieved, most researchers have used conventional measurement of fracture toughness by indentation. The fracture toughness (Kic) from the micro-hardness indentation method can be calculated by means of the following equation [73] ... 

However, more recently a new brittleness rationalized index, denoted and expressed in Jim , has been introduced by Quinn and Quinn from the National Institute of Standards and Technology (NIST) as the ratio of the deformation energy per unit volume to the fracture energy per unit surface area. This brittleness index is more accurate than the previous one because it includes three intrinsic properties of the material rather than only two. Therefore, brittleness can be described in terms of the micro Vickers hardness (HV), Young s modulus (E), and the fracture toughness of the ceramic materials (X, ), as described in the following rationalized Quinn s equation ... 

Equations (5.11) and (5.12) relate flaw sizes that are produced by impact on glass to the measured hardness via the fracture toughness parameter. 

Because WC is oxidized to WO3 at high cutting speeds and this oxide is volatile, in order to cut hard steels, substantial amounts of TiC are added to some WC-Co grades. Some hardness data for cemented carbides is given in Table 6.23 along with other carbide data, and equations (5.51), (5.52), and (5.55) can be used to determine fracture toughness parameters from indentation hardness measurements. 

Nitrogen containing glasses, 224-225 equation for fracture toughness, 225 Knoop hardness, 224 Young s modulus, 225 hardness, 229 modulus, 229... 

The glass density (d) was measured on powdered samples by the pycnometry method with an accuracy of 0.005 g cm Young s modulus ( ) and Poisson s ratio (y) were measured by the pulse-echo technique on 4 mm thick rectangular specimen. Vickers indentations (load of 9.8 N apphed during 15 s), were performed to estimate both Meyer s hardness (H) and the indentation fracture toughness (Kc) by means of the following equations ... 

In TPE, the hard domains can act both as filler and intermolecular tie points thus, the toughness results from the inhibition of catastrophic failure from slow crack growth. Hard domains are effective fillers above a volume fraction of 0.2 and a size <100 nm [200]. The fracture energy of TPE is characteristic of the materials and independent of the test methods as observed for rubbers. It is, however, not a single-valued property and depends on the rate of tearing and test temperature [201]. The stress-strain properties of most TPEs have been described by the empirical Mooney-Rivlin equation... 

Thus, toughness, measured and expressed by Kic, is dependent on the elastic modulus, E, of the material, its hardness, H, (microindentation is often preferable for the proper evaluation of the indentation crack), crack length, c, and the applied load. Anstis et al. [11] employed a two-dimensional fracture mechanics analysis. The crack length, c, is measmed from the center of the impression to the crack tip in meters E is in GPa and H is the Vickers hardness in GPa. The height of the opposite triangular faces is h. It is clear that under small indentation loads, only small cracks form, as indicated schematically in Fig. 2.12. Actual Vickers indentation cracks are shown in Fig. 2.13. Equation (2.8) is often also expressed as ... 

Grain boundary (Cont.) nitrogen glass phases, 224 Knoop hardness, 224 toughness, 225 orientation, 199 phases in Si)N4, 223 specific fracture energy, 198, 258 equation, 200... 

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