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Chapter VIII Micro-hardness studies…
Where, E is the Young’s modulus and H is the hardness.
However, there are several reports on cracking around indentations in
several materials. PETN and RDX are important plastic explosive materials.
The fracture mechanism of indentation cracks was studied by Hagan and
Choudhari [99] by using the formulation suggested by Lawn and Fuller [97] as
follows:
P C 3/2 = ((2 E/(1-v 2 )) 1/2
316
(8.16)
Where, P is the load of indenter, C is the length of crack, E is the Young’s
modulus, ν is the Poisson’s ratio and is the coefficient of function between the
indenter and indented material, which is generally obtained by rubbing against
standard hard surface. The fracture toughness of ferrites has been studied by
Johnson et al. [100]. They used Vickers indenter and applied the formula
proposed by Evans and Charles [98]. Moreover, they hypothesized that the
large cations, Ca +2 and Fe +2 on the grain boundaries cause locally-distorted
structure which is an easy fracture path. Ferrites exhibit high strength and
fracture toughness but also experience grain boundary fracture in contrast to
trans-granular fracture in weaker counterparts. Altogether, fracture toughness
of doped bismuth oxide electrolytes have been reported by Sammes [101].
Burnett and Page [102] have studied crack propagation and patterns around
Vickers indentation mark on sapphire and glass with and without ion
implantations. They also determined the fracture toughness Kc by using the
relation proposed by Lawn and Co-workers [103-104] as follows:
Kc = 0.0139 (E/H) 1/2 P/C 3/2 (8.17)
Where, H is the hardness, E is the modulus of the elasticity, P is the load and C
is the crack length.