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Chapter VIII Micro-hardness studies…
A statistical model for ideal crack initiation using Vickers indentations
has been suggested by Dal Maschio et al [105]. Using such model it is possible
to calculate the threshold load, defined as the load at which there is a 50%
fracture probability, from experimental evaluations.
The toughness of a material denotes its resistance to fracture. For a
solid containing a well-developed crack of specified dimension, the fracture
toughness, Kc determines the fracture stresses in uniform tensile loading. The
fracture mechanics of the indentation process has provided an equilibrium
relation for well-developed crack extending under a center-loading condition.
P
3
l
2
.. . K for l > d/2 (8.18)
..
0
c
Where, P is the load, l is the crack length measured from the center of the
indenta-tion mark to the crack end, d the diagonal length of the indentation
impression and β0 the indenter constant equal to 7 for the Vickers indenter
[106-108].
Shaskol’skaya et al [109] and Guin et al [110] have reported
measurements of both hardness and cracking in KDP and deuterated KDP
crystals. They also identified two types of slip systems in KDP; the first system
consisted of slip planes (110), (101), (112) and (123) with common Burgers
vectors /2; the second slip system was identified as (010). Marion [111]
has reported values of fracture toughness in KDP crystals as 0.2 MPa.m 1/2 .
More recently, Fang and Lambropoulos [112] studied Vickers and Knoop
hardness of KDP crystals on (100) and (001) faces. The cracks were observed
for large loads values on the both faces, however, the cracks were longer on
the (100) faces than the (001) faces. Assuming the elastic and plastic isotropy
the crack sizes were analyzed and fracture toughness Kc were measured. They
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