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Chapter VIII Micro-hardness studies…
8.7 Proportional Specimen Resistance (PSR) model
Bradt [15] explained the ISE with the help of the general model i.e.
“Proportional Specimen Resistance” (PSR). According to PSR model micro-
hardness can be described with two components, which are the frictional
forces between the test specimen and the indenter faces and the elastic
resistance of the test specimen. The indentation load P is related to
indentation size d, as,
P = a1d + a2d 2
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(8.12)
Where, the coefficient a1 is contribution of proportional specimen
resistance to apparent micro-hardness and a2 coefficient is related to the load
independent micro-hardness or load independent constant. The parameter a1
characterizes the load dependence of hardness [15] and it is suggested that
the a1/a2 can be considered as measure of the residual stress and these are
connected with defect. The term a1d has been attributed to the specimen
surface energy [86], the deformed surface layer [87], the indenter edges
acting as plastic hinges [88] and the proportional specimen resistance [15,
89]. Modifying equation (8.12),
P/d = a1 + (Pc / d0 2 ) d (8.13)
Where, Pc is the critical applied test load above which micro-hardness become
load independent and do is the corresponding diagonal length of the
indentation. The applicability of the PSR model to describe the observed ISE
in relatively wide range of applied test loads can be examined by the linearity
between P/d and d. The term a2 is not related to ISE. Rather, it is related to
the load independent micro-hardness and is equal to Pc/d0 2 [90]. Plot of P/d