Abstract :
The use of normalized porosity in models for the porosity dependence of mechanical
properties is addressed first for the frequently used power law expression for such
dependence, i.e., E/E0 = (1 − P)n where E is the property of interest at any volume fraction
porosity (P) and E0 is the value of E at P = 0. Normalizing P by PC, the value of P at which
the property of interest inherently goes to zero, giving E/E0 = (1 − P/PC)n, clearly calls
attention to the importance of PC values <1 (e.g., potentially as low as ∼0.2), a fact long
known but inadequately recognized. Serious problems from the arbitrary use of both n and
PC as fitting parameters with little or no guidance as to the dependence that n and PC
(which is microstructurally sensitive) have on the type of porosity are shown. Further,
porosity normalization of the power law model indicates at best limited compression of
different porosity dependences into a single universal porosity dependence function and
little distinguishing of property dependences as a function of the type of porosity. However,
normalized porosity of minimum solid area (MSA) models gives a single universal porosity
dependence. The difference in responses to P normalization of the two modeling
approaches is attributed to their being based respectfully on little or no pore character and
on detailed pore character. Thus, P normalization may be a valuable tool for evaluating
porosity models, but must be applied in a more rigorous fashion, i.e., PC determined
primarily by measurement and correlation with the type of porosity (as with MSA models)
and not as an arbitrary fitting parameter as used in the evaluations of the power law model.
C 2005 Springer Science + Business Media, Inc.
