Use of normalized porosity in models for the porosity dependence of mechanical properties

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 P_C, the value of P at which the property of interest inherently goes to zero, giving E/E₀ = (1−P/P_C)ⁿ, clearly calls attention to the importance of P_C 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 P_C as fitting parameters with little or no guidance as to the dependence that n and P_C (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., P_C 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.