This theoretical approach to quality is important, because it allows a foundry engineer or casting user to establish the absolute quality of a casting; which is imposed by the onset of necking; and to determine whether further improvements are possible. It also allows us to understand better, from a scientific point of view, what microstructural features deter- mine casting quality.


Effect of Inclusions and Porosity on Quality


A detailed study of the tensile properties of copper con- taining second phase particles and porosity defects was presented in 1962 by Edelson and Baldwin.13


Controlled


amounts of porosity (and other defects) were introduced into copper-based alloys, produced by sintering metal pow- ders. A detailed analysis of their results showed that the volume fraction of defects was the governing variable. The size or the shape of defects was not important. Further- more, the most sensitive indicator of defect concentration was the elongation to fracture in tensile specimens. A fig- ure from their study is reproduced in Figure 8. It shows the relative loss in ductility as a function of the volume fraction of defects. The ductility was determined from the reduction in area of the tensile specimen, and compared to a standard sample having a one percent concentration of defects (i.e., f = 0.01).


This result shows that the elongation to fracture (and qual- ity) is extremely sensitive to the presence of defects, but it suffers from two limitations. Firstly, the form of the plot does not allow us to estimate accurately the quality of rela- tively ‘defect free’ material. Secondly, it is not clear that this result applies to high quality, net-shaped castings. Cáceres and Selling14


have shown that the tensile properties of cast-


ings do not correlate well with measurements of volumetric porosity content. In commercial castings the distribution of porosity and other defects is non uniform, and tensile failure occurs at the weakest spot. As a consequence, the concentra- tion of defects found on the fracture surface may be three to twenty times the average volumetric concentration. Another approach is needed.


Cáceres and Selling presented a model for the growth of a plastic instability inside a tensile specimen, when a certain area fraction (f) of porosity was present on a planar section of an otherwise defect-free material. An equation was de- rived for the loss of elongation and strength caused by these defects. Their equation correlated well with experimental measurements of the elongation to fracture and the area frac- tion of defects found on the fracture surface of Al-Si-Mg alloy samples. These results were later extended by Caceres and Sigworth,15


who derived the equation: (1-f) = qn en(1-q) Equation 6


This equation relates the relative loss in ductility of a tensile sample (value of q) to the area fraction of de- fects present, f. Considering equation [2], the resulting loss in tensile strength is equal to:


Equation 7


Figure 9 shows a plot of these two equations for A356- T6 alloy (that is, for a value of n equal to 0.1). Note that even very small amounts of defects in a material have a significant effect on elongation. The ultimate tensile strength is affected much less. For example, a concen- tration of defects of only 0.1% (f = 0.001) results in a loss of 15% in elongation, while the reduction in UTS is hardly measurable. With 1% area fraction of defects (f = 0.01) the elongation is reduced by 40%, but the ultimate tensile strength is decreased by only 5 %.


Figure 8. Loss of elongation associated with defects.13 International Journal of Metalcasting/Winter 11


Figure 9. Theoretical effect of defect concentration (f) on elongation and UTS.


13


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