of failure for a level of elongation, P(Ef)
parameters requiring analysis. In Fig. 3(c), this data is plot- ted as a distribution of Ef
from Eqns 2-6 is replaced by the strain term, Ef
Here it is very important to point out that the Weibull modu- lus of Ef
, and in Fig. 3(d) as a probability . Here the stress term .
is actually less for the 82 m/s melt velocity than for
the 26 m/s condition, irrespective of the fact that this trend is opposite to that observed for the tensile strength. These differences are evident in Fig. 3(d), and the consequences of this observation are that even though the values of elongation are greater in all samples tested in the 82 m/s condition, the distribution of values is broader, and it may then follow that the distribution of flaw sizes was increased simply because a greater proportion of samples are of higher relative qual- ity. As may be appreciated, tensile strength does not need to change as much to result in a large change in elongation, as tensile strain increases. In these cases therefore, the Weibull
) are also very important measures of quality. (Posi- tion parameter for this alloy is discussed in more detail later in the section on the effects of alloy chemistry).
modulus as well as the values of the position parameters (σo and Efo
It therefore seems clear that this technique provides a ver- satile representation of the quantifiable differences between the two casting conditions. Furthermore, this approach al- lows for a robust evaluation for what may be considered to be “safe” from a design perspective for multiple parameters.1 In contrast to the values of µ-3σ presented in Table 2, which are applicable only to the specific geometry of the casting tested, the results from the Weibull analysis are able to be scaled to cope with different specimen volumes, geometries and loading conditions (Eqns 8-11).
use of the ludwik-Holloman Equation
Further investigation of quality in the A380 high pressure di- ecastings was conducted using the techniques developed by Cáceres,9,10
based on the Ludwik-Holloman equation (Eqn
13). Values of K and n defined by Eqn 13 were determined for each of the two data sets, (i.e., the 25 samples for each of the two melt velocities tested). Values of n were deter- mined by first converting all 25 of the 0.2% proof stress and tensile strength data points to their true stress values, and all elongation data points to true strain values. All of the results
Figure 2. Fracture surface of an average sample produced at 82 m/s at different magnifications (see text for details). Note that the size of the primary composite defect present on the fracture surface is significantly reduced when compared to the sample produced at 26 m/s.
42 International Journal of Metalcasting/Summer 2011
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