lowest allowable UBS must be zero) gives: the property x, and setting xu (2)
The above equation can be converted into a linear represen- tation by taking the natural logarithm to both sides of the equation twice to yield the following form:
(3)
This equation is in the form y = mx + c; therefore, the Weibull modulus m can be determined from the slope of a plot of ln(ln[l–Pf,n
probability of failure. This can be estimated by a commonly applied method:
]) against Fn , where Pf,n (4)
the y-axis of the straight line used to determine the Weibull modulus (m). Since, from Eq. (3) y = m ln F0
F0 = exp(y/–m). The usefulness of this analysis is that the Weibull modu-
lus m is a single value that shows the spread of properties, in this case, UBS of the FPB test. Higher Weibull modu- lus shows a narrower spread of properties, which indicates that the casting process is associated with low numbers of defects in the final casting and a greater reproducibility of properties. In this work the Weibull method was used to analyze the FPB test results for the magnesium control arm samples to evaluate each casting process.
results and discussion
Microporosity was observed in the tested specimens, ranging in size from 5 to 20µm. Most of pores had the aspect ratio of approximately 0.5. The near neighbor distance of the poros- ity is in the range of 30 to 70µm, depending on the casting group. Table 1 lists the average porosity analysis results for each casting process. From these results, it is evident that microporosity is not a major defect for all castings. Figures 7 (a) and (b) show the average area percentage of porosity and grain size distribution for each sample for different casting groups, respectively. The T-Mag and squeeze cast processes show fewer pores than do the LPPM and ablation processes. The average area percentage of porosity was in the range
40 (a)
In this equation, n is the number of the result when all re- sults are ordered in an ascending fashion, and N is the total number of results. The scale parameter represents the fail- ure UBS below which 63.2 pct of the samples failed. This value is denoted F0
and was obtained from the intercept on at x = 0, then
is a measure of the
= 0 (which assumes that the
of 0.1 – 2.0 wt% for all samples from different casting pro- cesses. Larger grains were found in the T-Mag cast (300 ± 50µm), compared with LPPM (100 ± 20µm), ablation (100 ± 30µm), and squeeze cast (20 ± 10µm). It would be expected that the ablation casting show the smallest grain size due to the high cooling rates. The control arms were heat treated and hence does not reflect as cast conditions in Figure 7(b).
Except the microporosity, different types of defects were identified, including sponge shrinkage, gas pores, and crack- like defects. In general, all four casting groups present some sponge shrinkage. Gas pores with large size diameters were also found in some samples for each casting group. The long crack-like defects were found only in the squeeze casting samples. Figure 8 shows the typical metallographic images for each casting process. The sponge shrinkage defects were found in the squeeze cast (Figure 8[a]), LPPM (Figure 8[b]) and T-Mag (Figure 8[c]) samples. Separated irregular pores were found in the ablation (Figure 8[d]) samples.
(b)
Figure 7. (a) Area percentage of porosity, (b) Grain size, for samples from different casting processes, with the exception that second dendrite arm spacing (SDAS) was measured for the squeeze cast sample.
International Journal of Metalcasting/Fall 2011
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