In order to interpret the cumulative frequency (which rep- resents the y-axis) of the variable x, the P(x), a commonly applied method was used:
Equation 3
In this equation the reorganized ‘n’ data points (ascend- ing order) are assigned a ranking of j in the range of (1-n), such that each point has a ranking P(j) on the cumulative frequency plot. A combination of this ranking for P(x) data set with the previously described equation (2) yields the Weibull plot.
Chill #2, Iteration #5
The usefulness of this analysis comes from the realization that different distributions of data of variable ‘x’ will yield different amounts of scatter in the data sets. The Weibull modulus ‘m’ in equation (2) is a quantitative measure of this scatter, such that the greater the value of ‘m’, the steeper the slope of the Weibull plot, and the smaller the scatter in the data. This translates into a narrower range of the analyzed property. The smaller the value of ‘m’ on the other hand, the shallower the slope of the Weibull plot, which implies a large scatter in the analyzed data. This in turn makes accu- rate predictions of the material property that much more dif- fi cult. As a result, it becomes evident that the ‘m’ parameter in the Weibull analysis is a powerful tool in the tensile data analysis, and material reliability in particular.
Cross section taken for LOM.
See Figure 5a ►
Chill #2, Iteration #5
the Chill #2 (iteration #5) directly below the fracture surface. Cross-section taken is indicated on the fractured surface. Additional Scanning Electron Microscopy / Secondary Electron (SEM/SE) micrographs of the fractured surface were taken as indicated on the fracture surface images (dashed box regions). Included is a high magnifi cation image with a 200 µm bar scale.
Figure 3b. Secondary Dendrite Arm Spacing (λ2 36 International Journal of Metalcasting/Winter 10
), and porosity measurements on the tensile bar cross-sections from
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