A cumulative frequency distribution of a random variable x can be represented using the three parameter form of the Weibull equation:


Equation 1


P(x) is the cumulative frequency distribution of a random variable x, in this case either UTS, or El.TOT


mum allowable value of the analyzed variable, which in this case is 0 for both stress and strain data; θ is the scale param- eter, also referred to as the characteristic value; and m is the shape parameter, also known as the Weibull modulus.


; xo Chill #1, Iteration #2 is the mini-


Equation (1) can be converted into a linear representation by applying the ‘ln’ operator to both sides of the equation to yield the following form:


Equation 2 was made to calculate the slope m in each case.


In this form the equation can be interpreted by the linear form ‘y = mx + b’, where a variable y is plotted in the do- main x to give a line with slope m, and a y-intercept at b. By applying this approach a plot of (y vs. x) was constructed for both the UTS data and the El.TOT


data sets, and a liner best-fi t


Cross section taken for LOM.


See Figure 4a


►


Chill #1, Iteration #2


Figure 3a. Secondary Dendrite Arm Spacing (λ2


), and porosity measurements on the tensile bar cross-sections from


the Chill #1 (iteration #2) 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.


International Journal of Metalcasting/Winter 10 35


Page 1  |  Page 2  |  Page 3  |  Page 4  |  Page 5  |  Page 6  |  Page 7  |  Page 8  |  Page 9  |  Page 10  |  Page 11  |  Page 12  |  Page 13  |  Page 14  |  Page 15  |  Page 16  |  Page 17  |  Page 18  |  Page 19  |  Page 20  |  Page 21  |  Page 22  |  Page 23  |  Page 24  |  Page 25  |  Page 26  |  Page 27  |  Page 28  |  Page 29  |  Page 30  |  Page 31  |  Page 32  |  Page 33  |  Page 34  |  Page 35  |  Page 36  |  Page 37  |  Page 38  |  Page 39  |  Page 40  |  Page 41  |  Page 42  |  Page 43  |  Page 44  |  Page 45  |  Page 46  |  Page 47  |  Page 48  |  Page 49  |  Page 50  |  Page 51  |  Page 52  |  Page 53  |  Page 54  |  Page 55  |  Page 56  |  Page 57  |  Page 58  |  Page 59  |  Page 60  |  Page 61  |  Page 62  |  Page 63  |  Page 64  |  Page 65  |  Page 66  |  Page 67  |  Page 68  |  Page 69  |  Page 70  |  Page 71  |  Page 72  |  Page 73  |  Page 74  |  Page 75  |  Page 76  |  Page 77  |  Page 78  |  Page 79  |  Page 80  |  Page 81  |  Page 82  |  Page 83  |  Page 84  |  Page 85