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Unformatted text preview: This treatment has been excerpted from “The Science and Design of Engineering Materials”, 2nd edition, by Schaffer, Saxena et al, McGraw Hill, 1999. **************************************************** Mechanical properties such as hardness will usually follow normal distributions represented by: } ] / ) )[( 2 / 1 exp{( ]} ) 2 ( /[ 1 { ] / ) [( 2 s x s s x p μ π μ = ] / ) [( σ μ x p where is the probability for the property possessing a particular value of x, x is a specific value for the property μ is the mean value for that property and s is the standard deviation for the series of measured values continued... An example of such a distribution is given by a study problem from W.D. Callister’s “Materials Science and Engineer: An Introduction”, 4th edition, Wiley, 1997, problem 6.50: ****************************************************** To the right are tabulated a number of Rockwell B hardness values, which were measured on a single steel specimen. Compute average and standard deviation hardness values. ********************************** Ε = 47.3 x av = 85.3 1.00 1.0 86.3 0.81 0.9 84.4 2.25 1.5 86.9 0.01 0.1 85.2 1.21 1.1 86.4 0.04 0.2 85.5 3.24 1.8 83.5 6.25 2.5 87.8 0.36 0.6 84.7 21.16 4.6 80.7 3.61 1.9 87.2 0.81 0.9 86.2 6.25 2.5 82.8 0.25 0.5 88.3 0.00 0.00....
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 Spring '11
 Mecholsky
 Normal Distribution, Standard Deviation, Cumulative distribution function, MPa, standard normal deviate, nµ

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