Turbochargers Are Us, a new start-up company, hires you to design their new turbocharger. They explain that they want to replace their metallic superalloy turbocharger with a high-tech ceramic that is much lighter for the same configuration. Silicon nitride may be a good choice, and you ask Ceramic Turbochargers, Inc. to supply you with bars made from a certain grade of Si3N4. They send you 25 bars that you break in three-point bending, using a 40-mm outer support span and a 20-mm inner loading span, obtaining the data in the following table.

(a) Calculate the bend strength using σf = (1.5 · F · S) (t2· w), where F = load, S = support span (a = 40 mm loading span and b = 20 mm in this case), t = thickness, and w = width,and give the mean strength (50% probability of failure) and the standard deviation.

(b) Make a Weibull plot by ranking the strength data from lowest strength to highest strength. The lowest strength becomes n = 1, next n = 2, etc., until n = N = 25. Use F= (n - 0.5) N where n = rank of strength going from lowest strength n = 1 to highest strength n = 25 and N = 25. Note that F is the probability of failure. Plot ln [1 (1 - F)] as a function of ln sf and use a linear regression to find the slope of the line which ism: the Weibull modulus. Find the characteristic strength (s0) (63.2% probability of failure).