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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.
Bar
Width (mm)
Thickness (mm)
Load (N)
1
6.02
3.99
2510
2
6.00
4.00
2615
3
5.98
2375
4
5.99
4.04
2865
5
4.05
2575
6
6.01
2605
7
4.01
2810
8
5.95
4.02
2595
9
3.97
2490
10
3.96
2650
11
6.05
2705
12
2765
13
2680
14
2725
15
6.03
2830
16
3.98
2730
17
6.04
4.03
2565
18
5.96
19
5.97
20
2745
21
2895
22
2525
23
2660
24
3.95
25
2640
(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).
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