hw_09_sol_0

# hw_09_sol_0 - MechEng 382 Winter 2009 Homework #9 Solutions...

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MechEng 382 Winter 2009 Homework #9 Solutions 1. [ Dowling , Prob. 11.1] Estimate the constants C and m for the straight line portion of the data of Fig. 11.3. Solution m = 3 . 19 C = 1 . 77 × 10 - 9 mm / cycle / ( MPa m ) m Figure 1: Data for Prob. 1 [ Dowling , Fig. 11.3]. 1

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MechEng 382 Winter 2009 Homework #9 Solutions 2. [ Dowling , Prob. 11.4] Representative data points are given in Table P11.4 (Fig. 2 ) from the results of tests at R = 0 . 1 on 2124-T851 aluminum. Figure 2: Data for Prob. 2 , after [ Dowling , Table P11.4]. (a) Plot these points on log-log coordinates, and obtain approximate values of constants C and m for Eq. 11.10. Solution Remark The approximations for C and m will vary considerably. (b) Use a log-log least-squares ﬁt to obtain reﬁned values of C and m . Solution m = 2 . 90 C = 5 . 18 × 10 - 8 mm / cycle / ( MPa m ) m 2
MechEng 382 Winter 2009 Homework #9 Solutions 3. [ Dowling , Prob. 11.37] Consider the center-cracked plate of AISI 4340 steel of Ex. 11.4 (Prob. 2 ), with the same initial crack size of a i = 1mm , but let the cyclic forces be half as large—that is, P min = 40 and P min ax = 120kN . (a) Estimate the crack length at failure. Solution a f = 0 . 0288m (b) Calculate the life using Eq. 11.32. Do you expect this result to be reasonably accurate? Explain why or why not.

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## This note was uploaded on 09/28/2010 for the course MECHENG 382 taught by Professor Thouless during the Winter '08 term at University of Michigan.

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hw_09_sol_0 - MechEng 382 Winter 2009 Homework #9 Solutions...

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