The S-N diagram for a titanium alloy is shown in the figure. Calculate the fraction of life consumed by the following sequence of loadings: 15,000 cycles at 80 MPa 120,000 cycles at 60 MPa 3,500,000 cycles at 50 MPa Maximum stress (ksi) 160 140 120 100 80 60 40 20 10³ 10+ 10³ 10⁰ Cycles to failure 107

digit number x:8

A cylindrical 1045 steel bar (see the figure below) is subjected to repeated compression- tension stress cycling along its axis. If the load amplitude is 23,000 N, calculate the minimum allowable bar diameter (in mm) to ensure that fatigue failure will not occur. Assume a factor of safety of 2.0. Maximum stress, S (MPa) 700 600 500 400 300 200 100 0 4340 steel 104 Ti-5Al-2.5Sn titanium alloy 70Cu-30Zn brass EQ21A-T6 Mg alloy 105 1045 steel Ductile cast iron 107 2014-T6 Al alloy 108 10⁹ 106 Cycles to failure, N Data taken from the following sources and reproduced with permission of ASM International, Materials Park, OH, 44073: ASM Handbook, Vol. I, Properties and Selection: Irons, Steels, and High-Performance Alloys, 1990; ASM Handbook, Vol. 2, Properties and Selection; Nonferrous Alloys and Special- Purpose Materials, 1990; G. M. Sinclair and W. J. Craig, "Influence of Grain Size on Work Hardening and Fatigue Characteristics of Alpha Brass," Transactions of ASM, Vol. 44, 1952.

The stresses on the surface of a hard bronze component are shown in the figure below. The yield strength of the bronze is σY = 345 MPa.a) What is the factor of safety predicted by the maximum-shear-stress theory of failure for the stress state shown? Does the component fail according to this theory?b) What is the value of the Mises equivalent stress for the given state of plane stress?c) What is the factor of safety predicted by the failure criterion of the maximum-distortion energy theory of failure? Does the component fail according to this theory?