Materials for engineering, 3rd Edition - (Malestrom)

Problems 223
conditions is 200 kJ mol –1 , estimate the time to rupture of a similar
specimen under the same stress at 600°C, discussing any assumptions
you make.
[Answer: 1.6 × 10 5 hours]
8. A nickel alloy bolt is used to hold together furnace components. The
bolt is initially tightened to a stress σ 1 and must be re-tightened if the
stress falls below a critical level σ c . The alloy creeps according to
equation [2.19]: derive an expression for the time required between retightenings.
Calculate the maximum time between re-tightenings at 500°C if the
bolt must not exceed 1 / 3 of its yield stress of 600 MPa and if σ c is taken
to be 100 MPa. In an attempt to extend the time between re-tightenings,
the safety factor is ignored and the bolt is tightened to 60% of its yield
stress. What re-tightening time will this give?
(For this alloy, n = 4.6, σ o is unity, Q = 270 kJ mol –1 ˙ε o = 8 × 10 –36
s –1 and Young’s modulus is 215 GPa).
[Answers: 379 days and 46 days]
9. Using equation [2.23], calculate the number of cycles for fatigue failure
(N f ) when the following materials are subject to a cyclic stress amplitude
equal to 0.8 of their yield stress: normalized 0.15% carbon steel, peak
aged 7075 AlZnMg alloy, and a quenched and tempered NiCrMo 4340
steel.
[Answers: 4.65 × 10 5 cycles; 1.064 × 10 5 cycles; 833 cycles]
10. The rate of fatigue crack growth in a certain alloy follows the Paris
power law (equation [2.31]). A wide plate of this material failed by
growth of a fatigue crack from one edge under a constant stress amplitude.
Fatigue striations were 2 µm apart on the fracture crack surface at a
distance of 4 mm from the edge and 5.5 µm apart at a distance of 9 mm
from the edge. Determine the value of m in equation [2.31], given that
Y equals unity in equation [2.30].
[Answer: 2.49]
11. Calculate the energy dissipated per cycle of stress when the following
materials are subjected to elastic vibrations at a stress amplitude of
31 MPa:
(a) mild steel of Young’s modulus 200 GPa and specific damping capacity
2.28.
(b) cast iron of Young’s modulus 170 GPa and specific damping capacity
28.
Which material would be more appropriate for use for the manufacture
of a lathe bed, and why?
[Answers: (a) 5.48 kJ; (b) 79.1 kJ]
12. At a temperature close to its glass transition, a certain cross-linked
amorphous polymer is found to deform under uniaxial stress σ according