Page 464 - Mechanical Behavior of Materials

464 Chapter 9 Fatigue of Materials: Introduction and Stress-Based Approach

σ y p
r
σ x
T
τ xy
t

σ
y
p
pr/t
p
0 time
0 time

σ pr/(2t)
T x
0
time

0 time
−τ xy
y
Tr/J
x
0 time
2τ
1 −1 xy
θ = tan
p 2 σ − σ y
x
θ p
σ 45
2
0 time
σ
1

Figure 9.41 Combined cyclic pressure and steady torsion of a thin-walled tube with closed
ends. The principal directions oscillate during each cycle.

compared with the τ xy caused by torsion. Additional complexities could exist. For example, the
bending moment in Fig. 9.40 or the torque in Fig. 9.41 could also be cyclic loads, and the frequency
of cycling of the bending or torsion could differ from that of the pressure.

9.8.1 One Approach to Multiaxial Fatigue

Consider the simple situation where all cyclic loads are completely reversed and have the same
frequency, and further where they are either in-phase or 180 out-of-phase with one another. Also,
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