Cyclic Material Behaviour

1
Cyclic Material Behaviour

• Stress-Strain response of most materials under
  cyclic loading is different than under single
  (monotonic) loading.
• For fatigue analysis, it is necessary to consider
  the cyclic material behaviour for strength and
  life calculations.
• Fatigue itself is a process of crack initiation
  and growth due to cyclic loading.

2
Monotonic Engineering Vs. True Stress-Strain
Curves
Typical service region less than 2 difference.
3
Cyclic Stress-Strain Curves

• For cyclic loading, we will always be using true
  stress, s, and true strain, e.
• However, for most calculations we ignore the
  difference between engineering values (S,e) and
  true values (s,e)

4
Cyclic Vs. Monotonic Stress-Strain
For Steels Su /Sys lt1.2 - Cyclically Softens
Su/Sys gt1.4 - Cyclically Hardens
5
Elastic and Plastic Strain
A
C
ep
ee
e
6
Cyclic Hysteresis Behaviour
F
B
E
C
D
7
More Cyclic Stress-Strain Curves
8
Cyclic Hysteresis Behaviour
s
Range
Stress range, Ds
Amplitude
e
Dep
Dee
Strain range, De
9
Equation for s-e Curve
k
Log(Ds/2)
n
Log(Dep/2)
10
Equation for s-e Curve
s
e
11
Reversed Cyclic Straining

• Bauchinger Effect After being plastically
  strained in one direction the stress-strain curve
  of a metal in the opposite sense is lower than
  the initial stress-strain curve.
• Memory The stress for reversed plasticity is
  generally lowered because of the dislocation
  pile-ups and their back stresses left by the
  initial straining. The stress-strain path follows
  the initial path whenever the prior maximum or
  minimum strain level is exceeded.
• Masings Hypothesis Masing suggested (before
  dislocations were observed) that the
  stress-strain curve for reversed straining
  MEASURED FROM THE POINT OF REVERSAL would be the
  cyclic curve scaled by a factor of 2.

12
Bauchinger Effect
13
Masings Hypothesis
Reversed s-e curve
Ds, Ds/2
Cyclic s-e curve
De, De/2
14
Memory
15
Tracking Strain Sequences in s-e Space

• Most components subjected to cyclic loading are
  susceptible to fracture by fatigue cracking and
  can be monitored with strain sensors (e.g.,
  resistance foil strain-gauges)
• Hence, it is common to obtain service load
  spectra in strain units.
• The strain data must be mapped into s-e space for
  the specific material to do fatigue analysis.

16
Simple Strain History
e
time
17
Sequence Effects in Strain History
18
Closed Loop Strain Spectrum