Even if you design mechanical components satisfying mechanical strength criteria it may fail due to a phenomenon called fatigue. Historically many design disasters have happened by neglecting effect of Fatigue.In this video lecture we will learn how to predict and quantify fatigue effect.
Detailed description of above video lecture is given below
A Wire Breaking problem
To understand what is fatigue let’s consider this metal wire. You have to break it. So how will you break it? Will you pull it from both ends or will you bend the wire upward and downward repetitively.
|Fig.1 Two methods to break metal wire, Either bend it upward and downward repetitively or pull it|
Reason Behind Fatigue Failure - Crack Propagation
When you bend it downwards bending stress induced is in the wire cross section. There will be tension at top area and compression at bottom area. When wire is at equilibrium there will not be any stress on wire cross section. When wire is bending upwards there will be compression at top and tension at bottom.
|Fig.2 Stress variation in wire cross-section, as wire is bent downward and upward|
|Fig.3 Stress variation at a point is plttod on stress vs time graph|
Fatigue Failure in Real Life Engineering Problems
|Fig.4 Some practical cases which could result in fatigue failure, if not designed properly|
The same phenomenon can happen for axle of this motor where it is undergoing fluctuating stress due to gravity effect of this mass. A rail wheel when it is in contact with with the track produces a high contact stress, but when the wheel rotates stress gets relieved. When it comes back to original position again contact stress arises. So this also is a case of fluctuating stress case. Again will lead to fatigue failure if we do not design it carefully. Same is the case with a gear pair. Here contact stress arised at contact point fluctuates with time.
Effect of Stress Amplitude on Number of Cycles - S N Curve
This is the most important part in fatigue analysis. Relationship between stress amplitude and number of cycles it can execute before it fails. As you can guess as stress amplitude increases number of cycles for failure decreases. We will draw number of cycles in x axis, Stress amplitude in y axis. Both in logarithmic scale. Let’s start with the maximum stress a material can withstand, its ultimate stress. So this will happen, as you increase the stress even before completing one cycle the material will get broken. If you decrease the stress amplitude it will execute more number of cycles before it fails. Decreasing stress further even more number of cycles.
|Fig.5 Number of cylces for fatigue failure increases with decrease in stress amplitude|
|Fig.6 Stress amplitude Vs number of cycles, green region represents safe design area|
Fatigue Failure, when there is no Complete Stress Reversal
The case we discussed had complete stress reversal. What will be maximum stress limit for this case ?. When stress reversal does not happen. It has got a mean value and amplitude.
|Fig.7 Fluctuating stress case which is not fully reversed|
|Fig.8 Use of Goodman diagram to find safe stress amplitude when stresmm mean value is not zero|