Table of Contents
- Abstract
- Fluctuating Load vs. Static Load
- Endurance Strength
- Types of Fluctuating Loads
- Wohler Diagram or S-N Diagram || Analysis of Completely Reversed Stress
Abstract
In this article we shall discuss about fluctuating loads; how they differ from static loads; their types and general flow of steps to be followed while designing a mechanical component against fluctuating loads.
Whenever the magnitude of load varies with respect to time and/or changes its direction, it is called fluctuating load. In real life scenario, most of the components that we use and manufacture, are all subjected to fluctuating loads. Therefore, this study becomes absolutely indispensable. This article shall give you a clear idea about how we design components against fluctuating loads (especially in case of completely reversed fluctuating loads) and why do we do so.
Fluctuating Load vs. Static Load
We are all familiar with basic types of loadings such as a rod from which a load is hanged. It is a typical example of a static loading (tensile). It is such a loading, whose magnitude and nature (tensile/compressive/shear, etc.) do not change with time. In such a case it becomes very easy to predict the life of the specimen and it is also easy to design such a component which can sustain static tensile or compressive loads, using simple equations like Hooke’s Law. We can easily calculate the strain or deformation that will be produced as an effect of a particular applied load.
But, when loads vary with time, things become complex. Consider the rim of a vehicle and visualize a point on it. As the wheel rotates, the point also moves along a circle. At an instant it might be at the top where load is less, but when it reaches the bottom part, it presses against the road and consequently the load on it increases. This is a case of fluctuating load.
Life of components subjected to fluctuating loads cannot be accurately predicted with the help of any equation or formula. Based on decades of research and observations, certain frameworks have been developed which can help us estimate the life of components subjected to fluctuating loads.
Endurance Strength
For static loading, failure is generally defined when the material deforms more than a certain limit or when it crosses its yielding point stress and starts to deform permanently. But, in case of fluctuating loads, failure can occur at significantly lower levels of stresses and the failure is often ‘sudden’ and ‘total’. Such a failure is called fatigue failure.
The stress levels at which a component fails, when subjected to fluctuating loads, is called its Endurance Strength. Generally, the empirical value of Endurance Strength is taken to be half of the Ultimate Tensile Strength, for an ideal specimen. But, for a real life specimen, Endurance Strength can be significantly lower.
The size of specimen, surface roughness of specimen and presence of irregularities like notches on the specimen can further reduce its endurance strength. With presence of notches and irregularities, stress concentration increases and can serve as a potential failure point. There are various values taken into account in lieu of these factors to predict the endurance strength correctly.
Again, as mentioned before, study of specimen under fluctuating loads is a probabilistic approach. If we want to be more sure that a component will sustain a load then we have to assume even lesser values of endurance strength. On the contrary, if we assume that the endurance strength is slightly higher and design it accordingly, there will be lesser probability of the specimen to survive the test. To account for this, we use Reliability Factor. It is designed in such a way that, if we want more reliability, value of endurance strength will reduce and vice-versa. In other words, if we consider the material to be weaker than what it actually is (underestimate its strength) then there will be more chance of it to meet our expectation standards (as it is actually stronger than what we assumed it to be). It can be further understood by the following example:
Suppose a material’s inherent strength is to bear 10 units of load. But we assume that it can carry only 8 units, then its reliability to actually carry 8 units will be high. But if we assume that it can carry 9.9 units, then its reliability to carry 9.9 units will be lesser because, we are uncertain if the actual strength of the material is 9 or 10 or 11 units. This is the probabilistic approach that we use.
Types of Fluctuating Loads
Load fluctuations can be of various types. In some cases load variations might be periodic or cyclic, just like in our example of the rim of a wheel, the loading pattern repeats itself after every rotation of the wheel. In some specific cases of cyclic loading, the maximum value of tensile load reached is equal to the maximum value of compressive load. In such a case, the mean stress will be zero (See following paragraph). Such a loading is called completely reversed loading.
In some other cases, we may have some other pattern of fluctuation and in some cases, the fluctuations may be totally random, but random fluctuations are beyond the scope of our discussion and we will stick to the cyclic stress variations, specifically to completely reversed loadings only.
For numerical analysis, we just need the mean value of stress and the maximum stress amplitude. It can be very easily calculated if we know the value of maximum and minimum stresses that the specimen is subjected to. Suppose, the maximum value of stress = S1 and the minimum value of stress = S2. (Use the appropriate sign convention, such as negative for compressive and positive for tensile.)
Then, Stress Amplitude = (S1-S2)/2
and, Mean Stress = (S1+S2)/2.
Example
Suppose, it is observed that the stress is fluctuating and the maximum values reached is 100Mpa (tensile) and 50 Mpa (compressive). Then, S1= 100 Mpa and S2= -50 Mpa.
Stress Amplitude = 75 Mpa (tensile) & Mean Stress =25 Mpa (tensile).
Wohler Diagram or S-N Diagram || Analysis of Completely Reversed Stress
Assume that we have a case of completely reversed stress. That is, S1=S2 and both are of opposite nature. In such a case, Mean Stress=0. And, Magnitude of Stress Amplitude=S1=S2.
Till now, we have understood that a component which is subjected to loads below the range of its Endurance Strength, will not fail. In other words, it will have infinite life, that is, no matter how many cycles of fluctuating loads are applied, it will still survive.
But, what will happen if the stress amplitude crosses the endurance strength? Will the specimen fail (break) instantly? Well, as per the findings of Wohler, it won’t. It will, instead have a finite life, that is, it will fail, but after enduring some cycles of this fluctuating stress. And, precisely, its life will be less than 1 million stress cycles.
Wohler, after conducting many experiments, suggested this S-N diagram, in which we have logarithm of Stress Amplitude on one axis and the logarithm of N (no. of stress cycles) on the other. And from this plot, if we know the Stress Amplitude, we can very well define the life of the specimen, that is, the number of stress cycles for which the component will survive.
The more the stress amplitude exceeds the endurance strength, the lesser will be its life.
For, Stress Amplitude<Endurance Strength, the component shall have infinite life
For, Stress Amplitude=Endurance Strength, life will be exactly 1 million stress cycles.
And, for Stress Amplitude>Endurance Strength, life of component < 1 million stress cycles.