A colleague asked me to help her with some Fatigue hand calculations on a simple test piece. No problem I thought – quite straightforward, except it did not turn out that way and I discovered a hole in my understanding that is critically important to getting correct Fatigue life predictions! Hence I have written this blog so that you don’t fall into the same trap as me! Here is the simple uniaxial test set up – a turned plain carbon test piece subject to a 20kN axial tensile load and fixed at the end. The maximum P1 stress is 278 MPa ... Now for the Fatigue study. I set up a Fatigue ‘Event’ which was ‘Fully Reversed’ and used the ‘Derived ASME carbon steel’ curve in the material properties for the SN curve. As the ‘Event’ was ‘Fully Reversed’ the mean stress is zero so there is no need for a correction factor.
The result shows that the specimen would fail after about 8,699 cycles … Everything at this stage was fine. I could prove that the stress matched my hand calculations and the number of cycles to failure matched the data in the SN curve at the 278 MPa stress … You can see that the N value at 278 MPa will be slightly less than 10,000 cycles. However, I wanted to show that the life would be significantly reduced if the loading was not ‘Fully Reversed’ but ‘Zero Based’. This is because a ‘Fully Reversed’ event is in compression for 50% of the time and compression does not open fatigue cracks (hence why we use compressive surface treatments as a means of increasing fatigue life). I copied the ‘Fully Reversed’ Fatigue Study and swapped the event from ‘Fully Reversed’ to ‘Zero Based’. I knew that this would create a positive means stress so also added in a Gerber ‘Mean Stress Correction Factor’ and was confident that the Life would now be less than the 8,699 cycles. To my surprise the Life came out at 56,347 – over six times longer! I checked and double checked and finally realised my mistake.
The stress study was set up with 20kN static load. This implied that when fully reversed the alternating stress amplitude was actually 40kN as shown by this diagram … It is the alternating stress amplitude that is important. When you swap to a ‘Zero Based’ condition the alternating stress amplitude is only 20kN i.e. halved … This simple fact means that you cannot just swap ‘Fully Reversed’ with ‘Zero Based’ if you want to compare the difference in Fatigue Life (all else being the same). You are then not comparing ‘apples with apples’. The solution is either to double the force in the static study (which seems counter-intuitive) or else use the ‘Scale Factor’ in the Fatigue Event set up. I had observed this option before but not appreciated its significance. It allows you to effectively scale the stress results in the parent stress study. Here is what I did …
This means that the alternating stress amplitude is now 40kN in the ‘Zero Based’ event as it was in the ‘Fully Reversed’. We must also recognise that the mean stress is now positive and correct this with the Gerber ‘Mean Stress Correction Factor’ in the study Properties. The final result is a Life of 1,363 cycles …
This is now much lower than the original life and is correct. Here is a table of the 3 results. You can see how critical this is to get right … Andy Fulcher
Technical Manager