Its happened to us all at one time or another: we have been a victim, of stress failure. I myself for example have been enduring a failure of sorts, my tibia broke, and broke at a very important intersection, which required surgery... But, most of us have been observant of a less painful failures:
Failures such as
- A rake breaking in our hands
- Or a board snapping under our feet
- Or even a crack in our go kart frame.
The failure can be traced to some event of high load, or obvious miss-application of design intent:
For example:
- Jumping the go kart
- Or trying to move rocks with the rake
- Or jumping on a board that was too thin
Each one of these instances are descriptions of failure. The funny thing is we can predict failure by assimilating the right information (which is readily available) and using mathematical relationships.
Sounds fancy and complicated, but it really means this:
Things have their breaking point, we can predict this breaking point relatively easily.
So lets get to it...
First of all a basic understanding of how to evaluate failure is needed.
The Science of Failure
Science is a system of thought which relies on cause and effect relationships.
Translation: A cause (a go kart flying at obscene speeds) flies over a jump and lands on all for wheels, but suddenly drops to the ground making ugly scraping sounds (the effect).
What other variables are there to this problem? Well what is the problem exactly? A broken frame!
To the untrained eye, the failure would be perceived to be because the go kart went over the jump, when in reality the failure is because the frame could not handle the jump load.
What Failed?
So what is it about the frame that caused it to fail?
That begs the question, what was the failure exactly?
The frame cracked the tubes underneath the seat and basically ripped the tubes in half and the go kart bent down and scraped on the ground.
So the tubes, cracked, and tore and bent.
To evaluate the problem further, we see that the tube (individually) has a wall thickness, or section of material. This section of material tore, or ripped apart.
Key To Failure
The ripping apart ability of material is key to understanding the basis for what is called stress. In fact most materials have the ability to be stretched, or compressed. Stress is evaluated as the amount of force divided by the area that the force is acting on that the material can take.
Stress = Force/Area
So for example, a solid cable (.0625 inches in diameter wire) is hanging from the ceiling. I put a 100 pound load on the cable. The stress in that cable is 100 pounds divided by the cross sectional area of the cable, or 100 pounds/PiR^2 or 100lbs/ .003 in^2 = 32594 psi
To predict whether the cable would snap or not, the stress would have to be around 36000 psi. Well as you can see, we are really close to 36000 psi and any light bump of the weight would cause it to SNAP!
What we did was little prediction. A .0625 cable can only hold so much load, and 100 pounds is about it!
Okay, how did I know that? Because scientists have observed that steel (mild steel that is) breaks consistently at around 36000 psi stress. In fact special pieces of equipment are designed to just cause material samples to fail, day in and day out. What they are doing is validating material samples made at foundries, and steel mills so that guys like you and me can predict and make things with relative assurance that the gokart we are making will not break in half.
So to recap, stress is defined as Force per unit area or
Stress = Force/Area
It is vital to understand that the area of a part relates to the overall strength of the part, because forces flow through this area.
We understand this very well, when we pick up a large rubber band and compare it to small rubber band. The main difference between the two is the cross sectional area of the rubber band. The larger rubber band has more area to work with, and therefore exerts more force when stretched.
If we were to put 3 small rubber bands together we may equal the same force as the large rubber band, that is because the larger rubber band has 3 times as much area as the smaller rubber bands.
So stress is the force that a section of area can take. Once the force exceeds that areas capacity to hold load it snaps, breaks, or stretches then snaps!
Next time... Sectional Area and the relationship to failure
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