Strain Energy Release During Fracture -Where does it go?

[jstluise]

When a bolt is pulled in tension and eventually fractures, is all the built up strain energy dissipated in the formation of the new surfaces? Does any energy do into accelerating the broken halves of the bolt?

Imagine that two plates are bolted together. As the two plates are forced apart, the bolt deforms and eventually yields/fractures. When the fracture occurs, the bolt will be shot out from the joint. I believe that it is the release of the elastic potential energy built up in the plates that is causing the bolt halves to accelerate, and that the energy dissipated in the fracture has no influence on the bolt accelerating. Is this correct?

Thinking about it another way: imagine the two plates in the above scenario are infinitely stiff. When they are forces apart so that the bolt fractures, will the bolt move at all? Or will the bolt just break and remain mostly still? (I guess this is assuming the rest of the bolt is infinitely stiff as well; if not there could be built up energy in the deformation of the bolt head that could accelerate the bolt once it breaks)

I hope that makes sense!

 

[Filip Larsen]

You could perhaps try establish some equations for energy and, thus, speed of a bolt assuming all stored energy from the load is converted to kinetic energy in the bolt, and then run a calculation for the situation you have in mind? I ran a few numbers on the back of an envelope (well, actually it was a block of paper) and was a bit surprised about the result.

 

[jstluise]

You could perhaps try establish some equations for energy and, thus, speed of a bolt assuming all stored energy from the load is converted to kinetic energy in the bolt, and then run a calculation for the situation you have in mind? I ran a few numbers on the back of an envelope (well, actually it was a block of paper) and was a bit surprised about the result.

Thanks for the reply. Could you summarize your results?

What we are trying to figure out is out of all the energy put into the system to break the bolt (area under force/displacement curve), how much of that is dissipated in the fracture of the bolt, and how much of it is dissipated in the mechanism that is pulling the bolt apart.

A Frangibolt is a device that is placed between two bolted plates. When activated, the Frangibolt expands until there is enough built up force to break the bolt. When the bolt breaks, it is the potential energy present in the Frangibolt that we are worried about, which is leftover from the energy dissipated in the fracture.

 

[Filip Larsen]

I am not a mechanical or materials engineer, but it only took a few minutes with a textbook to establish a simple model for the energy U stored in a bolt as a function of the load force F, bolt area A, elasticity module E and clamp length L (grip length in your case), as

$$U = \frac{F^2 L}{2 A E}$$

which can be combined with an expression for the kinetic energy of the bolt. You should be able to derive the combined result easily. If you use a bolt with a built-in weak spot (i.e. different cross sections along the length of the bolt), you may have to derive a more accurate U expression for that.

When inserting data for a 10 mm diameter standard steel alloy bolt with an "effective length" of 30 mm loaded with 70 kN over a grip of 10 mm, I get an energy of around 22 J and a maximum speed of around 34 m/s, which was higher than I had expected. I did not make any additional calculations to check my results, though, so it may be that I have made a mistake.

 

[jstluise]

I am not a mechanical or materials engineer, but it only took a few minutes with a textbook to establish a simple model for the energy U stored in a bolt as a function of the load force F, bolt area A, elasticity module E and clamp length L (grip length in your case), as

$$U = \frac{F^2 L}{2 A E}$$

which can be combined with an expression for the kinetic energy of the bolt. You should be able to derive the combined result easily. If you use a bolt with a built-in weak spot (i.e. different cross sections along the length of the bolt), you may have to derive a more accurate U expression for that.

When inserting data for a 10 mm diameter standard steel alloy bolt with an "effective length" of 30 mm loaded with 70 kN over a grip of 10 mm, I get an energy of around 22 J and a maximum speed of around 34 m/s, which was higher than I had expected. I did not make any additional calculations to check my results, though, so it may be that I have made a mistake.

I see what you did, but that stored energy is only considering the elastic deformation of the bolt. What you are describing is essentially the elastic potential energy (1/2*k*x^2) using the equivalent spring constant from the bolt properties.

If the bolt all of a sudden broke (i.e. no energy went into fracturing), then (I think) it makes sense to say this will be the energy that is converted into kinetic energy. So, in the case of a real brittle material, this is probably a good estimate of the kinetic energy.

But, with a material that has some plastic deformation before fracture, you are going to loose some energy in the deformation of the bolt. Thus, the total energy inputted into the system is dissipated in the fracture/deformation, and the rest is converted to kinetic energy.

I'm beginning to think that just looking at the force/displacement curves for breaking a bolt will tell me everything I need to know. The area under the curve is the energy put into the system. For example, looking at this force/displacement curve:

If you almost reach the point of fracture, but let off the force, you will recover based on the elastic modulus. The rest of the area was energy wasted in plastically deforming the bolt. So, that leads me to think that once fracture occurs, the energy (green) is available for conversion from potential to kinetic.

That is the only thing that makes sense to me right now, without getting into fracture mechanics. But, I could be totally wrong.

 

[Filip Larsen]

For what it is worth I agree with your description. Note that the area of the green section is indeed the expression I gave earlier with F being the ultimate tensile strength, that is, the expression effectively "ignores" any energy lost due to plastic deformation.

 

[jstluise]

For what it is worth I agree with your description. Note that the area of the green section is indeed the expression I gave earlier with F being the ultimate tensile strength, that is, the expression effectively "ignores" any energy lost due to plastic deformation.

Ah yes, thanks for pointing that out. Glad we are on the same page.

 

[AlephZero]

Note that the area of the green section is indeed the expression I gave earlier with F being the ultimate tensile strength, that is, the expression effectively "ignores" any energy lost due to plastic deformation.

That's right. The only energy you can recover is from the elastic strain energy in the bolt. You already used the plastic strain energy in stretching the bolt permanently. You can't use it again.

I think the estimate of 34 m/s velociity is a bit high. You didn't state what you assumed for the mass of the broken piece (don't forget the bolt head, for example). Some energy will go into vibrations in the bolt and the flanges, as well as the "rigid body" motion of the bolt. But broken bolts can certainly "fly" a long way if they get "launched" cleanly, without catching on the side of the bolt holes etc.

We once had an unexpected failure of something similar to a very large bolt, that was being tested in a vacuum tank and filmed with a high speed camera, so we could measure what happened. The impact on the lid of the tank (about 10 feet diameter) wrecked the lid, We calculated that without the lid, it would have gone through the roof of the building and reached an altitude of about 1500 feet

 

[jstluise]

Thanks for responding, AlephZero.

Some energy will go into vibrations in the bolt and the flanges, as well as the "rigid body" motion of the bolt. But broken bolts can certainly "fly" a long way if they get "launched" cleanly, without catching on the side of the bolt holes etc.

I think you are onto what originally made me start thinking about this. When the broken bolt is launched, is it from the built up potential energy from the joined material forcing the bolt apart? Or is it somehow from the strain energy in the bolt?

This goes back to the scenario I mentioned in the my first post: you have two infinitely stiff plates being joined by a bolt. The two plates are forced apart, stretching the bolt to failure. When the bolt breaks, there will be no stored energy in the plates (right?), so will the bolt be launched out? Where does the elastic strain energy go?

We once had an unexpected failure of something similar to a very large bolt, that was being tested in a vacuum tank and filmed with a high speed camera, so we could measure what happened. The impact on the lid of the tank (about 10 feet diameter) wrecked the lid, We calculated that without the lid, it would have gone through the roof of the building and reached an altitude of about 1500 feet

Scary!

 

[Cowpoke]

I would imagine the resulting force is a result of both the bolt's and the plate's potential energies being released simultaneously. The material of which the plate was constructed, and the tensile strength of the bolt could possibly give you the numbers needed to calculate how much each contributed to the bolt's acceleration.

Jim

 

[jstluise]

I would imagine the resulting force is a result of both the bolt's and the plate's potential energies being released simultaneously. The material of which the plate was constructed, and the tensile strength of the bolt could possibly give you the numbers needed to calculate how much each contributed to the bolt's acceleration.

Jim

I can totally understand how the potential energy in the plate could cause the bolt to accelerate and shoot out; the plate is essentially a spring in compression that is all of a sudden released when the bolt breaks.

But, when the bolt is being pulled apart, it is always in tension like an extension spring. So why would the energy in the bolt cause it to shoot outwards? The only thing I can think of would be the reaction happening between the bolt head and the plate; as the broken piece of the bolt contracts toward the head of the bolt and it is this momentum that accelerates the bolt. Think of shooting a rubber band off the tip of your finger; your finger is acting as the plate, the loop of rubber band around your finger is acting as the bolt head, and your release hand is acting as the bolt fracturing.

 

[Cowpoke]

aah yes it seems I was thinking unidirectionally. Now this is bugging me as well.

 

[jstluise]

The analogy I made with the rubber band shooting makes the most sense to me thus far. Assuming that the each half of the broken bolt are the same mass, and the plates are infinitely stiff, then the elastic potential energy in the bolt divided in half and each half of the bolt will be slingshotted out away from each other.

Now considering the stiffness of the plates, and I get a bit confused. Imagine the point right before the bolt is going to break...you have the stored elastic potential energy in the bolt, but now you have stored elastic potential energy in the plates. So that means there is more energy in the system? i.e. you did more work to both stretch the bolt AND compress the plate? The dynamics get a bit more messy, but I imagine a model could be made with just masses and springs prior to release (fracture).

Hmmm, more to think about...