Impact force in the Charpy test

[FEAnalyst]

Hi,

could you tell me how to calculate approximate value of impact force during Charpy test (pendulum hitting sample) ? The only formulas that can be found in literature for this test are maximum velocity $v=\sqrt{2gh}$ and work done for fracture $K=mgR(cos \beta - cos \alpha)$. But it should be possible to calculate the value of this force somehow. I guess that this case can be generalized to pendulum impact problem but I don't know any sufficient equations for that too.

Thanks in advance for your help

 

[jrmichler]

You know the kinetic energy before and after impact, and the momentum before and after impact. You can find the duration of impact using high speed video. You can measure the acceleration of the pendulum during impact, and the duration of impact, using an accelerometer.

As a PhD student, you have access to all of the above. In order to use these tools, you need to think about the physics of what is happening instead of looking for "the equation". After you understand what is happening, you will be able to find or derive the equation(s) needed.

 

[FEAnalyst]

Thanks for reply. So far these are only theoretical considerations since I don't use such tests in my research. I just wonder if we can calculate the approximate impact force in Charpy test measuring only the duration of impact. Would it be enough to use the following formula: $F=\frac{\Delta p}{\Delta t}=\frac{m \cdot \Delta v}{\Delta t}$ , where $v=\sqrt{2gh}$ ? Or maybe it won't work here and there are some better equations ?

 

[jrmichler]

A student at your level should be able to be able to derive these types of equations from basic principles, to verify the results, and to defend what they have done to a critical audience. A simple problem such as this is good practice.

Hint: Consider some edge cases:
1) A highly ductile specimen that does not fracture.
2) A perfectly brittle specimen with high modulus of elasticity.
3) A perfectly brittle specimen with high strength and low modulus of elasticity.

 

[FEAnalyst]

Unfortunately it's neither my area of previous master's degree studies nor of my current research topics but I'll try to analyze this problem in more detail as it's really interesting for me. So far I was omitting more advanced aspects related to strenght of materials or fracture mechanics and only focusing on general derivation of impact force.
Do you know some papers about force in Charpy tests ? I haven't found anything useful.

 

[russ_watters]

Do you know some papers about force in Charpy tests ? I haven't found anything useful.

This doesn't surprise me. I don't see how it could be useful. Why is it useful to you?

The main issue I see is that the force is not going to be constant and may not even have a clearly defined function (linear, quadratic). So a single number (average) may mean even less than plotting the curve and trying to identify the function.

 

[FEAnalyst]

Just out of curosity. I thought that there will be some info about pendulum impact force calculations available in the internet.

I totally agree that this will be highly nonlinear, dynamic event and the force definitely won't be constant. Actually this could be solved using explicit dynamics Finite Element Analysis code but I am looking for (very simplified and approximate) analytical solution. Even something as simple as this: https://www.wired.com/2014/07/how-do-you-estimate-impact-force/ or this: https://www.engineeringtoolbox.com/impact-force-d_1780.html but for pendulum. It seems that I have to use the equations that I've mentioned before.