Colision and deformation between 2 objects

[builder16]

I am a forensic engineer trying to find the solution to a physics / metallurgy problem. No one in my office seems to know how to approach the problem. I was hoping I could get an answer from the folks in the forum. Please help.

A 440C steel ball having a diameter of 1.0” is propelled horizontally and collides with a metal plate having the dimensions 10” x 10” x 2” thick. The initial velocity of the ball is 60 feet per second. Assume that the ball impacts the plate at its direct center. Also assume that the plate is stationary and held rigidly in place. The material properties of the steel ball are as follows: UTS = 285,000, .2%YS = 275,000, Elongation = 2%, Reduction of area = 10%, Rc hardness = C57.
Determine the force at impact. Determine the size of the indention made (diameter and depth) in the metal plate after impact. Repeat the calculations for the following materials:

Block material 1: Type 440C
Block material 2: Lead:
Block material 3: Copper

Finally, determine the coefficients of restitution in all three cases.

 

[elegysix]

Honestly, in my opinion, I think it would be best to actually do it and just measure it. There are a lot of factors here which make this a complex problem. Unless you absolutely need a model dependent on material properties, buying the balls and plates is probably the easiest way to go.

If you insist on a model though, I would start by taking the initial energy, and supposing some % of that energy did work on the plate. that's because some energy goes into debris, sound, heat and deforming the projectile. At this point, you should realize that if you even manage to build a model, you'll end up doing an experiment to determine the %.

So either way you're doing the experiment - I'm going to assume you're going to go the easier route and just measure it.

Good luck

 

[AlephZero]

Model it with some industry standard software for example LS-DYNA.

Given the assortment of parameters in your OP, this looks more like a homework question to me than a "real life" scenario. In that case, review your course notes or textbook to find out what empirical formulas you are supposed to use.

 

[builder16]

Thank you. We intend to model it this week. I'm not sure if we have LS-DYNA but I'll check. Prior to the modeling I was trying to obtain some equations that relate elastic impact / deformation to the size and depth of the resultant indentation.