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.

 

[PJC01]

I would approach this problem by first analyzing the properties of the materials involved. In this case, we have a 440C steel ball and three different block materials: 440C steel, lead, and copper. Each material has its own unique properties that will affect the outcome of the collision.

To determine the force at impact, we can use the equation F=ma, where F is the force, m is the mass of the steel ball, and a is the acceleration. Since the steel ball is propelled at a constant velocity of 60 feet per second, we can use the equation v^2=u^2 + 2as to find the acceleration. Here, u is the initial velocity of the ball and s is the distance traveled, which is the diameter of the ball (1 inch) divided by 2. Once we have the acceleration, we can plug it into the first equation to find the force at impact.

To determine the size of the indentation made in the metal plate, we can use the equation for impact force, F= (4/3)E*sqrt(R), where E is the Young's modulus of the material and R is the radius of the indentation. We can use the material properties provided to calculate the Young's modulus for each material and then solve for R.

For the coefficients of restitution, we can use the equation e= (v2'-v1')/(v1-v2), where v1 and v2 are the initial velocities of the ball and block respectively, and v1' and v2' are the velocities after impact. We can use the equations for velocity and acceleration to calculate the velocities before and after impact.

In summary, to solve this physics/metallurgy problem, we need to analyze the properties of the materials involved, use relevant equations to calculate the force at impact, size of the indentation, and coefficients of restitution for each material. These calculations will provide valuable insights into the collision and deformation between the steel ball and the metal plate. I hope this helps in finding a solution to your problem.