Estimating the damage to a material based on force or kinetic energy

[Pyreaus]

I'm programming a game in which I'd like to simulate the real world physics of an attack using primarily medieval style weapons. Think dwarf fortress, but rather than assigning damage numbers we're calculating force or kinetic energy. Getting that much is easy enough since I can find the mass of real world analogues as well as cutting or striking surface areas, etc. Currently I can calculate the kinetic energy or force and with force get pressure across the striking surface. I tried to doing kinetic energy/distance cubed but I wasn't sure what distance to use for that and it seemed to be a bit janky.

Here is an example of the data I pulled for a 20lbs sledgehammer:

	Mass	Strike Length	Strike Width	Total Length	Impact Velocity	Impact Area	Force	Kinetic Energy	Pressure 1
F-International	10.99961	0.08255	0.08255	0.9652	24.255476	0.0068145025	2668.007764	3235.689914	391519.0821

The velocity I used is based on a 'soft cap' of swing speed I determined based on data like professional baseball batter swings and things like that.

(That's all in metric)
I also have some datasheets on metal like this: http://www.postdiluvian.org/~mason/materials/steel_strength.html
or lumber like this: https://www.conradfp.com/pdf/ch4-Mechanical-Properties-of-Wood.pdf

And I used a formula I found for shear strength of metal: Force require = thickness * perimeter * shear strength of the material
However that came out with unrealistically high numbers:

Impact Area	Layer Thickness	Yield Strength	Tensile Strength	Force to Yield	Force to Shear
0.3302	0.001	26000	47000	59192.8678	107002.4918
		179263682	324053579

Showing it'd take 107 kN to break a hole in a one millimeter steel plate (And not even a very strong blend of steel, relatively speaking) using a sledgehammer. It'd take 59 kN just to deform it, according to this calculation! This seems totally unrealistic since steel can obviously be cut using much less force using a band or circular saw, so I feel like using the Yield/Tensile strengths is the wrong approach here. Does anyone have some suggestions as to how to handle this problem? Finding pre-existing explanations on stuff like this is pretty hard.

Any help would be appreciated!

 

[hutchphd]

Strike length ?? width?? What do these mean...and pulled from where?

 

[Pyreaus]

It's the surface area of the striking surface. So for the example there that's a sledgehammer with a 3.25" by 3.25" head, so the striking surface is 3.25" squared. I used the dimensions of an actual sledgehammer. But that's not the part I need help with.

 

[hutchphd]

How did you obtain the force??

 

[Pyreaus]

I said in the description that I created an estimate of the effective maximum speed someone can swing something and the impact at the tool end based on the effective reach of the tool. I estimate 100ms deceleration time so, y'know, mass times acceleration.

 

[hutchphd]

Why 100 ms? It makes no sense to agonize over the rest of the calculation and "spitball" this number.

 

[Pyreaus]

No offense but it's not the part I'm asking for help with. I also just calculated kinetic energy because I don't need to 'guess' at a deceleration time for that. Do you have any opinion on the rest of it?

 

[hutchphd]

You don't nee the
No offense but it's not the part I'm asking for help with. I also just calculated kinetic energy because I don't need to 'guess' at a deceleration time for that. Do you have any opinion on the rest of it, because this is sort of tangential to what I need help with.

My opinion is that you need to state clearly what quantities you wish to know and show in detail your best attempts to calculate them. Then maybe we can help.

 

[Pyreaus]

As I stated in the original post I need help with estimating the effects on various materials using the kinetic energy or force of a strike. I tried to calculate it by converting both into pressure and testing it against the yield/tensile strengths of materials from a table, but I wasn't sure what distance to use in the kinetic energy -> pressure formula, since that requires a volume and a striking area is a surface area, not a volume. I also tried converting the yield/tensile strengths into 'forces required' but that comes out with similarly odd numbers. I am asking if I should be using a different value than yield/tensile strength or if there is some other value I should be using. When you cut metal, what do I use to determine how hard a metal is to cut? Is it tensile strength? Something else?

 

[hutchphd]

It is probably tensile strength and shear modulus but the geometry is vastly different and a blade is designed to concentrate force onto a very very small area (that"s what they do!) so not really salient here.

I tried to calculate it by converting both into pressure and testing it against the yield/tensile strengths of materials from a table, but I wasn't sure what distance to use in the kinetic energy -> pressure formula, since that requires a volume and a striking area is a surface area, not a volume. I also tried converting the yield/tensile strengths into 'forces required' but that comes out with similarly odd numbers

This is not sufficient for me to help! You are certainly correct to look at the yield/ tensile properties.
In fact a standard way to test sheet steel is to use gravity to swing a hammer at it. Or drop a ball on it. I'm quite certain there are reams of data that answer this question. You might have to particularize it a little but why don't you try to find test data for something close and then you can tweak it.. Mechanical materials acceptance testing or something like that

 

[Pyreaus]

I can reconfigure the calculations to use a blade instead of a hammer but the game needs to have various types of weapons. The example I had already handy was that of a hammer. The issue for me was that it seemed odd that, using a 20lbs sledgehammer, the calculations were showing you wouldn't be able to dent a 1mm steel plate. I gathered that, as a result, the 'perimeter times thickness times tensile strength' I was using wasn't going to give accurate results, so I wondered if there was some other metric I could use. The metals table for example doesn't give a shear modulus on steel, just aluminum, so I'm not sure what to do with it. I've been trying Google-fu for a while and thought maybe someone on here might know since I've been directed here a few times while google searching. I can try looking up that stuff but it's surprisingly hard to find data on 'hitting stuff with hammers or swords' lol.

To Clarify: The calculation's the same just different surface area. A 1kg blade puts out a lot more /pressure/ than a hammer but has like 1/4 the force, which makes sense to me at least.

 

[jrmichler]

Search sheet metal dent resistance for a good place to start. The second hit was particularly good - it's a master's thesis on the subject.

 

[Pyreaus]

Search sheet metal dent resistance for a good place to start. The second hit was particularly good - it's a master's thesis on the subject.

The simulation thesis seems like it'd be useful, especially since he provides a formula:
F0 = K1 * σy * t^a where F0 is the denting force require for 0.1 mm dent depth, K1 is material constant, Yσ is yielding strength, t is the sheet thickness and a is geometric constant

However, I'm not sure where to get the material constant for other steel blends or other metals or if the geometric constant is only the same when using the same size and thickness of steel plate he used. Maybe I missed something when I read it over? If not, is there somewhere I could get that information?