I Is There a Curve For a Material's Surface Area vs. UTS

AI Thread Summary
The discussion revolves around the physics of materials in relation to a tabletop game design, specifically focusing on the relationship between surface area and ultimate tensile strength (UTS). The creator's diagram suggests that smaller surface areas may offer greater resistance to deformation due to a higher ratio of bonds per particle. There is a question about whether kinetic energy focused on a small area can penetrate armor effectively, as the resistance may be proportionately greater than that of larger areas. The conversation also touches on the definition of UTS and the meaning of elongation percentage in materials, clarifying that a 20% elongation indicates a material can stretch to 120% of its original length before breaking. Understanding these concepts is crucial for accurately representing armor mechanics in the game.
gibberingmouther
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I drew a diagram in order to help figure out something for a tabletop game I'm putting together.

My question is about the physics of materials, and is not directly about the fictitious psychic/magic abilities in my game world.

I drew a diagram consisting of dots representing particles and lines connecting the particles to represent bonds. Real atoms don't bond together exactly like this, I understand that, but this diagram seemed to suggest that a material would put up more proportional resistance for a smaller surface area because there are more bonds resisting deformation in proportion in a smaller surface area than to a larger one. That's just what I figured from my diagram.

I started drawing an example of the diagrams I had drawn in Paint and then Paint.Net but apparently my computer got a virus(es) from somewhere because both of those apps are now seriously malfunctioning. I don't go to shady websites or anything, but my laptop, once a workhorse, is having some issues lately...

Basically, the ratio of bonds connecting 9 particles to the particles surrounding those 9 particles (ratio of bonds around those 9 particles to the 9 particles) is smaller than the ratio of bonds connecting 4 particles to the particles surrounding those 4 particles (ratio of bonds around the 4 particles to the 4 particles). To me, this implied that there should be a curve with surface area on the x-axis and ultimate tensile strength on the y axis. A small surface area (not the cross sectional area, or thickness, you consider with tensile strength) will have the maximum ratio of UTS to surface area, and it the curve should taper out into a horizontal line.

This is important for how armor works in my game. Does kinetic energy focused into a small area not always penetrate because that small area resists more proportionately than a larger area?

Or am I wrong and the graph I suggested is pretty much just a horizontal line?

If it can be approximated as a horizontal line, how does something like steel plate resist pointy things like swords or arrowheads?
 
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What's UTS? Ultimate Tensile Strength? Can you give a quantitative definition please? Thanks.

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Yes, I meant "ultimate tensile strength."

Here's a chart showing some UTS values for steel alloys: https://www.amesweb.info/Materials/Steel-Tensile-Yield-Strength-Chart.aspx

What does the "elongation %" mean, by the way? If you have a sheet of steel with a certain thickness and pull at it, a 20% elongation means it will elongate to 120% before breaking? Do I understand correctly?
 
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