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

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SUMMARY

The discussion centers on the relationship between a material's surface area and its ultimate tensile strength (UTS), particularly in the context of designing armor for a tabletop game. The user posits that a smaller surface area may provide greater resistance to deformation due to a higher ratio of bonding connections, suggesting a curve where surface area is plotted against UTS. They seek clarification on whether this relationship approximates a horizontal line and how materials like steel plates resist penetration from pointed objects. Additionally, they request a quantitative definition of UTS and clarification on the concept of elongation percentage in steel.

PREREQUISITES
  • Understanding of ultimate tensile strength (UTS) in materials science
  • Familiarity with the concept of surface area in relation to material properties
  • Basic knowledge of material bonding and atomic structure
  • Awareness of mechanical properties of steel alloys
NEXT STEPS
  • Research the mathematical modeling of surface area versus ultimate tensile strength in materials
  • Study the mechanical properties of various steel alloys, focusing on UTS and elongation
  • Explore the physics of material deformation under stress, particularly in armor applications
  • Investigate the impact of surface area on the penetration resistance of different materials
USEFUL FOR

Material scientists, game designers, engineers, and anyone interested in the mechanical properties of materials, particularly in the context of armor design and performance.

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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