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

In summary, the conversation is about the physics of materials in relation to a tabletop game. The speaker drew a diagram to represent bonds between particles and noticed that a smaller surface area has a higher ratio of bonds to particles, suggesting a potential correlation between surface area and ultimate tensile strength. The speaker also mentions issues with their computer and provides a chart of ultimate tensile strength values for different steel alloys. They also ask for a quantitative definition of ultimate tensile strength and clarification on the meaning of "elongation %."
  • #1
gibberingmouther
120
15
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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  • #2
What's UTS? Ultimate Tensile Strength? Can you give a quantitative definition please? Thanks.

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  • #3
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?
 

1. What is UTS and how does it relate to a material's surface area?

UTS stands for Ultimate Tensile Strength and is a measure of a material's maximum resistance to breaking under tension. The surface area of a material is important in determining its UTS because a larger surface area means more surface for stress to act upon, which can lead to a lower UTS.

2. Is there a direct relationship between a material's surface area and UTS?

There is no direct relationship between a material's surface area and UTS. While a larger surface area can lead to a lower UTS, there are other factors that can also affect a material's UTS, such as its composition, structure, and processing techniques.

3. Can a material's surface area be manipulated to improve its UTS?

In some cases, manipulating a material's surface area can improve its UTS. For example, increasing the surface area through processes such as cold working or heat treatment can result in a stronger material. However, it is not the only factor that determines a material's UTS and other methods may need to be used to improve it.

4. How does a material's surface area affect its strength-to-weight ratio?

A material's strength-to-weight ratio is a measure of its strength relative to its weight. Generally, a larger surface area can lead to a lower strength-to-weight ratio as it adds weight to the material without necessarily increasing its strength. However, this can also depend on other factors such as the material's density and overall structure.

5. Is there a specific curve that can be used to predict a material's surface area vs. UTS?

There is no specific curve that can accurately predict the relationship between a material's surface area and UTS. This is because it depends on various factors, including the type of material, its composition, and processing techniques. Experimental data and analysis would need to be conducted to understand the specific relationship for a particular material.

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