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Name: Anonymous
Status: Student
Age: 14
Location: N/A
Country: N/A
Date: April 2004


Question:
I was wondering does everything get weaker the thinner you make it and does it get stronger the thicker you make it.

In other words is possible to have a thick material be flexible and a thin material be sturdy?



Replies:
Yes, everything gets both stronger and stiffer (they are different ideas) when it gets thicker.

However, there is a wide range of strengths and a wide range of stiffnesses in various materials. When we want a part to be thin and strong at the same time, we choose the strongest materials we have, and that's the best we can do. When we want flexibility and thickness, we try to find something rubbery but fairly strong, and that's the best we can do. There are limits to what we can currently do, in both directions.

Imagine what you can do with good steel, like piano wire, and that's fairly near the stiffest and strongest we can do. Sapphire, Diamond, Silicon Carbide are stiffer and harder, but maybe not stronger for pulling forces (tension).

Tungsten Carbide is harder. Kevlar and graphite strings are a little stronger. Carbon nanotube fibers will be much stronger, if we ever invent them. There's no firm limit to how flexible a rubbery material can be, but it's strength tends to decline simliarly. Flexiblity with better strength tends to be done with fancy shaping of thin, stiff, strong materials.

A stong steel cable may break at tension of over 100,000 pounds per square inch of thickness ("psi"). That's it's strength. The same cable will stretch about 1% per 30,000 psi. That's it's stiffness with respect to stretching.

A rubber rod may break at less than 1000 pounds per square inch of thickness, much less, if it is tearing from a little cut at one side. The same rubber rod might stretch about 1% per 1 psi. (guessing that number.) Looks like rubber gives you more stretch for a given strength. And it stretches farther before breaking.

Look for "elastic modulus" or "bending modulus", for flexibility numbers.
Look for "yield stress" or "break strength" or "ultimate strength" for strength numbers. some good places for numbers:

http://www.lib.umich.edu/dentlib/Dental_tables/toc.html, Elasmod.html, Ulttensstr.html

http://www.maropolymeronline.com/Properties/modulus_values.asp

Strength is: how hard do I have to stretch, squeeze, or bend to make it permanently break or bend ? (It won't spring back.) Stiffness is: how hard do I have to stretch, squeeze, or bend to make it temporarily bend a certain percentage of it's size? (It will spring back.) For all low to medium forces, Stiffness is what you notice. (Opposite terms are Flexibility, Elasticity.) Then when higher forces exceed the Strength, irreversible deformation or breaking occur.

Stress and Strain mean different things, too. Stress is the force density, in pounds-force per square inch or Newtons per square meter. "how hard were you pushing?" Strain is the percentage deformation that results from a stress. "how much did it give?"

For a given material, strength depends a lot on quality. You can buy cheap 30kpsi steel bolts, or you can buy expensive "Grade 8" 80kpsi+ steel bolts. But stiffness is difficult to influence more than 20%.

Both cheap and expensive bolt have the same degree of spring-stretch for small forces. Steel is 3 times stiffer than aluminum, and ceramic is 3-4 times stiffer than glass.

Engineering fanciness in sculpting the shapes often helps out. A beam made of ten thin sheets of spring steel, free to slide on each other, will be 10 times more flexible than one thick sheet, for the same total thickness. A soft (and weak) rubber pad can be stronger and stiffer in one direction if there are steel wires inside, running in that direction only. But it's still flexible in the vertical and cross-wise directions. Making big triangles out of thin rods creates a structure which is stronger and stiffer than the same rods just piled side-by-side. Tubes of rolled-up sheet are stiffer than the same sheet sliced and stacked densely. Bubbles are another example of fanciness - you have Polystyrene foam for rigidity and some other foams for flexibility.

Hopefully this will give you some tools to design things you have in mind.

Jim Swenson



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