Why Are Some Materials Strong?
Strength
Why do solids have different strengths? What is strength? How does strength relate to stiffness?
Your first guess may be to say that strength depends on the interatomic bonds in materials. A strong material has strong bonds and a weak one has weak bonds. This is not the case however. The Young's Modulus of a material is related to the stiffness of the interatomic bonds in a material. The strength of a material in bulk is not related to the strength of interatomic bonds however. The only link between bulk strength and bond strength is that you can make a weak bulk material using strong interatomic bonds, but you can't make a strong bulk material using weak interatomic bonds.
What Is Strength?
Before we talk about strength, we need to first define it. Strength is how hard it is (how much force is required) to break an object. It should not be confused with stiffness which is how springy, floppy, flexible etc.. an object is (this is measured by the Young's Modulus of the material).Here are some examples so you can get a feel for the differences between stiffness and strength.
A biscuit is weak and stiff.
Steel is strong and stiff.
Nylon is strong and flexible.
Jelly is weak and flexible.
Tensile And Compressive Strength
Another detail to note is that in this post we will be talking about tensile strength. This is the stress (force per unit area) needed to break an object by pulling it apart.This is different and a lot simpler than compressive strength as there are a lot more ways to break something by squashing it.
If it has a low Young's Modulus, it may squash out sideways as if it was putty. If it has a high Young's Modulus, then this kind of failure would likely be explosive and the material may explode out sideways.
If the material is long and thin, it may buckle under the pressure and snap in two.
The material may also crumple like a box and so you cannot just assign one compressive strength to a material. For this reason, we will only talk about tensile strength in this post.
Energy
As you pull a material apart, you are applying a force across the distance that you stretch it. This means you are doing work. The law of conservation of energy means that this energy must be converted into another form. Assuming the material does not make sounds and does not get hotter, the work done will be stored as strain energy.This means strain energy is a potential energy caused by the material being stretched. If the force is then removed, the surface will revert back to normal and the energy will mostly be dissipated as heat.
This is because a key idea in physics is that all systems try to minimize their potential energy. Think of a ball in the air. A ball tries to minimize its gravitational potential energy and so tries to fall towards the center of the Earth. This is the minimum total potential energy principle.
Surface Tension
Now we have to think about surface tension.
Surface tension in a fluid is its tendency to acquire the least surface area possible. This is why water often stays as drops on surfaces as this formation has a lower surface area than if it was evenly spread on the surface.
The easiest explanation for why fluids have surface tension revolves around energy. A molecule in the center of a fluid is in contact with as many neighboring molecules as possible. A molecule on the surface on a liquid however, is in contact with about half of the molecules compared to a central one. Molecules in contact with a neighbor are in a lower energy states than molecules with no neighbors and so molecules in the center have lower energy than molecules on the surface.
For a liquid to minimize its energy state, the number of molecules on the surface must be minimized as these have high energy. Minimizing this means the surface area of the liquid is minimized. The shape which minimizes the surface area is a smooth sphere (the reason why all the liquids we see are not spheres is because other forces such as gravity also influence their shape). Any curvature in the surface results in a greater surface area and therefore a higher energy. This means the surface pushes back against any curvature in the same way that a ball resists being raised (through gravity) in an attempt to minimize it's gravitational potential energy.
Through this argument, you can see that solids also have surface tensions. The molecules on the surface on a solid also have more energy than molecules in the center and so the solid tries to minimize this energy by minimizing its surface area. The difference between this and surface tension in a liquid is that a solid is much more rigid and so we do not notice that there is a force trying to minimize the solids surface energy.
Now think of an insect walking on water.
When an insect goes on water, its surface is dimpled and therefore becomes extended. This means its surface energy increases as work is done against tension to extend the surface. Conservation of energy can be used and you will notice that the increase in surface energy will be equal to the decrease in potential energy.
There will be a maximum sized insect that can walk on it and any heavier insects would just sink. This is the same with a solid. This force required is the stress which will separate two adjacent layers of atoms.
Cutting a material increases its energy. This means the energy used in separating the material is equal to the energy stored in the new surfaces of the material.
What Is Strength
σ = 2√GE/x
is the equation that tells you the stress required to break a material
G is the surface energy of the solid per square meter
E is the Young's Modulus of the material
x is the distance between two adjacent layers of atoms
The small issue with this is that to derive this equation, it is assumed that Hooke's Law is true up to failure. For large strains however, it follows the interatomic curve which is gives about half the extension Hooke's law suggests. This means roughly
σ = √GE/x
This tells us that the surface energy of a solid, it's Young's Modulus and the distance between adjacent layers of atoms are what determine when it will fracture (the stress required to break it).
Reality
The weird thing is that the value from the equation is usually 100 - 1000 times bigger than the strength of bulk materials.David Griffiths and Ben Lockspeiser decided to investigate glass to see why this is the case since it has a very easy fracture mechanism. They drew fibers of glass, found their Young's Modulus's easily by mechanical experiment and then approximated the spacing between the glass atoms at 2 - 3 Angstrom (Å) units (1 Angsrom is 0.1 nanometers). Now they just needed to measure its surface energy.
Another advantage of glass is that it has no sharp melting point, it gradually changes from a solid to a liquid, becoming less viscous as temperature increases. This means there is no big change in molecular structure and so there is no big change in surface tension and therefore energy.
You can easily measure the surface tension of molten glass by heating the end of a glass rod so a blob forms. You then have to measure the force needed to extend the end as this force will only need to overcome surface tension. They did this and when they brought this together with glass's Young's Modulus and atom spacing, they found that strength was increasing as fibers became thinner. Strength was roughly inversely proportional to thickness. They then realized that the theoretical strength of glass was the same as very thin glass.
The next step was to work out why most materials fell short of this theoretical strength.
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