I used to think that the padlock design of using many layers of metal stacked to form the main body was a cost-cutting consideration. This was my assumption before I came across the idea that it was really a way to make the lock stronger. It might have been from a TV commercial which showed a bullet penetrating a lock in slow motion. This was many, many years ago, but I have always wondered about that. Although anectodal, my experience finds that really sturdy, heavy duty equipment usually has a nice solid frame or enclosure. I'm not counting things like cars that are designed with "crumple zones", because in such cases weight is a major factor. I'm thinking about manufacture where weight isn't an issue, like padlocks. Does anyone have knowledge of something that would support this claim?
[Physics] Is a laminated padlock really stronger than a solid one, and if so, why
everyday-lifeforcesmaterial-science
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http://www.physicsforums.com/archive/index.php/t-37701.html says
"Most of the strength of a cylinder comes from the outer portions. I think the contribution goes like the cube of the radial position. So, if you took a solid rod and drilled out a half the volume from the center, you do not lose half the strength. Strength to weight ratio is better for a hollow pipe than a solid rod."
The definition for the second moment of inertia $I_c$ for a filled and hollow cylinder can be found on http://en.wikipedia.org/wiki/Second_moment_of_area: $$I_c=\int\!\!\!\!\!\int_A y^2 \textrm{d}x\textrm{d}y=\int_0^R\!\!\!\!\!\int_0^{2\pi} r^2 \textrm{d}\phi\ r\textrm{d}r=\frac{\pi r^4}{4}$$
The surface area of the filled cylinder is: $$A=\pi r^2$$
Compare filled and hollow cylinder of equal mass: $$s_c=\frac{I_c}{A}=\frac{r^2}{4}$$, cylinder with fractional internal radius $r_i=xr_o$ and $x<1$: $$s_h=\frac{I_h}{A}=\frac{r^4(1-x^4)}{4r^2(1-x^2)}=\frac{r^2(1-x^2)(1+x^2)}{4(1-x^2)}=\frac{r^2(1+x^2)}{4}>s_c$$.
This means a hollow cylinder is stronger than a rod of equal mass and the same material. A hollow cylinder with a bigger inside diameter is better. In the limit $x\rightarrow 1$ the hollow cylinder is twice as strong. Note that this limit isn't physically viable as it would be an cylinder with infinite radius and infinitesimally thin wall. However it is useful to define the upper limit of the second moment of inertia. I didn't expect the increase in strength only a factor of two.
I've been having a play with some granulated and some icing suger (I think "icing sugar" is the same as "powdered sugar") and the thing that strikes me is that icing sugar is less free flowing than granulated sugar. I would guess this is the reason for the density difference.
You mention in a comment that the packing fraction for spheres does not depend on the size of the spheres. This is true, but spheres will only get anywhere near the theoretical packing fraction if they can slide over each other freely and rearrange themselves into a close packed array. If the spheres stick together your get a flocculate that will have a much lower packing fraction.
So my suggestion is that in icing sugar the grains have a tendancy to stick together rather than flow freely over each other. I'd guess this is just down to particle size. Assuming the adhesion between grains is a surface phenomenon then the adhesive strength won't increase with grain size, so the increased mass and size of larger grains makes them easier to pull apart mechanically. The adhesion might be due to Van der Waals forces, or it could be due to an adsorbed water layer making the grain surface slightly sticky.
Response to comment:
The relationship between sediment density and flocculation is well known in the colloid science world (I was a colloid scientist in a previous life) and indeed it's used in industrial processes. For example this patent describes using flocculation to stabilise zeolite slurries. Although it covers zeolite grains in water the principle is exactly the same. If the slurry is not flocculated all the zeolite grains settle into a close packed sediment at the bottom of the tanker and you can't get them out. If you make the zeolite grains stick together they for a less dense sediment (just like the icing sugar forms a less dense powder).
In industry at least most colloid scientists work with fluid suspensions, and sugar while technically still a suspension, is a suspension of solids in air. The way to probe the effect of particle adhesion on powder density would be to control the grain-grain adhesion and show that changes the density. However I don't know how you would do that for a system in air. In fluids it's easy because you can adsorb surfactants and polymers onto the grain surfaces.
It would be interesting to see what density powders were formed in vacuum. If an adsorbed water layer is responsible for the stickiness it should be reduced in vacuum so the powder density will increase. Also you could try vibrating the powder. If particle adhesion has caused formation of a less dense aggregate then vibrating the powder should increase the density because it has will separate adhered grains.
Best Answer
The multi-layered structure protects against impact fracture.
If you hit an object very hard, you can create a crack; stresses will concentrate at that crack, and make it easier for the crack to propagate (think of the little notch in the ketchup packet: that's where you can tear the plastic...)
Now if you have a solid body (of anything), then that crack can continue to grow. But if you laminate, then the crack will hit the end of one lamina, and stop. That means that a laminated object will be much more impact resistant: it's easy to initiate a crack on the outermost surface (for example with a carbide-tipped object), but it's much harder to do so on an inner surface (which your tool cannot reach).