What factors determine the maximum penetration of an axe through a metal sheet?

[Nick23]

Imagine an axe going through a sheet of metal, both made of the same probe.
On the basic level of language - the axe goes through the sheet.
On the next level of language - due to pressure, delivered by the edge of the blade, the bonds between the molecules of the metal sheet begin to tear.
But what happens on the next level ?

Why do molecules spread out upon the impact of kinetic force ? Why does the matter that is thinner, tuns out to be more pliable ? Why does the blade edge powered by velocity and mass resists deformation much better, if the pressure to it and the sheet is the same ?

 

[Doug Huffman]

Pressure is force per area. As area is sharpened to an infinitesimal, the force becomes very large.

 

[Drakkith]

Why do molecules spread out upon the impact of kinetic force ?

The force applied to them exceeds the force holding the molecules together and they give way, first by elastic deformation, then by plastic deformation.

Why does the matter that is thinner, tuns out to be more pliable ?

In order for the metal to bend, it has to have somewhere to go. If you hit a thin sheet of metal with a hammer, the metal will bend and change its shape by moving away from the point of impact. If you have a really thick piece of metal, the thin layer that takes the initial impact has nowhere to go, so the force of the impact is transmitted through to the underlying metal. This drastically increases the amount of force required to deform the metal since more of the material is absorbing the force and you need more energy to break or alter all of those bonds.

Think about a thin sheet of metal as a lot of molecular layers placed on top of one another. A single layer is only one molecule thick, and it can bend in almost any way, including completely backwards to lay on top of itself. Now, consider two layers. If we bend one edge of the metal upwards, the lower layer has to move a larger distance and wrap around the upper layer, so it is pulled apart in addition to being bent. Since the layers are bonded to each other, this means you have to break molecular bonds somewhere in order for the metal to bend. This breaking of bonds requires a lot of energy. A sheet of metal has millions or billions of these layers, so you need a lot of energy to break them. That's why thick pieces of metal are much harder to bend or break than thin pieces.

This is also why wire cables are made up of many thin strands of wire. When you bend the cable, the outside wires are able to slip past each other and move, which prevents them being stressed and pulled apart, which would break the cable after only a few bending actions.

Of course, that's all a very, very simplistic explanation. Metallic bonding is not quite the same as I've explained above, but I think my explanation hits somewhere around the mark.

Why does the blade edge powered by velocity and mass resists deformation much better, if the pressure to it and the sheet is the same ?

The molecules at the edge of the blade are forced backwards by the impact, but like I explained above they have nowhere to go so the axe doesn't bend or break like the sheet of metal does. Well, it doesn't bend anywhere close to as much as the sheet of metal does. The molecules on the edge of the axe are usually pushed sideways by the force of the impact since there are no other molecules occupying those spaces, but only a relatively small portion of the impact energy goes into this.

 

[sophiecentaur]

Why does the blade edge powered by velocity and mass resists deformation much better, if the pressure to it and the sheet is the same ?

Materials tend to be stronger in compression than under tension. The edge of the axe blade is under pressure but the acute angle of the blade is producing tension in the bottom of the crack that it forms. The force needed to cause the split will depend upon the actual width of the workpiece so the deformation can be greater in the crack with a narrow piece, making the wedged tool more effective. The sides of the vee are easier to push apart with a thin piece so the stress where the blade edge is pushing will be greater.

 

[mfb]

Imagine an axe going through a sheet of metal, both made of the same probe.

While you can do that for a while (see previous posts for the reasons), it will make your axe blunt over time. Usually tools are made out of material that is stronger than the materials they are designed for.

 

[sophiecentaur]

While you can do that for a while (see previous posts for the reasons), it will make your axe blunt over time. Usually tools are made out of material that is stronger than the materials they are designed for.

Although tools are usually tougher than the stuff they work on the 'tool' tends to have the advantage over the work material so you can actually work on hard material with a softer tool material. They 'cleave' diamonds with a steel chisel and that relies on the crystal structure which has comparatively weak 'cleavage planes'.
But the "tearing" that's in the question doesn't even need a cutting tool. It's the geometry of the situation when a tear forms, that puts maximum stress at the bottom of the vee. We've all tried to tear plastic food packets that just refuse to tear in one place but, move to a different place on the edge (or bite it) and it gives in so easily- all you need is that initial tiny tear.

 

[Nick23]

Thank you all for such detailed replies, it's been really helpful. I need to read more on physics )

It's the geometry of the situation when a tear forms

- In my understanding, this sums it up best. Thank you sophiecentaur.

 

[sophiecentaur]

I plan to write a book about this to help people understand the subject better.

"Tears without tears"

 

[Nick23]

Awesome ! One more question then. If the axe is heated, it will penetrate easier (like an armor-piercing sabot round), but it will also deform easier. How do they calculate the temperature at which the maximum penetration will be possible while maintaining the situation at which geometry of piecing remains intact ?

 

[sophiecentaur]

Awesome ! One more question then. If the axe is heated, it will penetrate easier (like an armor-piercing sabot round), but it will also deform easier. How do they calculate the temperature at which the maximum penetration will be possible while maintaining the situation at which geometry of piecing remains intact ?

I would bet they base the design on measurements at least as much as calculation.
The situation with ordnance is a lot different from that of tools, which need to be used many times. If the axe were to deform after one operation, it could be useless for the next job.