Gungnir

Let's take into account that the GPa of steel is anywhere between 190-210. However GPa is a measurement of square meters. We are currently working in centimeters, so lets go ahead and convert that over. .0127 m. is the current amount, and we will multiply that by our GPa here to get 2.413 GPa of stress would generally overpower a .0127 m. piece of steel. However, unfortunately this does not take into account the structural integrity of a cylinder.

So lets go ahead and use our functions to calculate the hoop, radial and axis stress of the product utilizing our information we've gathered so far. That's .861 GPa for the hoop stress, 0.689 GPa for the radial stress and 0.086 GPa for the axis stress.

A blade's contact surface area is generally around 4/16ths to 3/16ths of an inch depending on contact zone of the blade, as the blade tapers down when you get to the end. As we are using a different metric system, lets convert those inches over. 3/16ths of an inch is approx 0.477 cm., or 0.00476 m.

Beautiful! We have a stress level for the varying areas of the cylinder. Now all we have to do is calculate the Pa of an attack. How do we do that, you ask? Simple. We will use Newton's second law of motion in order to derive the number of N of an attack from a standard Gladius, which is approximately 1kg. We will assume that the swordsman is proficient, and can swing the blade at 22.352 m/s^2.

So that is N = Kg*m/s^2. You will find that a single sword strike from a Gladius that met the specifications from above would have 22.352 newtons of force.

Now that we have the newtons, its time to derive the Pa. 1 Pa is the N/m^2. Luckily, we have already derived the m of the surface area of the contact area of the Gladius as 0.00476 m, and our newtons have been determined to be 22.352. This part is simple math, and gives us 0.000986538 GPa from a sword strike at that level. This amount does not come close to the amount of force it would take to chop through a sheet of metal at .0127 m., let alone snap one in half.

However, the problem with this is that this does not take into account other forces and vectors from a circular nature; levers and fulcrums can easily change the output of newtons on an attack. Well, it was fun learning some things with you. Feel free to ask me any questions I might be able to try to explain with math in the future. Turns out we didn't use hoop, axis or radial stress levels, but if you would like to we could definitely explore those subjects as well. It would most certainly be my pleasure.