Fissure Energy/Force Equation

Question

For this, I am trying to understand if it is a measure of force (Newtons) or energy (Joules ) of when fissures are created, Fissures are where the ground is being torn up either by volcanic ventilation, or otherwise.

So whether it is measured in force or energy, I wish to know what is the best equation for this phenomenon to occur.

So the information I have that would further this is the area is 20.58 m^2, the depth is 30,000 m. and it happened in just a second.

I thought it would be used for Tensile Strength with Silicon with the yield strength of 180 MPa.

Answer 1

Force is used to (try to) move objects apart. Energy is expended as the objects move and thereby separate. In a pure physics sense, until an object moves, absolutely no work energy is expended. You can push on a wall all you want with as much force as you want but, unless the wall moves, you do no work.

A stress-strain curve of a materials is a map of force to cause a deformation. The area under the curve is a map of the energy to cause the deformation. Up to the yield stress, the area is resilience. This is the energy expended to cause elastic deformation of the material. Because the stress strain curve is a straight line in the elastic region, the functional form of resilience $R$ is

$$R = \sigma_y \epsilon_y / 2 = \sigma_y^2 / 2E $$

where $\sigma_y$ is yield stress, $\epsilon_y$ is yield strain, and $E$ is Young's (elastic) modulus.

A further stress-strain function happens up to breaking. The total area under the stress-strain curve to break is toughness. The stress strain curve is not linear in this region. Integration methods are required.

The fissure forms because the material breaks, not because it reaches the end of its elastic deformation. The force needed is the obtained from the true breaking stress of the material. The energy required is obtained as the toughness of the material.

Ductile materials have a yield, a tensile, and a breaking stress. The tensile strength is the point where the material begins to neck. Think chewing gum stretched ... necking is where the gum thins.

Perfectly brittle materials have no yield. They just fail after elastic deformation. The toughness is the resilience in this case.

Many cases for materials that show only modest if any ductility and no necking assign the yield stress as the failure stress and ignore breaking stress. The toughness is greater than resilience, but the distinction is not a hard one.

Resilience and toughness may appear to have the same units as stress (e.g. Pa = N/m$^2$). In reality, a better unit designation for both is energy per unit volume (e.g. J/m$^3$).