Editing Structural geology (section)

==Characterization of the mechanical properties of rock==
The mechanical properties of rock play a vital role in the structures that form during deformation deep below the earth's crust. The conditions in which a rock is present will result in different structures that geologists observe above ground in the field. The field of structural geology tries to relate the formations that humans see to the changes the rock went through to get to that final structure. Knowing the conditions of deformation that lead to such structures can illuminate the history of the deformation of the rock.

Temperature and pressure play a huge role in the deformation of rock. At the conditions under the earth's crust of extreme high temperature and pressure, rocks are [[Ductility|ductile]]. They can bend, fold or break. Other vital conditions that contribute to the formation of structure of rock under the earth are the [[Stress (mechanics)|stress]] and strain fields.

===Stress-strain curve===
Stress is a pressure, defined as a directional force over area. When a rock is subjected to stresses, it changes shape. When the stress is released, the rock may or may not return to its original shape. That change in shape is quantified by strain, the change in length over the original length of the material in one dimension. Stress induces strain which ultimately results in a changed structure.

Elastic deformation refers to a reversible deformation. In other words, when stress on the rock is released, the rock returns to its original shape. Reversible, linear, elasticity involves the stretching, compressing, or distortion of atomic bonds. Because there is no breaking of bonds, the material springs back when the force is released. This type of deformation is modeled using a linear relationship between stress and strain, i.e. a [[Hooke's law|Hookean]] relationship.

:<math> \epsilon = \frac{\sigma}{E} </math>

Where σ denotes stress, <math> \epsilon </math> denotes strain, and E is the [[elastic modulus]], which is material dependent. The elastic modulus is, in effect, a measure of the strength of atomic bonds.

[[Plastic Deformation|Plastic deformation]] refers to non-reversible deformation. The relationship between stress and strain for permanent deformation is nonlinear. Stress has caused permanent change of shape in the material by involving the breaking of bonds.

One mechanism of plastic deformation is the movement of dislocations by an applied stress. Because rocks are essentially aggregates of minerals, we can think of them as poly-crystalline materials. Dislocations are a type of crystallographic defect which consists of an extra or missing half plane of atoms in the periodic array of atoms that make up a crystal lattice. Dislocations are present in all real crystallographic materials.

===Hardness===
Hardness is difficult to quantify. It is a measure of resistance to deformation, specifically permanent deformation. There is precedent for hardness as a surface quality, a measure of the abrasiveness or surface-scratching resistance of a material. If the material being tested, however, is uniform in composition and structure, then the surface of the material is only a few atomic layers thick, and measurements are of the bulk material. Thus, simple surface measurements yield information about the bulk properties. Ways to measure hardness include:

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* [[Mohs Scale]]
* [[Dorry abrasion test]]
* [[Deval abrasion test]]
* [[Indentation hardness]]
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Indentation hardness is used often in metallurgy and materials science and can be thought of as resistance to penetration by an indenter.

===Toughness===
Toughness can be described best by a material's resistance to cracking. During plastic deformation, a material absorbs energy until fracture occurs. The area under the stress-strain curve is the work required to fracture the material. The toughness modulus is defined as:
 
:<math> M_t = \frac{2}{3} \sigma_{UTS} \; \epsilon_f </math>

Where <math> \sigma_{UTS} </math> is the ultimate tensile strength, and <math> \epsilon_{f} </math> is the strain at failure. The modulus is the maximum amount of energy per unit volume a material can absorb without fracturing. From the equation for modulus, for large toughness, high strength and high ductility are needed. These two properties are usually mutually exclusive. Brittle materials have low toughness because low plastic deformation decreases the strain (low ductility). Ways to measure toughness include: [[Page impact machine]] and [[Charpy impact test]].

===Resilience===
Resilience is a measure of the elastic energy absorbed of a material under stress. In other words, the external work performed on a material during deformation. The area under the elastic portion of the stress-strain curve is the strain energy absorbed per unit volume. The resilience modulus is defined as:

:<math> M_R = \frac{(\sigma_y)^2}{2E} </math>

where <math> \sigma_y </math> is the yield strength of the material and E is the elastic modulus of the material. To increase resilience, one needs increased elastic yield strength and decreased modulus of elasticity.