Basically the force exerted

F is in N, A0 is in m^2 (or in^2) 
Stress is in N/m^2 (= 1 Pa)

Basically the change in length, as a result of stress

Can be tension, compression, shear, rotational.

Same as tensile test, except you get negative strain (length gets smaller)

For most materials stressed in tension and at relatively low levels: 

E is the modulus of Elasticity (in GPa or psi)
- metals and ceramics have similar E's, with ceramics having a slightly larger E generally
- polymers have a very low E
- when stress and strain are proportional, elastic deformation occurs (no permanent deformation)

As temperature increases, E decreases (for most materials, except for some rubbers).

where G is modulus of elasticity

Elastic strain is manifested as stretching of interatomic bonds. The stronger the bonds are, the more force (so more strain) required to pull the bonds apart: 

E is the slope of the above graph.

Basically the ratio of the lateral and axial strains.

Capacity of a material to absorb energy when it is deformed elastically, and then upon unloading, to have this energy recovered. 

Permanent, nonrecoverable deformation.  On the atomic scale, bonds break with atom neighbors, and reform with new neighbors - called "slip"

Point at which plastic deformation begins (aka proportional limit). Point P on graph:

Measure of the degree of plastic deformation that has been sustained at fracture.

Maximum stress the material can ever take. Point M (with fracture at point F):

Several definitions:
- resistance to fracture when a crack (defect) is present 
- ability of material to absorb energy and plastically deform before fracturing