Stress is defined as a force applied over an area, and has the dimensions F/A.
Shear is a stress that results from the opposition of forces that are not aligned (F/A).
Strain is defined as deflection divided by the original dimension, and is a measure of
deformation, that is, the differential change in size, shape, or volume of a material. Strain is dimensionless.
The
modulus of elasticity is stress divided by strain.
Lithostatic stress or
confining pressure is
uniform stress that operates equally in all directions in rocks. Confining pressure is due to the burden of overlying rock, just as seawater exerts equal pressure from all directions at depth.
Differential or
divertorial stress results from
compressional or
extensional tectonic stresses that are
not equal from all directions:
tensional stress (stretching),
compressional stress (squeezing), or
shearing stress (side to side shearing). Compressional stresses act along the direction of maximum principal stress, whereas extensional stresses act along the direction of minimum principal stress.
For the mutually orthogonal directions along which stress is applied, the
▪ maximum principal stress direction is designated σ
1 ,
▪ minimum principal stress direction is σ
3 , and
▪ intermediate principal stress direction is designated
σ2 .
▪ normal stress, directed perpendicular to a given plane is designated, σ
η▪ shear stress, directed parallel to a given plane is designated, σ
τ▪ vector components of stress can be expressed according to Cartesian coordinate system as 9 components (x,y, z combinations) relative to the 3 mutually perpendicular x-y-z axes
Materials differ in their responses to stress, depending upon composition, conditions of temperature and confining pressure, and strain rate. However, regardless of intrinsic degrees of brittle or ductile qualities, all strained materials pass through 3 successive stages of deformation:
elastic,
ductile, and fracture (failure, or
brittle deformation). Provided that the
strain rate is sufficiently slow to allow minerals to accommodate structurally, minerals can adjust to applied stresses by a variety of mechanisms.
In
elastic deformation, rock changes shape by a very small amount and the deformation is
not permanent. Elastic deformation occurs only with small differential stresses, which are less than the rock's yield strength. Rock adjacent to failed rock in earthquakes propagates seismic waves by elastic deformation, then springs back to its original shape in elastic rebound. For this reason, structural damage to rocks and formations provides the only evidence of passage of past seismic waves.
In
ductile deformation, rock deeper than
10-20 km is subjected to enormous lithostatic stress, and the high temperatures of burial render the hot rock softer and more malleable. At these depths, in the lower continental crust and mantle, rock undergoes plastic deformation and flows in response to application of a differential stress that is stronger than its yield strength. Rock undergoes ductile deformation by gradual creep along crystal grain boundaries and planes within crystal lattices. Ductile deformation in generates
folding and ductile
shear zone features, such the
dynamic metamorphic
mineralogical and
textural changes seen in
foliated schistose,
banded,
lineated, and
augen-structured dynamic metamorphic rocks,
mylonites,
distorted porphyroclasts and
mica fish,
phyllonites.
In
brittle deformation close to the Earth's
surface, where rocks are comparatively cool, rock behaves in a brittle fashion, fracturing in response to differential stress greater than the rock's yield strength. Rock failure and fracture generates
faulting,
brecciation,
pseudotachlites, cataclasis, and
slickenside striations. Rock adjacent to the failed rock springs back to its original shape in the elastic rebound that is responsible for earthquakes.
Labels: brittle, ductile deformation, elastic, modulus of elasticity, shear zones, strain, stress
