Transcript Strain: Making ordinary rocks look cool for over 4 billion years

Strain: Making ordinary rocks
look cool for over 4 billion years
Goals: To understand homogeneous,
nonrecoverable strain, some useful
quantities for describing it, and how we
might measure strain in naturally deformed
rocks.
Deformation vs. Strain
Deformation is a reaction to differential stress.
It can involve:
a) Translation — movement of rocks
b) Rotation
c) Distortion — change in shape and/or size.
Distortion = Strain
Folded single layer can serve as an example
of deformation that involves translation,
rotation, and distortion.
Recoverable vs.
nonrecoverable strain
• Recoverable strain: Distortion that goes
away once stress is removed
– Example: stretching a rubber band
• Nonrecoverable strain: Permanent
distortion, remains even after stress is
removed
– Example: squashing silly putty
Strain in 2-D
• Elongation (e) change in length of a line
– e = (L - L0)/ L0
L = deformed length
L0 = original length
– Elongation often expressed as percent of the
absolute value, so we would say 30%
shortening or 40% extension
Strain in 2-D
Strain ellipse: Ellipse formed by subjecting a
circle to homogeneous strain
Undeformed
Deformed
The strain ellipse
2 principal axes — maximum and minimum
diameters of the ellipse.
If volume is constant, average value of axes =
diameter of undeformed circle
=
Stretch (S): Relates elongation to the strain
ellipse
S = 1 + e = 1 + [(L - L0)/ L0]
Maximum and minimum principal stretches (S1
and S2) define the strain ellipse
S1 = 1 + e1
and
S2 = 1 + e2
S2
S1
The strain ratio is defined as S1/S2
• Magnitude of shape change recorded by
strain ellipse.
• Because it is dimensionless, the strain ratio
can be measured directly without knowing L0.
S2
S1
Strain in 3-D
• For 3-D strain, add a third axis to the strain
ellipse, making it the strain ellipsoid
• The axes of the strain ellipsoid are S1, S2,
and S3
• S1, S2, and S3 = Maximum, intermediate,
and minimum principal stretches
Three end-member strain ellipsoids
Constriction
S1 > S2 = S3
Plane strain
S1 > S2 > S3
Flattening
S1 = S2 > S3
We can plot 3-D strain graphically on a Flinn
diagram
Use the strain ratios — S1/S2 and S2/S3
Flinn
Diagram
We can also describe the shape of the finite
strain ellipsoid using Flinn’s parameter (k)
– k = 0 for flattening strain
– k = 1 for plane strain
– k = ∞ for constrictional strain
Activity
• As a group, measure S1/S2 and S2/S3 of
the flattened Silly Putty, Sparkle Putty, and
Fluorescent Putty balls from Monday
• Plot these results individually on a Flinn
diagram. Use different symbol for each
putty type
• Calculate Flinn’s parameter for the Silly
Putty
Strain rate (ė)
Elongation per second, so
ė = e/t and units are s-1
Calculate strain rate for your three putty
types
Natural strain markers
Sand grains, pebbles, cobbles, breccia
clasts, and fossils
Must have same viscosity as rest of rock