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: Translation — movement of rocks Rotation 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) ė = e/t and units are s-1 Elongation per second, so 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