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

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

2. Goals: To understand homogeneous, nonrecoverable strain, some useful quantities for describing it, and how we might measure strain in naturally deformed rocks.

3. 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

4. Folded single layer can serve as an example of deformation that involves translation, rotation, and distortion.

5. 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

6. 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

7. Strain in 2-D Strain ellipse: Ellipse formed by subjecting a circle to homogeneous strain Undeformed Deformed

8. 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 =

9. 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

10. 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

11. 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

12. Three end-member strain ellipsoids Constriction S1 > S2 = S3 Plane strain S1 > S2 > S3 Flattening S1 = S2 > S3

13. We can plot 3-D strain graphically on a Flinn diagram Use the strain ratios — S1/S2 and S2/S3

15. Flinn Diagram

16. 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

17. 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

18. Strain rate (ė) Elongation per second, so ė = e/t and units are s-1 Calculate strain rate for your three putty types

19. Natural strain markers Sand grains, pebbles, cobbles, breccia clasts, and fossils Must have same viscosity as rest of rock