Structures Exam 2

Homogenous strain

All parts of material undergo same magnitude and direction of strain

Inhomogeneous strain

Deformation varies across material

Elongation formula (part added)

e = (lf - lo) / lo

Stretch formula (final length / original length)

S = 1 + e

Stretch along X direction

greater or equal to 1; positive elongation

Stretch along Z direction

less than or equal to 1; negative elongation

Angular shear (psi)

Change in angle measured between two initially perpendicular lines

Shear strain (gamma)

Tangent of angular shear (psi)

Volumetric strain

Change in volume / Original volume

Volumetric strain = 1

(Stretch X) (Stretch Y) (Stretch Z) = 1

Plane strain

X > Y = 1 > Z; intermediate strain elipsoid; k = 1

Constrictional strain

X > Y = Z; prolate ellipsoid; k > 1

Flattening strain

X = Y > Z; oblate ellipsoid; k < 1

k-value

K-value = (a - 1) / (b - 1)

Strain

Internal change of points in a body relative to one anothe

Translation

Rigid body movement between locations

Rotation

Rigid body turning without shape change

Finite strain

Accumulated strain after the entire deformation history

Incremental strain

Infinitesimally small amount of strain occurring in single instant

Strain path

History and sequence of all incremental strains; adds to finite strain

Finite strain ellipses

Only perfectly align with each other if strain path is entirely coaxial (pure shear)

Pure Shear (coaxial)

The principal strain axes (X and Z) do not rotate during deformation; lines parallel to X and Z do not rotate

Simple Shear

Principal strain axes constantly rotate during deformation

Lines of No Instantaneous Stretch

Two perpendicular lines that divide the instantaneous shortening field from the instantaneous lengthening field (X for pure shear, + for simple shear, they don’t rotate)

Hooke’s Law for Elastic Behavior

Stress = Youngs Modulus (E) * Strain

Equation for Linear (Newtonian) Viscous Behavior

Stress = Viscosity * Strain Rate

Perfectly Plastic Behavior

Zero strain before yield stress is reach; continuous strain after yield stress is reached

Graphs for elastic and plastic hehavior

Elongation (e) = x, Stress = y, Young’s Modulus (E) = slope

Graph for viscous behavior

Strain rate = x, Stress = y, Viscosity = slope

Poisson’s ratio for viscous behavior

Viscosity = | elongation perpendicular to stress / elongation parallel to stress |

Increasing temperatures _____ ductility

Increases

Increasing confining pressure ____ ductility

Increases

Increasing strain rate _____ ductility

Decreases

Increasing fluid pressure ____ ductility

Decreases

Cataclastic flow

Physical crushing, fracturing, and sliding of grains past one another. It occurs at shallow depths and low temperatures. Not localized at meso scale. Ductile at macro scale, brittle at micro scale.

Crystal plasticity

Movement of crystal defects at high P/T causes strain

Diffusional mass transsfer

Movement of atoms due to fluids (pressure solution) or high P/T and small grain size (Coble/NH) causes strain

Vacancies

When atoms are missing in crystal lattice; allows for climb

Interstitial impurities

Extra atom is squeezed between crystal lattice; blocks edge dislocation at low temp

Substitutional impurities

Incorrect atom in crystal lattice; blocks edge dislocation at low temp

Edge dislocation (crystal plasticity)

When extra-half plane of atoms is wedged within crystal lattice

Dislocation glide (crystal plasticity)

Shear stress causes slip along glide plane (perpendicular w/ half-plane; intersects at bottom edge)

Cilmb (crystal plasticity)

Obstacle in dislocation, bottom atom in half-plane drops into adjacent vacancy, moving up glide plane (favored by high T)

Undulose extinction (crystal plasticity)

Dislocations pile up due to obstacles. Without climb, they gradually bend the crystal lattice, leading to smooth extinctional differences.

Subgrain formation (crystal plasticity)

Climb (and cross-slip) resolves dislocation pile-up, creating vertical dislocation walls that break up grains into sections with externally distinct, internally uniform extinction

Conditions favoring cataclastic flow

Shallow upper crust and upper fault zones (Low T, Low Pc, Low Sigmad)

Conditions favoring crystal plasticity

Mid crust to lithospheric upper mantle (High T, High Pc, High Sigmad)

Conditions favoring pressure solution diffusion

Upper to mid crust (fluids, low–med T)

Conditions favoring Coble creep diffusion

Lower crust to upper mantle (dry, high T, extremely small grains)

Conditions favoring Nabarro-Herring Creep

Lower crust to lower mantle (dry, extreme T, small grains)

Fluid dislocation diffusion

Atoms dissolve into fluid in high stress boundaries and precipitate at low stress boundaries

Coble creep diffusion

Atoms migrate from high to low stress along grain boundaries

Nabarro-Herring creep diffusion

Atoms migrate from high to low stress along solid crystal interior

Dislocation Glide Equation (hypothetical crystal plasticity when no glide obstacles)

Strain rate = A e^(stress) e^( -activation energy / RT)

Dislocation Creep Equation (crystal plasticity irl with glide obstacles)

Strain rate = A (stress^n) e^( -activation energy / RT)

Coble Creep Equation for dry diffusion

Strain rate = A (stress) e^( -activation energy / RT) * grain size^(-3)

Nabarro-Herring Creep equation for dry diffusion

Strain rate = A (stress) e^( -activation energy / RT) * grain size^(-2)

``Hinge line

Line of maximum curvature along surface of fold

Limbs

Relatively straight sides of a fold located between hinges

Inflection points

Points o limbs where direction of curvature reverses.

Axial surface

Plane connecting all hinge lines of stacked folded layers

Crest/Trough

Highest and lowest geographic points of folds

Amplitude

Half the height of a fold measured from crest to trough

Wavelength

Distance between two adjacent hinges of same orientation

Profile plane

2D cross-section of fold perpendicular to the hinge line.

Interlimb angle Angle between the tangent of inflection point on each limb

Enveloping surface

Imaginary plane tangent to all crests/troughs of a fold train.

Antiform

A fold that closes upward

Synform

A fold that closes downward

Anticline

A fold with the oldest rocks in its center

Syncline

A fold with the youngest rocks in its center

Fold facing

Direction where layers get progressively younger along axial surface

Cylindrical fold

Fold in which hinge line is straight with a consistent trend and plunge

How to test for a cylindrical fold on a stereonet

Cylindrical if poles of bedding planes align along one great circle (pi circle).

How to find the fold axis on a stereonet

Find pole to the pi circle

Fold vergence

Direction upper fold limb points (perfectly opposes dip direction of fold limbs)

Parasitic folds

Smaller, higher-order folds developed on the limbs of a larger fold

S and Z folds

Asymmetric parasitic folds on opposite limbs of a major antiform

M/W folds (significance)

Symmetric parasitic folds found at the hinge of a major fold; marks axial surface

Isogon

A line connecting points of equal dip on fold bedding

Parallel fold

Consistent layer thickness (t)

Similar fold

Consistent thickness parallel to the axial surface (T)

Axial-planar foliation

Cleavage parallel to axial surface