Week 3 Flashcards
Types of shear in homogeneous PLANE strain (k=1)
PURE
SIMPLE
Pure shear
Decrease z
Increase x
Same y
/\V=0
Fixed principle axes = coaxial
Pure shear structures
Symmetric
Strain ellipse looks squished
Material lines rotate towards x-axis
Simple shear
No length change
No strain
TRANSLATE upper block // to shear zone margins (SHEAR PLANE)
Principal axes rotat = non-coaxial
Simple shear structures
Asymmetric
Strain ellipse ‘skewiff’
Material lines rotate in same sense as x-axis i.e. towards the shear plane
Angular shear, Ψ =
change in angle between 2 originally perpendicular lines after deformation
Shear strain, γ =
tanΨ
Kinematic vorticity, W(k) =
total angular velocity of material lines:strain rate
Kinematic vorticity in pure shear
= 0
- angular velocities of material lines cancel
Kinematic vorticity in simple shear
= 1
- angular velocities > 1
“Spectrum of plane strain deformations”
Pure –> simple –> rigid rotation
increasing W(k) –>
Shear zones
Strain highest at centre
Domains homogeneous
Zone itself heterogeneous
What plane must you observe shear zones in?
THE X-Z PLANE
Stereograph steps:
- Count to strike and mark
- Spin mark to nearest pole
- Count IN to dip
- Follow circle line
= plane for line
= dot for plunge/azimuth
- Count 90’ from line = pole to plane
Assumption with vorticity
The e.g. coral originally grew perpendicular to the bed
How must we view shear sense indicators in order to determine sense of shear?
In the XZ principal plane of finite strain
δ-type porphyroclasts
Rotate more rapidly than they deform = supersimple shear
σ-type porphyroclasts & mica fish
Deform more rapidly than/as rapidly as they rotate = simple to subsimple shear
‘Toothpaste effect’
During pure shear strain, the boundaries between deformed/undeformed rocks must form discontinuities = strain compatibility problem (continuity across shear zone boundaries is lost)
- shear zone has to extrude laterally while wall rock remains undeformed
= CRUSTAL DEFORMATION ZONES SHOULD BE DOMINATED BY SIMPLE SHEAR, ALTHOUGH DEVELOPMENTS OF FAULTS AND OTHER STRUCTURES MAY DEPART FROM THIS
i.e. shear zone will parallel boundaries is not compatible with (cannot accommodate) pure shear
Why doesn’t the ‘toothpaste effect’ occur during simple shear?
The shear plane is a surface of no finite strain
Also applies to heterogeneous strains - easy in simple shear to vary strain with no holes, overlaps developing
What is required for the state of strain in two adjacent layers to be compatible?
The section through their respective strain ellipsoids parallel to their interface must be identical
What do/do not stereographic projections preserve?
DO: angular relationships between lines and planes
DON’T: spatial relationships
