Rheology Flashcards
Homogeneous vs inhomogeneous
material
A homogeneous material has the same composition, texture, properties etc. everywhere.
Strictly homogeneous materials are rare in geology.
Statistic homogeneity is scale-dependent
Might be statistically homogeneous at outcrop and sample scale and inhomogeneous at microscopic scale
Isotropic vs anisotropic material
isotropic
same mechanical properties in all directions
reacts to stress identically regardless of the directions
Anisotropic
stress required to deform the material depends on the direction of the stress
-ie more stress is required to deform parallel to foliation
Elastic and anelastic behaviour
-no permanent distortion, strain recoverable
Elastic behavior:
strain is recoverable, add stress, it deforms, take away the stress the rock goes back to original form. This is instantaneous
Anelastic behavior:
-not an instantaneous change, it takes time to recover back to original form
The ease or difficulty of elastic behavior is measured by various modulus
Uniform hydrostatic pressure producing a uniform dilation:
Bulk modulus or modulus of incompressibility (K = ∆σ/∆v)
Uniaxial compression or tension: Young’s modulus (E = σ/ε)
Simple shear: Modulus of rigidity
(G = σs/γ)
What is Hookean elasticity and what does this mean for shear stress
This is when the relationship between stress (σ) and strain (ε) is linear
The decline in shear stress happens beyond the elastic limit when the material starts behaving plastically or fails
There is no permanent deformation or failure in Hookean materials, so shear stress does not reach a maximum and decline
Elastic - Elastic Limit - Permanent Initially, the material behaves elastically (Hookean).
At the elastic limit, it starts to deform permanently (plastic deformation).
Beyond this, strain accumulates permanently.
Viscous and plastic behaviour
strains are permanent and nonrecoverable
Ideally viscous behaviour
- the resulting strain rate (έ) is proportional to the applied stress.
σ = ηέ
(η is Newtonian viscosity, a material constant)
- show deformation throughout wherever a deviatoric stress is present.
-Materials with little internal structures (e.g., water) tend to behave in an inideally viscous manner, whereas crystalline materials rarely do
ideally plastic material
- does not deform if stress is below a critical value (σc) and cannot maintain a stress greater than σc. At σc it continuously deforms in a permanent manner.
-strain only takes place in localized regions where the critical value of stress is reached.
Brittle and ductile behaviour
Brittle behavior:
-Loss in cohesion
-break in cohesion across marked discontinuities
Ductile behavior:
-no loss of cohesion
-strain is distributed in a smoothly varying manner throughout the deforming mass
Brittle-ductile transition
- not a clear boundary
In geology,
- requires specification of the scale of observation.
- Ductility: capacity for undergoing permanent change of shape without fracturing at the scale of observation.
ie, microscopically brittle behavior may produce macroscopically ductile flow
describe the ductile behavior of rocks (strain hardening and softening)
Strain hardening:
gradual rise in the stress required to produce further deformation at the same strain rate.
- At lower T or higher strain rate (rapid deformation)
- atoms don’t have time to rearrange, dislocations pile up, making further deformation harder
The material becomes stronger but less ductile - At higher T or lower strain rate (slow deformation)
No Strain Hardening → Steady-State Deformation
material deforms at a constant stress level without hardening.
-atoms have time to rearrange
-dislocations continuously eliminated via recovery / recrystallization, material does not harden
Easier to deform (i.e. less stress is required) at higher T or lower strain rate.
Strain softening:
gradual decrease in the stress required to produce further deformation at the same strain rate
Creep behaviour: Flow under constant stress
Constant stress or creep experiments:
Deformation begins at a relatively high-strain rate (primary or transient creep) – steadily decreases
– constant strain rate (steady state;
secondary or steady-state creep)
– strain rate increases again (due to fracture or recrystallization; tertiary or accelerating creep)
What is steady state deformation and at what scale is it applicable in geology
Deformation at a constant strain rate and at a constant stress.
Deformation of rocks in the crust may approximate steady state on a large scale.
-> Locally may be non-steady state deformation but most theoretical modeling of deformation assumes steady state deformation.
During steady-state creep, the stress is related to the strain rate by a power law:
έ = A exp -(Q/(RT))σN
έ = Strain rate
A = the frequency factor,
Q = activation energy for certain deformation mechanism
R = gas constant
T = temperature in degrees K
N = stress exponent
N = 1 (Nabarro-Herring creep):
- material is behaving as a perfectly viscous fluid.
- Crystalline material when the mechanism of deformation is diffusion of vacancies through the grains from one grain boundary to another
N > 1
- Most crystalline materials at moderate temperatures (e.g. half the melting point)
- Commonly N = 3 or 5
- creep is probably controlled by dislocation motion.
Factors affecting brittle or ductile behaviour
Temperature
strain rate (opposite effect to that of temperature)
-> at low t or high strain, limited atom movement, more brittle
-> at high t or low strain, more atom movement allowed, more ductile
confining & pore fluid pressure
high confining pressure → compression inhibits crack growth, more ductile
(this is why crust is brittle and mantle is ductile)
pore-fluid pressure
high pore-fluid pressure → fluids push cracks open, more brittle
material
- different bond structures behave differently
- stronger bonds (ionic, covalent) less atom movement, more brittle
- metallic bonding, mobile dislocations, more ductile
- layered structures (Mica & Clay minerals), easy slip along planes, more ductile
Rheology of the lithosphere
depth ->increasing t and p
-> rock strength increases
with increasing depth:
brittle, brittle-ductile transition, ductile
Homologous temperature
ratio of material temperature to melting temperature
uses melting temperature as the standard to compare different materials
ie if two materials are 50% to the melting temperature, they should behave similarly
-makes it possible to compare deformation of materials with different melting temperature
eg., ice and olivine should behave similarily at TH = 0.95
-> ice at -14ºc (TH=.95) should behave similarly to olivine at 1744ºc (also TH=.95)
competence
denote contrast in strength
competent and incompetent are relative to each other
the competent material is able to support a higher deviatoric stress (more difficult to deform) than an incompetent material
eg, quartzite vs shale
-q is competent and s is incompetent
stronger material than q vs q
- stronger material is competent and q is incompetent
