1/6<112>pairs Matrix (L12)

GBSource

Twin

Orthorhombic

Reordering

12

Ni

Al

Cubic (L12)

Possible Micromechanical Model For Microtwinning

Possible Micromechanical Model For Microtwinning

Energy of the 2-layer pseudotwin (~600 mJ/m2 ?)

Energy of the 2-layer true twin(15 mJ/m2 ?)

Possible Micromechanical Model For Microtwinning

Energy of the 2-layer pseudotwin (~600 mJ/mol?)

Energy of the 2-layer true twin(15 mJ/mol?)

ttttpt tKt ).exp()()(

Possible Micromechanical Model For Microtwinning

At steady state doing a work balance for a forward progress of b, we get:

bdtK

bdtbdlb

ttttpt

2

22

).exp()(

)()(

d2

l =Applied Stressb = Burgers Vector(t) = Fault Energypt =Pseudo Twin Energytt = True Twin EnergyK = Parameter determining the reordering

kinetics (K=Dord/x2, where x is a measure of the short range diffusion length)

t = timeTertiaties sheared athermally creating pseudotwins

Secondaries sheared athermally creating faults that eventually reorder into true twins

Unsheared ’

A pair of identical Shockleys on adjacent slip planes

Possible Micromechanical Model For Microtwinning

Velocity for diffusion-mediated glide:

Assumptions:• the energy penalty due to the twin

decreases exponentially with time• the shear of secondary ’ is thermally

assisted while the shear of tertiary ’ is athermal.

• the effective stress driving the shear of the secondary ’ is given by:

Strain rate:

Microstructure Parameters:

Obtain from direct TEM measurements

Key Model Parameters:

Obtain from transient creep experiments

or modeling

tptptptwin vb

).(

)(ln

2

2

2tttpeff

ttpttpordtp fb

f

x

bDv

tp

pttertiary

frictiontertiaryeff

b

f

3

Possible Micromechanical Model For Microtwinning

Applied Stress = 420 MPaTemperature = 950Kpt = 300 mJ/m2

tt = 20 mJ/m2

Dord/x2 = 0.18/sFriction Stress = 25 MPa

Applied Stress = 420 MPaTemperature = 950Kpt = 300 mJ/m2

tt = 20 mJ/m2

Dord/x2 = 0.18/sFriction Stress = 25 MPa

Effective stress dependence on tertiary volume fraction (for a given applied stress)

Velocity dependence on tertiary volume

fraction (for a given applied stress)

Possible Micromechanical Model For Microtwinning

Temperature = 950Kpt = 300 mJ/m2

tt = 20 mJ/m2

Dord/x2 = 0.18/sf2 = 0.3Friction Stress = 25 MPa

Dislocation velocity vs Effective Stress. Stress exponent of velocity for low stresses is very close to unity. When the

stress is large enough to athermally shear the secondaries, then there is “power-law” breakdown.

Possible Micromechanical Model For Microtwinning

If tertiary volume fraction is assumed to drop exponentially with time, then the transient creep behavior can be predicted