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ANELASTICITY Some Background, Mechanisms and Recent Work

ANELASTICITY Some Background, Mechanisms and Recent Work. Aaron Vodnick MSE 610 4/25/06. Why I Care. - From room temp, heat to zero stress and hold. - Thin Cu Film on a Si Substrate. - Temperature represents total strain. - Stress increases with time.

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ANELASTICITY Some Background, Mechanisms and Recent Work

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  1. ANELASTICITY Some Background, Mechanisms and Recent Work Aaron Vodnick MSE 610 4/25/06

  2. Why I Care - From room temp, heat to zero stress and hold. - Thin Cu Film on a Si Substrate - Temperature represents total strain - Stressincreases with time - Stress proportional to elastic strain So… there’s some anelastic mechanism here I want to understand

  3. Conditions for Ideal Elasticity • Each level of applied stress has a unique equilibrium value of strain • The equilibrium response is achieved instantaneously (phonon velocity) • The response is linear (doubling the stress doubles the strain) s E 2s s e e 2e First – Ideal Elasticity Hooke’s Law Isotropic: Anisotropic: e t s t - Easing conditions allows us to generalize elastic behavior

  4. Conditions for Ideal Elasticity Conditions for Anelasticity • Each level of applied stress has a unique equilibrium value of strain • The equilibrium response is achieved instantaneously (phonon velocity) • The response is linear (doubling the stress doubles the strain) • Each level of applied stress has a unique equilibrium value of strain • The equilibrium response is achieved only after the passage of sufficient time • The response is linear (doubling the stress doubles the strain) Equilibrium strain. Load Removed Load Applied Complete Recoverability t Anelasticity Relax the 2nd condition for Ideal Elasiticity e

  5. Other Behaviors Sometimes people use the term “Anelastic” when it isn’t appropriate

  6. E2 E1 Describing Anelasticity: SLS Standard Linear Solid Describing stress-strain behavior: 2 1 General linear equation describing model

  7. Apply Constant Strain Apply Constant Stress s0 e eR sR e0 t E2 t E1 SLS Creep Behavior Equation Describing Behavior Where t’s are time constants and ER is the relaxed modulus

  8. f Dynamic Behavior f is the “loss angle” or “internal friction” –the angle the strain lags the stress. It is a measure of energy absorbed in each cycle Dynamic tests give behavior over short times – but can relate to relaxations • Common Measurement methods: • Resonant Vibrations • Wave propagation Can calculate activation energies by measuring internal friction as a function of temperature

  9. Characterization

  10. Some Mechanisms

  11. Snoek Relaxation • Interstitial Relaxation • Defect Symmetry: • - For point defect relaxations, defects must have a symmetry less than lattice • BCC Octahedral interstitial have tetragonal symmetry (not cubic) • - Creates an “Elastic Dipoles” (three types) • Dipole can “feel” external stresses • These types of point defects don’t exist in FCC crystals. Can get relaxations with point defect pairs.

  12. Snoek Relaxation Diffusion to z-sites e Saturation Equal distribution • Consider a tensile stress along the Z axis of a [001] crystal • Tetragonal axis of z-sites elongates • Tetragonal axis of x,y-sites shortens • Driving force to diffuse to low energy sites • Kinetic process time

  13. Grain Boundary Sliding (Grain) Shear stresses act across grain boundaries • Viscous slip occurs at boundary (Dx) • Grain corners sustain more of shearing force • Stress at corners provide driving force for reverse slip The potential relaxation strength is given by: So, the potential relaxation is >50% of the initial strain. (this is big) Remember: So:

  14. Grain Boundary Sliding Relationship with Stacking Fault Energy • Grain boundaries composed of dislocations • Sliding may be associated with dislocation motion • Stacking fault energy represents dislocation “width” when it spreads • -- These models are not very realistic because it ignores strong interactions of dislocations with boundaries

  15. Grain Boundary Sliding Effect of Solutes Solid Solution • Second peak appears and grows with impurity addition • Boundaries contain steps/ledges • Migration smoothes boundaries • Occurs by solute drag at high concentration • Rate controlling step is slower of two Pure Metal Cu – 0.1% Ni Cu – 0.5% Ni Self Diffusion migration Sliding

  16. Final Configuration Dislocations Example of dislocation in thin metal film • Dislocation is anchored at film surfaces • Segments bow and exert force f on Jogs • Diffusion occurs to drag jogs to final configuration • Line tension restores initial configuration upon removal of stress Pinning points could also be things such as dragged solute atoms Choi and Nix, 2006

  17. Thin Film Measurement • Si cantilevers microfabricated and coated with films to be tested • Electrostatic force from AC voltage vibrates cantilever • AC voltage turned off, decay of velocity is measured • Internal friction from rate of amplitude decay • Determine activation energy from frequency dependence on peak temp. Internal Friction Choi and Nix 2004 and 2006

  18. Final Statements • Anelasticity is in fact mind numbing • Few people have cared about it since before the seventies • There is some new interest in determining mechanisms governing material behaviors on small scales • Any time-dependent, reversible, processes can cause anelasticity

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