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Topics. Couple creep with wrinkling cracking diffusion. What came first, chicken or egg?. Chicken is egg’s way to make more eggs. Systems dynamics. s. SiGe island under compression. Strained SiGe island. glass. Si. Yin et al., J. Appl. Phys. 2003. Two Relaxation Modes.

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  1. Topics Couple creep with • wrinkling • cracking • diffusion What came first, chicken or egg? Chicken is egg’s way to make more eggs. Systems dynamics

  2. s SiGe island under compression Strained SiGe island glass Si Yin et al., J. Appl. Phys. 2003

  3. Two Relaxation Modes Before annealing Expansion Wrinkling • Small islands expand • Large islands wrinkle and fracture

  4. Stress as a function time s Liang et al. Acta Mater. 50, 2933 (2002)

  5. Film on elastic substrate a Film on viscous layer Gradual loss of constraint Viscous layer   h Constraint, and its gradual loss Free-standing film  a  h l ~ a

  6. elastic film: plane stress dx  h  H viscous layer: pure shear Diffusion-like equations. Effective diffusivity: 2D Shear Lag Model Huang, Prevost, Suo, Acta Mater. 50, 4137 (2002)

  7. Length scale = Dimensional consideration Analytical solution (Laplace transform) • Gradual loss of constraint: • When t = 0, K = 0 • When t = ∞, K = ∞ • Delayed growth when K = Kc Stationary long crack, blanket film K(t)

  8. y L time x L 2a L L t = 10.0 K = 0.441 t = 0.05 K = 0.264 t = 1.0 K = 0.604 t = 3.0 K = 0.722 Stationary finite crack, island film

  9. Length scale Time scale Steady velocity Steady Crack Growth viscous underlayer Liang, Huang, Prévost, Z. Suo, Experimental Mechanics 43, 269 (2003).

  10. Kc Subcritical V-K curve Kth Subcritical Cracking and Creep Crack Velocity, V Stress Intensity Factor, K

  11. Liang, Huang, Prevost, Suo, Experimental Mechanics, 43, 269 (2003). Ratcheting-Induced Stable Crack (RISC) Huang, Suo, Ma, Fujimoto, J. Mater. Res, 15, 1239 (2000). Begley, Evans, J. Appl. Mech., 68, 513 (2001). Tensile Film Ratcheting Layer Cyclic temperature

  12. n-creep Power law creep underlayer Delayed crack growth Liang, Zhang, Prevost, Suo, Int. J. Fracture. In press

  13. Examples of stress generation INTEFACIAL PROCESS Deposition-induced compression (chemical potential excess) Solidification Oxidation-induced tension: Ni (chemical potential deficit) Oxidation-induced compression: Si Chason et al. PRL 88, 156103 (2002) NONRCIPROCAL DIFFUSION (Kirkendall effect) Diffusion couple: ZnCu COMBINED EFFECTS Selective oxidation: NiAl Selective evaporation: ZnCu Suo, Kubair, Evans, Clarke, Tolpygo Acta Materialia 51, 959 (2003)

  14. Coupled creep and diffusionin body of a single atomic species

  15. Suo, Kubair, Evans, Clarke, Tolpygo Acta Materialia 51, 959 (2003) Net flux is divergence-free net flux diffusion flux convection Strain-rate Diffusion-induced strain-rate (isotropic placement rule) Creep strain-rate Kinematics v N

  16. Energetics Define driving forces as energy-conjugates: power dissipation kinematic constraint power supply Suo and Kubair

  17. Kinetics diffusion creep

  18. A synthesis of Stokes’s creep and Herring’s diffusion Summary of equations for v and s

  19. Example: thick substratestress generation J

  20. Example: thin foillateral expansion/contraction 2H J is independent of force balance

  21. Coupled creep and diffusion in a binary solution

  22. Coupled creep and diffusion in a binary solution • A synthesis of • Stokes’s creep • Herring’s stress-driven diffusion • Darken’s nonreciprocal diffusion

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