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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.

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Presentation on theme: "Topics Couple creep with wrinkling cracking diffusion What came first, chicken or egg? Chicken is egg’s way to make more eggs. Systems dynamics."— Presentation transcript:

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

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

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

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

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

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

8 Stationary finite crack, island film x y L L LL 2a2a time t = 0.05 K = t = 1.0 K = t = 3.0 K = t = 10.0 K = 0.441

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

10 Subcritical Cracking and Creep Stress Intensity Factor, K Crack Velocity, V K th KcKc Subcritical V-K curve

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

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

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

14 Coupled creep and diffusion in body of a single atomic species

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

16 Energetics Define driving forces as energy-conjugates: Suo and Kubair power dissipationpower supplykinematic constraint

17 Kinetics diffusion creep

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

19 Example: thick substrate stress generation J

20 Example: thin foil lateral expansion/contraction J is independent of 2H force balance

21 Coupled creep and diffusion in a binary solution

22 A synthesis of Stokes’s creep Herring’s stress-driven diffusion Darken’s nonreciprocal diffusion


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