
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 Before annealing Expansion Wrinkling • Small islands expand • Large islands wrinkle and fracture
Stress as a function time s Liang et al. Acta Mater. 50, 2933 (2002)
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
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)
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)
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
Length scale Time scale Steady velocity Steady Crack Growth viscous underlayer Liang, Huang, Prévost, Z. Suo, Experimental Mechanics 43, 269 (2003).
Kc Subcritical V-K curve Kth Subcritical Cracking and Creep Crack Velocity, V Stress Intensity Factor, K
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
n-creep Power law creep underlayer Delayed crack growth Liang, Zhang, Prevost, Suo, Int. J. Fracture. In press
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)
Coupled creep and diffusionin body of a single atomic species
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
Energetics Define driving forces as energy-conjugates: power dissipation kinematic constraint power supply Suo and Kubair
Kinetics diffusion creep
A synthesis of Stokes’s creep and Herring’s diffusion Summary of equations for v and s
Example: thin foillateral expansion/contraction 2H J is independent of force balance
Coupled creep and diffusion in a binary solution • A synthesis of • Stokes’s creep • Herring’s stress-driven diffusion • Darken’s nonreciprocal diffusion