1. Thin Film Cracking Modulated by Underlayer Creep Rui Huang The University of Texas at Austin Collaborators: J. Liang, J.H. Prevost, Z. Suo

2. Creep and ratcheting induced cracks in thin films SiN film on Al (ratcheting) Huang, Suo, Ma, J. Mech. Phys. Solids 50, 1079 (2002) SiGe film on glass Huang, et al., Acta Mechanica Sinica (2002).

3. h l ~ a  a  Free-standing film Gradual loss of constraint due to creep Film on elastic substrate a h  Viscous layer  Film on viscous layer Stress relaxes in crack wake, but intensifies at crack tip; Gradual loss of constraint (G 2  G 1 )

4. Cracking of a brittle film on a viscous layer Will a pre-exist crack grow? When will a pre-exist crack grow? How fast will a crack grow? Viscous layer 

5. 2D Shear Lag Model   dx H h Diffusion-like equations, Elsasser, 1969. Rice, 1980. Freund and Nix, 1999. Xia and Hutchinson, 2000. Huang et al., 2001. Viscous layer: pure shear Elastic film: plane stress

6. Gradual loss of constraint: When t = 0, K = 0 When t  ∞, K  ∞ Long crack will grow after a delay (when K = K c ) Stationary long crack Length scale = Dimensional consideration: Analytical solution: (Laplace transform) K

7. Stationary short crack Longer cracks are subject to delayed fracture. 0 When t  0, 1 When t = ∞, Very short cracks will never grow,

8. Delayed fracture KcKc a Cracks never grow 0 a Crack grows t 0 acac tmtm

9. Effect of edge relaxation x y L L LL 2a2a time t = 0.05 K = 0.264 t = 1.0 K = 0.604 t = 3.0 K = 0.722 t = 10.0 K = 0.441 Huang, et al., Acta Mater. 50, 4137 (2002).

10. Growing Cracks Crack growth criterion: Time scale: Length scale:  = 500 MPa E = 100 GPa,  = 10 GPa-s, h = 0.1  m, and H = 1  m Representative values  = 4  m, t 0 = 16 s

11. Numerical simulation of crack growth Transient state Stationary crack Steady state growth

12. Steady state velocity of crack growth Steady velocity is approached after the crack grows by a distance ~  Crack velocity can be readily measured experimentally, and can be use to determine the viscosity of the underlayer. Viscous layer  h H Liang, Huang, Prévost, Suo, Experimental Mechanics. In press.

13. Subcritical cracking Know the subcritical cracking V-K curve of the brittle film Measure crack velocity to determine the underlayer viscosity. Stress Intensity Factor, K Crack Velocity, V K th KcKc Subcritical V-K curve Steady state set by two kinetic processes: underlayer creep Subcritical bond break

14. Crack in a micro-bridge Viscous layer Substrate Brittle film LL 00 Stress Intensity Factor, K Crack Velocity, V Bridge length, L LcLc Critical legnth:

15. Viscoelastic underlayer Elastic underlayer (Xia and Hutchinson, 2000) rubbery glassy viscoelstaic days weeks years KcKc a No initiation 0 Delayed fracture Instant initiation Suo, prevost, Liang, submitted.

16. Nonlinear creep Power law creep: Stationary long crack: Steady state velocity: Measure crack velocity to determine the creep law (B, n) for the underlayer. Liang, Zhang, Prevost, Suo, submitted to Acta Mater.

17. Thin Film Ratcheting Huang, Suo, Ma, Acta Materialia 49, 3039-3049 (2001). Strain per cycle Uni-directional shear substrate metal film cyclic temperature cyclic stress Y strain stress E Ratching-creep analogy:

18. Ratcheting-induced crack Liang, Huang, Prevost, Suo, Experimental Mechanics, in press. Tensile Film Ratcheting Layer Cyclic temperature Stress intensity factor of a stationary long crack: Steady state growth rate:

19. Summary Underlayer creep induces loss of constraint on cracks in thin films. –A long crack starts to grow after a delay. –Subcritical cracking, modulated by underlayer creep, attains a steady state crack velocity. Extensions to viscoelastic and nonlinear creep underlayers. Ratcheting-induced crack by analogy.