Surfaces form peaks and valleys to alleviate stress.

1
Model Development for FW Surface Roughening
Michael Andersen, Nasr M. Ghoniem, Shahram
Sharafat
University of California Los Angeles (UCLA)
Goal Predict crack formation by modeling
surface roughening
Crack Formation from Roughening
Sharp Interface Approach

• Surfaces form peaks and valleys to alleviate
  stress.
• Solid decreases elastic energy by growing tips
  (low stress) and deepening valleys (material with
  high elastic energy is removed).
• At a certain point valleys progress to cracks and
  traditional fracture mechanics can be used.

Grooving patterns can appear in long rows, but
notice that a crosshatch formation ends the
valleys from continuing indefinitely.
A better surface profile can be used from one of
the test facilities
Stress Sources

• 3D biaxial stress model is used, assuming
• Volumetric heat loading
• Shallow stress zone
• Material below stressed zone restrains motion.
• No constraint in 3rd dimension.
• Utilizing Jake Blanchards work
• A multiple pulse temperature profile can be used
  as well (T. Hunter)

Balance obtained between destabilizing surface
strain and stabilizing curvature.
Phase-field Modeling
The critical wavelength is useful in determining
if the peak is growing, as a wavelength exceeds
the critical value the tips and valleys grow to
stabilize the surface strain.

• Sharp interface calculations become cumbersome on
  the scale of a mm. Solution is to use a phase
  field at the transition of solid-vapor to
  facilitate numerical convergence..
• Solution is a summation of free energies from
  elastic (fe), gravity (fgravity), double well
  potential (fdw), and an equilibrium control (fc).
• F must then solve the relaxation equation
• Which leads to

Simulated phase field solution in a fracturing
sample.
H is the solid fraction function, 1 for solid and
0 for vapor as relative maxima and minima. G
accounts for the possibility for a phase
transition where the two minima 0,1 correspond to
the phases vapor and solid respectively.
L.O. Eastgate Phys.Rev.E,65
HAPL-Rochester, NY Nov. 8-9