Grain Boundary Cohesive Laws as a Function of Geometry

1
Grain Boundary Cohesive Laws as a Function of
Geometry
Valerie R. Coffman, James P. Sethna Cornell
University
2
Measuring Grain Boundary Energy and Fracture
Strength
Stress (Lennard-Jones Units)
-Measure energy and fracture strength for all
commensurate geometries -Cohesive Laws used in
FEM simulations
Strain
-2D Geometries described by 2 angles -3D
described by 5 parameters
3
Grain Boundary Energy
-Grain Boundary Energy has cusps for high
symmetry geometries -Devils staircase analogy
cusp singularity at all rationals
1
Energy (LJU)
0
?1?2
60
30
?1
?2
?1
?2
4
Grain Boundary Energy
-Dislocation added to high symmetry geometry
with Burgers vector b -For low angle grain
boundaries ? b / d E - ? log
(?) -Near high symmetry geometries E -
?-?0 log ?-?0
Energy (LJU)
?1?2
5
Peak Stress
Fracture toughness decreases abruptly when high
symmetry is broken
2.5
Perfect Crystals
2
?1?2
60
30
Stress (LJU)
?1
?2
Peak Stress
Strain
6
Peak Stress
-Added flaw nucleates fracture at stress
sc -Nucleation point feels stress of added
dislocations -Volterra solution gives speak(?)
sc - A(? - ?0)
Atomistic
nucleation pt
Stress (LJU)
Volterra Soln
?1?2
7
-Adding a flaw to a high symmetry grain boundary
is analogous to adding a flaw to a perfect
crystal -Energies have cusps at high symmetry
boundaries -Fracture toughness has
discontinuities everywhere -Self-similarity in
both functions
Thanks to Yor Limkumnerd, Anthony Ingraffea, Gerd
Heber, Wash Wawrzynek, Paul Stodghill, The
Adaptive Software Project