DIRECT SIMULATION OF SUBGRAIN DISLOCATION STRUCTURES Srinivasan M. Sivakumar and Michael Ortiz
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DIRECT SIMULATION OF SUBGRAIN DISLOCATION STRUCTURESDIRECT SIMULATION OF SUBGRAIN DISLOCATION STRUCTURES Srinivasan M. Sivakumar and Michael Ortiz
Graduate Aeronautical LaboratoriesCALIFORNIA INSTITUTE OF TECHNOLOGY
PATCHY SLIP Asaro (1983)
EQUAL CHANNEL ANGULAR EXTRUSIONEQUAL CHANNEL ANGULAR EXTRUSION
Process of shearing
• Route A : (=0o)• Route B : =90o
• Route C : =180o
• Route BC and BA –=90o or =270o
(Reinsertion angles)
Formation of -B2 & -A2 leaves
Formation of -B2-A2 subleaves
Formation of -A2&-C5 leaves
Reduction of lamellar sizes upon further deformation
LAMELLAR STRUCTURES (Cu)(Lee, et al. 2002)
• LARGE DEFORMATION SINGLE CRYSTAL PLASTICITY• STRONG LATENT HARDENING – SINGLE SLIP PLASTICITY• SEQUENTIAL LAMINATION CONSTRUCTION MIMICS THE
LAMELLAR DISLOCATION STRUCTURES OBSERVED• RANK-ONE CONVEXIFICATION ALGORITHM • NON-LOCAL EFFECTS USING DISLOCATION DENSITY TENSOR• KEY APPLICATIONS:
ALL SEVERE PLASTIC DEFORMN. PROCESSES (SPD) EXAMPLE: ECAE
Thanks to:Caltech’s ASCI ASAP CenterC.Tome and I. Beyerlein (LANL)Matt Fago (Caltech)Lydia Suarez (Caltech) and Marta Kahl (Caltech)
FCC – AL-CU ALLOY Shear strain=200%
CALCULATIONS FOR = 900 ECAE - SINGLE PASS
SINGLE CRYSTAL RESULTS (for a particular random orientation)
POLYCRYSTAL RESULTS
EVOLUTION OF CALCULATED POLE FIGURES EXPERIMENTAL
MULTIPLE LENGTH SCALE SEPARATIONS
AN APPLICATIONAN APPLICATION
(ECAE)
ELASTIC PLASTICWORK OF DEFORMATION
&
with
INFINITE LATENT HARDENING
SEQUENTIAL LAMINATESSEQUENTIAL LAMINATION - RANK-1
CONVEXIFICATION
KOHN, 1991
REGIONS OF
SINGLE SLIP
AUBRY & ORTIZ, 2003
INCREMENTAL VARIATIONAL
SCHEME
RADOVITZKY &ORTIZ, 1999
CRITERION FOR BRANCHING:
COMPATIBILITY
INTERFACES
EQUILIBRIUM EQUATIONS
X1
X2
x1
x2
Die Exit
Shear Plane
Die Entry
Reinsertion
CONFIGURATIONAL EQUILIBRIUM
(AN A POSTERIORI ESTIMATON OF SIZES)
ESTIMATED:
CALCULATED: