direct simulation of subgrain dislocation structures srinivasan m. sivakumar and michael ortiz

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: