Johannes Weertman

Dept. Mat. Sci. & Eng

Dept. Earth & Planetary Sci.

Northwestern University

Evanston, IL, USA

Leon Keer Symposium

Symi, Greece, July 2010

Free

y0

SSolid

Surface

y0

Solid

Former Free

y0

Solid

Surface

S

Free

y0

Solid

Surface

y0

Solid

Former Free

y0

Solid

Surface

Dislocation moving near

a free surface

bS

0

BbL

y0 vv

Empty Space

Solid

Empty Space

Solid

Free Free

SurfaceSurface

bL

y0

y

bS

0

B

Bb

bSB

LSByyy00

b

bLB

SLB

y0

y0

SB

LB

LB

SB

image

image

image

image

Solid Solid

Solid Solid

Former

Free Surface

bL

y0

y

bS

0

B

Bb

bSB

LSByyy00

b

bLB

SLB

y0

y0

SB

LB

LB

SB

image

image

image

image

Solid Solid

Solid Solid

Former

Free Surface

Free Surface

Problem Solved

Dislocation moving nearan interface

bS

0

A

BbL

y0

A A A

B B B

vv

bL

y0

y

bS

0

B

Bb

bSB

LSByyy00

b

bLB

SLB

y0

y0

SB

LB

LB

SB

B B B

B B B

image

image

image

image

SA

A

A

yy0 SB

LA

A A A

A A A

imageyy0 SB

SA

bLSA

image

bSLA

image

bLA

image yy0 LB

LA

yy0 LB

SA

(Similar set of equations for longitudinal dislocation)

Shear Dislocation

Shear Dislocation

Longitudinal Dislocation

Interface

Problem Solved

Reduction to

Stationary Dislocation

Near a

Free Surface

J. Dundurs and T. Mura, “Interaction between an edge dislocation and a circular

inclusion”, J. Mech. Phys. Solids, 12, 177-189 (1964).

[J. Dundurs and G. P. Sendeckyj, “Behavior

of an edge dislocation near a bimetallic interface”,

J. Appl. Phys., 36, 3353-3354 (1965).

J. Dundurs and G. P. Sendeckyj, “Behavior of an edge dislocation near a bimetallic

interface”, J. Appl. Phys., 36, 3353-3354 (1965).

For Free SurfaceA=B=1c2 = 0

A = B = 1

1 = space B

2 = empty space A

J. Dundurs and T. Mura, “Interaction between an edge dislocation and a circular

inclusion”, J. Mech. Phys. Solids, 12, 177-189 (1964).

Displacement solution constructed from Dundurs et al papers and converted

from vertical free surface to horizontal free surface

Total displacement fieldorigin at y = y0

Displacement solution constructed from Dundurs et al papers and converted

from vertical free surface to horizontal free surface

SUMMARY

The problem of a moving edge dislocation

gliding near an interface or free surface

can be solved with image dislocations if the

dislocations first are separated into

shear wave and longitudinal wave

dependent components.

Thank you for

listening to this

elementary dislocation

theory talk

SUMMARY