UNIVERSITY OF HYDERABAD

A SEMINAR ON

Stress fields around dislocations PRESENTATION

BY

VAMSI KRISHNA RENTALA12ETMM10

I M.TechMATERIALS ENGINEERING

SCHOOL OF ENGINEERING SCEINCES AND TECHNOLOGY

DislocationA dislocation is a crystallographic defect within a

crystal structure.It comes under line defect.Motion of dislocations results in plastic deformation.Dislocations produces deformation via

incrementally breaking bondsThere are mainly three types of dislocations.a) Edge dislocation b) Screw dislocation andc) Mixed dislocation

Edge dislocationAn edge dislocation is a

defect where an extra half-plane of atoms is introduced through the crystal, distorting nearby planes of atoms.

• Edge dislocations move in response to shear stress applied perpendicular to the dislocation line.

Screw dislocation• A dislocation in the lattice structure of a crystal in which the atoms are arranged in a helical pattern that is normal to the direction of the stress•The motion of screw dislocation is also a result of shear stress•Motion is perpendicular to direction of stress

Mixed dislocations•Dislocations exhibiting both edge and screw characteristics are known as mixed dislocations•These are the dislocations mostly encountered in real crystals•It is very difficult to have pure edge or pure screw dislocations.

How stress fields are produced around a dislocation?The atoms in a crystal containing a

dislocation are displaced from their perfect lattice sites and the resulting distortion produces a stress field around the dislocation.

The stress and strains in the bulk of the crystal are sufficiently small

How to calculate stress fields? Linear elasticity theory:•By assuming the crystalline materials to be elastically isotropic.•Although most crystalline solids are elastically anisotropic.

Elements of elasticity theorya) Displacement – a change in position.b) Strain - change in dimension to its original dimension c) Stress - resistance force per unit area

Types of stresses:i. Tensile stressesii. Compressive stresses and iii. Shear stresses

Simple model for screw dislocation.

The deformation field can be obtained by cutting a slit longitudinally along a thick-walled cylinder and displacing a surface by b parallel to the dislocation line.

Screw Dislocation

Stress field around a screw dislocation

0 yx uu )/(tan22

1 xybbuz

The screw dislocation is associated with shear stresses only

The stresses and strains are proportional to 1/r and therefore diverge to infinity as r 0Solids cannot withstand infinite stresses and for this reason the cylinder is shown as hollow with a hole of radius ro.

0 yxxyzzyyxx eeeee

rb

yxbyee zxxz

4

sin)(4 22

rb

yxbxee zyyz

4

cos)(4 22

0 yxxyzzyyxx

rGb

yxGby

zxxz

sin

)(2 22

rGb

yxGbx

zyyz

2cos

)(2 22

Simple model for edge dislocation.

The deformation fields can be obtained by cutting a slit longitudinally along a thick-walled cylinder and displacing the surface by b perpendicular to the dislocation line.

Stress field around an Edge Dislocation

Deformation of a circle containing an edge dislocation. The unstrained circle is shown by a dashed line. The solid line represents the circle after the dislocation has been introduced.

222

22

))(1(2)3(

yxvyxby

xx

Stress Field Due to Edge Dislocations

0 yzxy

xx

yy

Stress values in GPa

Left-right mirror symmetry

Up down ‘inversion’ symmetry

(i.e. compression goes to tension)

222

22

))(1(2)(yxv

yxbyyy

))(1( 22 yxvvby

zz

222

22

))(1(2)(yxv

yxbxxy

The largest normal stress is along the x-axis. This is compressive--- above slip plane. tensile---------- below slip plane.

xy shear stress is maximum in the slip plane, i.e. when y=0

xx

For an edge dislocation

ConclusionsMixed dislocation is a combination of pure edge and

pure screw components.In the cylindrical coordinate system, when r 0

then, the stresses and strains tends to infinity.For a positive edge dislocation, compressive

stresses are above the slip plane while the tensile stresses are below the slip plane and vice versa for negative edge dislocation.

ReferencesIntroduction to dislocations by D.Hull & D.J.BaconTheory of Dislocations book by Hirth & LotheElementary dislocation theory by Johannes Weertman

and Julia R.Weertman.Some information from wikipedia

Thank you