The document summarizes the presentation given by Vamsi Krishna Rentala on stress fields around dislocations. It first defines dislocations and the three main types: edge, screw, and mixed. It then describes how stress fields are produced by dislocations using linear elasticity theory. Simple models are used to illustrate the stress fields around screw and edge dislocations. Key results presented include the diverging stresses near dislocations and variations in stress type (tensile vs. compressive) above and below the slip plane for an edge dislocation. The document concludes by noting mixed dislocations contain both edge and screw components and summarizing some properties of stress fields.

1. A SEMINAR ON
Stress fields around dislocations
PRESENTATION
BY
VAMSI KRISHNA RENTALA
12ETMM10
I M.Tech
MATERIALS ENGINEERING
SCHOOL OF ENGINEERING SCEINCES AND TECHNOLOGY

2. Dislocation
 A 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 bonds
 There are mainly three types of dislocations.
a) Edge dislocation
b) Screw dislocation and
c) Mixed dislocation

3. Edge dislocation
 An 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.

4. 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

5. 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.

6. 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

7. 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 theory
a) 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 stresses
ii. Compressive stresses and
iii. Shear stresses

8. 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

9. Stress field around a screw dislocation
0 yx uu )/(tan
22
1
xy
bb
uz





10. 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 0
Solids cannot withstand infinite stresses and for this reason the
cylinder is shown as hollow with a hole of radius ro.
0 yxxyzzyyxx eeeee
r
b
yx
by
ee zxxz


 4
sin
)(4 22



r
b
yx
bx
ee zyyz


 4
cos
)(4 22



0 yxxyzzyyxx 
r
Gb
yx
Gby
zxxz



sin
)(2 22



r
Gb
yx
Gbx
zyyz




2
cos
)(2 22




11. 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

12. 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.

13. 222
22
))(1(2
)3(
yxv
yxby
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
yxby
yy






))(1( 22
yxv
vby
zz





222
22
))(1(2
)(
yxv
yxbx
xy







14.  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

15. Conclusions
 Mixed 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.

16. References
 Introduction to dislocations by D.Hull & D.J.Bacon
 Theory of Dislocations book by Hirth & Lothe
 Elementary dislocation theory by Johannes Weertman
and Julia R.Weertman.
 Some information from wikipedia

17. Thank
you