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