LECTURE #27 : 3.11 MECHANICS OF MATERIALS...
17
LECTURE #27 : 3.11 MECHANICS OF MATERIALS F03 INSTRUCTOR : Professor Christine Ortiz OFFICE : 13-4022 PHONE : 452-3084 WWW : http://web.mit.edu/cortiz/www • PLASTICITY IN METALS
Transcript of LECTURE #27 : 3.11 MECHANICS OF MATERIALS...
LECTURE #27 :3.11 MECHANICS OF
MATERIALS F03INSTRUCTOR : Professor Christine OrtizOFFICE : 13-4022 PHONE : 452-3084WWW : http://web.mit.edu/cortiz/www
• PLASTICITY IN METALS
SUMMARY : LECTURE #26I. Maxwell ModelI.A. Creep
I.B. Stress Relaxation
k
η
σο
σs=kεsεs=σo/k
σD=ηεDεD=(σo /η)t
•
σο
σ
t
σο
ε
t
t10
t10
σo/k
σo/k
(σo/η)t1
σo/η)
σ
t
σο
ε
t
t10
t10
σo/k
σo/k
(σo/η)t1
σo/η)
k
η
εο
σs=kεs
σD= ηεD
•
εο
k
η
εο
σs=kεs
σD= ηεD
•
εο
o
o o
CRPo
(t)
(t) tk
(t): C (t)Creep Compliance
σ σ
σ σε
η
εσ
=
= +
=
ε
t
εο
σ
t
0
0
ε
t
εο
σ
t
0
0
o
i
i o
Ro
(t)d
0dt
:k
(t) exp( t / )(t 0) k
(t): E (t)
Relaxation Time
Relaxation Modulus
ε εσ
τ σ
ητ
σ σ τσ σ ε
σε
=
+ =
=
= −= = =
=
τ0.37σi
σi
Stress versus Strain Curves for Elastic Materials*(*uniaxial tension)
σ
ε
σ
ε
Stress versus Strain Curves for Plastic Materials*Typical Stress versus Strain Curve For a Plastically Deforming
Material In Uniaxial Tension (e.g. annealed Cu)
σ
ε
Measuring the Onset of Plastic Deformation
σ
ε
Ε
σY
εY0.002
ε f
σ f
elastic plastic
failure
Ε
Stress versus Strain Curves for Plastic Materials*Typical Stress versus Strain Curve For a Plastically Deforming
Material In Uniaxial Tension (e.g. annealed Cu)
Elastic Strain Energy
σ
ε
Elastic Strain Energy
σ
ε
σ
ε
Plastic Deformation In Ductile Metals
THE EDGE DISLOCATION
extra half plane of atoms
••••••••
dislocation line
dislocation plane
Burger’s vector,
b ⊥ dislocationline =
lattice parameter or atomic spacing
slip or glide plane : defined byb and dislocation line
⊥dislocation core
••••••••
dislocation line
dislocation plane
Burger’s vector,
b ⊥ dislocationline =
lattice parameter or atomic spacing
slip or glide plane : defined byb and dislocation line
⊥dislocation core
CRYSTAL LATTICE
lattice strain
SLIP
•••••••••••••••••
•••••••••••••••••
•••••••••••••••••
•••••••••••••••••
•••••••••••••••••
•••••••••••••••••
•••••••••
•••••••••••••••••
•••••••••••••••••
•••••••••••••••••
•••••••••••••••••
•••••••••
τ
τ
slip plane
unstrained crystal lattice
SLIP
PLASTIC DEFORMATION IN SINGLE CRYSTALS
F
F
slip planes
edge dislocations
slip direction
Polycrystalline Plastic Deformationhttp://www.jwave.vt.edu/crcd/farkas/lectures/dislocations/tsld022.htm
