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

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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