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Lecture

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University of Michigan - Ann Arbor

Mechanical Engineering

MECHENG 382

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Winter

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Lecture 31 - Creep mechanisms
C REEP M ECHANISMS
Diffusional (linear) creep
• At low stresses creep occurs by diffusion provided.4M
• Gibbs free energy is proportional to normal stresses on grain boundaries
• Driving force for diffusion is gradient across grains of normal stresses on boundaries
• Consider a case of pure shear
• Normal tensile stress on “B” > normal tensile stress on “A”
∴ Energy of atoms on grain boundary “B” < energy on grain boundary “A”
∴ Atoms diffuse from “A” → “B”
• Creep is a shear driven process
Requires a difference in normal stress on boundaries of different orientations
• No creep under hydrostatic stress (same stress at “A” and “B”)
• Two diffusion routes between grain boundaries
(i) Lattice (bulk) diffusion creep
• Also known as “Nabarro-Herring” creep (1948/1950)
• Atoms move through the grain by bulk (lattice) diffusion
Width of diffusion path = grain size
ME382 - 9/iv/14 1 Lecture 31 - Creep mechanisms
(ii) Grain-boundary creep
• Also known as “Coble” creep (1963)
• Atoms move along the grain boundaries
Width of diffusion path = region of disorder of width δ between grains
b
• Key points for modeling
Diffusion is thermally activated
Both diffusion routes contribute simultaneously to creep
• Modeling gives the following equation for diffusional creep
⎡ ⎤
⎢ ⎥
ε = 14σ ΩHD olexp −Q /RT + ) δ b obexp −Q /RT )
H kT ⎢d 2 l d 3 b ⎥
⎢ lattice creep grain boundry ⎥
⎣ creep ⎦
3
where Ω = atomic volume (m )
k = Boltzmann’s constant (1.38 x 10 -2J.atom .K )-1
d = grain size (m) -1 -1
R = gas constant (8.31 J.mol .K )
T = absolute temperature (K)
3 -1
D ollattice diffusion coefficient (m .s ) 2 -1
δbD obboundary diffusion coefficient (m .s )
Q = activation energy for lattice diffusion (J.mol ) -1
l -1
Q b activation energy for boundary diffusion (J.mol )
• Important features of diffusional creep
i) Linear: ε ∝σ
ii) Thermally activated: ε ∝ exp(−Q/RT)
2
ME382 - 9/iv/14 Lecture 31 - Creep mechanisms
iii) Inversely dependent on grain size:
ε ∝1/d 2 for lattice creep

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