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Lecture

# Lecture31.pdf

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School
University of Michigan - Ann Arbor
Department
Mechanical Engineering
Course
MECHENG 382
Professor
All
Semester
Winter

Description
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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