Creep deformation of materials in light water reactors (LWRs) - Materials' Ageing and Degradation in Light Water Reactors - page 22

Table 3.1 Identifi cation of the particular mechanism of creep from
parameters n , p , Q c and A (Equation [3.16])

Creep mechanism n p Q c A

Nabarro-Herring (N-H) 1 2 Q L 12

Coble 1 3 Q gb 150

Harper-Dorn (H-D) 1 0 Q L 3 × 10 −10

Spingarn-Nix (S-N) 1 3 Q gb 75

Grain boundary sliding (GBS) 2 2 Q gb 200

Viscous glide 3 0 Q s 6

Dislocation climb 4-7 0 Q L 6 × 10 7

Power-law breakdown >7 - Q L -

processes. Power-law breakdown (PLB) occurs at relatively high stresses
equal to or greater than around 10 −3 E ( E is modulus of elasticity); this has
also been correlated with strain rates at or greater than 10 −9 D ( D is diffu-
sivity). 16 In this high stress and high strain rate regime, the creep-rates vary
with stress via an exponential function. While this region is observed in all
materials under appropriate conditions, the underlying mechanism of PLB
is still a moot factor.
In this table, Q gb is the grain boundary diffusion activation energy, Q L the
activation energy for lattice diffusion, and Q s the activation energy for solute
diffusion. As Table 3.1 suggests, a stress exponent value of unity (Newtonian
viscous) imply that the deformation mechanism could be Coble, N-H or
H-D creep. However knowledge of the grain size exponent or the activa-
tion energy would establish the right mechanism of creep. For example, a
stress exponent of 1 and activation energy equal to that for lattice diffusion
would suggest the mechanism of creep to be either N-H or H-D. But if the
grain size exponent is equal to 2, it would establish that the mechanism of
deformation is N-H. On the other hand, if the steady-state strain rate is
found to be independent of the grain size ( p = 0), the mechanism of creep
is H-D. The fact that the Coble creep mechanism is more sensitive to the
grain size and is controlled by the grain boundary diffusivity, it becomes
dominant at lower temperatures and/or smaller grain sizes while N-H creep
becomes predominant at relatively larger grain sizes and higher tempera-
tures. H-D creep becomes signifi cant at large grain sizes and bulk single
crystals. Thus, knowledge of the creep parameters would help in identifying
the exact mechanism of creep.

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3.3.1 The n = 1 regime

A stress exponent value of 1 suggests the mechanism of creep to be Coble,
N-H or H-D controlled. Recent studies have shown that the Spingarn-Nix