4.10.6.3.1 Linear viscoelastic creep model

Irradiation-induced (apparent) creep strain is con­ventionally defined as the difference between the dimensional change of a stressed specimen and an unstressed specimen irradiated under identical con­ditions. Early creep data was found to be well described by a viscoelastic creep model1,58-63 where

total irradiation creep (ec) = primary (transient)
creep + secondary (steady-state) creep.

ec = ^[1 — exp(-by)] + kay [12]

E0

where ec is the total creep strain; a, the applied stress; E0, the initial (preirradiated) Young’s modulus; y, the fast neutron fluence; a and b are constants (a is usually = 1); and k is the steady-state creep coefficient in units of reciprocal neutron dose and reciprocal stress.

Equation [13] thus conforms to the Kelly-Foreman theory of creep with an initially large primary creep coefficient, while the dislocation pinning sites develop to the equilibrium concentration, at which time the creep coefficient has fallen to the steady-state or secondary value. Early creep experiments in several

 

countries showed the primary creep saturated at approximately one elastic strain (a/E0) so that the true creep may be represented as a r і ec = + kay [13] E0 This is often normalized to the initial elastic strain and written as ec = 1 + kEog [14] in elastic strain units (esu) (esu is defined as the externally applied stress divided by the initial static Young’s modulus), or creep strain per unit initial elas­tic strain; kE is the creep coefficient in units of recip­rocal dose [United Kingdom ~ 0.23 x 10-20cm2n-1 EDN up to Tirr ~ 500 °С]. (EDN — equivalent DIDO nickel dose, a unit of neutron fluence used in the United Kingdom and Europe.)

 

where a is the applied stress; (dec/dy)0, the initial secondary creep rate; y, the fast neutron fluence; S(y), the structure factor, given by S(y) = Eg/Ep the ratio of the Young’s modulus at dose y to the Young’s modulus after the initial increase due to dislocation pinning. The structure factor, S(y), thus attempts to sepa­rate those effects due to dislocation pinning occurring within the crystallites and structural effects occur­ring ex-crystal through changes in the Young’s modulus. However, the effect of creep strain (tensile or compres­sive) on modulus is not considered when evaluating the structure term. The unstressed Young’s modulus changes are used to establish the magnitude of S(y).

 

4.10.6.3.3 The Kennedy model Kennedy et al66 replaced the structure term in the UK model with a parameter based on the volume change behavior of the graphite: ec = S + k'(y)ay [16] E0

 

where

 

У Г k'(g) = 4 1 0

 

/ DV /V0 ^ (DV / Vq )m

 

dy

 

[17]

Here, m is an empirical constant equal to 0.75 and k0 is the steady-state creep coefficient established from low dose creep experiments.

Although the Kennedy et al66 model was shown to perform well in the prediction of high-dose tensile creep data, it did not predict the compressive data nearly as well. Moreover, as with the UK model, the sign of the applied stress is not considered when evaluating the influence of structure change (as reflected in volume changes). The quotient in eqn [17] is evaluated solely from unstressed (stress — free) samples irradiation behavior. As discussed by Kelly and Burchell,51 the term (AV/Vmax) does not exist at low irradiation temperatures where graphites expand in volume.