The Kelly and Burchell50,51 model recognizes that creep produces significant modifications to the dimen­sional change component of the stressed specimen compared to that of the control and that this must be accounted for in the correct evaluation of creep strain data.

The rate of change of dimensions with respect to neutron dose g(n cm-2) in appropriate units is given by the Simmons’ theory2 for direction x in the unstressed polycrystalline graphite:

dXT + + F

ac — a, dg Xa dg

where ax is the thermal expansion coefficient in the x-direction, and ac and aa are the thermal expansion coefficients of the graphite crystal parallel and per­pendicular to the hexagonal axis, respectively, over the same temperature range. The term Fx is a pore generation term that becomes significant at interme­diate doses when incompatibilities of irradiation — induced crystal strains cause cracking of the bulk graphite.67 For the purposes of their analysis, Kelly and Burchell ignored the term Fx. The parameters (1/Xc)(dXc/dg) and (1/Xa)(dXa/dg) are the rates of change of graphite crystallite dimensions parallel and perpendicular to the hexagonal axis, and

dXT _ 1 dXc 1 dXa

dg Xc dg Xa dg 19

The imposition of a creep strain is known to change the thermal expansion coefficient of a stressed speci­men, increasing it for a compressive strain and decreasing it for a tensile strain compared to an unstressed control. Thus, the dimensional change
component of a stressed specimen at dose g(n cm 2) is given by

К—a, «г + і gX + f:

ac — a, dg X, dg

where a0x is the thermal expansion coefficient of the crept sample, and Fx0 is the pore generation term for the crept specimen. The difference between these two equations is thus the dimensional change correc­tion that should be applied to the apparent creep strain (the pore generation terms Fx and Fx0 were neglected):

[21]

The true creep strain rate can now be expressed as

de_ de0 a’x — Kx dXT

dg dg ac — a, dg 2

where e is the true creep strain and Є is the apparent creep strain determined experimentally in the con­ventional manner. Thus, the true creep strain (ec) parallel to the applied creep stress is given by

g. …

ec = e’c

0

where ec is the induced apparent creep strain, (ax — ax) is the change in CTE as a function of dose, (ac — aa) is the difference of the crystal thermal expansion coefficients of the graphite parallel and perpendicular to the hexagonal axis, XT is the crystal shape change parameter given above, and g is the neutron dose. The apparent (experimental) creep strain is thus given by

g

ec = ec +

0

Substituting for ec from eqn [13] gives the apparent (experimental) creep strain ec as

g.

ec = ES+ksg

with the terms as defined above.

The Kelly-Burchell model is unique in that it does take account of the sign of the applied stress in