II II II II II I - Waste Isolation Pilot Plant - U.S. Department of Energy

2
11
F=exp–1–~ 6 for q>&; . (4.12.8)
[[
Et
In ~ above equations, A and 8 are referred to as the workhardening and recovexy functions, respectively,
while .at is referred to as the transient strain limit. The workhardening and recovery functions are assumed to be
of the form
A=ctw+~wlo —
v
go
(Je
a=ar+pr log: .
()
The trimsient strain limit is a fimction of temperature and stress given by
()
m
(4. 12.10)
(4.12. 11)
E: = K. exp(c@) %
P
(4.12.9)
where Ko and c are constants. Finally, the evolution equation for the internal variable g is
~=(F–l)iS=E–6S . (4.12.12)”
To complete the generalization of the M-D constitutive model, an equivalent stress and flow rule for the creep
strain rate must be defined. These two definitions provide the necessary linkage among the three-dimensional
stress state, the creep strain rate, and the invariant creep relationships described earlier. According to Munson et
al. (1988), the Tresca stress generalization provides the most appropriate definition of the equivalent stress for rock
salt. With the Tresca stress generalization, the equivalent stress becomes
0: = 2&cos~ = tsl –03
(4.12.13)
where~ is the Lode angle defined
by
sin3V =
–3J3 ~
2J;f 2
In the two preceding equations, J2 and J3 are the second and third invariants of the deviatoric part of the stress
tensor, and 01 and 03 are the maximum and minimum principal stresses, respectively. The flow is assumed to be
associative so that the direction of = is normal to the Tresca flow surface. Unfortunately, the normal is undefined
as v = t ~ where sharp comers exist in the Tresca flow surface. At these locations, the flow is assumed to be
normal to the von Mises flow surface. The von Mises flow surface is characterized by a constant value of 6P
where
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