Creep deformation of materials in light water reactors (LWRs) - Materials' Ageing and Degradation in Light Water Reactors - page 43

In order to illustrate the effect of stress and temperature on transitions in
mechanisms it is necessary to suitably modify the creep equation. Sherby
analyzed steady-state creep-rate results using strain rate compensated by
diffusivity versus stress normalized by temperature-dependent modulus of
elasticity 16

n

ε

⎛
⎛

⎞

σ

[3.42 ]

A =

⎝

D E

so that different materials can be compared with each other. While this
equation seems to work well, it would be more appropriate to use dimen-
sionless strain rate as well, and Dorn and co-workers 4 proposed a dimen-
sionless equation that can appropriately describe the effect of changes in
stress, temperature and microstructure on mechanisms of creep. This equa-
tion known as the Bird-Mukherjee-Dorn (BMD) equation is given by

p n

ε kT

⎛
⎛ ⎝

b

⎞

σ σ

⎞

[3.43 ]

A

⎛
⎛ ⎝

= .

DEb dE

As shown in Fig. 3.16a, changes in stress and temperature for a given con-
stant microstructure of the material can reveal changes in the stress expo-
nent value. 60 At low normalized stress values, the deformation mechanism
appears to proceed with a stress exponent value of 1. At intermediate stress
values a stress exponent value of 2 corresponding to GBS is obtained. At
the highest normalized stress values, the mechanism of deformation oper-
ates with a stress exponent value of 5 corresponding to power-law creep.
The diffusivity value utilized for constructing the plot corresponds to the
lattice diffusion activation energy of titanium, and thus data at different
temperatures follow different curves in the GBS and viscous creep regimes
where the appropriate activation energy is that for grain boundary diffu-
sion. On the contrary, if one chooses to use the activation energy for grain
boundary diffusion, the data at high stresses will lead to different lines for
different temperatures. The BMD plot thus allows an easy understanding of
the transitions in creep mechanisms following changes in stress and temper-
ature. Such an analysis was found to be very useful in delineating various
creep mechanisms in Zr-based alloys as depicted in Fig. 3.16b. 73 Moreover,
such plots made for different materials would show the material behaviors
at equivalent loading conditions. 4

￿ ￿ ￿ ￿ ￿ ￿

Transitional creep mechanisms in class-A alloys

It is instructive to examine the transitions in creep mechanisms in solid
solutions of class-A type such as the results depicted in Fig. 3.10 where we