Hyperbolic-Sine Model

The hyperbolic-sine law is available in the form

{\dot{\bar{ε}}}^{c r} = A {(\sinh B \tilde{q})}^{n} \exp (\frac{Δ H}{R (θ - θ^{Z})}),

where:

${\dot{\bar{ε}}}^{c r}$: is the uniaxial equivalent creep strain rate, $\sqrt{\frac{2}{3} {\dot{ε}}^{c r} : {\dot{ε}}^{c r}},$
$\tilde{q}$: is the uniaxial equivalent deviatoric stress,
$θ$: is the temperature,
$θ^{Z}$: is the user-defined value of absolute zero on the temperature scale used,
$Δ H$: is the activation energy,
$R$: is the universal gas constant, and
$A$ , $B$ , and $n$: are other material parameters.

This model includes temperature dependence, which is apparent in the above expression; however, you cannot define the parameters $A$ , $B$ , $n$ , $Δ H$ , and $R$ as functions of temperature.

Depending on the choice of units, the value of $A$ might be very small for typical creep strain rates. If $A$ is less than 10⁻²⁷, numerical difficulties can cause errors in the material calculations. Therefore, use another system of units to avoid such difficulties in the calculation of creep strain increments.