**process creep#

Description#

This post calculation calculates creep damage at an instant \(t\) in relation to a variable \(T\), such as the integration of time between \(t_1\) and \(t\):

(125)#\[I(t) = (k+1) \int_{t_1}^t \left ( \frac{S-S_0}{A} \right )^r\]

with

(126)#\[S=(1-\alpha-\beta){\bf Mises}(\ten T)+\alpha{\bf Eig1}(\ten T) +\beta{\bf Trace}(\ten T)\]

where \({\bf Mises}(\ten T)\) indicates the second invariant of the deviatoric part of a tensor \(\ten T\), \({\bf Eig1}(\ten T)\) the maximum principal value, and \({\bf Trace}(\ten T)\) the trace (first invariant).

In accordance with the users choice, the result is given in terms of time to rupture or number of cycles to rupture. Two cases are envisioned:

  • \(I(t)\) attains 1 for a value of time between \(t_1\) and \(t_2\): the corresponding value is the time to rupture, and the number of cycles to rupture is set to one.

  • \(I(t_2)\) is less than 1: the time to rupture is obtained by superimposing a cyclic time and linear accumulation law. The number of cycles to failure is simply the inverse of \(I(t_2)\) and the time to rupture is obtained by multiplying this number by the length of loading considered.

Syntax#

**process creep \(~\,\) *var name [ *type scalar | tensor ] [ *express_life_as cycle | time ] [ *delay ] [ *scale lin | log ] [ *precision prec ]

name is the name of the variable to treat. The option *express_life_as is used to specify the output mode to be number of cycles or time to failure. With the option *delay a scaled stress measure is used: \(dS'=(S-S')/\tau\).

The user must furnish the coefficients S0, A, and r. Coefficients k, alpha and beta are optional with zero value by default. If it is used, the coefficient k must be a constant. One more supplemental coefficient tau is expected with the option *delay.

In the file problem.utp, we call the variable for time to rupture TC_S, and the number of cycles to rupture NC_S. If the output was put on a logarithmic scale, the names will be LTC_S and LNC_S. We generally prefer to work with log values when generating contour plots.

Creep damage is integrated using a second-order runge-kutta method. The precision required for integration can be specified by the optional *precision keyword. Default value is 1.e-4.

Example#

% Use stress tensor to compute time to failure and give
% a logarithmic output
**process creep
  *var sig
  *scale log
  *express_life_as time

% The following syntax is used in the material file :
**process creep
   A  1130.
   r    7.
   S0   0.
   alpha   0.3
   beta    0.

% ... but the coefficients may be non constant
**process creep
   A  temperature
   1130.   1050.
   2000.    700.
   ....