**process beremin#

Description#

This command performs the Weibull stress and the rupture probability according to the Beremin model (see Beremin F.M., “A local criterion for cleavage fracture of a nuclear pressure vessel steel”, Met. Trans. A, 14A, 2277–2287 (1983)). The Weibull stress is defined as:

(207)#\[\sigma_W = \left( \frac{1}{V_0}\int_{V,\, p>p_c} \sigma_I^m\,dV\right)^{1/m}\]

where \(V_0\), \(p_c\) and \(m\) are material parameters. \(\sigma_I\) is the stress tensor maximum principle stress. The integral is taken over the volume where the plastic strain is higher that a critical value \(p_c\). The rupture probability \(P_r\) is given by:

(208)#\[P_r = 1 -\exp\left(-\left(\frac{\sigma_W}{\sigma_u}\right)^m\right) = 1 -\exp\left(-\frac{1}{V_0}\int_{V,\, p>p_c} \left(\frac{\sigma_I}{\sigma_u}\right)^m\, dV\right)\]

\(\sigma_u\) is a material parameter.

Syntax#

**process beremin \(~\,\) *stress name1 \(~\,\) *strain name2

name1 is the name of the stress tensor and name2 the name of the inelastic deformation measure (scalar). The material file must contain the values \(V_0\), \(p_c\) \(m\) and \(\sigma_u\).

Example#

% input file
**process beremin
  *stress sig
  *strain epcum

% material file
**process beremin
  V0      10.
  m       20.
  sigma_u 1200.
  p_c     0.01