**process HCF#

Description#

This post-computation gives an evaluation of the equivalent stress to compare with the fatigue limit, in order to define the high cycle fatigue (HCF) resistance.

Four different criteria are implemented for HCF. The variables which provide the basis of the criterion are the hydrostatic pressure (for each of them), and a stress amplitude in terms of the von Mises invariant (for three of them), or in terms of a shear (in one case). In the following, the stress amplitude is designated \(Dsig\) (and defined in relation to stresses tensor), \(p_{max}\) the maximum hydrostatic pressure, and \(p_{mean}\) the mean value of hydrostatic pressure (\(p_{mean}=0.5(p_{max}+p_{min}\)).

The following criteria are implemented for the HCF model:

  • The criterion from Sines (mode SI) uses a coefficient \(b\) to calculate the equivalent stress:

    (147)#\[\sigma_eq = Dsig + b p_{mean}\]

  • The criterion due to Crossland (mode CR) uses a coefficient \(b\) to calculate its equivalent stress:

    (148)#\[\sigma_eq = (1-b) Dsig + b p_{max}\]

  • The criterion from Dang Van uses a coefficient \(b\). Its characteristic, if we compare the two first two models, resides in the combination of two variables at the same time. Two versions are implemented:

    • The classical model of Dang Van (mode DV) searches for the maximum value in all the physical space directions (\(\vect n\)), at all instants \(t_i\) of the equivalent stress. This is constructed from the current shear stress amplitude \(\tau\) and from the hydrostatic stress:

      (149)#\[\sigma_eq =\max(\vect n) \min (t_i){\left (~2 (1-b)~\tau (t_i)+3 b~p(t_i) ~\right )}\]

    • An alternative formulation of the Dang Van criterion (mode DV2) is also implemented. Following the same philosophy as previously, this modification provides a simpler evaluation because it uses a von Mises stress measure. Knowing the stress amplitude one can calculate the value \(\sigma_0\) corresponding to the loading path “center.” The critical variable \(DJ_{2}(t_i)\) then corresponds to the the von Mises invariant of the difference in current stress and \(\sigma_0\):

      (150)#\[\sigma_eq = \max (t_i) {\left (~2 (1-b)~DJ_{2} (t_i) + 3 b~p(t_i) ~\right )}\]

Syntax#

**HCF \(~\,\) *mode SI | CR | DV | DV2

The user must choose the mode of operation (SI, CR, DV, or DV2). The coefficient \(b\) must be defined in the material file. The post-computation produces an output for each input point at each time, which is the equivalent stress. The output variable name is HCF_mode.

Example#

**process HCF
  *mode DV2
  *var sig

% With the following definition in the material file
**process HCF  DV2
   b  0.3