**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 [U12].

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:

  \[\sigma_{eq} = Dsig + b p_{mean}\]

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

  \[\sigma_{eq} = (1-b) Dsig + b p_{max}\]

• 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:

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

  • 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 von Mises invariant of the difference in current stress and \(\sigma_0\):

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

Syntax

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

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.

*output_tau_p

to output the shear amplitude and the hydrostatic pressure \(\tau\) and \(p\), respectively. Only valid for DV mode, and the output names are tau_DV, and p_DV.

Example

**process HCF
  *mode DV2
  *var sig

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