**process fatigue_S#

Description#

Using the stress as critical variable, the formula implemented by this option predicts a fatigue life (Wöhler curve). Even though the criterion can be applied to any variable contained in the problem, the description of the equations is made in terms of stress.

The model is capable of taking into account a mean stress and a multi-axial loading history. The critical variables are the stress amplitude and the maximum stress (with generalization pertinent for multi-axial values), calculated over the time period specified by the user.

The model is written in terms of reduced stress (The components of the stress divided by the last stress under monotonic loading \(\sigma_u\)). The stress amplitude is noted , and the equivalent maximal stress is , and the mean trace is . The post computation returns a rupture in one cycle if attains the ultimate stress \(\sigma_u\), and an infinite number of cycles if is less than the fatigue limit \(\sigma_l\). Otherwise the number of cycles to failure \(N_f\) is defined as follows:

(145)#\[N_f=\frac{1}{{a(\beta+1)}} \left<\frac{\sigma_u-\Smax}{\Seq - \sigma_l'}\right> {\left(\frac{\Seq}{\overline{M}}\right)}^{-\beta}\]
(146)#\[\mbox{with } \sigma_l' = \sigma_l (1. - b_1 \Trmean) \quad; \quad \overline{M}= M (1. - b_2 \Trmean)\]

Syntax#

**process fatigue_S \(~\,\) *var name [ *type scalar | tensor ] [ *mode with_a | simple ] [ *normalized_coeff ] [ *use_eigen2 ] [ *scale lin | log ] [ *range section ]

name is the name of the subject variable if the computation (one would expect sig here). Using the extra keyword simple after the option *mode, the post-computation uses a simpler formulation where the ratio \(1/a(\beta+1)\) is included in the coefficient M.

The coefficients sigma_l, M, b1 and b2 can be optionally given in normalized form. If they are normalized (using the option *normalized_coeff) the expected names in the material files are changed to N_sigma_l, N_M, N_b1 and N_b2.

The other coefficients necessary to input are beta and a if the option with_a is given.

By default the equivalent max stress SMAX is the von Mises stress. Using the option *use_eigen2 makes SMAX equal the maximal eigen stress \(S_I\). Caution: in the **process fatigue_rainflow the default equivalent max stress SMAX is the maximal eigen stress \(S_I\).

Number of cycles to failure is given in the output, with the variable named NF_S. The user can ask that a logarithmic scale be used with the option *scale. If so the output will be named LNF_S.

Example#

**process fatigue_S
  *var sig
  *scale log

% The following syntax must be used in the material file :
**process fatigue_S
   M       2400.
   beta    5.
   sigma_l 120.
   sigma_u 450.
   b1  0.002
   b2  0.03