.. _R7.04.04:

**r7.04.04** Multi-axial fatigue initiation criteria
=========================================================

**Summary:**

In this note we propose a formulation of the criteria of MATAKE, DANG VAN and FATEMI - SOCIE and of the criteria in a formula adapted to the framework of the accumulation of damage under **period** and **non-period** multiaxial loading. These criteria can be used in the CALC_FATIGUE command.

The first part of this document is devoted to the criteria of MATAKE and DANG VAN adapted to periodic multiaxial loads. In this part, after discussing the concepts of endurance and damage accumulation and the general form of fatigue criteria, we describe the two DANG VAN and MATAKE (Critical Plan) models designed to perform damage accumulation calculations under multiaxial loading. It details the definition of the various shear planes associated with Gauss points or nodes, as well as the definition of a loading amplitude through the circle circumscribed to the path of the load in the shear plane. Finally, the criteria available in *Code_Aster* are presented.

In the second part we propose a formulation of the criteria of MATAKE, DANG VAN and FATEMI - SOCIE in the context of the accumulation of damage under non-periodic multiaxial loading. To define a cycle in the case of variable amplitude, we reduce the loading history to a one-dimensional function of time by projecting the tip of the shear vector onto an axis, and we use a cycle counting method. Here we choose method RAINFLOW. The criteria of MATAKE, DANG VAN and FATEMI - SOCIE adapted to the accumulation of damage under non-periodic loading are implemented in*Code_Aster*.

In addition to well-established criteria, Code_Aster has **formula criteria** allowing the user to build new criteria based on predefined quantities. This type of criterion is detailed in the third part of this document.

Finally, option VMIS_TRESCA makes it possible to calculate the maximum variation, over time, of a stress tensor according to the Von Mises and Tresca criteria.




.. toctree::
    :hidden:

    self

.. toctree::
    :maxdepth: 2
    :numbered:

    Introduction
    Pr_liminaires
    Crit_res_de_MATAKE__plan_critique__et_de_DANG_VAN
    Calcul_du_plan_de_cisaillement_maximal
    Calcul_de_la_demi-amplitude_de_cisaillement
    Crit_res___amplitude_variable
    Choix_des_axes_de_projection
    Projection_du_cisaillement
    Crit_res_en_formule
    Grandeur_et_composantes_introduites_dans_Code_Aster
    Autres_crit_res
    Conclusion
    Bibliographie
    Description_des_versions_du_document