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.

• 1. Introduction
• 2. Foreplay
  • 2.1. Endurance limit and accumulation of damage, uniaxial case
  • 2.2. Fatigue criterion, multiaxial case
  • 2.3. Definition of a loading amplitude in the multiaxial case
  • 2.4. Definition of the shear plane
• 3. Criteria for MATAKE (critical plane) and DANG VAN
  • 3.1. Criterion of MATAKE
  • 3.2. Criteria of DANG VAN
  • 3.3. MATAKE and DANG VAN modified for the accumulation of damage
• 4. Calculation of the maximum shear plane
  • 4.1. Expression of shear stresses in plane \(\Delta\)
  • 4.2. Exploring shear planes
• 5. Calculation of the shear half-amplitude
  • 5.1. Overview of the circumscribed circle calculation
  • 5.2. Description of the circle method passing through three points
  • 5.3. Criteria with critical plans
  • 5.4. Number of cycles at breakage and damage
• 6. Variable amplitude criteria
  • 6.1. MATAKE criterion changed
  • 6.2. Criteria of DANG VAN modified
  • 6.3. Criteria of FATEMI - SOCIE modified
• 7. Choice of projection axes
  • 7.1. Projection on an axis
  • 7.2. Construction of the second axis
• 8. Shear projection
  • 8.1. Case where axis 1 is the initial axis
  • 8.2. Case where axis 2 is the initial axis
  • 8.3. Definition of the module and orientation of the projection axis
• 9. Formula criteria
  • 9.1. For periodic charging
  • 9.2. For non-periodic charging
• 10. Quantity and components introduced in Code_Aster
  • 10.1. Calculated by CALC_FATIGUE
  • 10.2. Calculated by POST_FATIGUE
• 11. Other criteria
  • 11.1. Criterion VMIS_TRESCA
  • 11.2. Code_Aster components used
• 12. Conclusion
• 13. Bibliography
• 14. Description of document versions