r7.04.01 Estimation of lifespan in fatigue with a large number of cycles and in oligocyclic fatigue

Summary:

Most industrial structures are subjected to forces that vary over time which, repeated a large number of times, can lead to their breakage due to fatigue. In this note, we present the main functionalities of the POST_FATIGUE [U4.83.01] and/or CALC_FATIGUE [U4.83.02] and/or CALC_CHAMP [U4.81.04] commands that make it possible to estimate the endurance limit and the accumulation of damage of a part.

The various methods available are:

• linear accumulation: methods based on uniaxial tests (Wöhler, Manson-Coffin methods

and Taheri).

What these methods have in common is that they determine a damage value from the evolution over time of a scalar component characterizing, for the calculation of damage, the magnitude of stresses or deformations of the structure.

To do this, it is necessary to extract, by a cycle counting method, the elementary loading cycles undergone by the structure, determine the elementary damage associated with each cycle and determine the total damage by a linear accumulation rule;

• nonlinear accumulation: Lemaître method and Lemaître-Sermage method

These methods make it possible to calculate the damage \(D\) at each instant \(t\), from the data of the stress tensor \(\sigma (t)\) and the cumulative plastic deformation \(p(t)\);

• endurance limit: Crossland and Dang Van Papadopoulos criteria

These criteria apply to uniaxial or multiaxial loads under period stresses. They provide a criterion value that indicates whether or not there is fatigue. The equivalent constraints defined for these criteria can also be used to calculate the accumulation of damage.

Table of Contents

• 1. Introduction
• 2. Wöhler, Manson-Coffin, and Taheri methods
  • 2.1. Extraction of peaks
  • 2.2. Cycle-counting methods
  • 2.3. Damage calculation: Wöhler method
  • 2.4. Calculation of damage: Manson-Coffin method
  • 2.5. Damage calculation: Taheri method
  • 2.6. Calculation of total damage
  • 2.7. Conclusion
• 3. Calculation of generalized Lemaître damage
  • 3.1. Lemaître’s law generalized
  • 3.2. Identification of the parameters of generalized Lemaître’s law
• 4. Crossland and Dang Van Papadopoulos criteria
  • 4.1. Crossland criterion
  • 4.2. Dang Van Papadopoulos criterion
  • 4.3. Calculation of damage value
• 5. Conclusion
• 6. Bibliography
• 7. Description of document versions