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# Majid Hamid

**Grade: ** Master

**Thesis Title:**

Modeling High Cycle Fatigue Failure Using Continuum Damage Mechanics

**Year:** Sept. 2007- Feb. 2010.

**Abstract:**

High cycle fatigue is probably the most difficult phenomenon to handle within solid mechanics and is, by consequence, the main cause of failures of mechanical components in service. The difficulty comes from the early stage of damage which initiates defects at a very small micro- or nanoscale under cyclic stresses below the engineering yield stress. High-cycle fatigue is considered when the cyclic loadings induce stresses close to but below the engineering yield stress so that the number of cycles to initiate a mesocrack is “high,” that is larger than 105. The plastic strain is usually not measurable on a mesoscale but dissipation exists on a microscale to induce the phenomenon of damage.From the physical point of view, the repeated variations of elastic stresses in metals induce micro-internal stresses above the local yield stress, with dissipation of energy via microplastic strains which arrest certain slips due to the increase of dislocations nodes. There is formation of permanent micro slip bands and decohesions, often at the surface of the material, to produce the mechanism of intrusion-extrusion. After this first stage located inside the grains, where the microcracks follow the planes of maximum shear stress, there is a second stage in which the microcracks cross the crystal boundaries to grow more or less perpendicular to the direction of the maximum principal stress up to coalescence to produce a mesocrack.

The two-scale damage model based on this idea, that, fatigue damage is localized at the microscopic scale, a scale smaller than the mesoscopic one of the Representative Volume Element (RVE), this three-dimensional two scale damage model has been proposed for High Cycle Fatigue applications and has been extended to anisothermal cases and then to thermo-mechanical fatigue. The modeling consists in the micromechanics analysis of a weak micro-inclusion subjected to plasticity and damage embedded in an elastic meso-element. The consideration of plasticity coupled with damage equations at microscale, altogether with Eshelby–Kroner localization law, allows computing the value of microscopic damage up to failure for any kind of loading, 1D, 2D or 3D, cyclic or random, isothermal or anisothermal, mechanical, thermal or thermo-mechanical.

In this Paper, the continuum damage mechanics framework for high cycle fatigue initiated by Lemaitre and developed by R.Desmorat have been presented as a robust numerical scheme in order to validate the model numerically. To aim this target, a fully coupled constitutive two scale elastic-plastic-damage model is developed and implemented inside the finite element commercial code ABAQUS.

**Keywords:**Damage Mechanics; High Cycle Fatigue; FEM analysis; Two Scale Damage Model.