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139 Modeling High Cycle Fatigue Failure Using Continuum Damage Mechanics Majid Hamid m hamid@avadis org m hamid@me iut ac ir July 06 2010 Department of Mechanical Engineering Isfahan University of Technology Isfahan 84156 83111 Iran Degree M Sc Language Farsi Supervisors Mashayekhi Mohammad Assistant Professor Email mashayekhi@cc iut ac ir Khademizadeh Hasan Assistant Professor Email khademizadeh@cc iut ac ir 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 Even during the evolution of the damage there is no easy precursor to detect the danger of a failure 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 RVE of continuum mechanics The consideration of plasticity coupled with damage equations at microscale altogether with Eshelby Kr ner 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 The main advantage of developing a user subroutine inside a commercial finite element code is the access to a wide range of element types material models and other facilities such as efficient equation solvers

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