پياده سازي مدل آسيب غير محلي در مواد شكل پذير و كاربرد آن در فرايند براده برداري متعامد

چكيده انگليسي :

Implementation of Nonlocal Ductile Damage Model and Its Application in Orthogonal Cutting Process Adel Shams adel shams@gmail com 20st April 2011 Department of Mechanical Engineering Isfahan University of Technology Isfahan 84156 83111 IranDegree MSc Language FarsiMohammad Mashayekhi mashayekhi@cc iut ac irABSTRACTIn the present work a general framework for a nonlocal damage model based on the implicit gradient damage modelis developed and implemented using finite element method Continuum damage models describe the changes ofmaterial stiffness and strength caused by the evolution of defects in the framework of continuum mechanics Inmany materials a fast evolution of defects leads to stress strain laws with softening which creates seriousmathematical and numerical problems A standard implementation of constitutive equations which include strainsoftening behavior results in general unsatisfactory The reason for this is the observed dependency of the obtainedresults with mesh size and orientation especially in the neighborhood of localized damage area The finite elementsimulations of material instability problems converge to meaningful results upon further refinement of the finiteelement mesh since the width of the fracture process zone shear band is determined by the intrinsic material lengthscale while the classical continuum theories fail to address this problem This dependency can be explained by thechange of type of the equilibrium equations To avoid pathological localisation and mesh dependence and to incorporate length scale effects due tomicrostructure evolution the damage growth is driven by a nonlocal variable via a second order partial differentialequation This implicit gradient formulation introduces an additional partial differential equation of the Helmholtztype which is solved in a coupled fashion with the standard equilibrium equation The presented formulation whichconsists on a coupled finite element technique where two fields are interpolated nonlocal plastic strain anddisplacement is very effective in removing mesh dependency due to strain softening that affects the standard localmodels usually adopted for the analysis of ductile material behavior Implementing this coupled problem in a finite element program for small deformations follows standard routines elaboration of the weak form of the governing equations linearization and discretization The system of equations isincorporated in a full Newton Raphson incremental iterative solution strategy which makes use of a return mappingscheme with an elastic predictor plastic corrector procedure that only slightly differs from the commonly adoptedscheme by the addition of the nonlocal damage term To ensure quadratic convergence of the Newton Raphsonscheme Attention is mainly focused on the tangent operators that are required to update the stresses This thesiscovers a study on using nonlocal damage model in simulation of orthogonal metal cutting by finite element method The numerical examples presented in the following thesis have a twofold purpose to illustrate the effectiveness ofthe proposed nonlocal implicit gradient formulation in attenuating the mesh dependency in cutting simulationinvolving damage localization due to formation of primary shear band and propose a reliable separation criteria fororthogonal metal cutting To focus on effectiveness of the proposed nonlocal implicit gradient formulation on thecutting simulation a simple finite element model under plane strain deformation will be used to investigate themechanics of cutting from the incipient stage The use of nonlocal gradient damage models in cutting simulation analysis provides consistent and reliable FEMsimulation The use of nonlocal damage aims to obtain a clearer figure about the reliability of the separation criteriafor orthogonal metal cutting Keywords Nonlocal Damage Finite Element Method Length Scale Shear Band Localization Separation Criterion Orthogonal Cutting

شمس، عادل

پياده سازي مدل آسيب غير محلي در مواد شكل پذير و كاربرد آن در فرايند براده برداري متعامد

روش اجزاي محدود , طول مشخصه داخلي , باند برشي , محلي شدن آسيب , معيار جدايش