Modeling the Low Cycle Fatigue in Copper Single Crystal: Multiscale Dislocation Dynamics Simulations
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Modeling the Low Cycle Fatigue in Copper Single Crystal: Multiscale Dislocation Dynamics Simulations Micheal Kattoura and Mutasem Shehadeh Mechanical Engineering Department, American University of Beirut, Beirut, Lebanon ABSTRACT Multiscale dislocation dynamics plasticity (MDDP) model is used to investigate the evolution of dislocation microstructure in copper single crystals subjected to low cycle fatigue loading. Half cycle total plastic strain simulations are carried out at strain amplitudes ranging from 1×10-3 to 8×10-3. The initial hardening is investigated and the micro-structural cause behind it is presented. In addition, the loading history is presented and the effect of the initial micro-structure and dislocation distribution on the hardening behavior is studied. In addition, the evolution of the microstructures is examined. In depth analyses of the dislocation microstructures show that: 1) dislocation planes that are parallel and very close to each other are formed, 2) these walls contain dipoles that keep on zipping and unzipping during the first few cycles until they reach some stable zipping configuration. We can see that the hardening rate decreases with the increase of the number of cycles where we have large hardening rate in the first cycles then we reach to somehow constant stress. Our results are qualitatively in good agreement with recent experimental results of low cycle fatigue deformation. INTRODUCTION During the past several decades, extensive experimental works have been carried out to investigate the response of FCC single crystals to cyclic loading [1-6]. One of the main features of fatigue deformation is the localized nature of the induced plasticity. Hanriot et al [7] showed that intense slip bands appear on the surface of the tested specimen Ni based alloys. For section specimens on the other hand, the dislocation microstructure on the slip planes evolves with number of cycles from dislocation entanglements, followed by rough walls of dislocation dipoles and finally persistent slip bands (PSBs). The microstructural evolution in fatigued specimen can be linked with the mechanical response of the material. In single slip deformation, clear hardening effect is observed with the accumulation of plastic strain until the stress reaches a saturation stress value. Mughrabi [4] performed strain controlled fatigue experiments in Cu crystals oriented for single slip and established the famous cyclic stress–strain (CSS). Basinski and Basinski [2] attempted to form a picture of what has been learned over the years from some of the fundamental studies of cyclic deformation, with special reference to experimental studies. In addition to experimental studies, theories, models and computer simulations have been used mostly at the macro scale to investigate different aspects of fatigue deformation. Constitutive models have been proposed and used to explain the hardening and the extrusion formation in single slip deformation [8-11]. Finite element methods have been utilized to analyze various problems in
