219 research outputs found

    Size effects and idealized dislocation microstructure at small scales: predictions of a phenomenological model of Mesoscopic Field Dislocation Mechanics: Part I

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    A Phenomenological Mesoscopic Field Dislocation Mechanics (PMFDM) model is developed, extending continuum plasticity theory for studying initial-boundary value problems of small-scale plasticity. PMFDM results from an elementary space-time averaging of the equations of Field Dislocation Mechanics (FDM), followed by a closure assumption from any strain-gradient plasticity model that attempts to model effects of geometrically-necessary dislocations (GND) only in work-hardening

    Modeling dislocation sources and size effects at initial yield in continuum plasticity

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    Size effects at initial yield (prior to stage II) of idealized micron-sized specimens are modeled within a continuum model of plasticity. Two different aspects are considered: specification of a density of dislocation sources that represent the emission of dislocation dipoles, and the presence of an initial, spatially inhomogeneous excess dislocation content. Discreteness of the source distribution appears to lead to a stochastic response in stress-strain curves, with the stochasticity diminishing as the number of sources increases. Variability in stress-strain response due to variations of source distribution is also shown. These size effects at initial yield are inferred to be due to physical length scales in dislocation mobility and the discrete description of sources that induce internal-stress-related effects, and not due to length-scale effects in the mean-field strain-hardening response (as represented through a constitutive equation)

    Rigorous results on the threshold network model

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    We analyze the threshold network model in which a pair of vertices with random weights are connected by an edge when the summation of the weights exceeds a threshold. We prove some convergence theorems and central limit theorems on the vertex degree, degree correlation, and the number of prescribed subgraphs. We also generalize some results in the spatially extended cases.Comment: 21 pages, Journal of Physics A, in pres

    Size effects and idealized dislocation microstructure at small scales: predictions of a phenomenological model of Mesoscopic Field Dislocation Mechanics: Part II

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    In Part I of this set of two papers, a model of mesoscopic plasticity is developed for studying initial-boundary value problems of small scale plasticity. Here we make qualitative, finite element method-based computational predictions of the theory. We demonstrate size effects and the development of strong inhomogeneity in simple shearing of plastically-constrained grains. Nonlocality in elastic straining leading to a strong Bauschinger effect is analyzed. Stability of the time dependent, spatially homogeneous, simple shearing solution of PMFDM is studied. Results from thermal cycling of small scale beams/films with different degrees of constraint to plastic flow are presented showing size effects and reciprocal-film-thickness scaling of dislocation density boundary layer width

    Finite Element Modelling of Conventional and Hybrid Oblique Turning Processes of Titanium Alloy

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    AbstractThis study is a part of the on-going research at Loughborough University, UK, on finite element (FE) simulations of ultrasonically assisted turning (UAT) coupled with hot machining processes. In UAT, vibration is superimposed on the cutting tool movement, resulting in several advantages of the process, especially in machining of high-strength engineering materials. Direct experimental studies of machining processes are expensive and time consuming, especially when a wide range of machining parameters affects, complex thermo-mechanical high-deformation processes in machined materials. In recent years, a use of mathematical simulations and, in particular, FE techniques has gained prominence in the research community. These techniques provide an accurate and efficient modelling paradigm for machining processes. In the present work, thermo-mechanically coupled three-dimensional FE models of conventional, ultrasonically assisted turning and a new hybrid turning technique called hot ultrasonically assisted oblique turning for a case of titanium alloy are presented. A nonlinear temperature-sensitive material behaviour is incorporated in our numerical simulations based on the results of the split-Hopkinson pressure bar tests. The simulation results obtained at different cutting conditions are compared to elucidate main deformation mechanisms responsible for the observed changes in the material's responses to various cutting techniques

    Stability, quasinormal modes in a charged black hole in perfect fluid dark matter

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    In this work, we study time-like and null geodesics in a charged black hole background immersed in perfect fluid dark matter (PFDM). Using the condition for circular geodesics, we evaluate the energy (EE) and angular momentum (LL) in terms of the radius (rcr_c) of the circular orbits. The existence and finite-ness of EE and LL constrain the possible range of PFDM parameter (χ\chi) and the radius of the circular orbit (rcr_c). We then use the Lyapunov exponent (λ\lambda) to study the stability of the geodesics. Then we analyze the critical exponent (Îł\gamma) useful for determining the possibility of detection of gravitational wave signals. After that, we study the perturbation due to a massless scalar field in such a background and calculate the quasinrmal mode (QNM) frequencies and their dependence on PFDM parameter χ\chi and black hole charge QQ. Also, we compare the obtained QNM frequencies both in the exact case and in the eikonal limit. We also calculate the quality factor of the oscillating system and study its dependence on χ\chi and QQ. Finally, we evaluate the black hole shadow radius RsR_s and graphically observe the effect of χ\chi and QQ on it.Comment: 29 pages, 18 Figures; Comments are welcom