The effect of specimen size on the uniaxial deformation response of planar single crystals and polycrystals is investigated using discrete dislocation plasticity. The dislocations are all of edge character and modelled as line singularities in a linear elastic material. The lattice resistance to dislocation motion, dislocation nucleation, dislocation interaction with obstacles and dislocation annihilation are incorporated through a set of constitutive rules. Grain boundaries are modelled as impenetrable to dislocations. Two types of polycrystalline materials are considered: one that only has grains with a single orientation while the other has a checker-board arrangement of two types of grains which are rotated 90 • with respect to each other. The single crystals display a strong size dependence with the flow strength increasing with decreasing specimen size. In sufficiently small single crystal specimens, the nucleation rate of the dislocations is approximately equal to the rate at which the dislocations exit the specimens so that below a critical specimen size the flow strength is set by the strength of the initially present Frank-Read sources. On the other hand, grain boundaries acting as barriers to plastic deformation in polycrystalline specimens of the same size lead to a more diffuse deformation pattern and to a nearly size-independent response.
Take-down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim.Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons the number of authors shown on this cover page is limited to 10 maximum. AbstractThe plane strain indentation of single crystal films on a rigid substrate by a rigid wedge indenter is analyzed using discrete dislocation plasticity. The crystals have three slip systems at AE35:3 and 90 with respect to the indentation direction. The analyses are carried out for three values of the film thickness, 2, 10 and 50 mm, and with the dislocations all of edge character modeled as line singularities in a linear elastic material. The lattice resistance to dislocation motion, dislocation nucleation, dislocation interaction with obstacles and dislocation annihilation are incorporated through a set of constitutive rules. Over the range of indentation depths considered, the indentation pressure for the 10 and 50 mm thick films decreases with increasing contact size and attains a contact size-independent value for contact lengths A44 mm. On the other hand, for the 2 mm films, the indentation pressure first decreases with increasing contact size and subsequently increases as the plastic zone reaches the rigid substrate. For the 10 and 50 mm thick films sink-in occurs around the indenter, while pile-up occurs in the 2 mm film when the plastic zone reaches the substrate. Comparisons are made with predictions obtained from other formulations: (i) the contact sizeindependent indentation pressure is compared with that given by continuum crystal plasticity; (ii) the scaling of the indentation pressure with indentation depth is compared with the relation proposed by Nix and Gao [1998
Discrete dislocation plasticity analysis of the grain size dependence of the flow strength of polycrystals Balint, D. S.; Deshpande, V. S.; Needleman, A.; Van der Giessen, E. Take-down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim.Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons the number of authors shown on this cover page is limited to 10 maximum. AbstractThe grain size dependence of the flow strength of polycrystals is analyzed using plane strain, discrete dislocation plasticity. Dislocations are modeled as line singularities in a linear elastic solid and plasticity occurs through the collective motion of large numbers of dislocations. Constitutive rules are used to model lattice resistance to dislocation motion, as well as dislocation nucleation, dislocation annihilation and the interaction with obstacles. The materials analyzed consist of micron scale grains having either one or three slip systems and two types of grain arrangements: either a checkerboard pattern or randomly dispersed with a specified volume fraction. Calculations are carried out for materials with either a high density of dislocation sources or a low density of dislocation sources. In all cases, the grain boundaries are taken to be impenetrable to dislocations. A Hall-Petch type relation is predicted with Hall-Petch exponents ranging from %0.3 to %1.6 depending on the number of slip systems, the grain arrangement, the dislocation source density and the range of grain sizes to which a Hall-Petch expression is fit. The grain size dependence of the flow strength is obtained even when no slip incompatibility exists between grains suggesting that slip blocking/transmission governs the Hall-Petch effect in the simulations.
Micro-cantilevers are increasingly used to extract elastic and plastic material properties through controlled bending using a nanoindenter. Focused Ion Beam milling can be used to produce small scale single crystal cantilevers with cross-sectional dimensions on the order of microns, and electron backscatter diffraction (EBSD) allows cantilevers to be milled from a grain with a desired crystal orientation. Micro-cantilever bending experiments suggest that sufficiently smaller cantilevers are stronger, which is generally believed to be related to the effect of the neutral axis on the evolution of the dislocation structure. A planar model of discrete dislocation plasticity was used to simulate end-loaded cantilevers to interpret the behaviour observed in experiments. The model allowed correlation of the initial dislocation source density and resulting slip band spacing to the experimental load displacement curve. There are similarities between the predictions of this model and those of earlier discrete dislocation plasticity models of pure bending. However, there are notable differences, including a strong source density dependence of the size effect that cannot be explained by geometrically necessary dislocation (GND) arguments, and the effect of the cantilever stress distribution on the locations of soft pile-ups. The planar model was used to identify zero resolved shear stress isolines, rather than the neutral axis, as controlling the soft pile-up location, and source spacing as limiting the slip band spacing in the observed size effect; strengthening was much greater in the source-limited regime. The effect of sample dimensions and dislocation source density were investigated and compared to small scale mechanical tests conducted on titanium and zirconium. The calculations predict a scaling exponent n % 1 for the dependence of stress on size if size is normalised by the average source spacing and a term representing the size-independent flow stress is included, whereas the simple power-law form ordinarily used to fit experimental data significantly underestimates n.
This paper presents a novel plane-stress continuum damage mechanics (CDM) model for the prediction of the different shapes of forming limit diagrams (FLCs) for aluminium alloys under hot stamping conditions. Firstly, a set of uniaxial viscoplastic damage constitutive equations is determined from tensile experimental data of AA5754 at a temperature range of 350-550 C and strain rates of 0.1, 1.0 and 10 s À1 . The tests were carried out on Gleeble materials simulator (3800). Based on the analysis of features of FLCs for different materials forming at different temperatures, a plane-stress damage equation is proposed to take account the failure of materials at different stress-state sheet metal forming conditions. In this way, a set of multiaxial viscoplastic damage constitutive equations is formulated. The model is calibrated from the FLC data at temperature of 350 C and strain rate of 1.0 s À1 for AA5754. A good agreement has been achieved between the experimental and numerical data. The effect of the maximum principal stress, effective stress and hydrostatic stress on the materials failure features and on the shape of FLCs is studied individually and in combination. Using the newly developed plane-stress unified viscoplastic damage constitutive equations, the FLC of materials can be predicted at different temperatures and strain rate forming conditions.
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