Abstract: The relationships between a slip system in the parent lattice and its transform by twinning shear are considered in regards to tangential continuity conditions on the plastic distortion rate at twin/parent interface. These conditions are required at coherent interfaces like twin boundaries, which can be assigned zero surface-dislocation content. For two adjacent crystals undergoing single slip, relations between plastic slip rates, slip directions and glide planes are accordingly deduced. The fulfillment of these conditions is investigated in hexagonal lattices at the onset of twinning in a single slip deforming parent crystal. It is found that combinations of slip system and twin variant verifying the tangential continuity of the plastic distortion rate always exist. In all cases, the Burgers vector belongs to the interface. Certain twin modes are only admissible when slip occurs along an ãaã direction of the hexagonal lattice, and some others only with a ãc + aã slip. These predictions are in agreement with EBSD orientation measurements in commercially pure Ti sheets after plane strain compression.
Abstract: Finite element analyses of the overall mechanical response of metalâmatrix composites are carried out using three different models: standard crystal plasticity, crystal plasticity appended with a tangential continuity condition on the plastic distortion at matrix/particle interfaces, and a field dislocation mechanics model accounting for the presence and transport of polar dislocations. The focus is on assessing the effects of particle shape and size on the work hardening of the composite, as well as its loading path dependence. To a different amount, all models account for shape and size effects, and retrieve the Bauschinger effect. In standard crystal plasticity, the origin of these properties lies in Hadamard's compatibility conditions at the matrix/particle interfaces, but the size effects cannot be quantitatively predicted due to the absence of an intrinsic length scale. Supplementing crystal plasticity with the tangential continuity of the plastic distortion strongly enhances the particle shape and size effects, and the path dependence of the overall mechanical behavior. However, only the additional presence of polar dislocations in the third model allows quantitative prediction of the effects of size, by adding internal length scales (in relation with lattice incompatibility and dislocation transport) and dislocation microstructure building to the description of composite material straining.
Abstract: A grain-size dependent accommodation law for polycrystals is deduced from an inclusion/matrix problem (i.e., each grain is seen as embedded in a homogeneous equivalent medium) where plastic strain inside the inclusion is given as a discrete distribution of circular coaxial glide dislocation loops. The loops are assumed constrained at spherical grain boundaries. From thermodynamic considerations specific to a process of identical plastification in all the loops (considered as âsuper-dislocationsâ), an average back-stress over the grain is derived. In order to compute the very early stages of plastic deformation in a face-centred cubic polycrystal, this back-stress is incorporated into a diluted model in terms of concentration of plastic grains. Contrary to conventional mean-field approaches, a grain-size effect is obtained for the initial overall strain-hardening behaviour. This size effect results from an intrinsic contribution of intragranular slip heterogeneities on the kinematical hardening.
Abstract: In this paper, we derive the mechanical fields (internal stresses, elastic energy) arising from the presence of an inelastic distortion field representing a typical intra-granular âmicrostructureâ as the one observed during the plastification of metallic polycrystals. This âmicrostructureâ is due to the formation of discrete intra-granular plastic slip heterogeneities characterized by at least two internal lengths: the first one is the individual grain size which represents a stochastic parameter inherent to the processing route (prior working, annealing), and, the second one is the spatial distance between active slip lines or slip bands associated with inhomogeneous plastic slip in the interior of grains. These internal lengths can be observed and measured using conventional experimental techniques (EBSD, TEM, AFM). The micro-mechanical modeling of the mechanical fields associated with plastic slip events inside grains is performed with two different assumptions. The first one is based on the well-known Eshelbyâs problem of plastic inclusion where only the grain diameter is considered as internal length scale. This classical method considers homogeneous plastic distortion in the grain and leads to a uniform and grain size independent total strain field in the grain. The second method accounts for a non-uniform plastic distortion in the grain characterized by its discrete nature and the two aforementioned internal lengths. Both methods consider grains as spherical inclusions with a given diameter embedded in a homogeneous medium. For the second method, plastic slip is constrained by grain boundaries seen as impenetrable obstacles to dislocations. Thus, plastic strain is embodied by distributions of discrete circular glide loops. After writing the field equations and the free energy of the medium, a micro-mechanical formulation based on the Fourier transform method is developed. It is then found that in contrast with the mean-field approach, the internal stress fields as well as the elastic energy corresponding to different dislocation configurations depend on internal lengths associated to the deformed medium. Different possible configurations associated with intra-granular plastic flow due to circular glide dislocation loops are analyzed. Finally, the results are discussed with respect to the grain size dependence of the flow strength and the Bauschinger effect for plastically deforming polycrystals and perspectives to develop new microâmacro transition schemes accounting for internal length scales are sketched out.
Abstract: Aging of ice single crystals subjected to creep exhibits peculiar behavior. If the sample is unloaded after sufficient strain, a forward jump in creep rate is observed at reloading. Sequences of loading periods alternated with either increasing or decreasing unloading intervals were performed to document this phenomenon. During the tests, acoustic emission was recorded in order to characterize dislocation activity and spatial distribution. Predictions obtained from a field dislocation theory coupling the evolution of statistical and polar dislocation densities compare fairly well with experimental results. Polar dislocation density reflects lattice incompatibility and long-range internal stresses. The associated back-stress and its relaxation during aging are seen as the origin of the acceleration effect. The interplay between dislocation velocity enhancement and polar dislocation annihilation during aging controls the phenomenon, whereas statistical dislocations only play a minor role. The reverse relaxation deformation observed during unloading periods is reproduced well by the model.
Abstract: Plasticity, a key property in the mechanical behavior and processing of crystalline solids, has been traditionally viewed as a smooth and homogeneous flow. However, using two experimental methods, acoustic emission and high-resolution extensometry, to probe the collective dislocation dynamics in various single crystals, we show that its intermittent critical-like character appears as a rule rather than an exception. Such intermittent, apparently scale-free plastic activity is observed in single-slip as well as multislip conditions and is not significantly influenced by forest hardening. Strain bursts resulting from dislocation avalanches are limited in size by a nontrivial finite size effect resulting from the lamellar character of avalanches. This cutoff explains why strain curves of macroscopic samples are smooth, whereas fluctuations of plastic activity are outstanding in submillimetric structures.
Abstract: Metallic single crystals of hcp (Zn and Cd) and fcc (Cu) lattice structure with various crystallographic orientation were deformed in tension at room temperature. For the study of the intermittent, scale-invariant character of collective dislocation dynamics (crackling plasticity), initially discovered in ice samples, the acoustic emission technique was used. The AE event energy distributions always follow the power law given by P(E) â¼E - Ï E . The exponent Ï E. was calculated for all single crystals and its value is discussed with respect to a character of plastic deformation (single or multi-slip, hardening, twinning).
Abstract: Previous acoustic emission (AE) experiments on ice single crystals, as well as numerical simulations, called for the possible occurrence of self-organized criticality (SOC) in collective dislocation dynamics during plastic deformation. Here, we report AE experiments on hcp metallic single crystals. Dislocation avalanches in relation with slip and twinning are identified with the only sources of AE. Both types of processes exhibit a strong intermittent character. The AE waveforms of slip and twinning events seem to be different, but from the point of view of the AE event energy distributions, no distinction is possible. The distributions always follow a power law given by P(E)EâÏE, with ÏE = 1.5 ± 0.1, even when multi-slip and forest hardening occur. The exponent ÏE is in perfect agreement with those previously found in ice single crystals. Along with observed time clustering and interactions between avalanches, these results are new and strong arguments in favour of a general, SOC-type, framework for crystalline plasticity.
Abstract: The Hall-Petch (HP) law, that accounts for the effect of grain size on the plastic yield stress of polycrystals, is revisited in terms of the collective motion of interacting dislocations. Sudden relaxation of incompatibility stresses in a grain triggers aftershocks in the neighboring ones. The HP law results from a scaling argument based on the conservation of the elastic energy during such transfers. The Hall-Petch law breakdown for nanometric sized grains is shown to stem from the loss of such a collective behavior as grains start deforming by successive motion of individual dislocations.
Abstract: Previous acoustic emission experiments on creeping single crystals of ice showed that the dynamics of an assembly of interacting dislocations self-organized into a scale-free pattern characterized by power law distributions of avalanche sizes. In this paper, we investigate the possible incidence of temperature and microstructure on this emerging pattern. Temperature does not modify the nature of the critical dynamics. However, it seems to modify the avalancheâs relaxation owing to dislocationâphonon interactions. On the other hand, tests on polycrystals reveal the role of grain boundaries as barriers to dislocation motion hindering the emergence of the scale-free pattern, as well as the role of kinematic hardening as a polarized internal stress.
Abstract: Acoustic emission experiments on creeping ice as well as numerical simulations argue for a self-organization of collective dislocation dynamics during plastic deformation of single crystals into a scale-free pattern of dislocation avalanches characterized by intermittency, power-law distributions of avalanche sizes, complex space-time correlations and aftershock triggering. Here, we address the question of whether such scale-free, close-to-critical dislocation dynamics will still apply to polycrystals. We show that polycrystalline plasticity is also characterized by intermittency and dislocation avalanches. However, grain boundaries hinder the propagation of avalanches, as revealed by a finite (grain)-size effect on avalanche size distributions. We propose that the restraint of large avalanches builds up internal stresses that push temporally the dynamical system into a supercritical state, off the scale-invariant critical regime, and trigger secondary avalanches in neighbouring grains. This modifies the statistical properties of the avalanche population. The results might also bring into question the classical ways of modelling plasticity in polycrystalline materials, based on homogenization procedures.
