Tantalum plate and rod materials that demonstrate mild-to-strong anisotropic plastic flow during large deformation are analyzed in terms of tensorial property symmetry. Texture interrogations of these materials reveal duplex orientation components that have implications with regard to the symmetry realized during plastic deformation; specifically these materials show less symmetry than one would expect from a cursory examination of the texture. Mesoscale polycrystal simulations are performed to probe a general shape for the yield surface function based on a discrete orientation distribution representation of the material texture and previously established single-crystal deformation modes. The yield surface shape is mathematically represented in terms of second and higher-order tensors. A plastic compliance analysis is presented and applied to graphically map the deformation symmetry contained in these tensors for both ideal and real materials. Compliance results are shown to be consistent with finite element simulations of r-value specimens loaded in uniaxial tension.

Almansi and Green strain tensors are developed for use in large deformation molecular dynamics/statics simulations that employ Embedded Atom Method (EAM) potentials for metals. The strain tensors are formulated with respect to the deformation gradient. A scalar potential function is used with a weighting function that is dependent upon a cutoff radius for the deformation gradient. For a homogeneous or inhomogeneous deformation, a cutoff distance of one lattice parameter can be used to approximate local strain level. Inhomogeneous deformation reveals different results for Almansi and Green strain tensors indicating that the small strain assumption cannot be used to determine large atomic strains.

The use of transient mechanical tests such as repeated load relaxations and repeated creep tests provide some insight on the respective contribution of mobile dislocation densities and velocities to the plastic strain-rate and also on the hardening mechanisms. Improvements of the second technique are reported as well as results on Ni3Al polycrystals. Other materials (e.g. Cu, TiAl) are considered for comparison. Correlations are found between dislocation exhaustion rates, workhardening coefficients and the amplitude of yield point at reloading after the relaxations.

One has simulated by a finite element computation, the tensile plastic deformation of bcc aggregates with the same initial crystallographic texture but a different spatial distribution of orientations. The computations show fairly large differences between the simulations in terms of axial strain fields: one aggregate presents an homogeneous field, while another one localizes the strain in a narrow band. This “macroscopic effect” is then analyzed at the smaller scale of the crystallite by comparing local re-orientations, glide activity and stress levels. The influence of neighboring grains and of the “local”texture is thus shown. This is an effect that polycrystalline models (Taylor or self-consistent models) cannot account for.

Serrated plastic flows or propagating Portevin-Le Chatelier (PLC) bands in uniaxial tensile aluminum alloy sheet samples were analyzed by a 3D finite element model. A local dynamic strain aging viscoplasticity model motivated by dislocation dynamics was implemented in an ABAQUS user material subroutine. When the sheet metal was assumed to be spatially homogeneous, individual plastic deformation bands inclined about 50° with regard to the axial tensile loading were predicted by the model to propagate along the thin sheet sample, similar to the experimentally observed behavior of the solid solution strengthened alloy AA5182-0. When the sheet metal was assumed to be inhomogeneous by making a few material elements slightly harder or softer, the model predicted a propagating single neck formed by double shear bands, similar to the behavior of the precipitation strengthened alloy AA6111-T4.

Previous work using in-situ curvature measurement has shown a correlation between stress and microstructure during the early stages of thin film growth. The model presented here can be used to predict the curvature change of the substrate during part of this growth process. Curvature, and thus film stress, is measured in-situ during growth of sputter-deposited Pt on amorphous substrates. The average film stress is observed to be slightly compressive initially, followed by a change towards a tensile maximum, after which the stress becomes compressive again. Plan view TEM micrographs of Pt films of thicknesses up to 35 Å show the evolution of microstructure from isolated islands to a coalesced film. This evidence suggests that the tensile regime is due to island coalescence. The model calculates the curvature induced in a substrate during the tensile excursion associated with island coalescence, where discontinuous islands are modeled as a series of cracks in an otherwise continuous film. Quantitative measurements of island size and areal fraction covered are extracted from the TEM micrographs and used to predict the curvature during coalescence. The predicted stresses are shown to compare favorably with the measured stresses.

The evolution of the constitutive parameter, the mean slip distance, λ, is monitored during tensile deformation of 3.2 μm grain size aluminum at 200 K. Transmission electron microscopy (TEM) confirms that the grain size, D, sets an upper limit to λ.

Micro-indentation experiments have shown very strong size dependence of the indentation hardness, a phenomenon that cannot be explained by classical plasticity theories. A theory of mechanism-based strain gradient (MSG) plasticity has been developed based on the Taylor model in dislocation theories, and is intended for materials and structures whose dimension controlling plastic deformation falls roughly between 0.1 to 10 microns. The MSG plasticity theory is used in the present study to investigate the size effects observed in micro-indentation experiments. It is shown that the theory can indeed reproduce micro-indentation experimental data, thus providing an important self-consistent check of the MSG plasticity theory.

In this work a recently proposed gradient and rate-dependent crystallographic formulation is used to investigate the macroscopic behaviour of a precipitated single crystal. It relies on strain gradient concepts to account for the additional strengthening mechanism caused by presence of interfacial and geometrically necessary dislocations (GNDs). The total slip resistance is assumed to be due to a mixed population of mobile and sessile forest obstacles arising from both statistically stored dislocations (SSDs) and GNDs. The non-local crystallographic theory is implemented numerically into the finite element method. It requires the calculation of the slip rate gradients at the element level to determine the evolutionary behaviour of the GND densities, and a fully implicit numerical algorithm within a large strain kinematics framework and non-isothermal conditions. The effects of the relevant microstructural features (precipitate size, morphology and volume fraction) and deformation gradient-related length scales on the macroscopic behaviour is investigated and compared with experimental results.

Strain localization in mild steel submitted to a sequential loading paths is investigated at macroscopic, mesoscopic and microscopic scales. The experimental results demonstrate that the morphology of the localization and the nominal load-displacement curves depend on the microstructural anisotropy. A crystalline model using a finite element code is proposed. The anisotropy is described by a hardening matrix whose terms correspond to dislocation-dislocation interactions and depend on the evolution of the dislocation densities on the activated slip systems during the sequential tests. The strain localization predicted by this model fits with the experimental observation and allows us to assume that localization is correlated to the saturation on the activated slip systems.

Some recently-developed experimental techniques, such as in situ ultra-small-angle Xray scattering (USAXS), have demonstrated a capability for measuring aspects of dislocation structure evolution that are inaccessible to other experimental methods. However, no single technique can provide the entire range of information required by theoretical and computational researchers. It is only through the synergy of several experimental techniques (such as USAXS, transmission electron microscopy, and X-ray diffraction imaging) that much of the required quantitative information can be obtained. Ultimately, the development of additional new experimental techniques will also be required.

The plasticity of thin films and layers is of considerable technological interest. For instance, the relaxation of internal stresses in semiconducting epitaxial layers has been the object of many studies [1, 2]. This relaxation is usually treated via the concept of critical thickness, the latter being defined as the maximum layer thickness below which dislocations cannot spontaneously move and relax the internal stresses. The various internal stresses present in epitaxial layers (e.g. the misfit and elastic incompatibility stresses at the film/substrate interface and the image force in a free-standing film) can be computed within a continuum frame. However, the way they influence the motion of a dislocation has not yet been computed, even in a approximate manner. An useful approximation that allows treating the boundary condition at the surface of a free-standing film consists of making use of the concept of image dislocation. Then, the critical stress for moving a dislocation in a free-standing film is the same as that of a capped layer of thickness twice that of the film. To date, models and dislocation dynamics (DD) simulations are available that involve several levels of approximation for the treatment of the dislocation/interface and dislocation/surface interactions [3–7]. For reasons that are not clearly understood, however, these models predict critical thicknesses that are systematically larger than the expected ones. The comparison with experiment is, in addition, made difficult because stresses have to be artificially introduced to replace the internal stresses and approximations have to be done to treat the image stresses. In the present work it is shown that it is now possible to fully account for the contribution of the various sources of internal stresses to the critical stress for the motion of a threading dislocation. This is performed numerically with the help of a hybrid code that combines a DD code for the treatment of the dislocation dynamics and a Finite Element (FE) code for the treatment of the boundary conditions. In what follows, several applications of this discrete-continuum model (DCM) to the study of dislocation motion in epitaxial layers are presented. The motion of a dislocation in a thin film is considered, including the image force and successively adding a misfit stress and an elastic incompatibility stress at the film/substrate interface.

The deformation behavior of (0001) <1210> basal slip in single crystals of five different transitionmetal disilicides with the C40 structure has been investigated in the temperature range from room temperature to 1500°C in compression. These disilicides are found to be classified into two groups depending on the onset temperature for plastic flow. The low-temperature group, which consists of VSi2, NbSi2 and TaSi2, exhibits the onset temperature for plastic flow around 0.3 T/Tm (melting temperature) and deforms by a conventional shear mechanism. In contrast, the high temperature group, which consists of CrSi2 and Mo(Si,Al)2, exhibits the onset temperature around 0.6T/Tm and deforms by a synchroshear mechanism. Factors affecting the deformation mechanism in these C40 disilicides are discussed in terms of directionality of atomic bonding and the relative stability of the C40 phase with respect to the C11b phase.

Recently, we have designed and produced several transition metal Laves phases with low-temperature compressive ductility. These improved alloys demonstrate that manipulation of atomic-scale structure can have a drastic effect on meso-scale deformation behavior. To gain a basic understanding of the role of atomic-scale substitutions on the room temperature mechanical properties, a systematic investigation of the Laves ZrCr2-based alloy system alloyed with Hf, Nb, Ta and Ti was conducted and is reported here. Extensive room temperature ductility was obtained in the Hf-alloyed ternary Laves phase alloy system. Mechanical twinning is found to be the predominant deformation mode at room temperature in this alloy system. It is emphasized that Hf substitution in the Zr sublattice of ZrCr2 may play the most prominent role in changing the local electronic structure resulting in easier twinning.

Plastic response of a solid under stress depends on its crystallographic structure and morphology. Two of the major mechanisms of plasticity in metals are crystallographic slip and twinning. The purpose of this work is to analyze the influence of local stress distribution on slip and twin nucleation and propagation and to examine how this behavior depends on the interaction among slips, twins, and grain boundaries. We formulate a simple model in which slip and twin systems are defined at appropriate angles to each other. Plastic flow is treated as a Markovian stochastic process consisting of a series of local inelastic transformations (LITs) in the representative volume elements (RVE). The probabilities of LITs per unit time are defined in the framework of transition-state theory. By varying the types of allowed LITs and/or the scale of RVE, plastic deformation is modeled at different structural levels, from a small volume of single crystal to the aggregate response of an isotropic polycrystalline solid. An important feature of this model is that evolution of the internal stress distribution is traced explicitly throughout the simulation run. This allows us to examine conditions of slip and twinning in considerable detail. In particular, we observe that twinning occurs through a nucleation-and-growth mechanism whose rate is controlled by the size of the critical nucleus of the new phase.

The generation and motion of dislocations in high-purity single crystals of Mo have been observed in real time by deforming electron-transparent samples in-situ in a transmission electron microscope. At 300 K and at low levels of stress, a novel dislocation source was observed that generated a long, straight screw dislocation. The source was a dislocation tangle that existed in the annealed material. An edge dislocation emerged from the tangle, trailing behind it the screw dislocation. These screw dislocations were immobile at this stress level. At higher stresses, the same dislocation tangle generated many dislocations, but now by a pole mechanism. The nature of these tangles and the source operation mechanisms will be described.

Initial dislocation structure in annealed high-purity Mo single crystals and deformation substructure in a crystal subjected to 1% compression have been examined and studied using transmission electron microscopy (TEM) techniques in order to investigate dislocation multiplication mechanisms in the early stage of plastic deformation. The initial dislocation density is in a range of 106 σ 107 cm−2, and the dislocation structure is found to contain many grown-in superjogs along dislocation lines. The dislocation density increases to a range of 108 σ 109 cm−2, and the average jog height is also found to increase after compressing for a total strain of 1%. It is proposed that the preexisting jogged screw dislocations can act as (multiple) dislocation multiplication sources when deformed under quasi-static conditions. The jog height can increase by stress-induced jog coalescence, which takes place via the lateral migration (drift) of superjogs driven by unbalanced line-tension partials acting on link segments of unequal lengths. The coalescence of superjogs results in an increase of both link length and jog height. Applied shear stress begins to push each link segment to precede dislocation multiplication when link length and jog height are greater than critical lengths. This “dynamic” dislocation multiplication source is suggested to be crucial for the dislocation multiplication in the early stage of plastic deformation in Mo.

Using linear elastic dislocation dynamics simulations, we show that junction formation between dislocations from various interacting slip systems can be predicted by a simple self-energy calculation. We find that this prediction is robust: dislocation curvature and external stress produce little change in the simulation results for junction formation. One key to this success appears to be a separation of timescales, where movement of the far away dislocation arms (under, for example, external stress) is typically slow compared to the process of making a junction. The self-energy calculation we describe gives a rule for dislocation encounters which should allow a considerable saving in computational effort, allowing one to impose correct interaction outcomes without calculating the interactions in detail. We also find that dislocations often come together under attraction without forming a junction. The resulting “cross-linked” state provides an additional type of connection between dislocations. We include preliminary results on the persistence of junctions and cross-linked states under stress.

Dislocations are the elementary carriers of plastic flow and are ideally at the base of any physical model for plastic deformation. In the last few years, several 3-D simulations of Dislocation Dynamics (DD) have been devoted to the analysis of single crystal plasticity at small strains [1–5]. However, such DD simulations have some limitations which restrict their domain of application: (i) In many materials, there is a lack of accurate input regarding the mechanisms governed by the core properties of dislocations. (ii) The plastic strain amplitude that can be simulated is usually small (e.g. smaller than 1% in f.c.c. crystals). (iii) The boundary conditions of the simulations are generally rather crude and may introduce spurious size effects and various other artefacts. Most of the time, the questions of stress equilibrium and dislocations flux at the external surfaces are not addressed.

This paper concentrates on application of the so-called Discrete Dislocation Plasticity to high strain rate deformations. In particular the question is addressed if the DDP approach may capture the specific processes taking place at high strain rates. In particular the paper reports on tests of the validity of some approximations and provides some sample runs to show the applicability of the method. In assessing the results, one has to keep in mind two underpinning aspects: (1) the model is two-dimensional and (2) the results hold only in the regime where linear isotropic elasticity is valid. It was concluded that accelerations can not be neglected at very high strain rate deformations, both for the conventional and the relativistic case.