Dislocations In Crystalline Materials Research Articles

Direct comparison between experiments and dislocation dynamics simulations of high rate deformation of single crystal copper

A long standing challenge in computational materials science is to establish a quantitative connection between the macroscopic properties of plastic deformation with the microscopic mechanisms of dislocations in crystalline materials. Although the discrete dislocation dynamics (DDD) simulation method has been developed for several decades with the goal of addressing this challenge, a one-to-one comparison between the DDD predictions on single crystal stress–strain curves and experimental measurements under identical conditions has not been possible to date. Such a comparison is an essential step towards establishing a dislocation-physics based theory of plasticity and a multiscale framework of the plastic behaviors of crystalline materials. Here we provide direct comparisons between the stress–strain curves of Cu single crystals under high strain rate loading in the [001] and [011] directions obtained from miniaturized desktop Kolsky bar experiments and those from DDD simulations under identical loading conditions. With an appropriate set of parameters, DDD simulations can produce stress–strain curves that are in reasonable agreement with the experimental results. However, the dislocation mobility values needed to achieve this agreement are an order of magnitude lower than expected based on previous measurements and atomistic simulations. We hypothesize that this discrepancy could be caused by drag forces from jogs and point defects produced during the plastic deformation. Cross-slip of screw dislocations is also found to be necessary to capture the experimental stress–strain behavior, especially for the [011] loading direction. This work provides an example of how direct comparisons between DDD simulations and experimental measurements can provide new insight into the fundamental mechanisms of plastic deformation.

Direct atomic-scale imaging of a screw dislocation core structure in inorganic halide perovskites.

Topological defects such as dislocations in crystalline materials usually have major impacts on materials' mechanical, chemical and physical properties. Detailed knowledge of dislocation core structures is essential to understand their impacts on materials' properties. However, compared with imaging of core structures of edge dislocations, direct imaging of a screw dislocation core is challenging from the traditional edge-on direction because the atomic displacements are parallel to the screw dislocation line. Here, a screw dislocation with a Burgers vector 1/2[110] in orthorhombic CsPbBr3 nanocrystals is directly imaged at the atomic scale with the incident electron beam perpendicular to the dislocation line using aberration-corrected scanning transmission electron microscopy (STEM). The dislocation core is characterized by helical atomic planes along the dislocation line. Quantitative assessments of the change rate of the screw displacements reveal the dislocation line locate at a plane containing Cs and Br atoms. This study reveals the atomic structure of screw dislocation cores in CsPbBr3 and provides useful information for the understanding of structure-property relations of halide perovskites.

Scanning transmission electron microscopy image simulations of complex dislocation structures generated by discrete dislocation dynamics

Scanning Transmission Electron Microscopy Diffraction Contrast Imaging (STEM-DCI) has been gaining popularity for the identification and analysis of dislocations in crystalline materials due to its ability to supress undesirable image features that are often present in conventional TEM images. However, there does not yet exist a robust body of work demonstrating expected contrast in these imaging conditions. A novel approach for the simulation of STEM-DCI images was developed using a modified form of the scattering matrix formalism. This algorithm was used to simulate a variety of dislocation configurations generated using three-dimensional discrete dislocation dynamics.

An efficient 2D discrete dislocation Dynamics-XFEM coupling framework and its application to polycrystal plasticity

A new efficient framework coupling the two dimensional (2D) discrete dislocation dynamics (DDD) and the extended finite element method (XFEM) is developed for modeling the dynamic evolution of multiple dislocations in crystalline materials with abundant interfaces/surfaces. By a specially introduced stress calculation scheme with cut-off radius and virtual elements, the present algorithm can capture interaction between neighboring dislocations accurately although no time-consuming dislocation-core enrichment is employed. Since it is not sensitive to the FE mesh size and large XFEM time step can be used, its efficiency is evidently improved compared with other DDD frameworks. Due to the merits of XFEM itself, the present DDD-XFEM scheme can treat intractable surface/interface problems conveniently, with no additional image stress calculation as in the DDD-FEM superposition framework and special plastic-strain distribution near the surfaces/interfaces as in the discrete-continuous method (DCM) needed. For these, it can be used to model plastic behaviors of crystals with abundant interfaces/surfaces (i.e. grain/phase boundaries and crack/void surfaces). To show the ability of present DDD-XFEM scheme, it is used to simulate the mechanical responses of polycrystalline aluminum with assumed rigid and penetrable grain boundaries. A three-stage model for dislocation penetrating through grain boundary (DPTGB) is suggested. The results show that the present DDD-XFEM scheme can capture the formation of dislocation pile-ups and thus the Hall-Petch effect successfully. The DPTGB can decrease the flow stress and hardening rate evidently; moreover, it can weaken the grain size effect and may enhance the cyclic stress relaxation of polycrystals greatly.

Symmetry-Adapted Yield Criterion for Non-Schmid Materials

The current form of the effective yield criterion that is used to describe non-Schmid behavior of dislocations in crystalline materials is not invariant under the simultaneous change of the slip direction and the slip plane normal as dictated by crystallography. Here, we explore the consequences of this symmetry on the derivation of the effective stress. This is defined by a linear combination of six stress functions that are represented by their Maclaurin series. Only the lowest order terms that obey this symmetry are retained, which results in a homogeneous effective stress of order two. It is shown that the quadratic terms can be further eliminated by resolving the respective stresses into another coordinate system in the zone of the slip direction. The application of the ensuing linear yield criterion to body-centered cubic and hexagonal close-packed metals shows under which conditions the non-Schmid stress terms become significant in predicting the onset of yielding. In the special case, where the contributions of all non-Schmid stresses vanish, this model reduces to the maximum shear stress theory of Tresca.

Collision cascades interact with an edge dislocation in bcc Fe: a molecular dynamics study.

The interactions of an edge dislocation (ED) with collision cascades induced by 5 keV primary knocked-on atoms (PKAs) towards the ED in bcc Fe are studied using classical molecular dynamics (MD) simulations. It is found that the number and distribution of the residual point defects are related to the distance between the initial PKAs and the ED. Based on this result, we provide a comprehensive summary of four characteristic phenomena for cascade–ED interactions, including few interactions, the formation of a vacancy cluster, the sink effect for point defects, and the sub-cascade area affection, depending on the overlap of the peak cascades' area with the ED line. Then a qualitative model is proposed to clearly elucidate the underlying mechanisms of the four situations. Considering that dislocations constitute an essential part of the micro-structure of crystalline solids, our work demonstrates that: the pre-existing dislocations in crystalline materials could induce diverse effects under irradiation environments, which should be taken into account for designing and improving the radiation resistant materials.

Dynamics of screw dislocations: A generalised minimising-movements scheme approach

The gradient flow structure of the model introduced in Cermelli & Gurtin (1999, The motion of screw dislocations in crystalline materials undergoing antiplane shear: glide, cross-slip, fine cross-slip. Arch. Rational Mech. Anal.148(1), 3–52) for the dynamics of screw dislocations is investigated by means of a generalised minimising-movements scheme approach. The assumption of a finite number of available glide directions, together with the “maximal dissipation criterion” that governs the equations of motion, results into solving a differential inclusion rather than an ODE. This paper addresses how the model in Cermelli & Gurtin is connected to a time-discrete evolution scheme which explicitly confines dislocations to move at each time step along a single glide direction. It is proved that the time-continuous model in Cermelli & Gurtin is the limit of these time-discrete minimising-movement schemes when the time step converges to 0. The study presented here is a first step towards a generalisation of standard gradient flow theory that allows for dissipations which cannot be described by a metric.

Dislocation structures and electrical conduction properties of low angle tilt grain boundaries in LiNbO3

Dislocations in crystalline materials constitute unique, atomic-scale, one-dimensional structure and have a potential to induce peculiar physical properties that are not found in the bulk. In this study, we fabricated LiNbO3 bicrystals with low angle tilt grain boundaries and investigated the relationship between the atomic structure of the boundary dislocations and their electrical conduction properties. Observations by using transmission electron microscopy revealed that dislocation structures at the (0001) low angle tilt grain boundaries depend on the tilt angle of the boundaries. Specifically, the characteristic dislocation structures with a large Burgers vector were formed in the boundary with the tilt angle of 2°. It is noteworthy that only the grain boundary of 2° exhibits distinct electrical conductivity after reduction treatment, although LiNbO3 is originally insulating. This unique electrical conductivity is suggested to be due to the characteristic dislocation structures with a large Burgers vector.

Diffusion Effects Induced by Dislocations in Crystalline Materials Subjected to Large Strains

Abstract. We reconsider here the FEM-algorithm for solving the initial and boundary value problems performed within the viscoplastic constitutive framework and proposed in our paper [1]. The problems concerning the deformation of a sheet composed of a single fcc-crystal, generated by different slip systems simultaneously activated, are solved numerically for an in-plane stress state. The variational formulation is associated to the incremental equilibrium equations and is coupled with an update procedure for the state variables, which are described by the differential type equations, as well as for the non-local evolution equations of the dislocation densities. The length scale parameter is introduced into the model through the diffusion-like parameter which enters the evolution equations for dislocation densities. For more accuracy of the simulation, the shape functions have been chosen polynomials with higher than one degree. We do not consider that once a slip system was activated it remains active for the rest of simulation. The activation condition is a key point in the numerical algorithm. As a numerical example, we perform a tensile test of a rectangular and non-rectangular metallic sheet, comparring the results of the simulation when two, respectively eight slip systems are considered.

X-ray line profile analysis—An ideal tool to quantify structural parameters of nanomaterials

For a long time the shift and broadening of Bragg profiles have been used to evaluate internal stresses and coherent domain sizes, i.e. the smallest crystalline region without lattice defects. Modern technology provides both enhanced detector resolution and high brilliance x-ray sources thus allowing measurements of x-ray peaks with a high resolution in space and time. In parallel to the hardware, also diffraction theories have been substantially improved so that the shape of Bragg profiles can be quantitatively evaluated not only in terms of the crystallite size and its distribution, but also in terms of the density, type and arrangement of dislocations, twins and stacking faults. Thus state-of-the-art x-ray line profile analysis enables the thorough characterization especially of nanostructured materials which also contain lattice defects. The method can be used also to prove the existence of dislocations in crystalline materials. Examples of nanostructured metals, polymers and even molecular crystals like fullerenes are given.

Interface Effects on the Mechanical Properties of Nanocrystalline Nanolaminates

AbstractNanocrystalline nanolaminate (ncnl) structures are widely used in the study of physical properties in order to engineer materials for a variety of industrial applications. Often, novel and interesting mechanical behaviours that are found in nanolaminate materials can be linked with two characteristic features of structure. These are the layer pair spacing and the grain size. For the case of nanolaminates synthesized by physical vapor deposition processes, the layer spacing corresponds with the repeating sequence of layer pairs and can be referred to as composition wavelength. The grain size is the average width of the tapered columnar structure along the growth direction. Since the mechanical properties of strength and hardness are known to functionally vary with the separation between dislocations in crystalline materials, both structural features can potentially contribute to the total interfacial area and the characteristic separation of interfaces that mitigate dislocation motion. In this investigation, the individual contribution of layer pair spacing and grain size to the total interfacial structure are each quantified in an assessment of strength and hardness. A model is proposed for the total interfacial area of the material volume under plastic deformation that can quantify the interfacial area contribution from the layer pairs and the grain size. It is anticipated that each structural feature can potentially dominate the plastic deformation of the nanolaminate as dependent upon the specific layer pair spacing, the grain size, and the extent of plastic deformation.

Energetics of homogeneous nucleation of dislocation loops under a simple shear stress in perfect crystals

We present an analysis of homogeneous nucleation of a dislocation loop under an applied simple shear stress in a perfect crystal. By using a variational boundary integral method together with an interlayer potential in the Peierls-Nabarro (P-N) framework, we have determined the saddle-point configurations of embryonic dislocation loops and their associated activation energies under stress levels up to the ideal shear strength. The results, for typical materials such as Au, Cu, Al, and Si, indicate that energy barriers are far too high to suggest that thermal motion could play a role in nucleation of a dislocation loop in perfect crystals under usual stress levels, markedly below the ideal shear strength. These new findings broaden the earlier understanding of homogeneous nucleation of dislocations in crystalline materials and have significant implications on a number of existing models based on the mechanism of dislocation nucleation in deformation and fracture.

Disclination loops observed in ion irradiated NiMo amorphous films and their fractal characteristics

Ni 65Mo 35 amorphous alloy films were obtained by 200 keV xenon ion mixing of multilayered NiMo films at room temperature with doses greater than 7 × 10 14 Xe/cm 2. When the dose was increased to 7 × 10 15 Xe/cm 2, corresponding to the amorphous-to-crystalline phase transition, many odd lines were observed, for the first time, in transmission electron micrographs of the ion mixed amorphous matrix. After excluding other possible explanations, these lines were attributed to disclination loops, which can be considered as an analogue of dislocations in crystalline materials. Scaling analysis showed that the loops featured self-similarity and had a common fractal dimension, D f, of 1.20 for a particular length scale.

Localized Shear Deformation of Amorphous Metals

ABSTRACTThe characteristics of localized deformation in amorphous metals are reviewed. All the available evidences seem to suggest that dislocations are responsible for shear localization. These dislocations seem to require a stress concentration for their nucleation. Once nucleated, they are capable of producing both forward and reverse shear in a narrow band, much like the dislocations in crystalline materials.