Deformation Of Crystalline Solids Research Articles

Grain boundary plasticity initiated by excess volume

Grain boundaries (GBs) serve not only as strong barriers to dislocation motion, but also as important carriers to accommodate plastic deformation in crystalline solids. During deformation, the inherent excess volume associated with loose atomic packing in GBs brings about a microscopic degree of freedom that can initiate GB plasticity, which is beyond the classic geometric description of GBs. However, identification of this atomistic process has long remained elusive due to its transient nature. Here, we use Au polycrystals to unveil a general and inherent route to initiating GB plasticity via a transient topological transition process triggered by the excess volume. This route underscores the general impact of a microscopic degree of freedom which is governed by a stress-triaxiality-based criterion. Our findings provide a missing perspective for developing a more comprehensive understanding of the role of GBs in plastic deformation.

Situating the Vector Density Approach Among Contemporary Continuum Theories of Dislocation Dynamics

Abstract For the past century, dislocations have been understood to be the carriers of plastic deformation in crystalline solids. However, their collective behavior is still poorly understood. Progress in understanding the collective behavior of dislocations has primarily come in one of two modes: the simulation of systems of interacting discrete dislocations and the treatment of density measures of varying complexity that are considered as continuum fields. A summary of contemporary models of continuum dislocation dynamics is presented. These include, in order of complexity, the two-dimensional statistical theory of dislocations, the field dislocation mechanics treating the total Kröner–Nye tensor, vector density approaches that treat geometrically necessary dislocations on each slip system of a crystal, and high-order theories that examine the effect of dislocation curvature and distribution over orientation. Each of theories contain common themes, including statistical closure of the kinetic dislocation transport equations and treatment of dislocation reactions such as junction formation. An emphasis is placed on how these common themes rely on closure relations obtained by analysis of discrete dislocation dynamics experiments. The outlook of these various continuum theories of dislocation motion is then discussed.

Elastic interaction-induced anisotropic growth of dislocation loop arrays

The elastic interactions and reactions of dislocations lead to the formation of complex dislocation substructures, which is critical to the strain hardening and fatigue failure. Phase field dislocation dynamics simulations are conducted as a first step to understand the elastic interactions between dislocation loops. When the interloop spacing is small, the elastic interactions with neighboring loops become strong, rendering the edge segments strongly pinned, while allowing for the screw segments to propagate more easily. The interactions are found to result in an anisotropic stress distribution around the dislocation loops, leading to the formation of arrays of long, straight edge dislocations that could act as barriers to subsequent slip. Furthermore, the effect of initial loop size and applied strain rate on the elastic interaction-induced anisotropic pinning effect is investigated and discussed. The results are important for coarse-graining dislocation substructures formation into continuum level models of deformation in crystalline solids.

Defects in olivine

Abstract. Olivine, a ferromagnesian orthosilicate, is the most abundant mineral in Earth's upper mantle and is stable down to the olivine–wadsleyite phase transition, which defines the 410 km depth mantle transition zone. Olivine also occurs in crustal environments in metamorphic and hydrothermal rocks and is expected to be the major mineral constituent of the Martian and Venusian mantles. The olivine atomic structure is also used in materials science to manufacture lithium batteries. Like any other crystalline solid, including minerals, olivine never occurs with a perfect crystalline structure: defects in various dimensions are ubiquitous, from point, line, and planar defects to three-dimensional (3-D) inclusions. In this contribution, I review the current state of the art of defects in olivine and several implications for key processes occurring in Earth's mantle. Intrinsic and extrinsic point defects are detailed, exemplifying the astonishing diversity of atomic impurities in mantle-derived olivine. Linear defects, one of the key defect types responsible for ductile deformation in crystalline solids, are examined in light of recent progress in 3-D transmission electron microscopy, which has revealed an important diversity of dislocation slip systems. I summarize the principal characteristics of interface defects in olivine: the free surface, grain and interface boundaries, and internal planar defects. As the least-studied defects to date, interface defects represent an important challenge for future studies and are the main application of numerical simulation methods in materials science. I provide an overview of melt, fluid, and mineral inclusions, which are widely studied in volcanology and igneous petrology. Special attention is given to new crystalline defects that act as deformation agents: disclinations (rotational defects) and the potential occurrence of disconnections in olivine, both of which are expected to occur along or near grain boundaries. Finally, I detail outstanding questions and research directions that will further our understanding of the crystalline specificities and paradoxes of olivine and olivine-rich rocks and ultimately their implications for the dynamics of Earth's upper mantle.

Crystal imperfections in ice Ih.

In this paper, we present an overview of crystal imperfections in ice Ih. Due to its molecular nature, the fundamental asymmetry of the hydrogen bond, and proton disorder, crystal defects in this condensed form of water reveal a complexity not usually seen in atomic crystalline solids. The discussion is organized in terms of the spatial extent of the defects. We start with zero-dimensional imperfections such as the molecular vacancy and interstitial, Bjerrum, and ionic defects, as well as possible defect complexes that can be formed from them. Subsequently, we turn to the properties of dislocations, which are the one-dimensional disturbances that carry plastic deformation in crystalline solids. Finally, we discuss two-dimensional defects such as stacking faults and grain boundaries and discuss to what extent the latter are similar to other interfaces in ice Ih such as the free surface. We conclude with an outlook at the road ahead, discussing future challenges toward understanding the role of crystal defects in the macroscopic behavior of ice Ih.

Origin of Elastic–Plastic Deformation Invariant

We consider the autowave mechanism of evolution of a localized plastic deformation of crystalline solids of different origins. It is found that localization of the plastic flow is determined by the relation between elastic and plastic phenomena in deforming materials. It is shown that the main parameter of deformation processes is the elastic–plastic deformation invariant, viz., a dimensionless quantity connecting quantitatively the parameters of elastic waves and self-sustained waves (autowaves) of localized plastic deformation. The correctness of this statement is verified for metals, alkali-halide crystals, and rocks. The physical origin of the invariant is explained on the basis of thermodynamic considerations.

Supersonic Dislocation Bursts in Silicon.

Dislocations are the primary agents of permanent deformation in crystalline solids. Since the theoretical prediction of supersonic dislocations over half a century ago, there is a dearth of experimental evidence supporting their existence. Here we use non-equilibrium molecular dynamics simulations of shocked silicon to reveal transient supersonic partial dislocation motion at approximately 15 km/s, faster than any previous in-silico observation. Homogeneous dislocation nucleation occurs near the shock front and supersonic dislocation motion lasts just fractions of picoseconds before the dislocations catch the shock front and decelerate back to the elastic wave speed. Applying a modified analytical equation for dislocation evolution we successfully predict a dislocation density of 1.5 × 1012 cm−2 within the shocked volume, in agreement with the present simulations and realistic in regards to prior and on-going recovery experiments in silicon.

Assembling an alkyl rotor to access abrupt and reversible crystalline deformation of a cobalt(II) complex.

Harnessing molecular motion to reversibly control macroscopic properties, such as shape and size, is a fascinating and challenging subject in materials science. Here we design a crystalline cobalt(II) complex with an n-butyl group on its ligands, which exhibits a reversible crystal deformation at a structural phase transition temperature. In the low-temperature phase, the molecular motion of the n-butyl group freezes. On heating, the n-butyl group rotates ca. 100° around the C–C bond resulting in 6–7% expansion of the crystal size along the molecular packing direction. Importantly, crystal deformation is repeatedly observed without breaking the single-crystal state even though the shape change is considerable. Detailed structural analysis allows us to elucidate the underlying mechanism of this deformation. This work may mark a step towards converting the alkyl rotation to the macroscopic deformation in crystalline solids.

Sharp interface model of creep deformation in crystalline solids

We present a rigorous irreversible thermodynamics treatment of creep deformation of solid materials with interfaces described as geometric surfaces capable of vacancy generation and absorption and moving under the influence of local thermodynamic forces. The free energy dissipation rate derived in this work permits clear identification of thermodynamic driving forces for all stages of the creep process and formulation of kinetic equations of creep deformation and microstructure evolution. The theory incorporates capillary effects and reveals the different roles played by the interface free energy and interface stress. To describe the interaction of grain boundaries with stresses, we classify grain boundaries into coherent, incoherent and semicoherent, depending on their mechanical response to the stress. To prepare for future applications, we specialize the general equations to a particular case of a linear-elastic solid with a small concentration of vacancies. The proposed theory creates a thermodynamic framework for addressing more complex cases, such as creep in multicomponent alloys and cross-effects among vacancy generation/absorption and grain boundary motion and sliding.

Analysis of the misoriented structures in the model copper-copper compound formed by explosion welding

The existing concepts of the mechanisms of forming fragmented structures under the conditions of severe plastic deformation of crystalline solids are analytically reviewed. The translational and rotational plasticity modes that develop at micro- and mesoscopic structural levels, respectively, are sequentially taken into account. This allows us to correctly describe the morphological features of the evolution of fragmented structures, to predict misorientation spectra for various fragmentation mechanisms, and to determine the partial contribution of each mechanism in the cases where several deformation grain refinement mechanisms are involved in fragmentation. The computer simulation of deformation-induced misorientation spectra that was developed using these concepts is a new method for studying the physical nature of structure formation processes, and this method can be applied for various materials, temperature-rate deformation conditions, and technological loading schemes. As an example, we comprehensively consider the formation of fragmented structures under the extreme conditions of explosion welding of commercial-purity copper plates. A comparison of the model misorientation spectra calculated for a reference structure and the fragmented structure in the near-contact zone of the welded joint with the existing experimental data demonstrates the efficiency and reliability of the proposed method.

Uniaxial stress-driven coupled grain boundary motion in hexagonal close-packed metals: A molecular dynamics study

Stress-driven grain boundary (GB) migration has been evident as a dominant mechanism accounting for plastic deformation in crystalline solids. Using molecular dynamics (MD) simulations on a Ti bicrystal model, we show that a uniaxial stress-driven coupling is associated with the recently observed 90°GB reorientation in shock simulations and nanopillar compression measurements. This is not consistent with the theory of shear-induced coupled GB migration. In situ atomic configuration analysis reveals that this GB motion is accompanied by the glide of two sets of parallel dislocation arrays, and the uniaxial stress-driven coupling is explained through a composite action of symmetrically distributed dislocations and deformation twins. In addition, the coupling factor is calculated from MD simulations over a wide range of temperatures. We find that the coupled motion can be thermally damped (i.e., not thermally activated), probably due to the absence of the collective action of interface dislocations. This uniaxial coupled mechanism is believed to apply to other hexagonal close-packed metals.

Irreversible thermodynamics of creep in crystalline solids

We develop an irreversible thermodynamics framework for the description of creep deformation in crystalline solids by mechanisms that involve vacancy diffusion and lattice site generation and annihilation. The material undergoing the creep deformation is treated as a non-hydrostatically stressed multi-component solid medium with non-conserved lattice sites and inhomogeneities handled by employing gradient thermodynamics. Phase fields describe microstructure evolution which gives rise to redistribution of vacancy sinks and sources in the material during the creep process. We derive a general expression for the entropy production rate and use it to identify of the relevant fluxes and driving forces and to formulate phenomenological relations among them taking into account symmetry properties of the material. As a simple application, we analyze a one-dimensional model of a bicrystal in which the grain boundary acts as a sink and source of vacancies. The kinetic equations of the model describe a creep deformation process accompanied by grain boundary migration and relative rigid translations of the grains. They also demonstrate the effect of grain boundary migration induced by a vacancy concentration gradient across the boundary.

Intersection of screw dislocations in fcc crystals during torsional deformation

Dislocation reactions, including dislocation intersections during various processes in crystals, play an important and often crucial role. This is most pronounced during plastic deformation of crystalline solids, which attracts particular interest from researchers. Intersection of screw dislocations in fcc crystals during their deformation by uniaxial tension and compression was studied by A. Cottrell [1]. It was shown that the intersection of similar screw dislocations moving toward each other results in the formation of interstitial thresholds on them; in the case of intersection of opposite screw dislocations, vacancy thresholds are formed on them.

Glide of edge dislocations in tungsten and molybdenum

The glide of a dislocation is the fundamental process of plastic deformation in crystalline solids. For body-centered-cubic (bcc) metals, the three-fold core dissociation of screw dislocations has attracted much attention and investigation. In this paper, we present a molecular dynamics study of glide of edge dislocations in bcc tungsten and molybdenum. On the {1 1 0} glide planes, the Peierls–Nabarro stress (PNS) of the edge dislocation is found to be (3.75–5.0)×10 −4 μ and (1.25–2.50)×10 −4 μ for tungsten and molybdenum, respectively, where μ is the shear modulus. On the glide planes {1 1 2}, these two numbers are (8.13–8.75)×10 −4 μ and (3.75–5.0)×10 −4 μ along one direction, and (1.13–1.38)×10 −3 μ and (6.25–8.75)×10 −4 μ along the opposite direction. The asymmetry of the PNS on the {1 1 2} planes is attributed to the asymmetrical dislocation core structure. During the glide process on {1 1 0} planes, the three constituent planes of an edge dislocation displace in sequence. The glide on {1 1 2} planes involve two such subsequent displacements, since the core consists of two non-equivalent planes.

Fully reversible, dislocation-based compressive deformation of Ti3SiC2 to 1 GPa.

Dislocation-based deformation in crystalline solids is almost always plastic. Here we show that polycrystalline samples of Ti3SiC2 loaded cyclically at room temperature, in compression, to stresses up to 1 GPa, fully recover on the removal of the load, while dissipating about 25% (0.7 MJ x m(-3)) of the mechanical energy. The stress-strain curves outline fully reversible, rate-independent, closed hysteresis loops that are strongly influenced by grain size, with the energy dissipated being significantly larger in the coarse-grained material. At temperatures greater than 1,000 degrees C, the loops are open, the response is strain-rate dependent, and cyclic hardening is observed. This hitherto unreported phenomenon is attributed to the reversible formation and annihilation of incipient kink bands at room-temperature deformation. At higher temperatures, the incipient kink bands dissociate and coalesce to form regular irreversible kink bands. The loss factor for Ti3SiC2 is higher than most woods, and comparable to polypropylene and nylon. The technological implications of having a stiff, lightweight machinable ceramic that can dissipate up to 25% of the mechanical energy per cycle are discussed.

Modeling Deformation of Polycrystalline Rocks

The finite element method is a powerful complement to polycrystal plasticity theory for modeling the non-uniform deformation of crystalline solids. Polycrystal plasticity provides a micro-mechanical model for slip-dominated plastic flow and serves as a constitutive theory for deformation simulations (Kocks et al. 1998). The finite element method offers a numerical means to solve partial differential equations, such as the field equations of elasticity or plasticity (Zienkiewicz et al. 1989). The two can be combined in different ways depending on the goals of a modeling effort. ### Length scales Finite elements and polycrystal plasticity may be applied to the detailed modeling of a collection of grains that represent a sample of the material. In this case, there are one or more finite elements discretizing each grain and balance laws for momentum and mass are applied at the level of individual crystals. A second combination of finite elements and polycrystal plasticity is to embed polycrystal theory within a finite element formulation for physical systems that are far larger than the dimension of a grain. Polycrystal plasticity serves as a constitutive theory in essentially the same way as continuum elastoplasticity models. Balance laws are applied at the larger continuum scale. We refer to these as small-scale and large-scale applications, respectively. Care must be exercised in assuring consistency between the macroscopic material element volume and the polycrystal dimensions. With respect to characterizing these applications, it is useful to define a geometric parameter, ζ , as the relative sizes of a finite element and a crystal. Allowing h to be a characteristic dimension of an element and d to be the representative grain size the parameter ζ simply is h / d . Here, large ζ implies large numbers of crystals in each element; small ζ implies many elements within each crystal. For small-scale applications, there is a …

Connecting atomistic and mesoscale simulations of crystal plasticity

A quantitative description of plastic deformation in crystalline solids requires a knowledge of how an assembly of dislocations — the defects responsible for crystal plasticity — evolves under stress1. In this context, molecular-dynamics simulations have been used to elucidate interatomic processes on microscopic (∼10−10 m) scales2, whereas ‘dislocation-dynamics’ simulations have explored the long-range elastic interactions between dislocations on mesoscopic (∼10−6 m) scales3. But a quantitative connection between interatomic processes and behaviour on mesoscopic scales has hitherto been lacking. Here we show how such a connection can be made using large-scale (100 million atoms) molecular-dynamics simulations to establish the local rules for mesoscopic simulations of interacting dislocations. In our molecular-dynamics simulations, we observe directly the formation and subsequent destruction of a junction (a Lomer–Cottrell lock) between two dislocations in the plastic zone near a crack tip: the formation of such junctions is an essential process in plastic deformation, as they act as an obstacle to dislocation motion. The force required to destroy this junction is then used to formulate the critical condition for junction destruction in a dislocation-dynamics simulation, the results of which compare well with previous deformation experiments4.

The nature of large-scale correlations in plastic flow

The nature of large-scale correlations in the locations of the centers of plastic flow during the deformation of crystalline solids is discussed. It is shown that regularities in the generation and development of such centers can be described as various types of autowaves arising from processes of self-organization. Examples are presented of the excitation-wave and phase-wave types of autowave processes experimentally observed during the deformation of single-crystal and polycrystalline metals and alloys. Some numerical parameters of the autowave processes are estimated.

The self-excited wave nature of the instability and localisation of plastic deformation

The nature of the localisation of plastic flow observed during deformation of crystalline solids is discussed. The nucleation and evolution of the zones of strain localisation have been shown to reveal certain trends which could be described as autowaves of different kinds initiated by the processes of self-organization. Examples of self-excited wave processes, e.g., phase and excitement waves, that were observed experimentally by the deformation of mono- and polycrystalline metals and alloys are cited. Some of the numerical parameters of self-excited wave processes have been evaluated.

Erratum: Theoretical analysis of R-line shifts of ruby subjected to different deformation conditions

A theoretical approach to analyzing ruby R-line wavelength shifts under different types of deformation (uniaxial-strain compression and tension under shock loading, hydrostatic compression, and uniaxial-stress compression) and for different crystallographic orientations is presented. A symmetry-adapted representation of the various loading conditions in conjunction with crystal-field theory, but no point-ion model, is used to relate the shift of the R lines to deformation. The parameters needed in the model are obtained from shock-wave-compression data along the c and a axes. Without further iteration, these parameters are used in a consistent manner to analyze all remaining data: shock-wave-tension results, hydrostatic results, and uniaxial-stress results for different crystal orientations. Very good agreement is obtained between theoretical predictions and measurements. Changes in local site symmetry have been related to macroscopic deformation. For nonhydrostatic loading, effects of crystal orientation are important in analyzing R-line wavelength shifts. Suggestions for using ruby calibration at high pressures in diamond-anvil-cell measurements are presented. Implications of the present work for understanding shock-wave deformation in crystalline solids are indicated.