Dislocation Slip or Phase Transformation Lead to Room-Temperature Plasticity in Diamond: Comment on Plastic Deformation of Single-Crystal Diamond Nanopillars
Despite decades of extensive research on mechanical properties of diamond, much remains to be understood in term of plastic deformation mechanisms due to the poor deformability at room temperature. In a recent work in Advanced Materials, it was claimed that room-temperature plasticity occurred in <001>-oriented single-crystal diamond nanopillars based on observation of unrecovered deformation inside scanning electron microscope. The plastic deformation was suggested to be mediated by a phase transition from sp3 carbon to an O8-carbon phase by molecular dynamics simulations. By comparison, our in-situ transmission electron microscopy study reveals that the room-temperature plasticity can be carried out by dislocation slip in both <100> and <111>-oriented diamond nanopillars. The brittle-to-ductile transition is highly dependent on the stress state. We note that the surface structure may play a significant role in the deformation mechanisms as the incipient plasticity always occurs from the surface region in nanoscale diamonds.
Tension-compression asymmetry is a notable feature of plasticity in bcc single crystals. Recent experiments reveal striking differences in the plasticity of bcc nanopillars for tension and compression. Here we present results from molecular dynamics simulations of nanopillars of bcc Fe in tension and compression. We find that a totally different deformation mechanism applies in each cases: dislocation glide in compression and twinning in tension. This difference explains experimentally-observed asymmetry in the nanopillar morphology.
In this paper, compressive loading effects on the plasticity of Al-Cu alloy varying the crystal orientation of Al and alloying element (Cu) percentage are investigated using molecular dynamics approach. The alloying percentage of Cu are varied up to 10% in <001>, <110> and <111> crystal loading direction of Al. Our results indicate that the alloy nanopillar has highest first yielding strength and strain along <110> and <001> direction, respectively. Further, the dislocation density and dislocation interaction are studied to explain the compressive stress strain behavior of the alloy nanopillar…
Molecular dynamics (MD) is employed to investigate the plastic deformation mechanisms of single crystalline yttria-stabilized tetragonal zirconia (YSTZ) nanopillars under uniaxial compression. Simulation results show that the nanoscale plastic deformation of YSTZ is strongly dependent on the crystallographic orientation of zirconia nanopillars. For the first time, the experimental explored tetragonal to monoclinic phase transformation is reproduced by MD simulations in some particular loading directions. Three distinct mechanisms of dislocation, phase transformation, and a combination of dislo…
In this paper, we investigate plasticity in irradiated FeCrAl nanopillars using discrete dislocation dynamics simulations (DDD), with comparisons to transmission electron microscopic (TEM) in situ tensile tests of ion and neutron irradiated commercial FeCrAl alloy C35M. The effects of irradiation-induced defects, such as a/2 111 and a 100 type loops and composition fluctuations representative of phase separation in irradiated FeCrAl alloys, are investigated separately as well as superposed together in simulations. We explore the effects of defects on the stress-strain behavior, specifically yi…
Specimen- and grain-size effects on nanoscale plastic deformation mechanisms and mechanical properties of polycrystalline yttria-stabilized tetragonal zirconia (YSTZ) nanopillars are studied by molecular dynamics simulations. Through uniaxial compression of YSTZ columnar nanopillars, intergranular and transgranular deformation mechanisms are investigated. Cooperative intergranular deformations including grain boundary sliding and migration, grain rotation, and amorphous phase formation at grain boundaries are revealed. Results also reveal formation of partial dislocations, which act as splitte…
Plastic deformation of micron and sub-micron scale specimens is characterized by intermittent sequences of large strain bursts (dislocation avalanches) which are separated by regions of near-elastic loading. In the present investigation we perform a statistical characterization of strain bursts observed in stress-controlled compressive deformation of monocrystalline Molybdenum micropillars. We characterize the bursts in terms of the associated elongation increments and peak deformation rates, and demonstrate that these quantities follow power-law distributions that do not depend on specimen or…
Si nanopillars of less than 50 nm diameter have been irradiated in a helium ion microscope with a focused Ne$^+$ beam. The morphological changes due to ion beam irradiation at room temperature and elevated temperatures have been studied with the transmission electron microscope. We found that the shape changes of the nanopillars depend on irradiation-induced amorphization and thermally driven dynamic annealing. While at room temperature, the nanopillars evolve to a conical shape due to ion-induced plastic deformation and viscous flow of amorphized Si, simultaneous dynamic annealing during the …
Molecular dynamics simulations performed on <110> Cu nanopillars revealed significant difference in deformation behavior of nanopillars with and without twin boundary. The plastic deformation in single crystal Cu nanopillar without twin boundary was dominated by twinning, whereas the introduction of twin boundary changed the deformation mode from twinning to slip consisting of leading partial followed by trailing partial dislocations. This difference in deformation behavior has been attributed to the formation of stair-rod dislocation and its dissociation in the twinned nanopillars.
Prior to macroscopic yielding, most materials undergo a regime of plastic activity that cannot be resolved in conventional bulk deformation experiments. In this pre-yield, or micro-plastic regime, it is the initial three dimensional defect network that is probed and the intermittently evolving microstructure admits small increments in plastic strain. By reducing the sample size, this intermittent activity becomes increasingly apparent and can be routinely observed through small-scale mechanical testing. In some cases, the intermittent activity was shown to exhibit aspects of scale-free behavio…
As an extension to strain-gradient models of size-dependent plastic behaviour, this work proposes a model for a stress-gradient theory. The model is distinguished from earlier works on the topic by its being embedded in a thermodynamically consistent framework. The development is carried out in the context of single-crystal plasticity, and draws on thermodynamically consistent models for single-crystal conventional and strain-gradient plasticity. The model is explored numerically using the example of torsion of a thin wire comprising a face centred cubic crystal, and its behaviour compared wit…
Ice plasticity has been thoroughly studied, owing to its importance in glaciers and ice sheets dynamics. In particular, its anisotropy (easy basal slip) has been suspected for a long time, then fully characterized 40 years ago. More recently emerged the interest of ice as a model material to study some fundamental aspects of crystalline plasticity. An example is the nature of plastic fluctuations and collective dislocation dynamics. 20 years ago, acoustic emission measurements performed during the deformation of ice single crystals revealed that plastic flow proceeds through intermittent dislo…
This work presents a detailed experimental-numerical analysis of a low-carbon dual-phase steel microstructure, revealing evidence of significant anisotropic plastic deformation in lath martensite. A careful determination of the habit plane orientations in the present martensitic variants demonstrates that the observed traces of plastic slip coincide with the directions of the corresponding habit planes. To study the local lath martensite plastic activity, a dedicated substructure-enriched crystal plasticity based model is exploited. Compared with conventional bcc crystal plasticity, the model …
The work considers the effect of deformation on the exhaustion of the plasticity resource of steel 45 after the drawing deformation. The results of theoretical and experimental studies of damage accumulation are listed. A possibility of employment of a scanning electron microscope to observe submicropores is demonstrated.
In order to efficiently explore the nearly infinite composition space in multicomponent solid solution alloys, it is important to establish predictive design strategies and use computation-aided methods. In the present work, we demonstrated the density functional theory calculations informed design routes for realizing transformation-induced plasticity (TRIP) and twinning-induced plasticity (TWIP) in Cr-Co-Ni medium entropy alloys (MEAs). We systematically studied the effects of magnetism and chemical composition on the generalized stacking fault energy surface (gamma-surface) and showed that …
The statistics and origin of the first discrete plastic event in a one dislocation dynamics simulation are studied. This is done via a linear stability analysis of the evolving dislocation configuration up to the onset of irreversible plasticity. It is found, via a fold catastrophe, the dislocation configuration prior to loading directly determines the stress at which the plastic event occurs and that between one and two trigger dislocations are involved. The resulting irreversible plastic strain arising from the instability is found to be highly correlated with these triggering dislocations.
The purpose of continuum plasticity models is to efficiently predict the behavior of structures beyond their elastic limits. The purpose of multiscale materials science models, among them crystal plasticity models, is to understand the material behavior and design the material for a given target. The current successful continuum hyperelastoplastic models are based in the multiplicative decomposition from crystal plasticity, but significant differences in the computational frameworks of both approaches remain, making comparisons not straightforward. In previous works we have presented a theory …
The mode I crack tip asymptotic response of a solid characterised by strain gradient plasticity is investigated. It is found that elastic strains dominate plastic strains near the crack tip, and thus the Cauchy stress and the strain state are given asymptotically by the elastic K-field. This crack tip elastic zone is embedded within an annular elasto-plastic zone. This feature is predicted by both a crack tip asymptotic analysis and a finite element computation. When small scale yielding applies, three distinct regimes exist: an outer elastic K field, an intermediate elasto-plastic field, and …
Mechanical deformation of nanopillars displays features that are distinctly different from the bulk behavior of single crystals: Yield strength increases with decreasing size and plastic deformation comes together with strain bursts or/and stress drops (depending on loading conditions) with a very strong sensitivity of the stochasticity character on material preparation and conditions. The character of the phenomenon is standing as a paradox: While these bursts resemble the universal, widely independent of material conditions, noise heard in bulk crystals using acoustic emission (AE) technique…
The paper presents analytical or semi-analytical solutions for the formation and evolution of localized plastic zone in a uniaxially loaded bar with variable cross-sectional area. A variationally based formulation of explicit gradient plasticity with linear softening is used, and the ensuing jump conditions and boundary conditions are discussed. Three cases with different regularity of the stress distribution are considered, and the problem is converted to a dimensionless form. Relations linking the load level, size of the plastic zone, distribution of plastic strain and plastic elongation of …
Voids can limit the life of engineering components. This motivates us to understand local plasticity around voids in a nickel base superalloy combining experiments and simulations. Single crystal samples were deformed in tension with in-situ high angular resolution electron back scatter diffraction to probe the heterogeneous local stress field under load; the reference stress is informed by crystal plasticity finite element simulations. This information is used to understand the activation of plastic deformation around the void. Our investigation indicates that while the resolved shear stress …
There is a long standing technological problem in which a stress dwell during cyclic loading at room temperature in Ti causes a significant fatigue life reduction. It is thought that localised time dependent plasticity in soft grains oriented for easy plastic slip leads to load shedding and an increase in stress within a neighbouring hard grain poorly oriented for easy slip. Quantifying this time dependent plasticity process is key to successfully predicting the complex cold dwell fatigue problem. This work uses a novel approach of in situ synchrotron X-ray diffraction during stress relaxation…
We predict a strongest size for the contact strength when asperity radii of curvature decrease below ten nanometers. The reason for such strongest size is found to be correlated with the competition between the dislocation plasticity and surface diffusional plasticity. The essential role of temperature is calculated and illustrated in a comprehensive asperity size-strengthtemperature map taking into account the effect of contact velocity. Such a map should be essential for various phenomena related to nanoscale contacts such as nanowire cold welding, self-assembly of nanoparticles and adhesive…
We study three structurally different states of nanocrystalline 316 steel and show that the state, where boundaries containing excess concentration of alloying elements are combined with mobile dislocations in grain interiors, allows maintaining extraordinarily high strength and remarkably enhanced plasticity. Underlying mechanisms featuring interaction between the segregations and mobile dislocations are discussed.
The first plastic event occurring in discrete intermittent plasticity, as for example a pop-in seen in nano-indentation, is evaluated with extreme value statistics. It is found that when the same deformation is repeated many times, the average of the stress at this first event is related to the deforming volume via an exponentially truncated power-law. The present work demonstrates this trend and the expected Weibull fluctuation around it. The statistical formalism is shown to apply to the nano-indentation data of Morris {\em et al}, Phys. Rev. Lett. 106, 165502 (2011), as well as to dislocati…
In this work the relation of plastic and rheological material models is analysed in the framework of non-equilibrium thermodynamics. After a short summary of the basic notions of classical elasticity and plasticity the traditional thermodynamic treatment of plasticity by Ziegler is introduced, where the plastic deformation is an internal variable, leading to the reduction of thermostatic stress. Then a simple thermodynamic treatment of static and dynamic friction follows, because the continuum generalization of these phenomena leads to viscosity and plasticity in our interpretation. Finally, p…
A thermal activation model to describe the plasticity of bulk metallic glasses (Derlet and Maaß, Phil. Mag. 2013, DOI: 10.1080/14786435.2013.826396) which uses a distribution of barrier energies and some aspects of under-cooled liquid physics is developed further. In particular, a log-normal distribution is now employed to describe the statistics of barrier energies. A high temperature mean-field description of homogeneous macro-plasticity is then developed and is shown to be similar to a thermal activation picture employing a single characteristic activation energy and activation volume. In m…
Power law fluctuations and scale free spatial patterns are known to characterize steady state plastic flow in crystalline materials. In this Letter we study the emergence of correlations in a simple Frenkel-Kontorova (FK) type model of 2D plasticity which is largely free of arbitrariness, amenable to analytical study and is capable of generating critical exponents matching experiments. Our main observation concerns the possibility to reduce continuum plasticity to an integer valued automaton revealing inherent discreteness of the plastic flow.
Elastoplastic lattice models for the response of solids to deformation typically incorporate structure only implicitly via a local yield strain that is assigned to each site. However, the local yield strain can change in response to a nearby or even distant plastic event in the system. This interplay is key to understanding phenomena such as avalanches in which one plastic event can trigger another, leading to a cascade of events, but typically is neglected in elastoplastic models. To include the interplay one could calculate the local yield strain for a given particulate system and follow its…
Results of recent large-scale molecular dynamics simulations of dislocation-mediated solid plasticity are campared with predictions of the statistical thermodynamic theory of these phenomena. These computational and theoretical analyses are in substantial agreement with each other in both their descriptions of strain-rate dependent steady plastic flow and of a transient stress peak associated with initially small densities of dislocations. The comparisons between the numerical simulations and basic theory reveal inconsistencies in some conventional phenomenological descriptions of solid plasti…
Stressed dislocation pattern formation in crystal plasticity at finite deformation is demonstrated for the first time. Size effects are also demonstrated within the same mathematical model. The model involves two extra material parameters beyond the requirements of standard classical crystal plasticity theory. The dislocation microstructures shown are decoupled from deformation microstructures, and emerge without any consideration of latent hardening or constitutive assumptions related to cross-slip. Crystal orientation effects on the pattern formation and mechanical response are also demonstr…
We use considerations of energy balance and dissipation to derive a self-consistent version of the shear-transformation-zone (STZ) theory of plastic deformation in amorphous solids. The theory is generalized to include arbitrary spatial orientations of STZs. Continuum equations for elasto-plastic material and their energy balance properties are discussed.
In this work, distortion gradient plasticity is used to gain insight into material deformation ahead of a crack tip. This also constitutes the first fracture mechanics analysis of gradient plasticity theories adopting Nye's tensor as primal kinematic variable. First, the asymptotic nature of crack tip fields is analytically investigated. We show that an inner elastic region exists, adjacent to the crack tip, where elastic strains dominate plastic strains and Cauchy stresses follow the linear elastic stress singularity. This finding is verified by detailed finite element analyses using a new nu…
When submitted to large stresses at high temperature, usual crystals may irreversibly deform. This phenomenon is known as plasticity and it is due to the motion of crystal defects such as dislocations. We have discovered that, in the absence of impurities and in the zero temperature limit, helium 4 crystals present a giant plasticity that is anisotropic and reversible. Direct measurements on oriented single crystals show that their resistance to shear nearly vanishes in one particular direction because dislocations glide freely parallel to the basal planes of the hexagonal structure. This plas…
The standard way of modeling plasticity in polycrystals is by using the crystal plasticity model for single crystals in each grain, and imposing suitable traction and slip boundary conditions across grain boundaries. In this fashion, the system is modeled as a collection of boundary-value problems with matching boundary conditions. In this paper, we develop a diffuse-interface crystal plasticity model for polycrystalline materials that results in a single boundary-value problem with a single crystal as the reference configuration. Using a multiplicative decomposition of the deformation gradien…
A mechanism of perfect plasticity under low homological temperatures has been suggested. According to this mechanism, the phenomenon under study is of critical nature. It connects with percolation transition in the net of grain boundaries and with nonlocal interaction of fragments uniquely under simple shear mode. The mechanism is justified by general reasoning, mainly of geometrical character, and also by employing computational modeling and well-known experimental results.
The structure of the overall response of a metal polycrystal is analyzed under the assumption that activity on the slip systems of its constituents is governed by a generalized Schmid law. In the resulting macro-model of metal plasticity the overall rate of plastic deformation is related to the stress-gradient of the yield surface via a generalized, but still associated flow rule. While the overall rate of plastic deformation is no longer collinear with the stress-gradient of the yield surface, its deviation is characterized by an additional macro-variable, representative of the rate of the no…
We present a thermodynamic description of crystal plasticity. Our formulation is based on the Langer-Bouchbinder-Lookman thermodynamic dislocation theory (TDT), which asserts the fundamental importance of an effective temperature that describes the state of configurational disorder and therefore the dislocation density of the crystalline material. We extend the TDT description from isotropic plasticity to crystal plasticity with many slip systems. Finite-element simulations show favourable comparison with experiments on polycrystal fcc copper under uniaxial compression, tension, and simple she…
A phase field model for ductile fracture considering Hencky strain and finite J2 plasticity is presented using the nonlocal operator method. A variational derivation of J2 plasticity at finite strain with a phase field model is performed. The method includes a logarithmic strain tensor and an exponential mapping in the plasticity evolution. A spectral decomposition based algorithm for computing the first and second order derivatives of the composite matrix function is implemented. A consistent tangential stiffness matrix is derived and used in Newton-Raphson iterations. Several numerical examp…
Crystal plasticity is mediated through dislocations, which form knotted configurations in a complex energy landscape. Once they disentangle and move, they may also be impeded by permanent obstacles with finite energy barriers or frustrating long-range interactions. The outcome of such complexity is the emergence of dislocation avalanches as the basic mechanism of plastic flow in solids at the nanoscale. While the deformation behavior of bulk materials appears smooth, a predictive model should clearly be based upon the character of these dislocation avalanches and their associated strain bursts…
