Plastic Deformation Of Solids Research Articles

Bottom-up coarse-grain modeling of plasticity and nanoscale shear bands in α-RDX.

Computationally inexpensive particle-based coarse-grained (CG) models are essential for use in molecular dynamics (MD) simulations of mesoscopically slow cooperative phenomena, such as plastic deformations in solids. Molecular crystals possessing complex symmetry present enormous practical challenges for particle-based coarse-graining at molecularly resolved scales, when each molecule is in a single-site representation, and beyond. Presently, there is no published pairwise non-bonded single-site CG potential that is able to predict the space group and structure of a molecular crystal. In this paper, we present a successful coarse-graining at a molecular level from first principles of an energetic crystal, hexahydro-1,3,5-trinitro-s-triazine (RDX) in the alpha phase, using the force-matching-based multiscale coarse-graining (MSCG/FM) approach. The new MSCG/FM model, which implements an optimal pair decomposition of the crystal Helmholtz free energy potential in molecular center-of-mass coordinates, was obtained by force-matching atomistic MD simulations of liquid, amorphous, and crystalline states and in a wide range of pressures (up to 20GPa). The MSCG/FM potentials for different pressures underwent top-down optimization to fine-tune the mechanical and thermodynamic properties, followed by consolidation into a transferable density-dependent model referred to as RDX-TC-DD (RDX True-Crystal Density-Dependent). The RDX-TC-DD model predicts accurately the crystal structure of α-RDX at room conditions and reproduces the atomistic reference system under isothermal (300K) hydrostatic compression up to 20GPa, in particular, the Pbca symmetry of α-RDX in the elastic regime. The RDX-TC-DD model was then used to simulate the plastic response of uniaxially ([100]) compressed α-RDX resulting in nanoscale shear banding, a key mechanism for plastic deformation and defect-free detonation initiation proposed for many molecular crystalline explosives. Additionally, a comparative analysis of the effect of core-softening of the RDX-TC-DD potential and the degree of molecular rigidity in the all-atom treatment suggests a stress-induced short-range softening of the effective intermolecular interaction as a fundamental cause of plastic instability in α-RDX. The reported RDX-TC-DD model and overall workflow to develop it open up possibilities to perform high quality simulation studies of molecular energetic materials under thermal and mechanical stimuli, including extreme conditions.

A unified high-order Eulerian method for continuum simulations of fluid flow and of elastic–plastic deformations in solids

We develop a new high-order method for Eulerian simulations of solids undergoing large, elastic–plastic deformations. Thermodynamically consistent constitutive relations of classical hyperelasticity are used to describe the behavior of solids, liquids and gases in a unified manner. Two kinematic formulations, one based on the inverse deformation gradient tensor, and a second based on the symmetric Finger tensor, are used for tracking large deformations in solids. Simulations based on the Finger tensor are shown to be equivalent to those using the full inverse deformation gradient tensor at much lower computational expense. The numerical algorithm employs a 10th-order compact finite-difference scheme for spatial discretization and a 4th-order Runge–Kutta time-stepping scheme. An improved form of the Localized Artificial Diffusivity (LAD) method is used for numerical regularization of shocks and contact discontinuities. We show that this high-order numerical framework, previously used for simulations of fluid flows, is suitable for problems involving large deformations in elastic–plastic solids as well. Particular emphasis is laid on the choice of the artificial diffusivity parameters in order to sufficiently capture shocks and discontinuities in all the aforementioned continuum media with minimal added dissipation. Test cases in one and two dimensions are shown to demonstrate the feasibility and accuracy of the proposed approach. In particular, this choice of algorithms is shown to lead to excellent numerical resolution properties, and to preserve mass-consistency and curl/compatibility constraints with high order of accuracy. Potential extensions of this numerical framework include application to multi-material problems, involving compressible flow of fluids coupled to elastic–plastic deformations in solids, that are of significant engineering interest.

Grain size distribution in sheared polycrystals

Plastic deformation in solids induced by external stresses is of both fundamental and practical interest. Using both phase field crystal modeling and molecular dynamics simulations, we study the shear response of monocomponent polycrystalline solids. We subject mesocale polycrystalline samples to constant strain rates in a planar Couette flow geometry for studying its plastic flow, in particular its grain deformation dynamics. As opposed to equilibrium solids where grain dynamics is mainly driven by thermal diffusion, external stress/strain induce a much higher level of grain deformation activity in the form of grain rotation, coalescence, and breakage, mediated by dislocations. Despite this, the grain size distribution of this driven system shows only a weak power-law correction to its equilibrium log-normal behavior. We interpret the grain reorganization dynamics using a stochastic model.

Shear bands as translation-rotation modes of plastic deformation in solids under alternate bending

The paper studies the shear banding developing in corrugated surface layers of commercial titanium, hydrogenated Ti surface layers and high-purity aluminum foils glued onto commercial aluminum A7 plates against elastic deformation of their bulk under alternate bending at room temperature. In surface layers of commercial titanium under alternate bending up to fracture, plastic flow develops through microscale twinning against the background of dislocation substructure and shear banding is absent. Early in the alternate bending (up to N = 103 cycles which corresponds to strain ε∼ 55–60%), shear banding in hydrogenated Ti surface layers and Al foils is also absent. At N = 104–106 cycles, severe shear banding is detected in hydrogenated Ti surface layers and Al foils. Two types of meso- and macroscale shear bands are revealed and analyzed: planar shear bands with continuous misorientations in slightly corrugated surface layers and three-dimensional shear bands which propagate in highly corrugated surface layers. The latter shear bands are responsible for submicro- and/or nanofragmentation of material and culminate in plastic collapse and fracture of solids. Shear bands are treated as translation-rotation modes of plastic deformation in solids with high crystal lattice curvature. Shear banding is a multiscale noncrystallographic mechanism of a curved crystal lattice fragmentation that transforms an elastic lattice curvature of a deformed solid to its inelastic rotation.

A fluid structure interaction study of a viscous mechanism for energy absorption in protective structural panels

Sandwich panels designed to resist blasts and high-velocity impacts usually dissipate most of the delivered energy through inelastic deformation of solids. A concept is explored in this study to improve the energy absorption of such structures by the addition of a viscous mechanism. The mechanism relies on the fact that when a viscous liquid is forced through narrow passages at high speeds, it undergoes high shear rates that cause viscous energy dissipation. A simple test specimen in the form of a steel tube with capillaries attached at both ends was chosen for study. Both empty and liquid-filled test specimens were subjected to experimental and simulated drop-weight impact tests and simulated blast load tests. Fluid structure interaction analyses in the form of Coupled-Eulerian–Lagrangian simulations were performed to assess the energy dissipated both by solid plastic deformation and liquid viscous dissipation in the drop-weight and blast simulations. The liquid flow speeds generated by the applied loads were found to be a critical factor in determining the contribution of the viscous mechanism. The moderate liquid flow speeds generated by the drop-weight impacts resulted in negligible viscous energy dissipation. The simulated blast loads generated much higher liquid flow speeds and as a result the viscous energy contribution to the total absorbed energy in the test specimens approached 30%. The viscosity of the liquid has a major effect on the fraction of energy absorbed in the form of viscous dissipation. Results of this study support the viability of the concept of viscous-assist for improving the ability of protective panels and structures to withstand high-speed impact and blast loads.

Nonlinear wave processes in a deformable solid as a hierarchically organized system

Theoretical predictions and experiments demonstrate that solid state mechanics should consider, along with a structurally equilibrium 3D crystalline subsystem, a structurally nonequilibrium planar subsystem as a complex of all surface layers and internal interfaces with broken translation invariance. Primary plastic flow of a loaded solid develops in its structurally nonequilibrium planar subsystem as channeled nonlinear waves of local structural transformations that determine the self-organization law of multiscale plastic flow. These waves initiate mesoscale rotational deformation modes, giving rise to all types of microscale strain-induced defects in the planar subsystem. The strain-induced defects are emitted into the crystalline subsystem as an inhibitor of nonlinear waves of plastic flow in the planar subsystem. Plastic deformation of solids, whatever the loading type, evolves in the field of rotational couple forces. Loss of hierarchical self-consistency by rotational deformation modes culminates in fracture of material as an uncompensated rotational deformation mode on the macroscale.

Simulation of plastic deformation initiation in crystal materials under dynamic loading

In the last decade the scope of experimental and theoretical investigations into the initial stage of plastic deformation in solids has been expanded significantly. Nevertheless its atomistic mechanisms are as yet imperfectly understood. One of the major open questions concerns the existence of proto-defects, i.e. local structural distortions which provide the basis for the formation of conventional structural defects — carriers of plastic deformation. The investigations were applied to crystallines with different boundary types (free surfaces and grain boundaries) and different type of crystal lattice. The influence of loading intensity and deformation scheme was studied. Simulation was performed for various temperatures from 50 K to 500 K. It has been demonstrated that there is a certain threshold value of strain at which zones with local structural changes grow almost abruptly. A detailed analysis of atomic displacements at the stage of nucleation of local structural distortions (protodefects) has revealed that their formation is related with specific rearrangement in the first and second coordination spheres of one of the atoms. It is realized in the conditions of local expansion of the atomic volume.

Rheology of the Earth's mantle: A historical review

Historical development of our understanding of rheological properties of the Earth's mantle is reviewed. Rheological properties of the Earth's mantle control most of the important geological processes such as the style of mantle convection (e.g., stagnant lid versus plate tectonics) and the nature of thermal evolution. However, inferring the rheological properties of the Earth's mantle is challenging because of the presence of multiple mechanisms of deformation that have different dependence on time-scale (strain-rate), stress levels and other parameters. Through the integration of a broad range of observations including the elastic stiffness from tidal deformation and the viscosity from the concept of isostasy, a gross picture of rheological stratification of the Earth's mantle (a strong lithosphere, a weak asthenosphere and a strong layer below) was proposed in the mid-19th century. However, not only the physical basis for such a model was weak due to the lack of proper understanding of some materials science issues such as the interplay between elastic and viscous deformation but also the lack of understanding of temperature–depth relation associated with convection prevented our understanding of the rheological structure of the Earth's interior. Major progress occurred in the first half of the 20th century in our understanding of the atomistic mechanisms of plastic deformation in solids, and much of the theoretical framework on the plastic deformation of solids was established by late 1960s. Those developments provided a basis for scaling analyses that are critical to the applications of laboratory results to the Earth's interior. Major progress in laboratory studies on rheological properties occurred in the mid-1960s to the early 1970s in Griggs' lab using a new type of solid-medium high-pressure deformation apparatus to pressure ∼ 2 GPa and temperature ∼ 1600 K. The basic concepts such as the water weakening, non-linear rheology and deformation-induced lattice-preferred orientation were identified by their studies. However, large uncertainties in the stress measurements with this type of apparatus were recognized in the late 1970s and high-resolution experimental studies using synthetic samples were initiated in Paterson's lab in the mid-1980s using a high-resolution gas-medium deformation apparatus. However, experimental studies with such a gas-medium deformation apparatus can be conducted only at low pressures (< 0.5 GPa) and it is difficult to apply these low-pressure data to the Earth's interior deeper than ∼ 20 km. New experimental techniques to study rheological properties in Earth's deep interior have been developed during the last a few years. These techniques allow us to quantitatively study the rheological properties of Earth materials down to the lower mantle condition (∼ 24 GPa, ∼ 2000 K). Some geodynamic issues related to rheological properties are discussed including (i) the strength of the lithosphere and the origin of plate tectonics, (ii) the origin of the asthenosphere, and (iii) the deep mantle rheology and its influence on thermal history of Earth. Existing models on these topics are reviewed and new alternative models are discussed.

A New Approach to the Problem of Plastic Deformation of Solids

A New Approach to the Problem of Plastic Deformation of Solids

Fundamental role of nanoscale structural level of plastic strain in solids

A conceptual substantiation of the necessity to consider the nanoscale structural level of plastic strain in the physics of plasticity and strength of solids is presented. It is inferred that the fundamental mechanism of plastic strain is represented by local structural transformations (of the type of rearrangement of atomic clusters of various configurations) that occur in a loaded solid in local zones of tensile normal stresses. This mechanism determines generality of the nature of all possible kinds of plastic deformation of solids.

Development of accelerator-based γ-ray-induced positron annihilation spectroscopy technique

Accelerator-based γ-ray-induced positron annihilation spectroscopy performs positron annihilation spectroscopy by utilizing MeV bremsstrahlung radiation generated from an accelerator (We have named the technique “accelerator-based γ-ray-induced PAS,” even though “bremsstrahlung” is more correct here than “γ rays”. The reason for that is to make the name of the technique more general, since PAS may be performed by utilizing MeV γ rays emitted from nuclei through the use of accelerators as described later in this article and as in the case of positron lifetime spectroscopy [F.A. Selim, D.P. Wells, and J.F. Harmon, Rev. Sci. Instrum. 76, 033905 (2005)].) instead of using positrons from radioactive sources or positron beams. MeV γ rays create positrons inside the materials by pair production. The induced positrons annihilate with the material electrons emitting a 511-keV annihilation radiation. Doppler broadening spectroscopy of the 511-keV radiation provides information about open-volume defects and plastic deformation in solids. The high penetration of MeV γ rays allows probing of defects at high depths in thick materials up to several centimeters, which is not possible with most of the current nondestructive techniques. In this article, a detailed description of the technique will be presented, including its benefits and limitations relative to the other nondestructive methods. Its application on the investigation of plastic deformation in thick steel alloys will be shown.

Nonlinear strain theory of plastic flow in solids

We present a phenomenological time-dependent Ginzburg–Landau theory ofnonlinear plastic deformations in solids. Because the problem is very complex, wefirst give models in one and two dimensions without vacancies and interstitials,where large strains produce densely distributed slips but the mass densitydeviations remain small except near the tips of slips. Next we set up atwo-dimensional model including a vacancy field (or local free-volume fraction),where the sensitive dependence of the elastic shear modulus on the vacancydensity is relevant. In our simulation, if strains are applied to nearly defectlesssolids but in the presence of such an elastic inhomogeneity, the vacancydensity and the mass density can become considerably heterogeneous forlarge strains on spatial scales much longer than the atomic size. Thesestrain-induced disordered states are metastable or long lived once they arecreated.

The theory of theories and its implications for the understanding of plastic deformation

A general lesson learned in a scientific life time is presented, namely on how to judge the validity of a theory by the use of Occam's razor, and the application of this lesson to theoretical efforts in the area of the plastic deformation of solids.

A self-excited wave model of plastic deformation in solids

A self-excited wave model of plastic flow in crystalline solids is proposed. The experimental results pertaining to plastic flow in single crystals and polycrystals with different underlying mechanisms responsible for plastic deformation are summarized. The salient feature types of strain localization in the materials under consideration are captured and related to the respective steps on the deformation curves. The conditions at which the salient self-excited wave types of plastic deformation reveal themselves are determined. The applicability of the synergic self-organization approach to describing plastic deformation is substantiated. A self-excited wave model of plastic flow in materials with different underlying mechanisms of deformation is suggested.

A self-excited wave model of plastic deformation in solids

A self-excited wave model of plastic deformation in solids

Plastic deformation of solids viewed as a self-excited wave process

A self-excited wave model of plastic flow in crystalline solids is proposed. Experimental data on plastic flow in single crystals and polycrystalline solids involving different mechanisms have been correlated. The main types of strain localization in the materials investigated have been established and correlated with the respective stages of plastic flow curves. The best observing conditions have been defined for the major types of autowaves emerging by plastic deformation. The synergetic concepts of self-organization are shown to apply to description of plastic deformation. Suggested is a self-excited wave model of plastic flow in materials with different mechanisms of deformation.

Dislocation nucleation at nano-scale mechanical contacts

The plastic deformation of metals in highly localized stress fields is critical to macroscopic phenomena such as fracture, surface wear and adhesion where crack tips and surface asperities concentrate the applied stress. Controlled-probe contact techniques can be used to measure forces and displacements on the atomic scale, thereby directly exploring elastic and plastic deformation of solids at the nanometer level. In this study we use interfacial force microscopy to quantitatively examine the nano-scale elastic and plastic response of single crystal Au(111) surfaces using controlled-probe contacts with a range of radii extending down to 500 Å. Our results show that the stress at the plastic threshold increases with decreasing probe-tip radius. We apply a model for dislocation nucleation which reproduces the scaling behavior with tip radius and discuss deficiencies in the model and plausible reasons for the underestimation in quantitative stress values.

Functions with structure-mathematical objects for describing plastic deformation of solids

Functions with structure-mathematical objects for describing plastic deformation of solids

Model of track formation.

The developed theoretical model of track formation accounts for the influence of initial atomic displacements, momenta, and initial heating of atoms on the plastic deformation of solids near the trajectory of a penetrating fast heavy ion. These initial conditions result from the energy and momentum transfer from the excited electron subsystem to the ion one near the ion trajectory. The theoretical results obtained make it possible to investigate the dependencies of the anisotropic growth of amorphous alloys irradiated with high-energy heavy ions on the inelastic and elastic energy losses of the moving ion and on the irradiated temperature. A good agreement between these theoretical dependencies and existing experimental results was obtained.

Amorphization and new mechanisms of plastic deformation in solids

New microscopic mechanisms of plastic deformation in solids are considered, which are related to phase transitions. Special attention is paid to the relationship between local amorphization processes and deformation micromechanisms in crystalline and quasi-crystalline solids. In particular, theoretical models are proposed, which describe the new deformation micromechanism, related to solid state amorphization, as that capable of causing high-strain deformation in shock-loaded and quasi-statically deformed metallic crystals.