arXiv subjects

Valery I. Levitas

Publications and source records attributed to Valery I. Levitas.

27 records · Page 2Linked to original sources

arXiv2021

Nonlinear elasticity of prestressed single crystals at high pressure and various elastic moduli

A general nonlinear theory for the elasticity of pre-stressed single crystals is presented. Various types of elastic moduli are defined, their importance is determined, and relationships between them are presented. In particular, B moduli are present in the relationship between the Jaumann objective time derivative of the Cauchy stress and deformation rate and are broadly used in computational algorithms in various finite-element codes. Possible applications to simplified linear solutions for complex nonlinear elasticity problems are outlined and illustrated for a superdislocation. The effect of finite rotations is fully taken into account and analyzed. Different types of the bulk and shear moduli under different constraints are defined and connected to the effective properties of polycrystalline aggregates. Expressions for elastic energy and stress-strain relationships for small distortions with respect to a pre-stressed configuration are derived in detail. Under initial hydrostatic load, general consistency conditions for elastic moduli and compliances are derived that follow from the existence of the generalized tensorial equation of state under hydrostatic loading obtained from single crystal or polycrystal. It is shown that B moduli can be found from the expression for the Gibbs energy. However, higher-order elastic moduli defined from the Gibbs energy do not have any meaning since they do not directly participate in any known equations, like stress-strain relationships and wave propagation equation. The deviatoric projection of B can also be found from the expression for the elastic energy for isochoric small strain increments, and the missing components of B can be found from the consistency conditions. Numerous inconsistencies and errors in the known works are analyzed.

cond-mat.mtrl-sci↗

arXiv2021

Resolving puzzles of the phase-transformation-based mechanism of the deep-focus earthquake

Deep-focus earthquakes that occur at 350-660 km, where pressures 12-23 GPa and temperature 1800-2000 K, are generally assumed to be caused by olivine-spinel phase transformation (PT). However, there are many existing puzzles: (a) What are the mechanisms for jump from geological 10^-17-10^-15 1/s to seismic 10-10^3 1/s strain rates? Is it possible without PT? (b) How does metastable olivine, which does not completely transform to spinel at high temperature and deeply in the region of stability of spinel for over the million years, suddenly transforms during seconds and generates seismic strain rates 10-10^3 1/s? (c) How to connect deviatorically dominated seismic signals with volume-change dominated PT strain during PT? Here we introduce a combination of several novel concepts that allow us to resolve the above puzzles quantitatively. We treat the PT in olivine like plastic strain-induced (instead of pressure/stress-induced) and find an analytical 3D solution for coupled deformation-PT-heating processes in a shear band. This solution predicts conditions for severe (singular) transformation-induced plasticity (TRIP) and self-blown-up TRIP-PT-heating process due to positive thermomechanochemical feedback between TRIP and strain-induced PT. In nature, this process leads to temperature in a band exceeding the unstable stationary temperature, above which the self-blown-up shear-heating process in the shear band occurs after finishing the PT. Without PT and TRIP, significant temperature and strain rate increase is impossible. Due to the much smaller band thickness in the laboratory, heating within the band does not occur, and plastic flow after the PT is very limited. Our findings change the main concepts in studying the initiation of the deep-focus earthquakes and PTs during plastic flow in geophysics in general.

physics.geo-ph↗

arXiv2021

Review on phase transformations, fracture, chemical reactions, and other structural changes in inelastic materials

Review of selected fundamental topics on the interaction between phase transformations, fracture, and other structural changes in inelastic materials is presented. It mostly focuses on the concepts developed in the author's group over last three decades and numerous papers that affected us. It includes a general thermodynamic and kinetic theories with sharp interfaces and within phase field approach. Numerous analytical (even at large strains) and numerical solutions illustrate the main features of the developed theories and their application to the real phenomena. Coherent, semicoherent, and noncoherent interfaces, as well as interfaces with decohesion and with intermediate liquid (disordered) phase are discussed. Importance of the surface- and scale-induced phenomena on interaction between phase transformation with fracture and dislocations as well as inheritance of dislocations and plastic strains is demonstrated. Some nontrivial phenomena, like solid-solid phase transformations via intermediate (virtual) melt, virtual melting as a new mechanism of plastic deformation and stress relaxation under high strain rate loading, and phase transformations and chemical reactions induced by plastic shear under high pressure are discussed and modeled.

cond-mat.mtrl-sci↗

arXiv2020

Phase field theory for fracture at large strains including surface stresses

Phase field theory for fracture is developed at large strains with an emphasis on a correct introduction of surface stresses. This is achieved by multiplying the cohesion and gradient energies by the local ratio of the crack surface areas in the deformed and undeformed configurations and with the gradient energy in terms of the gradient of the order parameter in the reference configuration. This results in an expression for the surface stresses which is consistent with the sharp surface approach. Namely, the structural part of the Cauchy surface stress represents an isotropic biaxial tension, with the magnitude of a force per unit length equal to the surface energy. The surface stresses are a result of the geometric nonlinearities, even when strains are infinitesimal. They make multiple contributions to the Ginzburg-Landau equation for damage evolution, both in the deformed and undeformed configurations. Important connections between material parameters are obtained using an analytical solution for two separating surfaces, as well as an analysis of the stress-strain curves for homogeneous tension for different degradation and interpolation functions. A complete system of equations is presented in the undeformed and deformed configurations. All the phase field parameters are obtained utilizing the existing first principle simulations for the uniaxial tension of Si crystal in the [100] and [111] directions.

physics.app-ph↗

arXiv2020

Fifth-degree elastic potential for predictive stress-strain relations and elastic instabilities under large strain and complex loading in Si

Materials under complex loading develop large strains and often transition via an elastic instability, as observed in both simple and complex systems. Here, we present Si I under large strain in terms of Lagrangian strain by an $5^{th}$-order elastic potential found by minimizing error relative to density functional theory (DFT) results. The Cauchy stress-Lagrangian strain curves for arbitrary complex loadings are in excellent correspondence with DFT results, including elastic instability driving Si I$\rightarrow$II phase transformation (PT) and the shear instabilities. PT conditions for Si I$\rightarrow$II under action of cubic axial stresses are linear in Cauchy stresses in agreement with DFT predictions. Such elastic potential permits study of elastic instabilities and orientational dependence leading to different PTs, slip, twinning, or fracture, providing a fundamental basis for continuum simulations of crystal behavior under extreme loading.

cond-mat.mtrl-sci↗

arXiv2020

In situ quantitative study of plastic strain-induced phase transformations under high pressure: Example for ultra-pure Zr

The first in situ quantitative synchrotron X-ray diffraction (XRD) study of plastic strain-induced phase transformation (PT) has been performed on $α-ω$ PT in ultra-pure, strongly plastically predeformed Zr as an example, under different compression-shear pathways in rotational diamond anvil cell (RDAC). Radial distributions of pressure in each phase and in the mixture, and concentration of $ω$-Zr, all averaged over the sample thickness, as well as thickness profile were measured. The minimum pressure for the strain-induced $α-ω$ PT, $p^d_{\varepsilon}$=1.2 GPa, is smaller than under hydrostatic loading by a factor of 4.5 and smaller than the phase equilibrium pressure by a factor of 3; it is independent of the compression-shear straining path. The theoretically predicted plastic strain-controlled kinetic equation was verified and quantified; it is independent of the pressure-plastic strain loading path and plastic deformation at pressures below $p^d_{\varepsilon}$. Thus, strain-induced PTs under compression in DAC and torsion in RDAC do not fundamentally differ. The yield strength of both phases is estimated using hardness and x-ray peak broadening; the yield strength in shear is not reached by the contact friction stress and cannot be evaluated using the pressure gradient. Obtained results open a new opportunity for quantitative study of strain-induced PTs and reactions with applications to material synthesis and processing, mechanochemistry, and geophysics.

cond-mat.mtrl-sci↗

arXiv2019

Fatigue-resistant high-performance elastocaloric materials via additive manufacturing

Elastocaloric cooling, which exploits the latent heat released and absorbed as stress-induced phase transformations are reversibly cycled in shape memory alloys, has recently emerged as a frontrunner in non-vapor-compression cooling technologies. The intrinsically high thermodynamic efficiency of elastocaloric materials is limited only by work hysteresis. Here, we report on creating high-performance low-hysteresis elastocaloric cooling materials via additive manufacturing of Titanium-Nickel (Ti-Ni) alloys. Contrary to established knowledge of the physical metallurgy of Ti-Ni alloys, intermetallic phases are found to be beneficial to elastocaloric performances when they are combined with the binary Ti-Ni compound in nanocomposite configurations. The resulting microstructure gives rise to quasi-linear stress-strain behaviors with extremely small hysteresis, leading to enhancement in the materials efficiency by a factor of five. Furthermore, despite being composed of more than 50% intermetallic phases, the reversible, repeatable elastocaloric performance of this material is shown to be stable over one million cycles. This result opens the door for direct implementation of additive manufacturing to elastocaloric cooling systems where versatile design strategy enables both topology optimization of heat exchangers as well as unique microstructural control of metallic refrigerants.

cond-mat.mtrl-sci↗

arXiv2018

Twinning-induced pseudoelastic behavior in (MoW)$_{85}$(TaTi)$_{7.5}$Zr$_{7.5}$

We provide a critical atomistic evidence of pseudoelastic behavior in complex solid-solution BCC Mo-W-Ta-Ti-Zr alloy. Prior to this work, only limited single-crystal BCC solids of pure metals and quaternary alloys have shown pseudoelastic behavior at low temperatures and high strain rates. The deformation mechanisms investigated using classical molecular simulations under tensile-compressive loading reveal temperature-dependent pseudoelastic behavior aided by twinning during the loading-unloading cycle. The pseudoelasticity is found to be independent of loading directions with identical cyclic deformation characteristics during uniaxial loading. Additionally, temperature variation from 77 to 1500 K enhances the elastic strain recovery in the alloy.

cond-mat.mtrl-sci↗

arXiv2018

Deformation, lattice instability, and metallization during solid-solid structural transformations under general applied stress tensor: example of Si I -> Si II

Density functional theory (DFT) was employed to study the stress-strain behavior, elastic instabilities, and metallization during a solid-solid phase transformation (PT) between semiconducting Si I (cubic A4) and metallic Si II (tetragonal A5 structure) when subjected to a general stress tensor. With normal stresses ($σ_1$, $σ_2$, $σ_3$) acting along $\left<110 \right>$, $\left<1\bar{1}0 \right>$, and $\left<001\right>$, respectively, dictating the simulation cell, we determine combinations of 6 independent stresses that drive a lattice instability for the Si I$\rightarrow$Si II PT, and a semiconductor-metal electronic transition. Metallization precedes the structural PT, hence, a stressed Si I can be a metal. Surprisingly, a stress-free Si II is metastable in DFT. Notably, the PT for hydrostatic pressures is at 75.81 GPa, while under uniaxial stress it is 11.03 GPa (or 3.68 GPa mean pressure). Our key result: The Si I -> Si II PT is described by a critical value of the modified transformation work, as found with a phase-field method, and the PT criterion has only two parameters for a general applied stress. More generally, our findings are crucial for revealing novel (and more economic) material synthesis routes for new or known high-pressure phases under controlled and predictable non-hydrostatic loading and plastic deformation.

cond-mat.mtrl-sci↗