Phase Transformation Wave Research Articles

Thermomechanical coupling effect on the phase transition wave propagation in an SMA TiNi bar subjected to shock loading

Phase transition can strongly affect the stress wave propagation features. In this paper, the influence of temperature on the phase transformation wave (PTW) propagation was investigated theoretically and numerically with a thermo-mechanical coupling constitutive model and kinetic relation of the phase transition. The results showed that the temperature interface is also the phase transition threshold stress discontinuity. For shock wave propagating in the rod with fixed temperature interfaces, the transformation from shock wave to phase transition wave, then to an elastic wave was predicted due to the temperature interface effect, and an unloading elastic wave during loading was discovered induced by the boundary effect, which has barely been studied before. Moreover, for the adiabatic shock loading, phase transition wave front is not only a material interface, but also a temperature discontinuity. A loading shock wave with phase transition was predicted due to the second phase strengthening and an unloading shock wave with reverse transformation was generated arising from unloading path changing effect induced by adiabatic temperature rise across the transformation shock front. The theoretical analysis and simulation discloses the evolution of phase transition waves affected by temperature interfaces and reflect the intrinsic characteristic of phase transition materials with strong nonlinear behavior due to the dynamic thermo-mechanical coupling.

Structural phase transition and amorphization in hexagonal SiC subjected to dynamic loading

Understanding the dynamic behavior of silicon carbide (SiC) at extreme conditions is critical for applications such as coatings and armor. Revealing the plasticity and phase transition in SiC under intensive dynamic loading is among the key concerns. However, the effects of polytypes in SiC as well as the various loading conditions on its dynamic material responses are still not well understood. Here we carry out a series of large-scale molecular dynamics (MD) simulations to explore the inelastic responses of hexagonal SiC subjected to shock and ramp compression along the [0001] direction. The shock responses present three regimes sequentially as the shock particle velocity is increased from 0.5 km/s to 6 km/s: a single elastic wave, a multi-wave structure consisting of an elastic-plastic wave followed by two consecutive phase transition waves, and finally, an overdriven structural phase transformation wave. The original wurtzite structure is observed to transform into a 6-coordinated rock salt structure through a 5-coordinated intermediate structure. Furthermore, slip along the <112‾0> direction on the (0001) plane causes multiple stacking faults and amorphization when subjected to intense shock compression. The effects of temperature and strain rate on the material responses of hexagonal SiC are decoupled by performing ramp loading simulations. The results reveal that a lower temperature rise impedes atomic motion while a lower strain rate promotes it, highlighting a competitive effect. Besides, due to the limited availability of slip planes, dynamic compression can lead to the formation of nanograins in hexagonal SiC, and nanograins refinement with increasing shock intensity is observed. These results provide important insights into the deformation of SiC polytypes under extreme conditions and promote the understanding of the dynamic properties of hexagonal structure covalent materials.

Lithium Clustering during the Lithiation/Delithiation Process in LiFePO4 Olivine-Structured Materials.

Olivine-structured LiFePO4 is one of the most popular cathode materials in lithium-ion batteries (LIBs) for sustainable applications. Significant attention has been paid to investigating the dynamics of the lithiation/delithiation process in LixFePO4 (0 ≤ x ≤ 1), which is crucial for the development of high-performance LiFePO4 material. Various macroscopic models based on experimental evidence have been proposed to explain the mechanism of phase transition from LiFePO4 to FePO4, such as the shrinking core (i.e., core–shell) model, Laffont’s (i.e., new core–shell) model, domino-cascade model, phase transformation wave, solid solution model, many-particle models, etc. However, these models, unfortunately, contradict each other and their validity is still under debate. An atomistic model is urgently required to depict the lithiation/delithiation process in LixFePO4. In this article, we reveal the lithiation/delithiation process in LiFePO4 simulated by a computational model using the generalized gradient approximation (GGA + U) method. We find that the clustered configuration is the most energetically favorable, leading to co-operative Jahn–Teller distortion among the inter-polyhedrons that can be observed clearly from the bond patterns. This atomistic model not only offers answers to experimental results obtained at moderate or high rates but also gives the direction to further improve the rate capability of LiFePO4 cathode material for high-power LIBs.

Investigation of the Propagation of Stress Wave in Nickel-Titanium Shape Memory Alloys

Based on irreversible thermodynamic theory, a new constitutive model incorporating two internal variables was proposed to investigate the phase transformation and plasticity behavior in nickel-titanium (NiTi) shape memory alloys (SMAs), by taking into account four deformation stages, namely austenite elastic phase, phase transition, martensitic elastic phase, and plastic phase. The model using the material point method (MPM) was implemented by the FORTRAN code to investigate the stress wave and its propagation in a NiTi rod. The results showed that its wave propagation exhibited martensitic and austenitic elastic wave, phase transition wave, and plastic wave. However, a double-wave structure including the martensitic and austenitic elastic wave and plastic wave occurred when the martensitic elastic wave reached the phase transformation wave. Thus, the reflection wave at a fixed boundary exhibited a different behavior compared with the elastic one, which was attributed to the phase transition during the process of reflection. It was found that the stress increment was proportional to the velocity of phase transition wave after the stress wave reflection. In addition, the influences of loading direction and strain rate on the wave propagation were examined as well. It was found that the phase transition wave velocity increased as the strain rate increased. The elastic wave velocity of martensite under compressive conditions was larger than that under tensile loading. In contrast, the plastic wave velocity under compression was less than that subjected to the tensile load.

The Phase Transformation Wave and Conditions of Its Realization in Deformable Austenitic Steels Irradiated in a BN-350 Reactor

Experimental data on the influence of neutron irradiation on the plasticity characteristics of chromium–nickel austenite steels have been analyzed. Special attention is devoted to detection of anomalously high plasticity levels attained at some parameters of irradiation and deformation, which is explained by the formation and propagation of a “phase transformation wave” in the metastable steel. Necessary and sufficient conditions for the realization of this wave are formulated.

Волна фазового превращения в деформируемых аустенитных сталях, облученных в реакторе БН-350, и условия ее реализации

AbstractExperimental data on the influence of neutron irradiation on the plasticity characteristics of chromium–nickel austenite steels have been analyzed. Special attention is devoted to detection of anomalously high plasticity levels attained at some parameters of irradiation and deformation, which is explained by the formation and propagation of a “phase transformation wave” in the metastable steel. Necessary and sufficient conditions for the realization of this wave are formulated.

Shock-induced spall in single and nanocrystalline SiC

Shock-induced spall in SiC is investigated via high strain-rate loading molecular dynamics simulations. The dynamic response under different shock intensities is characterized along the low-index 3C-SiC crystallographic directions, [001], [110], and [111], and in a nanocrystalline sample with 5 nm average grain size. The simulation results show that all single crystal samples generate elastic, plastic, and structural phase transformation waves for increasing particle velocities in good agreement with previous investigations. However, crystal anisotropy effects affect the exact shock response and the corresponding wave structures. The Hugoniot elastic limit is significantly higher along the [111] and [110] directions while the patterns of plastic deformation, based on deformation twinning, contrast along the three crystallographic directions. The spall behavior, both for single and nanocrystalline samples vary from classical to micro-spall. The predicted spall strength is at maximum along the [111] direction, at 34 GPa, followed by the [110], and [001] directions, at 32 and 30 GPa, respectively. Nanocrystalline SiC displays a spall strength over 66.7% lower than single crystals. Spall strengths from direct and indirect methods agree well for both classical and micro-spall regimes after applying an elastic-plastic correction and considering the change in sound velocity, in particular for the case where the structural phase transformation occurs.

Interplay of plasticity and phase transformation in shock wave propagation in nanocrystalline iron

Strong shock waves create not only plasticity in Fe, but also phase transform the material from its bcc phase to the high-pressure hcp phase. We perform molecular-dynamics simulations of large, 8-million atom nanocrystalline Fe samples to study the interplay between these two mechanisms. We compare results for a potential that describes dislocation generation realistically but excludes phase change with another which in addition faithfully features the bcc → hcp transformation. With increasing shock strength, we find a transition from a two-wave structure (elastic and plastic wave) to a three-wave structure (an additional phase-transformation wave), in agreement with experiment. Our results demonstrate that the phase transformation is preceded by dislocation generation at the grain boundaries (GBs). Plasticity is mostly given by the formation of dislocation loops, which cross the grains and leave behind screw dislocations. We find that the phase transition occurs for a particle velocity between 0.6 and 0.7 km s−1. The phase transition takes only about 10 ps, and the transition time decreases with increasing shock pressure.

Intercalation dynamics in rechargeable battery materials: General theory and phase-transformation waves in LiFePO 4

A general continuum theory is developed for ion intercalation dynamics in a single crystal of rechargeable-battery composite electrode material. It is based on an existing phase-field formulation of the bulk free energy and incorporates two crucial effects: (i) anisotropic ionic mobility in the crystal and (ii) surface reactions governing the flux of ions across the electrode/electrolyte interface, depending on the local free energy difference. Although the phase boundary can form a classical diffusive “shrinking core” when the dynamics is bulk-transport-limited, the theory also predicts a new regime of surface-reaction-limited (SRL) dynamics, where the phase boundary extends from surface to surface along planes of fast ionic diffusion, consistent with recent experiments on LiFePO 4. In the SRL regime, the theory produces a fundamentally new equation for phase transformation dynamics, which admits traveling-wave solutions. Rather than forming a shrinking core of untransformed material, the phase boundary advances by filling (or emptying) successive channels of fast diffusion in the crystal. By considering the random nucleation of SRL phase-transformation waves, the theory predicts a very different picture of charge/discharge dynamics from the classical diffusion-limited model, which could affect the interpretation of experimental data for LiFePO 4.

Inelastic deformation and phase transformation of shock compressed silicon single crystals

Silicon crystals were shock compressed along the [100] and [111] orientations to stresses between 15.9 and 21.7GPa. Transmitted wave profiles exhibited considerable orientation dependence for elastic and inelastic waves but very little orientation dependence for the phase transformation wave. Following the phase transformation wave, the silicon was compressed ∼23%. This compression is significantly greater than the previously reported compressions for silicon shocked to similar stresses, and the present data are consistent with a completed phase transformation. The measured mechanical impedance of the transformed silicon matches the bulk impedance of the simple hexagonal phase of silicon reported in static high pressure studies.

Shock-induced phase transformations of iron studied with molecular dynamics

Molecular dynamics simulations are used to investigate the shock-induced phase transformation of iron at a certain initial temperature, which shows that the temperature lowers the threshold pressure of shock-induced phase transformation. Also, the evolution of the loading and unloading waves is calculated and analyzed, and it is found that the velocity of the inverse phase transformation wave(during ε phase →α phase)equals the longitudinal sound speed of the wave front and is less than that of the wave rear. The pressure and density of unloading traces is also calculated, which affords a good explanation to the evolution of the unloading waves, and the phase transformation band of unloading is obtained, which shows the hysteresis in the reverse transformation.

Simulation of an early stage of a conductor’s electrical explosion

Phase-transformation waves that may arise in a conductor in the course of an electrical explosion are considered. An estimate allowing one to predict the possibility of occurrence of several phase transformations at the front of the single wave is proposed. Mathematical simulation results are presented.

The structure of the phase transformation wave in the discrete model of a non-equilibrium phase transition

The structure of the wave of the phase transformation in the deterministic discrete model of non-equilibrium phase transitions is investigated. In this model each of the cells forming a two-dimensional lattice can be in one of three states: stable, metastable or excited. The transition into the stable state is allowed only through an intermediate excited state. The change of the phase state of each cell is initiated by the variation of a continuous parameter, the 'temperature', taking into account the energy exchange between cells, the phase stability regions and local rules in the neighbourhood of the cell. Taking the square and hexagonal lattices as examples, it is shown that this model possesses the following fundamental property: when the lifetime of the excited states is increased beyond a certain threshold, an abrupt change of the dynamics of the phase transition occurs. The wavefront then acquires a beam-like or fractal-like structure and, in the latter case, the system of cells has a quasicontinuous frequency spectrum of white or coloured noise. The application of this model to the description of non-equilibrium (explosive) crystallization in amorphous metals and semiconductors is discussed.

Longitudinal waves in an elastic medium with a piecewise-linear dependence of the stress on the strain

Longitudinal waves in an elastic body in which the derivative of the stress with respect to the strain (the coefficient of elasticity) can undergo a discontinuity are considered. Fronts can be propagated in such a body, in which a jumplike change in the coefficient of elasticity and the characteristic velocities occurs. It is shown that if the front velocity reaches the value of one of the velocities of the characteristics, reconstruction of the motion occurs, where the special case of the problem of the decay of a weak discontinuity of second-order arises, whereupon a change in the front velocity and type occurs. The problem under consideration is very similar to the problem of the behaviour of an elastic-plastic medium with hardening (although mathematically it does not the same as it), for which the front classification and certain solutions with front reconstruction are given in /1–3/. For a medium of different-modulus, a classification of the front is made in /4, 5/. Some of these fronts are identical with fronts in elastic-plastic media. Solutions of problems of the behaviour of weak first-order discontinuities in a different-modulus elastic body were examined in /4–7/. The paper by G.Ya. Galin, “Phase Transformation Waves” presented at the international conference “Modern Mathematical Problems of Mechanics and Their Application” (Moscow, 1987) was also devoted to flows with a change in properties of the medium.

Excitation of a phase-transformation wave in a metal under the action of a square surface heat pulse

We approximate the phase-transformation wave excited in a metal by the action of a square surface heat pulse when its surface density is given and the time of action is varied.