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Various phenomena (phase transformations (PTs), chemical reactions, microstructure evolution, strength, and friction) under high pressures in diamond-anvil cell are strongly affected by fields of stress and plastic strain tensors. However, they could not be measured. Here, we suggest coupled experimental-analytical-computational approaches utilizing synchrotron X-ray diffraction, to solve an inverse problem and find fields of all components of stress and plastic strain tensors and friction rules before, during, and after α-ω PT in strongly plastically predeformed Zr. Results are in good correspondence with each other and experiments. Due to advanced characterization, the minimum pressure for the strain-induced α-ω PT is changed from 1.36 to 2.7 GPa. It is independent of the plastic strain before PT and compression-shear path. The theoretically predicted plastic strain-controlled kinetic equation is verified and quantified. Obtained results open opportunities for developing quantitative high-pressure/stress science, including mechanochemistry, synthesis of new nanostructured materials, geophysics, astrogeology, and tribology.

 

Scale-free phase-field approach (PFA) at large strains and corresponding finite element method (FEM) simulations for multivariant martensitic phase transformation (PT) from cubic Si I to tetragonal Si II in a polycrystalline aggregate are presented. Important features of the model are large and very anisotropic transformation strain tensor εt = {0.1753; 0.1753; −0.447} and stress-tensor dependent athermal dissipative threshold for PT, which produce essential challenges for computations. 3D polycrystals with 55 and 910 stochastically oriented grains are subjected to uniaxial strain- and stress-controlled loadings under periodic boundary conditions and zero averaged lateral strains. Coupled evolution of discrete martensitic microstructure, volume fractions of martensitic variants and Si II, stress and transformation strain tensors, and texture are presented and analyzed. Macroscopic variables effectively representing multivariant transformational behavior are introduced. Macroscopic stress-strain and transformational behavior for 55 and 910 grains are close (less than 10% difference). This allows the determination of macroscopic constitutive equations by treating aggregate with a small number of grains. Large transformation strains and grain boundaries lead to huge internal stresses of tens GPa, which affect microstructure evolution and macroscopic behavior. In contrast to a single crystal, the local mechanical instabilities due to PT and negative local tangent modulus are stabilized at the macroscale by arresting/slowing the growth of Si II regions by the grain boundaries and generating the internal back stresses. This leads to increasing stress during PT. The developed methodology can be used for studying similar PTs with large transformation strains and for further development by including plastic strain and strain-induced PTs. 

Pressure-induced phase transformations (PTs) between numerous phases of Si, the most important electronic material, have been studied for decades. This is not the case for plastic strain-induced PTs. Here, we revealed in-situ various unexpected plastic strain-induced PT phenomena. Thus, for 100 nm Si, strain-induced PT Si-I to Si-II (and Si-I to Si-III) initiates at 0.4 GPa (0.6 GPa) versus 16.2 GPa (∞, since it does not occur) under hydrostatic conditions; for 30 nm Si, it is 6.1 GPa versus ∞. The predicted theoretical correlation between the direct and inverse Hall-Petch effect of the grain size on the yield strength and the minimum pressure for strain-induced PT is confirmed for the appearance of Si-II. Retaining Si-II at ambient pressure and obtaining reverse Si-II to Si-I PT are achieved, demonstrating the possibilities of manipulating different synthetic paths. 

The effect of initial microstructure and its evolution across the α→ω phase transformation in commercially pure Zr under hydrostatic compression has been studied using in situ x-ray diffraction measurements. Two samples were studied: one is plastically pre-deformed Zr with saturated hardness and the other is annealed. Phase transformation α→ω initiates at lower pressure for pre-deformed sample, suggesting pre-straining promotes nucleation by producing more defects with stronger stress concentrators. With transformation progress, the promoting effect on nucleation reduces while that on growth is suppressed by producing more obstacles for interface propagation. The crystal domain size reduces and microstrain and dislocation density increase during loading for both α and ω phases in their single-phase regions. For α phase, domain sizes are much smaller for prestrained Zr, while microstrain and dislocation densities are much higher. On the other hand, they do not differ much in ω Zr for both prestrained and annealed samples, implying that microstructure is not inherited during phase transformation. The significant effect of pressure on the microstructural parameters (domain size, microstrain, and dislocation density) demonstrates that their postmortem evaluation does not represent the true conditions during loading. A simple model for the initiation of the phase transformation involving microstrain is suggested, and a possible model for the growth is outlined. The obtained results suggest an extended experimental basis is required for better predictive models for the pressure-induced and combined pressure- and strain-induced phase transformations. 

Various phenomena (phase transformations, chemical reactions, and friction) under high pressures in diamond anvil cell are strongly affected by fields of all components of stress and plastic strain tensors. However, they could not be measured. Even measured pressure distribution contains significant error. Here, we suggest coupled experimental-analytical-computational approaches utilizing synchrotron X-ray diffraction, to solve an inverse problem and find all these fields and friction rules before, during, and after α-ω phase transformation in strongly plastically predeformed Zr. Due to advanced characterization, the minimum pressure for the strain-induced α-ω phase transformation is changed from 1.36 to 2.7 GPa. It is independent of the compression-shear path. The theoretically predicted plastic strain-controlled kinetic equation is verified and quantified. Obtained results open opportunities for developing quantitative high-pressure/stress science, including mechanochemistry, material synthesis, and tribology. 

The nanoscale multiphase phase-field model for stress and temperature-induced multivariant martensitic transformation under large strains developed by the authors in Basak and Levitas (J Mech Phys Solids 113:162–196, 2018) is revisited, the issues related to the gradient energy and coupled kinetic equations for the order parameters are resolved, and a thermodynamically consistent non-contradictory model for the same purpose is developed in this paper. The model considers N+1 order parameters to describe austenite and N martensitic variants. One of the order parameters describes austenite↔martensite transformations, and the remaining N order parameters, whose summation is constrained to the unity, describe the transformations between the variants. A non-contradictory gradient energy is used within the free energy of the system to account for the energies of the interfaces. In addition, a kinetic relationship for the rate of the order parameters versus thermodynamic driving forces is suggested, which leads to a system of consistent coupled Ginzburg–Landau equations for the order parameters. An approximate general crystallographic solution for twins within twins is presented, and the explicit solution for the cubic to tetragonal transformations is derived. A large strain-based finite element method is developed for solving the coupled Ginzburg–Landau and elasticity equations, and it is used to simulate a 3D complex twins within twins microstructure. A comparative study between the crystallographic solution and the simulation results is presented. 

Deep-focus earthquakes that occur at 350–660 km are 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 s⁻¹to seismic 10 − 10³ s⁻¹strain rates? Is it possible without PT? (b) How does metastable olivine, which does not completely transform to spinel for over a million years, suddenly transform during seconds? (c) How to connect shear-dominated seismic signals with volume-change-dominated PT strain? Here, we introduce a combination of several novel concepts that resolve the above puzzles quantitatively. We treat the transformation in olivine like plastic strain-induced (instead of pressure/stress-induced) and find an analytical 3D solution for coupled deformation-transformation-heating in a shear band. This solution predicts conditions for severe (singular) transformation-induced plasticity (TRIP) and self-blown-up deformation-transformation-heating process due to positive thermomechanochemical feedback between TRIP and strain-induced transformation. This process leads to temperature in a band, above which the self-blown-up shear-heating process in the shear band occurs after finishing the PT. Our findings change the main concepts in studying the initiation of the deep-focus earthquakes and PTs during plastic flow in geophysics in general.

 

Athermal resistance to the motion of a phase interface due to a precipitate is investigated. The coupled phase field and elasticity equations are solved for the phase transformation (PT). The volumetric misfit strain due to the precipitate is included using the error and rectangular functions. Due to the presence of precipitates, the critical thermal driving forces remarkably differ between the direct and reverse PTs, resulting in a hysteresis behavior. For the precipitate radius small compared to the interface width, the misfit strain does not practically show any effect on the critical thermal driving force. Also, the critical thermal driving force value nonlinearly increases vs. the precipitate concentration for both the direct and reverse PTs. Change in the precipitate surface energy significantly changes the PT morphology and the critical thermal driving forces. The critical thermal driving force shows dependence on the misfit strain for large precipitate sizes compared to the interface width. For both the constant surface energy (CSE) and variable surface energy (VSE) boundary conditions (BCs) at the precipitate surface, the critical thermal driving force linearly increases vs. the misfit strain coefficient for the direct PT while it is almost independent of it for the reverse PT. For larger precipitates, the critical thermal driving force nonlinearly increases vs. the precipitate concentration for the direct PT. For the reverse PT, its value for the CSE BCs linearly increases vs. the precipitate concentration while it is independent of the precipitate concentration for the VSE BCs. Also, for any concentration, the VSE BCs result in higher thermal critical driving forces, a smaller hysteresis range, and a larger transformation rate. The critical microstructure and thermal driving forces are validated using the thermodynamic phase equilibrium condition for stationary interfaces. 

Athermal resistance to the motion of a phase interface due to a precipitate is investigated. The coupled phase field and elasticity equations are solved for the phase transformation (PT). The volumetric misfit strain due to the precipitate is included using the error and rectangular functions. Due to the presence of precipitates, the critical thermal driving forces remarkably differ between the direct and reverse PTs, resulting in a hysteresis behavior. For the precipitate radius small compared to the interface width, the misfit strain does not practically show any effect on the critical thermal driving force. Also, the critical thermal driving force value nonlinearly increases vs. the precipitate concentration for both the direct and reverse PTs. Change in the precipitate surface energy significantly changes the PT morphology and the critical thermal driving forces. The critical thermal driving force shows dependence on the misfit strain for large precipitate sizes compared to the interface width. For both the constant surface energy (CSE) and variable surface energy (VSE) boundary conditions (BCs) at the precipitate surface, the critical thermal driving force linearly increases vs. the misfit strain coefficient for the direct PT while it is almost independent of it for the reverse PT. For larger precipitates, the critical thermal driving force nonlinearly increases vs. the precipitate concentration for the direct PT. For the reverse PT, its value for the CSE BCs linearly increases vs. the precipitate concentration while it is independent of the precipitate concentration for the VSE BCs. Also, for any concentration, the VSE BCs result in higher thermal critical driving forces, a smaller hysteresis range, and a larger transformation rate. The critical microstructure and thermal driving forces are validated using the thermodynamic phase equilibrium condition for stationary interfaces.