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  1. Abstract

    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.

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  2. Pressure-induced phase transformations (PTs) in Si, the most important electronic material, have been broadly studied. However, strain-induced PTs in Si were never studied in situ. Here, we revealed in situ various important plastic strain-induced PT phenomena. A correlation between the particle size's direct and inverse Hall-Petch effect on yield strength and pressure for strain-induced PT is found. For 100 nm particles, strain-induced PT Si-I³Si-II initiates at 0.3 GPa versus 16.2 GPa under hydrostatic conditions; Si-I³Si-III PT starts at 0.6 GPa and does not occur under hydrostatic pressure. Pressure in small Si-II and Si-III regions is ~5-7 GPa higher than in Si-I. Retaining Si-II and single-phase Si-III at ambient pressure and obtaining reverse Si-II³Si-I PT demonstrates the possibilities of manipulating different synthetic paths. The obtained results corroborate the elaborated dislocation pileup-based mechanism and have numerous applications for developing economic defect-induced synthesis of nanostructured materials, surface treatment (polishing, turning, etc.), and friction. 
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    Free, publicly-accessible full text available March 6, 2025
  3. The first study of the effect of the initial microstructure on its evolution under hydrostatic compression before, during, and after the irreversible α → ω phase transformation and during pressure release in Zr using in situ x-ray diffraction is presented. 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 but above volume fraction of ω Zr c = 0.7, larger volume fraction is observed for the annealed sample. This implies that the general theory based on the proportionality between the athermal resistance to the transformation and the yield strength must be essentially advanced. The crystal domain size significantly reduces, and microstrain and dislocation density increase during loading for both α and ω phases in their single-phase regions. For the α phase, domain sizes are much smaller for prestrained Zr, while microstrain and dislocation densities are much higher. For the cold-rolled sample at 5.9 GPa (just before initiation of transformation), domain size in α Zr decreased to ∼ 45 nm and dislocation density increased to 1.1 × 1015 lines/m2 , values similar to those after severe plastic deformation under high pressure. Despite the generally accepted concept that hydrostatic pressure does not cause plastic straining, it does and is estimated. During transformation, the first rule was found: The average domain size, microstrain, and dislocation density in ω Zr for c < 0.8 are functions of the volume fraction of ω Zr only, which are independent of the plastic strain tensor prior to transformation and pressure. The microstructure is not inherited during phase transformation. Surprisingly, for the annealed sample, the final dislocation density and average microstrain after pressure release in the ω phase are larger than for the severely pre-deformed sample. The significant evolution of the microstructure and its effect on phase transformation demonstrates that their postmortem evaluation does not represent the actual conditions during loading. A simple model for the initiation of the phase transformation involving microstrain is suggested. The results suggest that an extended experimental basis is required for the predictive models for the combined pressure-induced phase transformations and microstructure evolutions. 
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    Free, publicly-accessible full text available February 22, 2025
  4. Free, publicly-accessible full text available October 1, 2024
  5. Severe plastic deformations under high pressure are used to produce nanostructured materials but were studied ex-situ. Rough diamond anvils are introduced to reach maximum friction equal to yield strength in shear and the first in-situ study of the evolution of the pressure-dependent yield strength and radial distribution of nano structural parameters are performed for severely pre-deformed Zr.ω-Zr behaves like perfectly plastic, isotropic, and strain-path-independent and reaches steady values of the crystallite size and dislocation density, which are pressure-, strain- and strain-path-independent. However, steady states forα-Zr obtained with smooth and rough anvils are different, causing major challenge in plasticity theory. 
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    Free, publicly-accessible full text available September 2, 2024
  6. Severe plastic deformations under high pressure are used to produce nanostructured materials but were studied ex-situ. We introduce rough diamond anvils to reach maximum friction equal to yield strength in shear and perform the first in-situ study of the evolution of the pressure-dependent yield strength and nanostructural parameters for severely pre-deformed Zr. ω-Zr behaves like perfectly plastic, isotropic, and strain-path-independent. This is related to reaching steady values of the crystallite size and dislocation density, which are pressure-, strain- and strain-path-independent. However, steady states for α-Zr obtained with smooth and rough anvils are different, which causes major challenge in plasticity theory. 
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  7. Scale-free phase-field approach and corresponding finite element method simulations for multivariant martensitic phase transformation 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 transformation, which produce essential challenges for computations. 3D polycrystals with 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. 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 phase transformation and negative local tangent modulus are stabilized at the macroscale by arresting/slowing the growth of Si II regions by the grain boundaries. This leads to increasing stress during transformation. The developed methodology can be used for studying similar phase transformations with large transformation strains and for further development by including plastic strain and strain-induced transformations. 
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  8. 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. 
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  9. Severe plastic deformations (SPD) under high pressure, mostly by high-pressure torsion, are employed for producing nanostructured materials and stable or metastable high-pressure phases. However, they were studied postmortem after pressure release. Here, we review recent in situ experimental and theoretical studies of coupled SPD, strain-induced phase transformations (PTs), and microstructure evolution under high pressure obtained under compression in diamond anvil cell or compression and torsion in rotational diamond anvil cell. The utilization of x-ray diffraction with synchrotron radiation allows one to determine the radial distribution of volume fraction of phases, pressure, dislocation density, and crystallite size in each phase and the main laws of their evolution and interaction. Coupling with the finite element simulations of the sample behavior allows the determination of fields of all components of the stress and plastic strain tensors and volume fraction of high-pressure phase and provides a better understanding of ways to control occurring processes. Atomistic, nanoscale and scale-free phase-field simulations allow elucidation of the main physical mechanisms of the plastic strain-induced drastic reduction in phase transformation pressure (by one to two orders of magnitude), the appearance of new phases, and strain-controlled PT kinetics in comparison with hydrostatic loading. Combining in situ experiments with multiscale theory potentially leads to the formulation of methods to control strain-induced PT and microstructure evolution and designing economic synthetic paths for the defect-induced synthesis of desired high-pressure phases, nanostructures, and nanocomposites. 
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