Effect of hydrostatic pressure on the kinetics of alpha–omega phase transformation in zirconium

A three dimensional (3D) elastoplastic phase-field model, including strain hardening, is employed to study the effect of hydrostatic pressure in the range of 4–9 GPa on the kinetics of alpha–omega phase transformation in zirconium (Zr). The input data corresponding to pure Zr are acquired from experimental studies as well as by using the CALPHAD method. A decreasing incubation time, for the formation of omega variants, with increasing pressure is observed. Avrami (JMAK) equation is used to study the transformation kinetics by analysing the phase fraction plots predicted by the phase-field simulations. The estimated activation energy is in the range of 54–59 kJ mol−1 and decreases at an average rate of 992 J mol−1 per 1 GPa increase in pressure. The analysis of Avrami exponents, based on Cahn's approach, show that the transformation region can be divided into two distinct regions with a change in slope, which is attributed to the site saturation. It is concluded that in the first region where the exponents are above 3, the transformation proceeds by nucleation and growth. In the second region where the exponents are sub-unity, the transformation proceeds by growth of the existing variants.Post-print / Final draf

Grain growth phenomenon during pressure-induced phase transformations at room temperature

Significant grain growth is observed during the high-pressure phase transformations (PTs) at room temperature within an hour for various materials. However, no existing theory explains this phenomenon since nanocrystals do not grow at room temperature even over a time span of several years because of slow diffusion. Here, we suggest a multistep mechanism for the grain growth during $\alpha\rightarrow\omega$ PT in Zr. Phase interfaces and grain boundaries (GBs) coincide and move together under the action of a combined thermodynamic driving forces. Several intermediate steps for such motion are suggested and justified kinetically. Nonhydrostatic stresses due to volume reduction in the growing $\omega$ grain promote continuous growth of the existing $\omega$ grain instead of a new nucleation at other GBs. In situ synchrotron Laue diffraction experiments confirm the main predictions of the theory. The suggested mechanism provides a new insight into synergistic interaction between PTs and microstructure evolution.Comment: Main document: 16 pages, 4 figures; Supplementary document: 21 pages, 12 figure

Omega phase formation in ti–3wt

It is well known that severe plastic deformation not only leads to strong grain refinement and material strengthening but also can drive phase transformations. A study of the fundamentals of α → ω phase transformations induced by high-pressure torsion (HPT) in Ti–Nb-based alloys is presented in the current work. Before HPT, a Ti–3wt.%Nb alloy was annealed at two different temperatures in order to obtain the α-phase state with different amounts of niobium. X-ray diffraction analysis, scanning electron microscopy (SEM) and transmission electron microscopy (TEM) were applied for the characterisation of phase transitions and evolution of the microstructure. A small amount of the β-phase was found in the initial states, which completely transformed into the ω-phase during the HPT process. During HPT, strong grain refinement in the α-phase took place, as did partial transformation of the α- into the ω-phase. Therefore, two kinds of ω-phase, each with different chemical composition, were obtained after HPT. The first one was formed from the β-phase, enriched in Nb, and the second one from the α-phase. It was also found that the transformation of the α-phase into the ω-phase depended on the Nb concentration in the α-Ti phase. The less Nb there was in the α-phase, the more of the α-phase was transformed into the ω-phase

In Situ Analysis of the Phase Transformation Kinetics in the β-Water-Quenched Ti-5Al-5Mo-5V-3Cr-1Zr Alloy during Ageing after Fast Heating

Thermal treatments are the main route to achieve improvements in mechanical properties of β-metastable titanium alloys developed for structural applications in automotive and aerospace industries. Therefore, it is of vital importance to determine phase transformation kinetics and mechanisms of nucleation and precipitation during heat treatment of these alloys. In this context, the present paper focuses on the assessment of solid-state transformations in a β-water-quenched Ti-5Al-5Mo-5V-3Cr-1Zr alloy during the early stages of ageing treatment at 500 ◦C. In situ tracking of transformations was performed using high-energy synchrotron X-ray diffraction. The transformation sequence β + ω → α + α”iso + β is proposed to take place during this stage. Results show that isothermal α” phase precipitates from ω and from spinodal decomposition domains of the β phase, whereas α nucleates from ω, β and also from α” with different morphologies. Isothermal α” is considered to be the regulator of transformation kinetics. Hardness measurements confirm the presence of ω, although this phase was not detected by X-ray diffraction during the in situ treatment

In situ study of microstructure evolution and α → ω phase transition in annealed and pre-deformed Zr under hydrostatic loading

The detailed 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 a pre-deformed sample but for a volume fraction of ω Zr, c > 0.7, a larger volume fraction is observed for the annealed sample. This implies that the proportionality between the athermal resistance to the transformation and the yield strength in the continuum phase transformation theory is invalid; an advanced version of the theory is outlined. Phenomenological plasticity theory under hydrostatic loading is outlined in terms of microstructural parameters, and plastic strain is estimated. During transformation, the first rule is suggested, i.e., the average domain size, microstrain, and dislocation density in ω Zr for c < 0.8 are functions of the volume fraction, c 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 the average microstrain after pressure release in the ω phase are larger than for the severely pre-deformed sample. The results suggest that an extended experimental basis is required for the predictive models for the combined pressure-induced phase transformations and microstructure evolutions.This article is published as Pandey, K. K., Valery I. Levitas, Changyong Park, and Guoyin Shen. "In situ study of microstructure evolution and α→ ω phase transition in annealed and pre-deformed Zr under hydrostatic loading." Journal of Applied Physics 136, no. 11 (2024). doi: https://doi.org/10.1063/5.0208544

Nanomaterials by severe plastic deformation: review of historical developments and recent advances

International audienceSevere plastic deformation (SPD) is effective in producing bulk ultrafine-grained and nanostructured materials with large densities of lattice defects. This field, also known as NanoSPD, experienced a significant progress within the past two decades. Beside classic SPD methods such as high-pressure torsion, equal-channel angular pressing, accumulative roll-bonding, twist extrusion, and multi-directional forging, various continuous techniques were introduced to produce upscaled samples. Moreover, numerous alloys, glasses, semiconductors, ceramics, polymers, and their composites were processed. The SPD methods were used to synthesize new materials or to stabilize metastable phases with advanced mechanical and functional properties. High strength combined with high ductility, low/room-temperature superplasticity, creep resistance, hydrogen storage, photocatalytic hydrogen production, photocatalytic CO2 conversion, superconductivity, thermoelectric performance, radiation resistance, corrosion resistance, and biocompatibility are some highlighted properties of SPD-processed materials. This article reviews recent advances in the NanoSPD field and provides a brief history regarding its progress from the ancient times to modernity

Computational modelling of particulate composites using meshless methods

This thesis deals with the numerical simulation of particulate composites using one of the more stable and accurate meshless methods namely the element free Galerkin (EFG) method. To accurately describe the material inhomogeneities present in particulate composites, an extrinsic enrichment function is incorporated into the approximation of the EFG method which produces more versatile, robust and effective computational methodology. The effectiveness of the proposed numerical model is then investigated by employing the model to analyse different configurations of particulate composites. The accuracy and efficiency of this enriched EFG method are studied numerically by comparing the results obtained with the available analytical solutions and other numerical techniques. Further, it is demonstrated that the method developed in this work has the potential to efficiently model syntactic foam, a type of particulate composites. This is illustrated by performing multi-scale modelling using homogenisation technique which confirms satisfactory comparison of the numerical method with experimental results. To further explore the applicability of the developed methodology, an enriched or extended finite element method (XFEM) based technique, is applied to study crack inclusion and interaction of crack propagation with matrix and particles within particle reinforced composite material

Conceptual design of a breed & burn molten salt reactor

A breed-and-burn molten salt reactor (BBMSR) concept is proposed to address the Generation IV fuel cycle sustainability objective in a once-through cycle with low enrichment and no reprocessing. The BBMSR uses separate fuel and coolant molten salts, with the fuel contained in assemblies of individual tubes that can be shuffled and reclad periodically to enable high burnup. In this dual-salt configuration, the BBMSR may overcome several limitations of previous breed-and-burn (B$\&$B) designs to achieve high uranium utilisation with a simple, passively safe design. A central challenge in design of the BBMSR fuel is balancing the neutronic requirement of large fuel volume fraction for B$\&$B mode with the thermal-hydraulic requirements for safe and economically competitive reactor operation. Natural convection of liquid fuel within the tubes aids heat transfer to the coolant, and a systematic approach is developed to efficiently model this complex effect. Computational fluid dynamics modelling is performed to characterise the unique physics of the system and produce a new heat transfer correlation, which is used alongside established correlations in a numerical model. A design framework is built around this numerical model to iteratively search for the limiting power density of a given fuel and channel geometry, applying several defined temperature and operational constraints. It is found that the trade-offs between power density, core pressure drop, and pumping power are lessened by directing the flow of coolant downwards through the channel. Fuel configurations that satisfy both neutronic and thermal-hydraulic objectives are identified for natural, 5$\%$ enriched, and 20$\%$ enriched uranium feed fuel. B$\&$B operation is achievable in the natural and 5$\%$ enriched versions, with power densities of 73 W/cm$^3$ and 86 W/cm$^3$, and theoretical uranium utilisations of 300 $\mathrm{MWd/kgU_{NAT}}$ and 25.5 $\mathrm{MWd/kgU_{NAT}}$, respectively. Using 20$\%$ enriched feed fuel relaxes neutronic constraints so a wider range of fuel configurations can be considered, but there is a strong inverse correlation between power density and uranium utilisation. The fuel design study demonstrates the flexibility of the BBMSR concept to operate along a spectrum of modes ranging from high fuel utilisation at moderate power density using natural uranium feed fuel, to high power density and moderate utilisation using 20$\%$ uranium enrichment.Cambridge International & Churchill Pochobradsky Scholarship, Ford Britain Trust Travel Grant of the Cambridge University Engineering Department, Copisarow Travel & Conference Grant of Churchill Colleg