High Temperature Compression Tests Research Articles

Billet Size Optimization for Hot Forging of AISI 1045 Medium Carbon Steel Using Zener-Hollomon and Cingara-McQueen Model

This study investigates the effects of initial billet size variations on material flow behavior in hot forging processes, aiming to optimize the forging process using validated predictive models. Material and high-temperature compressive tests inform mathematical models, while simulations are conducted via the finite element method (FEM). Results align with the Zener-Hollomon and Cingara-McQueen approaches. The Arrhenius model predicts AISI 1045 steel flow stress with an R2 of 0.968 and an average absolute relative error (AARE) of 7.079%. The Cingara-McQueen equation achieves an R2 of 0.997 and an AARE of 2.960%. Reducing billets size from 260 mm to 230 mm decreases the material usage by up to 11.5%, while maintaining workpiece integrity. Experimental and simulated loads exhibit an AARE of about 2.69%, thereby indicating potential cost and efficiency improvements in hot forging processes.

High temperature electropalsticity in Aermet100 steel by decoupling electron wind effect

Aermet100 ultra-high strength steel (UHSS) is one of the highest strength-plasticity-matched metallic materials. It is widely used in critical load-bearing components in aerospace and weaponry. Compared to traditional forging processes, electropulsing assisted forming technology significantly enhances manufacturing efficiency and forming limits. Particularly in the forming of hard-to-deform materials into complex structures, it demonstrates significant application potential. However, quantitative studies on the decoupling of electron wind effects during high-temperature deformation and their impact on microstructural evolution, deformation mechanisms, and mechanical properties remain few reported, resulting in limiting the ability to select optimal process parameters in electropulsing assisted forming technology to precisely control material structure and properties. In this paper, the impact of varying degrees of electron wind effects on flow stress through high-temperature compression tests was investigated. The evolution of the microstructure was analyzed in conjunction with the thermodynamic and kinetic mechanisms of recrystallization. Moreover, the hitherto unexplained relationship between the activation of slip systems and texture components in Aermet100 UHSS is examined. Results indicate that with the enhancement of the electron wind effect, the flow stress of Aermet100 UHSS is reduced by 59.4 %. The electron wind effect not only reduces the activation energy for recrystallization but also enhances vacancy concentration, dislocation climb diffusion flux, and driving force, thus promoting continuous dynamic recrystallization. Furthermore, as the intensity of the electron wind effect increases to 0.85 Ew and above, S and Brass textures are observed for the first time. It is notable that the Dillamore texture, Brass texture, and S texture respectively activate specific slip systems (1‾ 10)[11 1‾], (0 1‾1‾)[11 1‾] and (110)[1‾ 11‾] during the hot deformation process of Aermet100 UHSS. This investigation sheds new insight into tailoring high temperature electroplasticity by regulating electron wind effects.

Multi-objective, multi-constraint high-throughput design, synthesis, and characterization of tungsten-containing refractory multi-principal element alloys

Refractory multi-principal element alloys (RMPEAs) have gained interest recently due to their superior properties at elevated temperatures, including outstanding yield and ultimate strengths, high thermal conductivity, and resistance to creep. RMPEAs can be designed to exhibit a wide range of properties by tailoring their composition. However, the vast chemical design space makes brute-force experimental screening inefficient and costly. In this work, we follow a closed-loop, iterative computational/experimental screening approach that combines computational alloy design methodologies with high-throughput synthesis and characterization tools to explore the vast RMPEAs space and design new RMPEAs that satisfy multiple objectives and constraints. In particular, we targeted compositions with yield strengths higher than 50 MPa at 2000 °C, W content of more than 30 at.% for high-temperature strength and operability up to 2000 °C, narrow solidification range for additive manufacturability, competitive ductility metrics, among other property constraints. We evaluated the mechanical properties and microstructure of 58 alloys designed in 5 batches, in both as-cast and homogenized conditions, synthesized using vacuum arc melting, utilizing scanning electron microscopy, X-ray diffraction, Vickers microhardness, nanoindentation, and high-temperature compression testing. Based on the microhardness screening experiments in each batch, the best-performing alloys were selected for scale-up. High-temperature compression at 1800 °C was performed in these alloys, demonstrating that the designed alloys exhibit up to five times higher yield strength than a pure tungsten benchmark. We conclude that W-containing RMPEAs designed in this study merit further consideration for next-generation structural materials for ultra-high temperature applications.

High-temperature effect on continuous glass fiber reinforced polypropylene multilayer composite and corrugated sandwich panels

The high-temperature mechanical behaviors of Multi-Layer Composite Panels (MCP) and Corrugated Sandwich Panels (CSP) of Continuous Glass Fiber-Reinforced Polypropylene (CGFRPP) are critical for their application in aerospace fields, which have been rarely mentioned in previous studies. High-temperature quasi-static tensile and compression tests on CGFRPP MCP are conducted first. The results showed that the tensile and compression strength, stiffness, and tensile modulus of MCP decreased with increasing temperature. The Gibson model was found to be more suitable for predicting the high-temperature mechanical performance of MCP after comparing the calculated results of different theoretical models with experimental data. Secondly, high-temperature planar compression tests were conducted on the CGFRPP CSP, revealing that the main failure modes were corrugated core buckling and delamination between the face panel and core material, with delamination being intensified at higher temperatures. Therefore, we proposed a strength theoretical model that considers structural buckling failure and interface delamination failure, and introduced the influence factor to evaluate the effect of interface delamination on structural strength.

Improvement of the strength of ternary eutectic V-Si-B alloys at ambient and high temperatures due to Cr additions

In the present study high-temperature compression tests on a chromium-alloyed ternary eutectic V-9Si-6.5B are reported. The ternary eutectic composition is located within the VSS (V solid-solution)-V3Si-V5SiB2 three-phase region of the respective V-rich corner of the phase diagram. The high-temperature compressive yield stresses were determined by the 0.5 % offset method and the plastic strain was obtained by subtracting the combined compliance of the testing machine and the specimen from the individually measured load-displacement curves. The microstructures in the as-cast and heat-treatment state (1400 °C / 100 hrs) were analyzed using SEM, EBSD and TEM observations. The effect of Cr on the ternary eutectic formation was studied. After compression testing, dislocation activities were observed in the VSS and V3Si phases, while the ternary intermetallic phases were dislocation-free. The high-temperature plasticity in the Cr-added ternary eutectic alloys V-9Si-6.5B+xCr is mainly governed the VSS phase which forms the major phase of the eutectic. Thus, Cr additions are found to contribute to solid-solution strengthening in the ternary eutectic alloys while strongly influencing the deformability by decreasing the temperature at which brittle failure occurs in the present compression experiments.

High temperature deformation behaviour and recrystallization mechanism of TiC/Ti6Al4V gradient material fabricated by laser directed energy deposition

Metal-ceramic gradient materials are of considerable interest due to their unique capability to integrate the ductility of metals with the mechanical strength and high-temperature resistance of ceramics, thereby reducing the risk of cracking induced by thermal stress. In this article, TiC/Ti6Al4V gradient materials were prepared through the laser directed energy deposition (LDED) process. Subsequently, high-temperature compression tests were performed at various temperatures to investigate the deformation behaviour and recrystallization mechanism of the gradient materials. The Zener-Holomon constitutive equation was then used to calculate the gradient material at 750–900 °C and 0.001–0.1 s−1 to obtain a deformation activation energy of 362.36 KJ·mol−1. The EBSD was used to analyze the microstructural evolution of the gradient material. The results indicate a significant reduction in the average grain size of the specimens after high-temperature compression, and a more random crystal orientation due to the occurrence of dynamic recrystallisation (DRX). The primary softening mechanism of TiC/Ti6Al4V gradient materials is discontinuous dynamic recrystallisation, with TiC primarily affecting the nucleation of discontinuous dynamic recrystallisation (DDRX) and the subsequent grain growth. The nucleation becomes easier with increasing TiC content. However, the TiC hinders the migration of grain boundaries, resulting in a smaller DDRX grain size. After high-temperature compression, the main slip system of the crystal is converted from Pri to Bas. Pyr is difficult to activate due to its high critical resolved shear stress.

Solidification and microstructure investigation on as-cast and annealed hypoeutectic Ti–Fe alloys

This work explored the solidification behavior, microstructure development, and resulting mechanical properties of hypoeutectic Ti–Fe alloys under both as-cast and annealed conditions. Ti-(27, 28, 29)Fe (wt%) alloys were synthesized through arc-melting, followed by annealing at 950 °C for 24 h and slow furnace cooling. The investigation procedures included thermodynamic calculations, differential scanning calorimetry, scanning electron microscopy, high-temperature laser-scanning confocal microscopy, X-ray diffraction, hardness measurements, and compression tests. The study demonstrated the efficacy of annealing treatments in reducing excess eutectic in the as-cast structure formed during solidification. Results from both thermodynamic calculation and experiment for the solidification process demonstrated reasonable agreement. The high β-stabilizing effect of Fe ensured the presence of the β phase at room temperature under both studied conditions. The solid-solution hardening of the β phase, coupled with the TiFe intermetallic, substantially contributed to the increased hardness and mechanical strength, although the increase in brittleness was noticeable in the as-cast state. Subsequent annealing enhanced plasticity but resulted in a reduction in strength, albeit maintaining yield strength at a considerable level, approximately 1450 MPa.

Effect of Alloying Elements on the High-Temperature Yielding Behavior of Multicomponent γ'-L12 Alloys.

The exceptional mechanical properties of Ni-based high entropy alloys are due to the presence of ordered L12 (γ') precipitates embedded within a disordered matrix phase. While the strengthening contribution of the γ' phase is generally accepted, there is no consensus on the precise contribution of the individual strengthening mechanisms to the overall strength. In addition, changes in alloy composition influence several different mechanisms, making the assessment of alloying conditions complex. Multicomponent L12-ordered single-phase alloys were systematically developed with the aid of CALPHAD thermodynamic calculations. The alloying elements Co, Cr, Ti, and Nb were chosen to complexify the Ni3Al structure. The existence of the γ' single phase was validated by microstructure characterization and phase identification. A high-temperature compression test from 500 °C to 1000 °C revealed a positive temperature dependence of strength before reaching the peak strength in the studied alloys NiCoCrAl, NiCoCrAlTi, and NiCoCrAlNb. Ti and Nb alloying addition significantly enhanced the high-temperature yield strengths before the peak temperature. The yield strength was modeled by summing the individual effects of solid solution strengthening, grain boundary strengthening, order strengthening, and cross-slip-induced strengthening. Cross-slip-induced strengthening was shown to be the key contributor to the high-temperature strength enhancement.

Prediction of ductile cracking in the titanium alloy forging process

Abstract The control of surface cracking in the forming of titanium alloy forgings is a significant problem in the forging industry. For titanium alloys, the formation of surface cracks is related to temperature, strain rate, and stress state. This study selected the widely used medium to high strength titanium alloy Ti-6Al-4V in the field of forging as the research material, and designed six different shapes of specimens for high-temperature tensile and compression tests. The mechanisms underlying crack formation were analyzed at the microscopic level, and the critical fracture displacement of these tests was extracted. Moreover, their critical fracture strains were obtained through simulations, and a High-temperature damage model was established based on the DF2016 model. The research results showed that cracks through void at grain boundaries propagate and aggregate to form, leading to a fracture mechanism characterized by ductile fracture through micro-pore aggregation. Simulation results demonstrate that the established model accurately predicts the crack of forgings.

Thermal Deformation Behavior and Microstructural Evolution of Multicomponent Mg-Li-Zn-Al-Y Alloys under Hot Compression.

High-temperature compression tests on Mg-11.5Li-2.5Zn-0.35Al-0.3Y (in wt.%) were carried out on a Gleeble-3500 thermal simulator. Flow stress and microstructural evolution were analyzed at different temperatures (T = 473 K, 523 K, 573 K, and 623 K) and strain rates (ε˙ = 1 s-1, 0.1 s-1, 0.01 s-1, and 0.001 s-1). On this basis, the constitutive model of the alloy was established using the Arrhenius-type constitutive model, and the thermal processing map of the alloy was drawn based on the DMM (dynamic material modeling) theory. The experimental results show that the flow stress of the Mg-11.5Li-2.5Zn-0.35Al-0.3Y alloy decreases with an increase in temperature and a decrease in strain rate. The grain size increases uniformly with the increase in temperature, while a sudden increase occurs with the decrease in strain rate. The predicted value of the model is compared with the experimental value to verify the correctness of the model, and the correlation coefficient, R = 0.9690, was calculated, which further proves the applicability of the model to the Mg-11.5Li-2.5Zn-0.35Al-0.3Y alloy. This alloy can be safely plastic-deformed 473 K~623 K and 0.001 s-1~1 s-1.

High Temperature Deformation of Harmonic Structure Designed CrMnFeCoNi High Entropy Alloy

The Harmonic Structure (HS) is a recently introduced concept that paves the way for engineering metallic materials to achieve superior mechanical performance. They consist of soft, coarse-grained regions surrounded in three dimensions by an interconnected network of hard, ultra-fine grained regions. In addition, from a structural materials point of view, high entropy alloys have attracted attention due to their unique mechanical properties. In the present study, the HS design was applied to a high entropy CrMnFeCoNi alloy (also called "Cantor alloy"). The HS-designed Cantor alloy was successfully fabricated by mechanical milling, which is one of the surface severe plastic deformation processes, and the subsequent sintering process. The mechanical properties of these HS and homogeneous (Homo) Cantor alloy compacts were investigated by high-temperature compression tests in the temperature range of room temperature (RT) and 1173K, under initial strain rates of 0.01 s-1, 0.001 s-1, and 0.0001 s-1. The stress-strain curves of the HS compacts showed a large initial increase in stress and then a rapid decrease with strain, while that of the Homo compact showed a gentle increase and a gradual decrease. EBSD observation of the deformed compacts revealed that the HS compacts were probably deformed not only by dynamic recrystallization, but also by grain boundary sliding during deformation. The strain rate sensitivity value m of the HS compacts was 0.541 (true strain: 0.2) at 1173 K. In other words, the HS compacts exhibited pseudo-superplastic deformation at these temperatures.

Effect of Microstructure Change on Mechanical Properties after High Temperature Forming of Ti-6Al-4V Alloy

Ti-6Al-4V alloy is not easy to machine complicated shapes due to its low thermal conductivity, so high-temperature forming techniques such as ring-rolling are being applied. When this high-temperature forming technology is applied, the microstructure is greatly changed by process variables, and the mechanical properties of the forming product are also different accordingly. In particular, in the case of the Widmanst tten structure, α lamellar spacing and colony size have a great influence on mechanical properties. Therefore, in this study, the most suitable process conditions were selected by performing a high-temperature compression test to apply the ring-rolling process to the Ti-6Al-4V alloy used as an aerospace material. After that, the microstructure of the forming product was observed, the effects of α lamellar spacing and colony size on the mechanical properties were confirmed, and the correlation between mechanical properties and microstructure was evaluated based on this.

Microstructure and Mechanical Properties of Al-Si Alloys Produced by Rapid Solidification and Hot Extrusion.

The paper presents the results of tests of rapid solidification (RS) aluminum alloys with the addition of silicon (5%, 11%, and 20%). Casting by melt-spinning on the surface of an intensively cooled copper cylinder allowed to obtain a metallic material in the form of flakes, which were then consolidated in the process of pressing and direct extrusion. The effect of refinement on structural components after rapid solidification was determined. Rapidly solidified AlSi materials are characterized by a comparable size of Si particles, regardless of the silicon content, and the shape of these particles is close to spheroidal. Not only Si particles are fragmented, but also the Al-Si-Fe phase, which also changed its shape from irregular with sharp edges to regular and spherical. The melt-spinning process resulted in a fine-grained structure compared to materials obtained by gravity-casting and extrusion. The influence of the high-temperature compression test on the mechanical properties of rapidly solidified materials was analyzed, and the results were compared with those of gravity-cast materials. An increase in strength properties was found in the case of the AlSi5 RS alloy by 20%, in the case of AlSi11RS by 25%, and in the case of the alloy containing 20% Si by as much as 86% (tensile test). On the basis of the homogeneity of the particle distribution determined by the SEM method, it was found that rapid solidification is an effective method of increasing the strength properties and improving the plastic properties of Al-Si alloys.

Microstructure and mechanical properties of TiC reinforced TZM composites prepared by spark plasma sintering

In this paper, TiC (1 wt%, 5 wt%, 10 wt%, 15 wt%)-reinforced TZM composites with high relative density and good mechanical properties were prepared by high energy ball milling and spark plasma sintering. The microstructure, element distribution, and phase composition of TZM-TiC composites were systematically analyzed and characterized. The mechanical properties of TZM-TiC composites were evaluated by microhardness test, room temperature compression test and high temperature compression test. The results proved that with the increase of TiC content, the size of Mo grains in TZM-TiC composites was significantly inhibited, and the morphology of the reinforcement phase changed from a spherical shape to a long stripe shape. Mo was found to be partially amorphous in TZM-TiC composites, and various second phases (TiC, Ti and Mo2C) were found in the TZM-TiC composites. Through two-dimensional mismatch theory and first-principle calculations, the strengthening effect of Mo-Mo2C interface was much higher than that of Mo-TiC and MoTi interface. The generation of amorphous Mo, the grain refinement and the second phase strengthening together significantly improve the micro-Vickers hardness and compressive strength of TZM-(10%, 15%)TiC composites, which contributes to the Vickers hardness of TZM-15%TiC reaching 885.77 HV, and the compressive yield strength of TZM-10%TiC composite reaching 2169.7 MPa. Besides, the TZM-10%TiC composite exhibits excellent thermal stability, and its compressive yield strength at 600 °C reaches 1880.7 MPa.

Evaluation of high-temperature formability for Ti-xMo-4Fe metastable beta alloys based on Mo contents

High-temperature formation technology is widely used to fabricate components with metastable β titanium alloys, a material characterized by balanced mechanical properties, including superb formability, corrosion resistance, and high strength. In high-temperature formation, it is crucial to control the formation conditions by linking the changes in those conditions caused by processing variables with microstructures and identifying the optimal conditions for high-temperature formation. As such, in this study, a Ti–Mo–Fe alloy was designed that is different from conventional metastable β titanium by adding molybdenum (Mo) and iron (Fe), which are relatively economical β stabilization elements. The mechanical characteristics of the alloy at room temperature were also examined by varying the Mo content, and a high-temperature compression test was conducted to evaluate its high-temperature characteristics and formability. The high-temperature compression test was performed at five different temperatures (700 °C, 750 °C, 820 °C, 900 °C, and 950 °C) to avoid β-transus and with four different strain rates 1 × 10−3/sec, 1 × 10−2/sec, 1 × 10−1/sec, and 1 × 100/sec. Then, the test results were utilized to create a processing map, which evaluated formability by examining plastic instability and energy distribution efficiency at different temperatures, strain rates, and reduction rates, the processing variables for high-temperature formation. Afterward, their connections with the microstructures were analyzed to determine the optimal conditions for the temperature formation of the newly designed Ti–Mo–Fe metastable β titanium alloy.

Effect of Sr addition on the high temperature deformation behavior and processing maps of Mg-7Sn alloy

The effect of strontium (Sr) addition (1 wt%) on the hot deformation behavior of Mg-7Sn (wt%) was investigated by performing high temperature compression tests in the temperature range of 300–450 °C and at strain rates of 0.05 s−1 – 5 s−1. The flow stress curves suggested the occurrence of dynamic recrystallization (DRX). The constitutive equation was developed using an Arrhenius-type hyperbolic sine equation. The addition of Sr to Mg-7Sn led to a decrease in the activation energy value, suggesting easy hot working as compared to Mg-7Sn alloy. The processing maps were further generated for both alloys at 0.2 strain (strain near peak stress). For both alloys, the high-efficiency domain appeared in the high temperature and high strain rate ranges. However, it was observed that the safe working region increased for Sr-added Mg-7Sn compared to Mg-7Sn alloy. The deformed microstructures from the safe region characterized using electron backscatter diffraction (EBSD) showed faster development of recrystallized grain in Mg-7Sn-1Sr alloy. Further, the EBSD maps depicted the occurrence of particle stimulated nucleation (PSN) in Mg-7Sn-1Sr alloy which was absent in Mg-7Sn alloy. The PSN occurrence with the addition of Sr is predicted to cause easy deformation and increase the recrystallization fraction in the Mg-7Sn-1Sr alloy. The unstable regions showed the presence of voids in both the alloys.

Research on the Impact Mechanical Properties of Real-Time High-Temperature Granite and a Coupled Thermal–Mechanical Constitutive Model

Studying the mechanical behavior of rocks under real-time high-temperature conditions is of great significance for the development of energy caverns, nuclear waste disposal projects, and tunneling engineering. In this study, a real-time high-temperature impact compression test was conducted on Sejila Mountain granite to explore the effects of temperature and external load on its mechanical properties. Based on the concepts of damage mechanics and statistics, a coupled thermal-mechanical (T-M) damage constitutive model was established, which considers the temperature effect and uses the double-shear unified strength as the yield criterion. The parameter expressions were clarified, and the accuracy and applicability of the model were verified by experimental data. The research results indicated that high temperatures had an obvious damaging and deteriorating effect on the strength of the granite, while an increase in impact velocity had an enhancing effect on the strength of the granite. The established constitutive model theoretical curve and test curve showed a high degree of agreement, indicating that the coupled T-M model can objectively represent the evolution process of damage in rocks and the physical meaning of its parameters is clear.

Effect of Al Concentration on Basal Texture Formation Behavior of AZ-Series Magnesium Alloys during High-Temperature Deformation

Magnesium and its alloys have been restricted in their industrial applications due to problems related to their formability. To overcome this issue, controlling the crystallographic texture is important, and the texture formation mechanism should be investigated in relation to factors including deformation conditions and solute atoms. In particular, the effects of solute atoms on the texture formation behavior should be further analyzed because they can considerably affect the deformation behavior. Thus, in this study, to clarify the effect of aluminum concentration on the texture formation behavior and microstructure, high-temperature uniaxial compression tests were conducted on three types of AZ-series magnesium alloys (AZ31, AZ61, and AZ91). Compression was conducted at 673 K and 723 K, with strain rates of 0.05 s-1 and 0.005 s-1, up to a true strain of -1.0. Cylindrical specimens were prepared from a rolled plate that had a (0001) basal texture and was compressed parallel to the c-axis of the grains. Consequently, work softening and fiber texture formation were observed in all the specimens. During the deformation, the development of grain boundaries, which is a typical characteristic of continuous dynamic recrystallization (CDRX), was observed, and the (0001) texture was highly developed with increasing Al content. Although each alloy was associated with the same deformation conditions and mechanisms, the AZ31 alloy exhibited a non-basal texture component. The stacking fault energy contributed to the generation of slip systems and gliding, and it was seen as the main reason for texture variation.

Construction of an Arrhenius constitutive model for Mg-Y-Nd-Zr-Gd rare earth magnesium alloy based on the Zener-Hollomon parameter and objective evaluation of its accuracy in the twinning-rich intervals

According to a high-temperature compression test of rare earth magnesium alloy (WE43), a strain-compensated constitutive model of the Arrhenius equation based on Zener-Hollomon parameters was established, and the rheological behaviors were predicted. The model exhibited relatively serious prediction distortion in the low-temperature and high-strain rate parameter interval, and its accuracy was still unsatisfactory even after modification by a correction operator considering the coupling of temperature and strain rate. The microstructure characterization and statistical analysis showed that a large number of twinning occurred in the parameter intervals with prediction deviation. The occurrence of twinning complicated the local internal stress distribution by drastically changing the crystal orientation and led to significant fluctuations in the macroscopic strain-stress and hardening curves relative to the rheological processes dominated by the dislocation and softening mechanisms, making the logarithm of the strain rate and stress deviate from the linear relationship. This twinning phenomenon was greatly influenced by the temperature and strain rate. Herein, the influence mechanism on twinning behavior was analyzed from the perspective of the interaction of dislocation and twinning.

Processing parameters optimization in hot forging of AISI 4340 steel using instability map and reinforcement learning

High-temperature compression tests of the AISI 4340 alloy were conducted at temperatures of 900–1200 °C, strain rates of 0.01–10 s−1, and true strain ranges between 0.01 and 1.00 to explore the hot deformation properties. The experiment result has been used to obtain stress-strain curves of the material. The instability map is built at each true strain based on the dynamic materials model and Prasad's instability criterion. On the top of the instability map, the deformation behavior obtained from finite element analysis (FEA) is schematically investigated in the deformation flow instability. A reinforcement learning-based optimization algorithm has been developed to derive the optimal processing parameter, including workpiece temperature and stroke speed in the manufacturing process. Q-learning was used to learn and explore the solution environment to achieve the optimum processing parameters that prevent defects from instability traits. The experiment results show that the algorithm successfully avoided the unstable domains. Optical photography and electron backscatter diffraction (EBSD) has verified the proposed approach's practicality with experimental observations of flow instability signs.