Improved Creep Resistance Research Articles

Microstructure optimization for improving creep resistance of additively manufactured Ni-based superalloy IN939 through heat treatment

Microstructure optimization for improving creep resistance of additively manufactured Ni-based superalloy IN939 through heat treatment

Effect of carbon content on the microstructure and stress rupture properties of a 4th-generation nickel-based single crystal superalloy

The balance between the stress rupture properties and castability of a 4th-generation Ni-based single crystal superalloy can be achieved by addition of appropriate carbon content. In this work, the effects of carbon content on the microstructure and stress rupture properties of a 4th-generation Ni-based single crystal superalloy were investigated in detail. The results showed that minor carbon addition could aggravate the dendrite segregation, while the addition of carbon had no obvious effect on the rafting and distortion of γ′ phase during stress rupture deformation. At 760 °C/810 MPa and 1100 °C/210 MPa, the stress rupture lives of the three experimental alloys initially increased and subsequently decreased with the increasing carbon content. However, under condition of 1140 °C/137 MPa, the increased carbon content resulted in the reduction of the stress rupture lives of alloy. It was discovered that minor carbon elements addition (0.045 wt%) can promote formation of interfacial dislocation networks and improve creep resistance at high temperatures. At intermediate temperature, the introduction of carbon could reduce the stacking fault (SF) energy of γ matrix, thus facilitating the formation of SFs in γ matrix. The M6Cgranular carbides precipitated at high temperature, which was considered to be beneficial to stress rupture properties.

Nanoindentation creep response of Ti–6Al–4V ELI alloy manufactured via laser powder bed fusion

The anisotropic creep response in both the XY and XZ planes of Ti–6Al–4V ELI manufactured by powder bed fusion (PBF) was examined under nanoindentation creep loading at room temperature, ranging from nm to μm scales. The stress exponent values of 4.06–4.30, rationalised through threshold stress, indicate that the creep behaviour is primarily dominated by dislocation gliding. Creep displacement results show that the anisotropic creep behaviour in the XY and XZ planes of the as-built, and heat treatment enhances the creep resistance of the XZ plane, while there is no significant difference in creep displacement between the as-built and heat-treated XY planes. Due to the higher dislocation density and compressive residual stress in the XY plane compared to the XZ plane, the creep resistance is higher in the XY plane for the as-built. It is highlighted that compressive residual stress is more relieved in the XY plane than in the XZ plane through heat treatment. The heat treatment results in improved creep resistance due to the formation of the Widmanstätten structure and β precipitates, which can impede dislocation movement under creep loading. The combination of residual stress and microstructural effects leads to anisotropic creep behaviour, suggesting that the anisotropy is inherited from the additive manufacturing process at micron scales.

Improved creep resistance of short carbon fiber reinforced polyetherimide composite by solution mixing method

Creep resistance is critical for ensuring the dimensional stability and safe operation of composite components. However, the creep resistance of short fiber reinforced thermoplastic composites has been rarely reported and that of the composites manufactured by conventional extrusion compounding combined with injection molding is kind of low. In this work, in order to address this issue, two short carbon fiber-reinforced polyetherimide (SCF/PEI) composites named respectively as SCF/PEIE and SCF/PEIS are prepared by both conventional extrusion compounding and our newly developed solution mixing method combined with injection molding. The solution mixing method involves the dispersion and mixing of carbon fibers within a PEI solution and allows for the retention of longer fiber lengths. Experimentally, the creep behaviors of the SCF/PEI composites were examined through tensile and flexural creep testing at various stress levels in a wide temperature range. Theoretically, the creep behaviors were characterized by employing the Schapery model and the time–temperature superposition principle (TTSP), and the impact of fiber length retention on creep resistance was quantitatively analyzed using the Fu-Lauke model. The results demonstrate that compared to the SCF/PEIE composite, the SCF/PEIS composite exhibits a higher creep fracture stress level (175 MPa) and a more extensive linear viscoelastic region (0–85 MPa) at room temperature. Furthermore, the SCF/PEIS composite was observed to have a significantly longer secondary creep stage at an elevated temperature of 210 °C. Overall, the creep resistance of the newly manufactured SCF/PEIS is significantly superior to that of the SCF/PEIE, which effectively extends the service life and operational capacity of injection-molded SCF/PEI composites.

Increasing heat resistance of a Mg-Sm-Zn alloy via minor gadolinium addition

The addition of minor gadolinium (Gd) into Mg-4Sm-0.6Zn-0.4Zr alloy significantly enhances high-temperature strength and creep resistance, such as a decrease in the minimum creep rate by approximately five times and an increase in the yield strength by around 40 MPa at 200 °C. The presence of Gd results in the co-precipitation of both prismatic β-type and basal γ-type phases during creep, whereas only the basal γ-type phase is present in the Gd-free alloy. The prismatic β-type and basal γ-type phases are oriented perpendicular to each other in space, creating a closed configuration that effectively blocks dislocation motions compared to single basal γ-type precipitates. Therefore, the improved creep resistance in the Gd-enriched alloy is mainly attributed to the co-precipitation of prismatic β-type and γ-type precipitates during creep. Furthermore, rare earth (RE) atoms inherently provide stable solute hardening at high temperatures, which contributes to the increased high-temperature strength. The addition of Gd also enhances grain boundary stability by promoting the formation of more Mg3RE phases, thereby further enhancing the creep strength. These findings offer insights into the development of highly creep-resistant Mg alloys with low RE concentrations.

Strength stability at high temperatures for additively manufactured alumina forming austenitic alloy

Several fast-spectrum nuclear reactors designed to generate high power (∼450 MWe) rely on forced convection of media such as supercritical CO2, sodium, or liquid lead to cool the nuclear core, operating at temperatures up to 600 °C. Cost-effective, high-strength Fe-based alumina forming austenitic (AFA) alloys are a promising candidate for the fabrication of critical nuclear components. This study investigated laser powder bed fusion (LPBF) processing of an AFA alloy composition optimized for improved creep resistance. Electron microscopy revealed an elongated grain structure along the build direction with a fine sub-grain cellular structure decorated with (Cr,Fe,Nb)23C6 carbide precipitates at the intercellular boundaries. At temperatures of 20–900 °C, the LPBF alloy's superior tensile properties compared to its arc-melted counterpart and other advanced steels (e.g., SS316) were attributed to the distribution of nano-sized carbide precipitates, whereas the high ductility was attributed to the LPBF alloy's elongated grain structure.

Effect of Ni-RGO nanosheets on the creep behavior of Sn–Ag–Cu composite solder joints

Creep damage of Sn–Ag–Cu micro-joints is inevitable in service, even at room temperature. In this study, Ni-decorated reduced graphene oxide (Ni-RGO) nanosheets were rationally selected as a promising reinforcement in Sn-3.0Ag-0.5Cu (SAC305) solder to improve creep resistance. Tensile creep tests were conducted on the Ni-RGO reinforced SAC305 micro-joints under 8–14 MPa stress at 100–150 °C by dynamic mechanical analysis (DMA) equipment. Micrography and fractography were observed using FESEM. The stress exponent (n) increased from 5.83 to 6.37, and the activation energy (Q) rose from 68.80 to 75.41 kJ/mol as 0.10 wt% Ni-RGO nanosheets were added into the SAC305 solder, indicating the occurrence of diffusion mechanism. By adding a trace amount of Ni-RGO nanosheets (no more than 0.10 wt%), the crack initiation was prone to occur at the wave-valley of the continuous scallop shaped interface, where the diffusion of vacancies occurred, resulting in hybrid-fracture features of quasi-cleavage and dimples. It can be concluded that the inclusion of trace amounts of Ni-RGO nanosheets can enhance the creep resistance of SAC305 micro-joints during service.

Microstructure and creep behavior of electron beam directed energy deposited TC11 titanium alloy

The creep behavior of TC11 titanium alloy prepared by electron beam directed energy deposition (EB-DED) under various temperatures and stresses was investigated. The results indicated that TC11 prepared by EB-DED maintained excellent creep resistance in the temperature range from 550 °C to 600 °C, compared with the forged TC and TA series titanium alloys. The creep process accelerated with increasing temperature and stress, leading to elevated creep rates and shortened creep lifetimes. The improved creep resistance was related to the multiscale microstructures, i.e., the primary β columnar grains, the refined α lamellar microstructure and the solid solution strengthening effect of Si element predominantly existing in a nearly fully dissolved state.

Kenaf/glass fiber‐reinforced polymer composites: Pioneering sustainable materials with enhanced mechanical and tribological properties

AbstractHybrid kenaf/glass fiber reinforced polymer composites have emerged as promising structural materials, garnering significant attention due to their unique blend of natural kenaf fibers and synthetic glass fibers. However, despite their potential, there remains a gap in the comprehensive understanding of their quasi‐static mechanical behavior, creep resistance, and fatigue performance. This paper addresses this gap by presenting recent advancements in studying these key properties of hybrid composites. Studies reveal that the combination of kenaf and glass fibers results in enhanced tensile, flexural, and impact strengths compared to individual fiber composites. Additionally, the hybridization offers improved creep resistance, with the glass fibers reinforcing the polymer matrix against deformation under sustained loads. Furthermore, investigations into fatigue properties demonstrate the resilience of hybrid composites to cyclic loading, contributing to prolonged service life in high‐stress environments. By elucidating the interplay between kenaf and glass fibers, this review underscores the potential of hybrid composites in various structural applications. The synergistic effects between natural and synthetic fibers offer a balance between sustainability, performance, and durability, making hybrid kenaf/glass fiber reinforced polymer composites a compelling choice for industries seeking lightweight, high‐performance materials in which aligns with the sustainable development goals (SDGs) especially on Goal 12.Highlights In composite engineering, combining glass and kenaf fibers could cut production costs, yield high‐performance materials, and promote green technology. Substituting part of the glass fiber with kenaf can enhance the strength‐to‐weight ratio and promote greater biodegradability in current synthetic composites. Quasi‐mechanical properties of hybrid kenaf/glass‐based composites was enhanced by optimal stacking sequences, filler addition, and fiber treatment. Failures due to fatigue and creep can be reduced by hybridizing kenaf/glass fiber composites can prevent in polymer composite due to enhance elastic modulus. Enhanced tribological performance of hybrid kenaf/glass‐based composites due to less damage in microstructure via good interlocking of kenaf and glass in matrix.

Influence of crystalline structure on creep resistance capability in semi-crystalline Polymers: A coarse-grained molecular dynamics study

In this study, we investigated the intrinsic correlation between the crystal configuration and persistent mechanical stability of semi-crystalline polymers. The creep resistances of microstructures with different grain sizes and the same crystallinity were evaluated using coarse-grained molecular dynamics simulations. It was demonstrated that under tensile loading at constant pressure, microstructures with larger grains have more pronounced resistance to molecular rearrangement and significantly delay creep deformation. The improved creep resistance can be attributed to two factors. First, larger crystal sizes result in an increased moment of inertia, reducing the angular velocity required for the rotational rearrangement of the crystalline phase. Second, the elongated crystalline stems enhance the resistance to intermolecular slippage, elevating the strain energy necessary to disrupt the crystalline structure. These findings reveal the molecular basis of creep resistance at the nanoscale and highlight the pivotal role of crystal morphology in enhancing the long-term mechanical integrity of polymers.

Microstructure evolution and assessment of creep behaviour of SiC nanoparticles dispersed squeeze-cast Mg-5.0Al-2.0Ca-0.3Mn alloy

The microstructural modification and creep behaviour of Mg-5.0Al-2.0Ca-0.3Mn (AXM520) alloy with SiC nanoparticles (SiCnp) dispersion have been investigated. The concentrations of the SiCnp are varied from 0.5 to 3.0 (wt.%), and the squeeze-cast nanocomposites (NCs) are abbreviated as NC0·5SiC, NC1·0SiC, NC2·0SiC and NC3·0SiC. The microstructures of the AXM520 alloy and NCs consist of a primary solid solution (α-Mg), a eutectic of α-Mg and (Mg,Al)2Ca (C36), and an Al8Mn5 phase. Additionally, the SiC phase is also present in the NCs. The continuous network of the C36 phase in the NCs is fragmented and becomes discontinuous with the increase in the fraction of the SiCnp. All the NCs revealed improved creep performance compared to the AXM520 alloy. The creep rate of the NCs decreases with the increase in the SiCnp content. The NC2·0SiC exhibited an improvement in creep resistance by 73.2 % compared to the alloy. However, the creep resistance deteriorated since the amount of the nanoparticles was further increased in the NC3·0SiC, leading to agglomeration. The stress exponents vary from 5.0 to 6.7, and activation energies vary from 89.8 to 101.8 kJ/mol, implying that the creep in the materials is controlled by the climb of dislocation assisted by the pipe diffusion. The pile-ups of dislocations took place around the C36 phase and near the SiCnp. The additional strengthening owing to the presence of the SiCnp in the NCs was responsible for their improved creep performance compared to the AXM520 alloy.

Recent Progress in Creep-Resistant Aluminum Alloys for Diesel Engine Applications: A Review.

Diesel engines in heavy-duty vehicles are predicted to maintain a stable presence in the future due to the difficulty of electrifying heavy trucks, mine equipment, and railway cars. This trend encourages the effort to develop new aluminum alloy systems with improved performance at diesel engine conditions of elevated temperature and stress combinations to reduce vehicle weight and, consequently, CO2 emissions. Aluminum alloys need to provide adequate creep resistance at ~300 °C and room-temperature tensile properties better than the current commercial aluminum alloys used for powertrain applications. The studies for improving creep resistance for aluminum casting alloys indicate that their high-temperature stability depends on the formation of high-density uniform dispersoids with low solid solubility and low diffusivity in aluminum. This review summarizes three generations of diesel engine aluminum alloys and focuses on recent work on the third-generation dispersoid-strengthened alloys. Additionally, new trends in developing creep resistance through the development of alloy systems other than Al-Si-based alloys, the optimization of manufacturing processes, and the use of thermal barrier coatings and composites are discussed. New progress on concepts regarding the thermal stability of rapidly solidified and nano-structured alloys and on creep-resistant alloy design via machine learning-based algorithms is also presented.

A microstructure-based constitutive model for creep rate and damage of oxide dispersion strengthened high-entropy alloy

Oxide dispersion strengthened (ODS) high-entropy alloys (HEAs) exhibit a great resistance to creep, which has a great application potential on the nuclear energy field. However, the classical creep model hardly considers the coupling effect of the cutting and Orowan bypassing mechanism as well as severe atomic lattice distortion in ODS HEAs, leading to low prediction accuracy. Here, we propose a dislocation theory-based constitutive model for strength and creep rate considering the climbing mechanism, shearing mechanism, and Orowan bypassing mechanism in ODS HEAs. In addition, the effects of the size and spatial distribution of the oxide particle on creep rate and strength are studied. The creep rate and yield strength obtained from the experiments and developed model are compared to verify the rationality and accuracy. The proposed model has demonstrated a high prediction accuracy, with the creep rate and yield strength achieving levels as high as 98.2 % and 98.1 %, respectively. The incorporation of oxide particles within a specific size range and volume fraction has been proven to significantly improve creep resistance. Interestingly, the fracture time has the potential to exceed 41 years, significantly surpassing that Zr-based alloys under the same conditions. This model would be utilized to predict the creep rate in response to a complex applied stress, offering theoretical guidance for the development of ODS HEAs with superior creep resistance for nuclear reactor cladding materials.

Increasing the cross-link density in a dual dissociative and associative polythiourethane covalent adaptable network improves both creep resistance and extrudability

There have been significant, recent reports of the effects of cross-link density on the relaxation dynamics and processability of exclusively associative covalent adaptable networks (CANs), also called vitrimers. Similar characterization is lacking for the substantial number of CANs that exhibit dual associative and dissociative dynamic covalent chemistries. Polythiourethane (PTU), which is a thiol-based analogue of polyurethane, is one such polymer class that exhibits both dissociative and associative dynamic chemistries. Here, we tune the cross-link density of PTU CANs by systematic incorporation of long-chain and short-chain thiols. As would be commonly expected, relative to networks with lower cross-link density, PTU networks with higher cross-link density exhibit improved creep resistance at 60 °C and 100 °C. However, we also observe faster elevated-temperature stress relaxation with increasing cross-link density, which is attributable to the dual nature of the PTU dynamic chemistry, with the associative dynamic mechanism being increasingly favored and becoming increasingly more rapid with increasing cross-link density. Because of this shift, our PTU CAN with the highest cross-link density undergoes facile melt extrusion at 150 °C; in contrast, our PTU CAN of lowest cross-link density cannot be melt extruded. Overall, this work highlights the significance of cross-link density in networks exhibiting two or more dynamic chemistries and how that may lead to otherwise unexpected outcomes, e.g., better processability at higher cross-link density.

Largely Improved Creep Resistance and Thermal-Aging Stability of Eco-Friendly Polypropylene High-Voltage Insulation by Long-Chain Branch-Induced Interfacial Constraints.

Polypropylene (PP)-based composites have attracted numerous attention as a replacement of prevailing cross-linked polyethylene (XLPE) for high-voltage insulation due to their ease of processing, recyclability, and excellent electrical performance. However, the poor resistances against high-temperature creep and thermal aging are obstacles to practical applications of PP-based thermoplastic high-voltage insulation. To address these problems, in this Letter, we synthesized an impact polypropylene copolymer (IPC) containing multifold long-chain branched (LCB) structures in phases, especially the interfaces between the PP matrix and the rubber phase. The results indicated that the structural stability of LCBIPC was significantly enhanced under extreme conditions. In comparison to IPC (without LCB structures), 24.1% less creep strain and 75.2% less unrecoverable deformation are achieved in LCBIPC at 90 °C. In addition, the thermal aging experiments were performed at 135 °C for 48 and 88 days for IPC and LCBIPC, respectively. The results show that the resistance against thermal aging was also enhanced in LCBIPC, which showed a 133% longer thermal aging life compared to IPC. Further results revealed that the interfacial layer between the PP matrix and the rubber phase was constructed in LCBIPC. The two phases are tightly linked by chemical bonds in LCB structures, leading to enforced constraints of the rubber phase at the micro level and better resistance performance against creep and thermal aging at the macro level. Evidently, the reported eco-friendly LCBIPC thermoplastic insulation shows great potential for applications in high-voltage cable insulation.

Double cross-linked 3D layered PBI proton exchange membranes for stable fuel cell performance above 200 °C

Phosphoric acid doped proton exchange membranes often experience performance degradation above 200 °C due to membrane creeping and phosphoric acid evaporation, migration, dehydration, and condensation. To address these issues, here we present gel-state polybenzimidazole membranes with double cross-linked three-dimensional layered structures via a polyphosphoric acid sol-gel process, enabling stable operation above 200 °C. These membranes, featuring proton-conducting cross-linking phosphate bridges and branched polybenzimidazole networks, effectively anchor and retain phosphoric acid molecules, prevent 96% of its dehydration and condensation, improve creep resistance, and maintain excellent proton conductivity stability. The resulting membrane, with superior through-plane proton conductivity of 0.348 S cm−1, delivers outstanding peak power densities ranging from 1.20–1.48 W cm−2 in fuel cells operated at 200-240 °C and a low voltage decay rate of only 0.27 mV h−1 over a 250-hour period at 220 °C, opening up possibilities for their direct integration with methanol steam reforming systems.

Improved creep resistance of Mo-V-Si-B alloys with a density below 8 g/cm³

Improving the efficiency of turbines for power plants and aircraft engines is an increasingly important research subject. Ternary Mo-Si-B alloys, consisting of a molybdenum solid solution (Moss) phase and two intermetallic phases Mo5SiB2 (T2) and Mo3Si, are able to combine balanced room temperature fracture toughness, high temperature creep strength and good oxidation performance. However, the high density (typically > 9 g/cm3) of this class of alloys is a drawback when used as structural materials for rotating components. In this study, high potential Mo-V-Si-B materials which provide a reduced density by about 17 % as compared with the reference alloy Mo-9Si-8B were investigated. A comparative characterization was carried out on sintered (FAST) and arc-melted Mo-40V-9Si-8B alloys. Compressive creep tests reveal competitive creep resistance of this new type of alloys in the application relevant temperature regime.

Analysis on the compressive creep behaviors of Mg–Y alloys with various grain sizes

The creep behaviors of a hot-rolled Mg-4.5 wt%Y alloy sheet in the grain size ranging from d = 10 μm to d = 160 μm were carefully investigated in this work. It was shown that both loading direction and grain size exhibited effects on the creep behavior. The creep resistance along the ND was always greater than that along the RD, and the increased grain size contributed to the improved creep resistance along both directions. For the fine-grained samples (d = 10 μm to d = 25 μm), the dominant mechanisms were independent of the loading direction, including grain boundary migration (GBM), cross-slip made by basal dislocations and prismatic dislocations, and <c + a > dislocations slipping on the prismatic planes. The undifferentiated dominant mechanisms led to the extremely low creep anisotropy. For the coarse-grained samples (d = 60 μm to d = 160 μm), the dominant mechanisms were different along two loading directions. Specifically, all RD samples shared the dominant mechanisms of cross-slip and {101‾2} twinning, while the dominant mechanisms of all ND samples were dislocation climb and <c + a > dislocations slipping on pyramidal planes. The easy activation of {101‾2} twinning replaced GBM and induced the creep anisotropy, resulting in a low incremental speed of creep resistance along the RD. Differently, the primary dislocation climb and pyramidal <c + a > slip brought a high incremental speed of creep resistance along the ND. Consequently, the coarsen-grained samples had a strong creep anisotropy.

The influence of γ′ morphology and size on stress rupture properties in Ni-base superalloy IN738LC

This study investigates the influence of γ′ precipitate morphology and size on the creep deformation of the cast superalloy IN738LC under conditions of 760–982 °C and 78–674 MPa. Two microstructures were obtained by different heat treatments. The analysis of the experiments show that, according to the applied stress at 760 °C and 871 °C, the S1A material, with a bimodal distribution with large cuboidal γ′ and small spherical γ′, exhibited the longer creep life compared to those with a monomodal distribution with spherical γ′ precipitates. In the creep test at 760 °C, the S1A material exhibited a stacking fault within the primary cuboidal-shaped γ′ phase. The main deformation mechanism observed was isolated stacking fault (ISF) formation. Conversely, for the S2A material, an extended stacking fault (ESF) was observed, where dislocations continuously traversed several γ′ and γ phases. At 871 °C in low-stress creep tests, the S1A alloy displayed a dislocation network resulting from thermal activation, with localized stacking faults. In the S2A alloy, three-dimensional dislocations generated by climb were primarily observed around spherical γ′ precipitates, accompanied by localized stacking faults. At 982 °C, both S1A and S2A alloys exhibited rafting under lower stress, displaying similar lifetimes. The formation of a regular dislocation network at the interface between γ′ and γ matrix and rafting of γ′ precipitate proved beneficial in improved creep resistance of the alloy.

Unexpected effects on creep resistance of an extruded Mg-Bi alloy by Zn and Ca co-addition: Experimental studies and first-principles calculations

In the present work, a new Mg-Bi based alloy is developed by the addition of Zn and Ca in equivalent atom fraction with Bi. Mg-Bi and Mg-Bi-Zn-Ca alloys were prepared by extrusion at a ram speed of 20 mm/s. Room temperature mechanical properties and creep behaviors at 423 K were investigated. The results show that Zn and Ca co-addition shows little influence on average grain size and texture intensity but changes the dispersive Mg3Bi2 into Mg2Bi2Ca particles in different sizes and a lower density. Twinning is largely activated during room-temperature deformation. Consequently, a slightly decreased proof strength but tripled elongation is shown at room temperature. Unexpectedly, large enhancement in creep resistance is detected after the co-alloying of Zn and Ca and the minimum creep rate is reduced by 10 to 20 times in the BZX621 alloy. Stress exponent n = 4–5 indicates that the creep is a dislocation-climb controlled type. Post-mortem characterization on microstructure shows slip of dislocation 〈c + a〉 are also largely found in B6 as well as BZX621 alloy and cross-slip is detected more severe in B6 alloy. Dynamic segregation and precipitation are also seen in both alloys. Bi-clusters are seen dispersive across the grains in B6 and so did the PFZs that could undermine creep resistance at the grain boundaries. By contrast, Zn-rich needle-like precipitates are developed at most “ends” of 〈c + a〉 dislocations, which would hinder the further dislocation motions and thus improve the creep resistance. First-principles calculations were adopted and the results show that the thermal stability and thermomechanical properties of Mg2Bi2Ca are much better than that of Mg3Bi2. Stacking faults energy is lowered down with the co-addition of Ca and Zn, which could inhibit the rate of dislocation climb and cross-slip. As a result, the improved creep resistance is obtained in the Mg-Bi-Zn-Ca alloys. Microstructural and controlling mechanism changes by thermal activation result in the unexpected enhancement in creep resistance with decreased room-temperature proof strength after co-addition. These findings could contribute to the development and optimization of creep-resistant Mg alloys in the future.