Yield Strength Research Articles

Process Parameter Optimization of Directed Energy Deposited QT17‐4+ Steel

AbstractThe feasibility of using argon‐atomized QT 17‐4+ stainless steel powder for directed energy deposition (DED) additive manufacturing is studied. The QT 17‐4+ steel is a novel martensitic steel designed based on the compositional modification of the standard 17‐4 precipitation‐hardened (PH) stainless steel. This modification aims to achieve better mechanical properties of as‐deposited components compared to the heat‐treated wrought 17‐4PH steel. In this study, QT 17‐4+ steel powder is used for DED, for the first time. The influence of laser power, laser scan speed, powder feed rate, and hatch overlap on the density is studied. The central composite design is used to determine the experimental matrix of these factors. The response surface methodology is used to obtain the empirical statistical prediction model. Both columnar and equiaxed parent austenite grain structures are observed. X‐ray diffraction analyses reveal a decrease in the percentage of retained austenite from 19% in the powder to 5% after DED. The microhardness of the DED processed sample in the as‐deposited state is slightly higher than that of wrought 17‐4PH steel either solution‐annealed or H900‐aged. A higher 0.2% yield strength, a lower ultimate tensile strength, and lower elongation are observed for the vertically printed test sample, when compared to the horizontal one.

Effects of Superheating Treatment on the Microstructure, Tensile and Thermal Conductivity Properties of Fe-Bearing Al-10Si-Mg Casting Alloy

In this study, we designed and manufactured a new Fe-bearing Al-10Si-Mg casting alloy (F alloy) and investigated its microstructure, mechanical properties, and thermal conductivity. Two types of Fe-bearing Al-10Si-Mg alloys were used: the Conventional-F alloy, injected at 720 ℃ and cooled by water quenching, and the Superheated-F alloy, heated to 820 ℃ and maintained at that temperature for 1 hour. Subsequently, it underwent a degassing process at 720 ℃ before being cooled by water quenching. Both the Conventional-F alloy and the Superheated-F alloy exhibited dendritic microstructures and Fe-intermetallic compounds. The Secondary Dendrite Arm Spacing (SDAS) of the Conventional-F alloy measured 32.4 μm, whereas the Superheated-F alloy measured 28.6 μm. Additionally, the average eutectic Si sizes were 10.3 μm for the Conventional-F alloy and 7.7 μm for the Superheated-F alloy. Fe-rich IMCs were observed in the eutectic region, with their size decreasing due to the superheating treatment. Tensile tests at room temperature were conducted at a strain rate of 10<sup>-3</sup>/s. The Conventional-F alloy exhibited a yield strength (YS) of 93.4 MPa, ultimate tensile strength (UTS) of 183 MPa, and an elongation (El.) of 6.4%. Conversely, the Superheated-F alloy displayed a YS of 115.4 MPa, UTS of 218.2 MPa, and an El. of 5.1%. The mechanical properties notably improved with the superheating treatment. Regarding thermal conductivity, the Conventional-F alloy exhibited 114.9 W/m·K, while the Superheated-F alloy displayed 153.7 W/m·K. This represents a roughly 14% increase compared to the thermal conductivity of the commercial Al-10Si-Mg material (Silafont36: 135.1 W/m·K). The effects of the Superheating Treatment on microstructural characteristics, deformation behavior, and thermal conductivity of the Fe-bearing Al-10Si-Mg casting alloys were discussed.

Dynamic reliability analysis of angular contact ball bearing based on maximum entropy quadratic fourth moment method*

ABSTRACT Bearing failure occurs when the dynamic contact stress exceeds the yield strength of the bearing material during operation. To minimise the risk of bearing failure, a new reliability theory method is proposed based on the stress-strength model of bearings, incorporating random input variables to analyse the reliability of angular contact ball bearings (ACBBs) and quantify their dynamic performance. The maximum entropy quadratic fourth moment method is used to calculate the probability distribution of maximum orthogonal shear stress-strength of bearing, and the maximum entropy principle is used to obtain the approximation of the minimum human error factors. Additionally, reliability-based sensitivity indices are derived to investigate the parametric significance of random input variables. Using B218 bearing as an example, the engineering application of this method in dynamic reliability and reliability-based sensitivity analysis is illustrated. Monte Carlo simulation is performed to verify the accuracy and effectiveness of the method to provide benchmark results. The results show that the Poisson’s ratio have a greater influence on the dynamic reliability of ACBBs than other parameters. Improving parameters such as ball diameter, raceway groove curvature radius and contact angle can also improve the reliability of bearings to some extent.

Tensile strength and immersion corrosion behavior of nano-ZnO, rare earth Gd reinforced Mg nanocomposites developed by novel stir ultrasonication process

This paper presents the tensile and immersion corrosion properties of Mg-Zn-0.2Gd-xZnO (x = 1, 1.5, 2 and 2.5 wt.%) alloy and nanocomposites developed by stir ultrasonication coupled with squeeze casting. The immersion corrosion tests were performed under the simulated body fluid (SBF) conditions. The microscopic measurements indicate that the examined alloys/nanocomposites exhibit a significant decrease in grain size when both alloying elements Gadolinium (Gd) and Zinc Oxide (ZnO) nanoparticles are added. The examination of the phase by XRD indicates the presence of α-Mg and Mg2Zn, Mg7Zn3 secondary phases, which act as barriers against corrosion. The study confirmed that the incorporation of nanoparticles ZnO content ranging from 1 to 2.5 wt. % leads to a notable enhancement in yield strength (140 to 230 MPa). From the immersion corrosion test, the nanocomposites with the inclusion of 2 wt. % ZnO ceramic nanoparticles resulted in the highest level of corrosion resistance with a corrosion rate of 0.049 mm per year. This nanocomposite also shows better wettability with improved hydrophilicity. The developed Mg based advanced nanocomposites have the potential to be used in load bearing implant applications as it exhibited high corrosion resistance characteristics.

Predicted Fracture Tendency of Naturally Occurring Aluminum Surface Coatings under Tensile Loading.

Naturally occurring coatings on aluminum metal, such as its oxide or hydroxide, serve to protect the material from corrosion. Understanding the conditions under which these coatings mechanically fail is therefore expected to be an important aspect of predictive models for aluminum component lifetimes. To this end, we develop and apply a molecular dynamics (MD) modeling framework for conducting tension tests that is capable of isolating factors governing the mechanical strength as a function of coating chemistry, defect morphology, and variables associated with the loading path. We consider two representative materials, including γ-Al2O3 and γ-Al(OH)3 (i.e., oxide and hydroxide), both of which form readily as aluminum surface coatings. Our results indicate that defects have a significant bearing on the strength of aluminum oxide, with grain boundaries serving to reduce the strain at failure from εzz = 0.300 to 0.219, relative to perfect single crystal. Our simulations also predict that porosity lowers the elastic stiffness and yield strength of the oxide. Relative to perfect crystal, we find porosity factors of 5%, 10% and 20% decrease the yield stress by 26%, 36% and 53%, respectively. MD predicts that perfect hydroxide and oxide single crystal have respective strains at failure of 0.08 and 0.31 under tensile uniaxial strain loading, and that the corresponding yield stresses are respectively 1.6 and 11.1 GPa. These data indicate that the hydroxide is substantially more susceptible to mechanical failure than the oxide. Our results, coupled with literature findings that indicate hot and humid conditions favor formation of hydroxide and defective oxide coatings, indicate the potential for a complicated dependence of aluminum corrosion susceptibility and stress corrosion cracking on aging history.

INFLUENCE OF THE TYPE OF MATERIAL OF DELAYED COKING REACTORS ON DAMAGE DURING OPERATION

The problem of increased damage to delayed coking reactors (DCRs) or coke drums in domestic and foreign oil refining practice is still relevant. To date, significant progress has been made abroad in understanding the mechanisms of damage to DCR; numerous measures have been formulated, tested for widespread use, and have been used for a considerable time to improve the resistance to operational damage of DCRs. There is an urgent need to adapt and use positive foreign experience in the domestic practice of designing and operating DCRs, which will allow for a significant reduction in their damageability. Among the measures to increase the resistance to operational damage of DCRs, the most important place is occupied by the determination of technical requirements for their material design. The article compares the technical requirements for the material design of the DCR in domestic and foreign design practice, and analyzes the operating experience of the DCR with different material designs. Data on recorded damage obtained during the operation of DCRs is presented, data on the chemical composition and mechanical properties of the materials used in the manufacture of DCRs, the results of technical diagnostics of DCRs are provided with illustrative materials of damage zones of DCRs. A comparison is made in the level of resistance to operational damage of DCRs with different material designs. The results of previously performed studies on mathematical modeling of the stress-strain state of the elements of DCRs are used, with verification of strength conditions. Recommendations for the material implementation of DCRs are provided. Proposals for changes in the technical requirements for the material design of the DCRs are formulated in terms of mechanical characteristics (yield strength) in the delivered state.

Effect of Carbon Content and Hard Phase Volume Fraction on Yield Strength in Friction Stir Processing of Low and Medium Carbon Steels

Effect of Carbon Content and Hard Phase Volume Fraction on Yield Strength in Friction Stir Processing of Low and Medium Carbon Steels

Mechanical Properties of an Ultrahard In Situ Amorphous Steel Matrix Composite

We report compression tests on micropillars manufactured from bulk specimens of partially devitrified SAM2×5 (Fe49.7Cr17.7Mn1.9Mo7.4W1.6B15.2C3.8Si2.4). Yield strength values of ≈6 GPa are obtained. Such a high strength can be attributed to the higher glass transition temperature (883 K) of this material, which impedes the multiplication of shear bands under loading, and to the presence of hard crystalline domains that result from devitrification of the amorphous powders during powder consolidation. The Vickers hardness of the specimens is found to be strongly correlated to the processing temperature and, hence to the volume of crystalline phases present in the specimens. As the processing temperature is increased, there is a reduction in free volume from the structural relaxation process in the amorphous alloy, leading to the eventual nucleation of crystalline phases of BCC Fe, Cr2B, Cr21.30Fe1.7C6, or Fe23B2C4, during the densification process. These results shed light on the relationship between nanocrystalline domains and the mechanical behavior of Fe‐based amorphous/crystalline composites.

Revealing the Enhancement Mechanism of Laser Cutting on the Strength–Ductility Combination in Low Carbon Steel

The strength–ductility mechanism of the low-carbon steels processed by laser cutting is investigated in this paper. A typical gradient-phased structure can be obtained near the laser cutting surface, which consists of a laser-remelted layer (LRL, with the microstructure of lath bainite + granular bainite) and heat-affected zone (HAZ). As the distance from the laser cutting surface increases, the content of lath martensite decreases in the HAZ, which is accompanied by a rise in the content of ferrite. Considering that the microstructures of the LRL and HAZ are completely different from the base metal (BM, ferrite + pearlite), a significant strain gradient can be inevitably generated by the remarkable microhardness differences in the gradient-phased structure. The hetero-deformation-induced strengthening and hardening will be produced, which is related to the pileups of the geometrically necessary dislocations (GNDs) that are generated to accommodate the strain gradient near interfaces. Plural phases of the HAZ can also contribute to the increment of the hetero-deformation-induced strengthening and hardening during deformation. Due to the gradient-phased structure, the low carbon steels under the process of laser cutting have a superior combination of strength and ductility as yield strength of ~487 MPa, tensile strength of ~655 MPa, and total elongation of ~32.7%.

Accurate prediction of aging effects on microstructure evolution and related mechanical strength of Mg-Zn alloys via multiscale simulations

Age strengthening is a common method to achieve superior mechanical properties employed in magnesium (Mg) alloys. However, the experimental approaches to examine the aging effects on mechanical properties are primarily based on trial and error, posing challenges for the design and development of high-strength Mg alloys. A promising solution to address this challenge is to establish an accurate prediction model for the aging effects on Mg alloys, covering the evolution of microstructure and corresponding mechanical properties. This paper introduces a multiscale simulation approach to accurately predict the aging effects on the Mg-2.3Zn (at.%) alloy. To begin, we establish a phase field model to simulate the microstructure evolution at 150 ℃, demonstrating precipitate growth during aging in alignment with experimental observations. Secondly, based on the microstructures obtained from phase field simulations, the corresponding yield strength is determined through finite element method simulations. The simulation successfully captures the peak-aged behavior of yield strength during aging, resulting in a yield strength of 167 MPa at the peak-aged state, with a deviation of less than 5 % from experimental results. In-depth analysis indicates that the peak value of total yield strength arises from the interplay between solid solution strengthening and precipitate strengthening. Furthermore, precipitate strengthening reaches a peak value at a specific aging time, deviating from the total yield strength. This deviation is primarily attributed to the effect of precipitate size on shear strengthening during aging. This study presents a general method for predicting the microstructure evolution and corresponding mechanical properties of alloys through multiscale simulations, offering valuable insights for designing and predicting the performance of metallic alloys.

The role of the preparation route on microstructure and mechanical properties of AlCoCrFeNi high entropy alloy

Nearly equiatomic AlCoCrFeNi alloy samples were prepared by induction melting and mechanical alloying (MA) combined with spark plasma sintering (SPS). The cast sample showed a dendritic microstructure composed of spinodally decomposed nanometric constituents of the B2 and BCC phases. The spark plasma sintered sample exhibited an ultrafine-grained microstructure of B2 phase and FCC solid solution and Cr23C6 carbides. The MA+SPS sample was strengthened by compressive stress-strain test up to a yield strength of 2029 ± 5 MPa, resulting significantly higher compared to 1366 ± 32 MPa of the cast sample. In addition to the higher compressive yield strength, the sintered sample exhibited a hardness of more than 130 HV higher compared to the cast alloy. On the other hand, the cast alloy showed high plastic deformation (29%) and significantly high ultimate compressive strength of 3072 ± 122 MPa. Together with these mechanical characteristics, the MA+SPS sample showed good thermal stability while preserving the mechanical properties even after annealing at 800 °C. This was not the case with the cast sample, in which ductility and ultimate strength significantly decreased upon annealing at 800 °C. A substantial yield strength reduction of both MA+SPS and cast samples was recorded when tested at 800 °C. Nevertheless, stress-strain curve trends were observed to be quite different between the two samples, thus suggesting dissimilar deformation mechanisms under high-temperature compression.

Simultaneous improvement of strength and ductility in near β Ti alloy with (α + β) hybrid structure via intermediate phases transformation

The influences of simultaneous precipitation of isothermal ω and O′ on deformation mechanisms and mechanical properties of near β Ti alloy Ti-5Al-3Mo-3V-2Cr-2Zr-1Nb-1Fe with (α + β) hybrid structure are revealed. During continuous heating, the phase transformation sequence in this alloy is β + αp + ω-embryos + O′ → β + αp + ωiso + O′ → β + αp + ωiso + O′ + αs → β + αp + αs. Low-temperature heat treatments from 200 °C to 400 °C are carried out to develop such intermediate phases. Upon aging at 200 °C and 300 °C, the isothermal ω and O′ domains are continuously generated. In comparison with solution state, the deformation behaviors of aged samples are altered, and the yield stress and ductility are simultaneously increased. When aged at 200 °C, the yield strength is increased by 13.8 %, and fracture elongation is increased by 63.2 %. When aged at 300 °C, the yield strength is increased by 18.2 %, and preserves large ductility same to solution state. This is due to the development of isothermal ω and O′ domains suppress long-range stress induced martensitic transformation during loading, and the deformation mechanisms evolve into dislocations slipping gradually. When the aging temperature increases to 400 °C, α precipitation takes place leading to an obvious decrement in ductility. Upon loading the primary α can also accommodate partly the strains and relax local stress concentration. The results in this work clearly proves that better mechanical properties can be achieved through tailoring intermediate phases generation.

Oxide/metal interface enhancement for improved dispersion strengthening mechanism in oxide-strengthened tungsten

The addition of secondary ceramic particles has shown to be effective in enhancing the mechanical properties of tungsten alloys. The diverse strengthening effects observed with various secondary particles necessitate further investigation. Herein, three ultrafine-grained, oxide-dispersed-strengthened tungsten alloys were prepared using solution combustion synthesis combined with low-temperature sintering. We thoroughly investigated the influence of Al2O3, La2O3, and Y2O3 on the microstructure and mechanical properties of tungsten, as well as their respective strengthening mechanisms. A detailed comparison revealed discrepancies between the yield strength experimentally measured and the theoretically predicted strength based on conventional grain refinement strengthening and dispersion strengthening theories, highlighting the significance of the intrinsic nature of dispersed oxides. Electron microscopy analysis and density functional theory calculations revealed that, compared to other oxides, the heterogeneous interface of Al2O3 with W exhibited minimal lattice distortion and the highest work of separation, resulting in a robust interface bonding. The prepared W-Al2O3 alloy showed exceptional performance with Vickers hardness HV0.2 of 698.9 and yield strength of 2488 MPa. Its yield strength surpassed that of W-Y2O3 and W-La2O3 alloys, as well as other commonly reported refractory metal materials.

Numerical Simulation Analysis of the Bending Performance of T-Beams Strengthened with Ultra-High-Performance Concrete Based on the CDP Model

In bridge reinforcement projects, damaged T-beams are the most common objects for reinforcement, yet the interface bonding and bending performance of UHPC reinforcement on T-beams have hardly been studied. To ensure the reliability and stability of UHPC-strengthened T-beams in practical applications, this study introduced a post-installed rebar bonding technique to efficiently connect T-beams with UHPC layers. Initially, using ABAQUS software [2020 version] for finite element simulation, this study investigated the effects of various post-installed rebar parameters (horizontal spacing, yield strength, diameter, and matrix concrete strength) on the shear performance of the UHPC and RC interface, obtaining the optimal connection parameters. Subsequently, by comparing shear formulas in domestic and international standards, a new UHPC-RC steel bar interface shear strength theoretical formula with 93.6% accuracy was derived. Finally, finite element simulations analyzed the impact of different post-installed reinforcing bar layout forms and longitudinal spacing, as well as UHPC-strengthened location and layer thickness, on the bending performance of damaged T-beams. The results showed a good match between simulation outcomes and experimental results, applicable for further reinforcement analysis of T-beams. When the horizontal spacing of post-installed rebars is 12d, with diameters ranging from 10 mm to 14 mm, their anchoring capability is efficiently utilized. A square form of a post-installed rebar with a longitudinal spacing of 300 mm effectively improves the ultimate bending load capacity of the strengthened beam. The simulation analysis and theoretical results help in the design and application of post-installed steel connections and UHPC-strengthened structures in UHPC-strengthened reinforced concrete T-beam structures.

Influence of heat treatment on the microstructure and mechanical properties of Al–Mg–Si alloy fabricated by double wires + arc additive manufacturing

Al-3.4Mg-1.7Si alloy single-pass and multi-layer thin wall components were fabricated with double wires + arc additive manufacturing procedure. Heat treatment was performed to further process the component. The microstructure and mechanical properties of the as-deposited and heat-treated components were comparatively investigated. After heat treatment, the grains grow up slightly, and the phase particles change to distribute semi-continuously, and a large number of nanoscale monoclinic β″ precipitated phases generate. The porosity increases to 0.0486% from as-deposited 0.0348%. The microhardness, ultimate tensile strength and yield strength are respectively improved by 25%,79%, and 228% with heat treatment process, with the hardness uniformity and elongation decreased.

Evolution of microstructure and texture and their influence on the strength of an accumulative roll bonded (ARBed) Al-Sc-Zr-Er-Ti alloy

Accumulative roll bonding (ARB) is an effective approach to improve the strength of metal sheets. This work studied the evolution of microstructure and texture and their influence on the strength of an ARBed Al-Sc-Zr-Er-Ti alloy, produced by multi-microalloying Sc, Zr, Er, and Ti into pure Al. A high-quality interface and a fine microstructure with an average grain size of ∼0.6 μm were achieved as by the ARB process. The Dillamore {4411} <11118> and the Copper {112} <111> components were sharpened in final texture as is common in ARB. However, after the 5th cycle, there was a new texture component along the α-fiber, at (φ1, Φ, φ2) ≡ (60°, 45°, 0°) in Euler space. The yield strength (YS) and tensile strength (UTS) increased with increasing the number of ARB cycles. The 7th ARBed Al-Sc-Zr-Er-Ti alloy had increased YS by 45% and UTS by 57%, respectively, compared to the initial cold rolled sheet. Strengthening was mainly attributed to dislocation strengthening, grain refinement and precipitation strengthening. There was little texture strengthening because of a strengthening and softening alternation with the change of ARB cycle.

Mechanically Controlled Landslide Deformation

AbstractMany landslide models assume a fully deformable body without any resistance against deformation. However, in reality, landslide bodies can display negligible to large deformation during motion. Examples for limited deformation include the prehistoric giant landslides of Flims and Köfels, or the Vajont landslide of 1963, where the structure of rock largely remained intact and the slides did not evolve into rock avalanches. Here, we propose a novel mechanical model for the controlled deformation of landslides. The model is based on the principle of material strength or resistance and includes a user‐specified function that reflects the mechanisms (internal friction, cohesion, viscosity, and yield strength) that act against the deformation induced by the free‐surface or the hydraulic pressure gradient of the landslide. This controls the landslide deformation and, in turn, also the motion and run‐out, and offers a unique possibility to describe the landslide motion ranging from a fully non‐deformable body sliding along the mountain slope to a completely fluidized motion without any resistance against the force associated with the free‐surface pressure gradient. The latter is the situation often considered for the motion of granular flows such as avalanches of snow or rock, or debris flows. The former can play a substantial role in the dynamics, however, has not yet been considered in mass flow simulations, severely limiting the applicability of those models. We demonstrate the performance of the new model and its applicability, also with the advanced open‐source computational mass flow simulation tool r.avaflow.

Effect of Temperature on the Tensile Deformation Mechanisms of a Fourth Nickel-Based Single Crystal Superalloys

This work conducted tensile experiments from room temperature to 1100 °Con a new fourth-generation single crystal superalloys along [001]. The effect of temperature on the tensile properties and deformation mechanism of the alloy were investigated. Results showed that the yield strength of the alloy reached its peak value (1017MPa) at 850 °C. From room temperature to 760 °C, the occurrence of stacking faults (SFs) was observed in the γ matrix channel. From the room temperature to 850 °C, the occurrence of stacking faults was observed in the γʹ phase. The interface dislocation networks appeared at 980 °C and above. At room temperature, stacking faults sheared γʹ phase, in which three types of stacking faults occurred, which controlled deformation process. The main deformation mechanism from 650 °C to 850 °C was the shearing of γʹ phase by stacking faults and super dislocations, and at 850 °C, stacking faults in different directions of propagation corresponded to the formation of Lomer-Cottrell locks (L-C locks), which greatly increased the yield strength. At 980 °C and 1100 °C, dislocation climbing and bypassing and anti-phase boundary (APB) coupled dislocation pair shear γʹ phase became the main deformation mechanism.

Advanced mechanical properties obtained via transition metals doped in CrFeNi medium entropy alloy

Medium entropy alloys (MEAs) have attracted significant interest due to their exceptional mechanical characteristics. This study employs molecular dynamics simulations to investigate the impact of transition metal (TM) elements doping on the mechanical properties of face-centered cubic (FCC) MEAs. We have doped 4% TM elements with pure MEA and analyze several mechanical characteristics such as lattice distortion, Yield strength, elastic constants and moduli, Vickers hardness, machinability index, and Kleinman parameters. The correlation between elastic moduli and doping implies a decrement in the stiffness of alloys. To confirm the ductility, a thorough assessment involving Poisson’s ratio, Cauchy’s pressure, and Pugh’s ratio are conducted. According to the anisotropy factor analysis, the presence of doping increases anisotropy in MEAs. The findings of our work suggest that the improved mechanical properties can be beneficial in the development of MEAs suitable for diverse applications.

Anisotropic Behavior and Temperature-Dependent Mechanical Properties of AA1060 Aluminum Alloy: A Comprehensive Microstructural Study

This study rigorously examines the AA1060 aluminum alloy's mechanical properties across different thermal conditions (298K to 77K) and orientations (RD-ND and TD-ND). Through annealing at 350°C for 50 minutes followed by extensive mechanical testing at ambient and cryogenic temperatures, the study delves into the microstructural evolution and deformation mechanisms utilizing Electron Backscatter Diffraction (EBSD) and Transmission Electron Microscopy (TEM). Findings indicate a pronounced increase in yield strength, tensile strength, and ductility with decreasing temperature. Notably, RD-ND oriented samples demonstrated enhanced mechanical strength over TD-ND oriented samples under both temperature regimes, underscoring the alloy's pronounced anisotropy. This comprehensive study illuminates the AA1060 alloy's temperature-dependent mechanical enhancements and anisotropic behavior, emphasizing the significant impact of microstructural orientation on its mechanical properties. The insights gained illuminate the AA1060 alloy's temperature-dependent and anisotropic behaviors, highlighting microstructural orientation's pivotal role in its mechanical properties, with profound implications for aluminum alloy application across varying temperature and stress conditions.