Increase Of Solution Time Research Articles

Numerical Prediction of Ship Resistance Based on Volume of Fluid Implicit Multi-Step Method

The Volume of Fluid (VOF) method is used in two-phase fluid flow problems of ship hydrodynamic calculations, to capture the motion and distribution of the gas–liquid free surface. To ensure solution stability and accuracy, numerical simulations typically require separate mesh refinement for the free surface or a reduced time step, resulting in a significant increase in solution time. This study aims to compare the drag and vessel attitude change calculations of the VOF implicit multi-step method with the traditional single-step method, and to verify the feasibility of the method in the numerical prediction of ship resistance and flow field analysis. The results show that an implicit multi-step method with a reasonable number of internal iterations could obtain results close to those of the single-step method with a reduced time step, and the error in trim angle was relatively large, about 2%, but the solving time was only about half that of the latter. The method could also capture the shape and location of waves on the hull, especially in the vicinity of the ship, while the distribution of the waves in the far field differed from those in the experiments to some extent.

Effect of solution treatment on static recrystallization of a post-deformed GH4586 superalloy

Solution treatment was carried on a post-deformed GH4586 superalloy in the solution temperature range of 1020°C to 1100°C and solution time of 2 h and 4 h. The results showed that the static recrystallization (SRX) occurred due to the residual distortion energy caused by high temperature deformation. With increasing solution temperature from 1020°C to 1100°C, the average grain size of γ matrix firstly decreased and then increased. With increasing solution time from 2 h to 4 h, the average grain size of γ matrix gradually increased from 24.2±3.2 μm to 30.9±3.8 μm. Grain boundaries and twinning boundaries are the main nucleated site for SRX. And when solution treated at 1020°C for 2 h, carbides can also become the preferential nucleation position. In addition, by analysing the relative deviation (v/vm ) distributions of Σ3 boundaries, it could be found that the higher solution temperature would lead to the increasing fraction of coherent Σ3 boundaries and the decreasing fraction of incoherent ones. Besides, the annealing twins nucleated and grew gradually during the migration of recrystallized grain boundaries, and their length fraction increased from 10.0% to 54.9% with increasing solution temperature.

Investigation on heat treatment of large-sized and complex AlSi9Mg aluminum alloy components formed by squeeze casting

AlSi9Mg aluminum alloy flywheel housing components were formed via squeeze casting and T6 heat treatment was applied to the formed components. The influence of solid solution temperature, solid solution time, aging temperature and aging time on the microstructure and mechanical properties of AlSi9Mg aluminum alloy components formed by squeeze casting were investigated. The results showed that T6 heat treatment changed the morphology of the eutectic silicon in the microstructure from long fibrous to short rods and round spheres. The spheroidization of eutectic Si phase was more obvious with an increase of solution temperature, and the eutectic Si phase not dissolved in the matrix became coarse and grew with an extension of solution time. In terms of mechanical properties, the tensile strength and elongation of AlSi9Mg specimens after heat treatment showed an increasing trend with a rise of solution temperature, but the yield strength decreased, while the three mechanical properties of specimens all improved first and then decreased with an increase of solution time, aging temperature and aging time. Comprehensive consideration of three mechanical properties showed that the optimal heat treatment process parameters in this experiment were solution temperature of 540 ℃, solution time of 180 min, aging temperature of 175 ℃ and aging time of 300 min. In addition, β''−Mg2Si strengthening phases and disc-shaped strengthening phases were precipitated during T6 heat treatment, which were also one of the reasons for the improvement of the casting properties.

Simultaneously Improving Strength and Ductility of Mg−3Li−8Gd−2Y−1.5Ag Alloy by Solution Treatment and Hot‐Rolling Process

The microstructure and mechanical properties of Mg−3Li−8Gd−2Y−1.5Ag (wt%) alloy at as‐cast state, as‐solution state, and as‐rolled state (three rolling reductions of 30, 50, and 70%) are investigated. With the increase in solution time at 520 °C, the dissolution of Mg24(Gd,Y)5 phase along the grain boundaries and the coarsening of grain size occur. The solution parameters of 520 °C/4 h are chosen in combination with microstructural evolution, grain size, and microhardness. The dynamic precipitation of irregular spherical‐like β1, needle‐like β′, fine β, and twins is observed after 30% hot rolling at 450 °C. With increasing the reduction to 70%, the number of β1, β′, and twins increases and massive stacking faults (SFs) appear in the twins. The strength and ductility of Mg−3Li−8Gd−2Y−1.5Ag alloy are simultaneously improved by the combination of solution treatment and hot‐rolling process due to the precipitation strengthening of β1 and β′, the formation of twins and SFs, and the fragmentation of Mg24(Gd,Y)5 phase along the grain boundaries.

Effect of solution time on the microstructure, precipitation behavior and mechanical properties of (Co0.5NiFeCrTi0.5 + SiC)p/7075Al hybrid composite

The effect of solution time on the aging behavior, corresponding microstructure and mechanical properties of the (Co0.5NiFeCrTi0.5 + SiC)p/7075Al hybrid composite was systematically studied. The hybrid composite was fabricated via squeeze casting, followed by solution treated for 1, 2, 4 and 6 h and subsequent artificial aging. Microstructural analysis revealed that the solution time had a significant effect on the second phase, HEA/Al interface, precipitation behavior and grains in the Co0.5NiFeCrTi0.5 high-entropy alloy (HEA) particle. The amount of the second phase dissolving into the Al matrix initially increased with the increase of solution time. However, there was no obvious change in the amount of the second phase after 4 h because only the insoluble Al7Cu2Fe phase was left in the matrix. The interface between the Al matrix and SiC particles in the hybrid Al matrix composites did not show significant changes with increasing solution time, whereas the interface between the Al matrix and HEA particles gradually grew. The peak-aged time of composites during artificial aging was gradually shortened with the increase of solution time, indicating that longer solution time could accelerate the precipitation kinetics. Composites solution treated for 2 and 4 h displayed the larger supersaturation of Mg and Zn atoms along with a higher density of precipitates than that of the AMC-1h composite at the peak-aged period. The peak-aged composite solution treated for 2 h showed the highest yield strength and tensile strength (551 and 652 MPa), followed by the composite solution treated for 1 h (495 and 608 MPa) and 4 h (469 and 551 MPa). However, the ductility gradually decreased with the increase of solution time due to the interface reaction between the Al matrix and SiC particles. The relationship between the solution time and precipitation behaviors in the vicinity of the SiC/Al and HEA/Al interface of hybrid composites were systematically studied. Our work provides new insights for the development of heat-treatable Al matrix composites reinforced by metallic particles.

Effect of multi-stage solution on microstructure and properties of Al–10.5Zn–2.05Mg–1.02Cu–0.2Zr–0.923Ti alloy extrusion

The effect of multi-stage solution on microstructure and properties was studied in Al–10.5Zn–2.05Mg–1.02Cu–0.2Zr–0.923Ti alloy extrusion. The microstructure, corrosion resistance, plasticity, hardness, and tensile properties of alloy were evaluated using metallographic microscope, X-ray diffraction analysis, micro-hardness tester, and microcomputer-controlled universal testing machine. The results show that the tensile strength and corrosion resistance of the alloy improve first and then deteriorate with increase of solution temperature and holding time, and 2# sample has the best mechanical properties (tensile strength is 711.159 MPa and elongation is 13%) and highest corrosion resistance of alloys. Furthermore, 2# sample has more uniform grains, more equiaxed crystals, and the low-angle grain boundaries, and the dislocation density and the dislocation strengthening contribution of alloy are relatively high. However, the grain grows and the dislocations were consumed with the increase of solution time and temperature, resulting in a decrease in dislocation density and dislocation strengthening contribution. It is indicated that alloy can achieve better comprehensive properties under solution treatment process (450 °C × 2 h + 460 °C × 2 h + 470 °C × 2 h + 480 °C × 2 h).

Nanolaser-based emulators of spin Hamiltonians

AbstractFinding the solution to a large category of optimization problems, known as the NP-hard class, requires an exponentially increasing solution time using conventional computers. Lately, there has been intense efforts to develop alternative computational methods capable of addressing such tasks. In this regard, spin Hamiltonians, which originally arose in describing exchange interactions in magnetic materials, have recently been pursued as a powerful computational tool. Along these lines, it has been shown that solving NP-hard problems can be effectively mapped into finding the ground state of certain types of classical spin models. Here, we show that arrays of metallic nanolasers provide an ultra-compact, on-chip platform capable of implementing spin models, including the classical Ising and XY Hamiltonians. Various regimes of behavior including ferromagnetic, antiferromagnetic, as well as geometric frustration are observed in these structures. Our work paves the way towards nanoscale spin-emulators that enable efficient modeling of large-scale complex networks.

Effect of Solution Heat Treatment on Microstructure and Mechanical Properties of Al-Mg-Si Alloy

Effects of different solution treatments on microstructure, texture and mechanical properties of 6A16 aluminum alloy sheet were investigated by electron back-scattered diffraction (EBSD) and tensile test. The results show that among the five solution treatments, with the increase of solution temperature and solution time, the average grain size increases and the yield strength of the alloy sheet gradually increases. The maximum elongation at break of the sheet is at 545 °C, and it increases with the increase of solution time. Therefore, the mechanical properties of the sheet are the best when the solution treatment is 545 °C for 5 min.

Microstructure, post thermal treatment response, and tribological properties of 3D printed 17-4 PH stainless steel

The intention of the present study is to investigate the effect of laser energy density on the microstructure, post-heat treatment response, and wear properties of additively manufactured 17-4 P H stainless steel. Microstructural characterisation techniques such as Scanning Electron Microscopy (SEM), X-ray Diffraction (XRD), Transmission Electron Microscopy (TEM), Electro Back Scatter Diffraction (EBSD) and thermal analysis methods such as Differential Scanning Calorimetry (DSC) and Dilatometry (DIL) were employed to attain the quantitative information about the microstructural evolution and phase transformation before and after conventional heat treatment (solution + aging). It was shown that applying higher energy density resulted in a slightly more retained austenite perhaps due to the lower cooling rate. The response of the 3D printed material to post-thermal treatment was affected by the initial energy density enabling us to control the final volume fraction of austenite. Significant grain refinement was observed in the heat-treated specimens. Solution treatment at 1040 °C led to the formation of retained austenite and precipitation of M23C6/M7C3 carbides (M = Cr, Mo) and NbC carbides. The increase of solution time from 1hr to 4 hrs increased the volume fraction of carbides (NbC, M23C6 and/or M7C3) precipitated during solution treatment and decreased the volume fraction of retained austenite due to the localised change in the chemical composition of the matrix around carbides and rise of Ms temperature. Subsequent aging at 472 °C for 1hr led to the precipitation of further carbides (and Cu-rich clusters) in the matrix forming Ni-rich regions promoting the formation of reverse austenite in the matrix. The amount of the precipitated carbides and reverse austenite was more severe in those samples solutionised at 1040 °C for 1hr rather than 4 hrs regardless of the initial energy density. The indentation results showed that the sample subjected to the lower energy density did not respond well to the conventional heat treatment on 17-4 PH stainless steels as expected; however, the increase of energy density improved the post-thermal treatment response. The reciprocating dry sliding wear resistance of the as-printed sample subjected to the energy density of 53.12 J/mm3 was considerably better than that of 73.40 J/mm3. We showed that the initial energy density of the additively manufactured samples could have a significant influence on the wear resistance of post-thermally treated samples and results in different wear behaviour. The main wear mechanism was oxidation and delamination of the iron oxide layer from the surface.

Research on Dynamic Corrosion Behavior and the Microstructure of Biomedical Mg–Y–Zn–Zr–Sr in Simulated Body Fluid Solution after Processing by Solution Treatment

Herein, as‐cast Mg–2Y–Zn–0.4Zr–0.3Sr alloy's solution treatment at 500 °C in the range of 10–35 h, and then cooled in 80° warm water, is used to investigate its dynamic corrosion behavior and surface morphology using a dynamic stimulating human environment device. Based on the result of corrosion behavior and microstructure, the alloy is mainly composed of α‐Mg and W‐phase (Mg3Zn3Y2) in Mg–2Y–Zn–0.4Zr–0.3Sr alloy. With the increase in solution time, the corrosion resistance is prompted due to the uniform microstructure and second phase dissolved into the matrix. The corrosion resistance of Mg–2Y–Zn–0.4Zr–0.3Sr alloy is increased by enhancing solution time before 25 h due to the uniformly distributed second phases and microstructure, which can alleviate the galvanic corrosion. However, increasing solution time exceeding 25 h reduces the corrosion resistance of the alloy due to coarse grains. Furthermore, twinning, which appears in grains interior after solution treatment, has a positive influence on corrosion resistance. Therefore, the good corrosion resistance of solution‐treated Mg–2Y–Zn–0.4Zr–0.3Sr alloy makes it excellent for biomaterial applications.

Adaptive spectral solution method for the Landau and Lenard-Balescu equations

We present an adaptive spectral method for solving the Landau/Fokker-Planck equation for electron-ion systems. The heart of the algorithm is an expansion in Laguerre polynomials, which has several advantages, including automatic conservation of both energy and particles without the need for any special discretization or time-stepping schemes. One drawback of such an expansion is the O(N3) memory requirement, where N is the number of polynomials used. This can impose an inconvenient limit in cases of practical interest, such as when two particle species have widely separated temperatures. The algorithm we describe here addresses this problem by periodically re-projecting the solution onto a judicious choice of new basis functions that are still Laguerre polynomials but have arguments adapted to the current physical conditions. This results in a reduction in the number of polynomials needed, at the expense of increased solution time. Because the equations are solved with little difficulty, this added time is not of much concern compared to the savings in memory. To demonstrate the algorithm, we solve several relaxation problems that could not be computed with the spectral method without re-projection. Another major advantage of this method is that it can be used for collision operators more complicated than that of the Landau equation, and we demonstrate this here by using it to solve the non-degenerate quantum Lenard-Balescu (QLB) equation for a hydrogen plasma. We conclude with some comparisons of temperature relaxation problems solved with the latter equation and the Landau equation with a Coulomb logarithm inspired by the properties of the QLB operator. We find that with this choice of Coulomb logarithm, there is little difference between using the two equations for these particular systems.

Effects of Heat-Treatment on Microstructures and Mechanical Properties of Hot Deformed TiB/Ti-6Al-4V Matrix Composites

In this paper, TiB reinforced Ti-6Al-4V matrix composites were successfully fabricated using a spark plasma sintering, hot rolling and heat treating process. (Transformed β-Ti + secondary α-Ti) domains were formed in TiB/TMCs after heat treatment. The size of these domains increases from 2.5 μm to 4.6 μm with the increase of solution time. The aspect ratio of whiskers monotonously decreases along with the solution time extending. The highest ultimate tensile strength of 1332 MPa and yield-strength of 1315 MPa were achieved by (940 °C, 15min+ water-quenching+537 °C, 4h) TMC.

A realistic energy optimization model for smart‐home appliances

Smart homes have the potential to achieve optimal energy consumption with appropriate scheduling. The control of smart appliances can be based on optimization models, which should be realistic and efficient. However, increased realism also implies an increase in solution time. Many of the optimization models in the literature have limitations on the types of appliances considered and/or their reliability. This paper proposes a home energy management scheduling model that is more realistic and efficient. We develop a mixed integer linear optimization model that minimizes the energy cost while maintaining a given level of user comfort. Our main contribution is the variety of specific appliance models considered and their integration into a single model. We consider the use of energy in appliances and electric vehicles (EVs) and take into account renewable local generation, batteries, and demand response. Our models of a shower, a fridge, and a hybrid EV consider both the electricity consumption and the conventional fuel cost. We present computational results to validate the model and indicate how it overcomes the limitations of other models. Our results, compared with the best competitors, provide cost savings ranging from 8% to 389% over a horizon of 24 hours.

Diagonalized Macromodels in Finite Element Method for Fast Electromagnetic Analysis of Waveguide Components

A new technique of local model-order reduction (MOR) in 3-D finite element method (FEM) for frequency-domain electromagnetic analysis of waveguide components is proposed in this paper. It resolves the problem of increasing solution time of the reduced-order system assembled from macromodels created in the subdomains, into which an analyzed structure is partitioned. This problem becomes particularly relevant for growing size and count of the macromodels, and when they are cloned in multiple locations of the structures or are used repeatedly in a tuning and optimization process. To significantly reduce the solution time, the diagonalized macromodels are created by means of the simultaneous diagonalization and subsequently assembled in the global system. For the resulting partially diagonal matrix, an efficient dedicated solver based on the Schur complement technique is proposed. The employed MOR method preserves frequency independence of the macromodels, which is essential for efficient diagonalization, as it can be performed once for the whole analysis bandwidth. The numerical validation of the proposed procedures with respect to accuracy and speed was carried out for varying size and count of macromodels. An exemplary finite periodical waveguide structure was chosen to investigate the influence of macromodel cloning on the resultant efficiency. The results show that the use of the diagonalized macromodels provided a significant solution speedup without any loss of accuracy.

Microstructure evolution during solution treatment of extruded Al-Zn-Mg profile containing a longitudinal weld seam

In this study, the microstructure evolution during solution treatment of extruded Al-Zn-Mg profile containing a longitudinal weld seam was firstly reported. The porthole die extrusion experiment was conducted to obtain the extruded profile. The solution treatment was performed at 470 °C for 15 min, 60 min and 120 min, respectively, and the aging was performed at 120 °C for 24 h. The secondary phase distribution, grain morphology, grain size and texture evolution of welding zone during solution were investigated. Moreover, the hardness and tensile properties after aging were analyzed. The results show that the solution for 15 min is sufficient for the dissolution of MgZn2 phase, while Al2CuMg and Al23CuFe4 phases cannot be dissolved even the solution time is prolonged to 120 min. The main texture components of {110}<111> and {110}<115> are formed after extrusion process, and these textures are remained after solution treatment. With increasing solution time, the intensity and volume fraction of texture firstly increases and then decreases. Furthermore, both the average size and aspect ratio of grains in welding zone increase with increasing solution time. The best hardness, tensile strength and elongation was obtained in the Al- Zn-Mg profile after solution treated for 15 min.

Modification of microstructure and tensile property of TiBw/near-α Ti composites by tailoring TiBw distribution and heat treatment

The 5.1 vol% TiB whisker reinforced Ti60 (near-α Ti alloy) composites were successfully fabricated by reaction hot pressing technology. In order to modify their microstructure and property, the effects of precipitates on the designed network structured composites were investigated by heat treatment without any deformation. The microstructure results show that the ordered α2 phase with the size of 5 nm–10 nm is precipitated from matrix due to high content of α stabilizing elements and the slow cooling rate after sintering process. The aging treatment can promote the precipitation of α2 phase in α phase matrix and the silicide in β phase matrix. In particular, the precipitates prefer to be formed near the TiB whiskers by providing the nucleation sites. The solution and quenching treatment above the β transus temperature can gradually dissolved these precipitates with increasing solution time. Both the solid solution and the aging treatment can improve the tensile strength of them due to the formation of martensite α′ phase and precipitation of silicide and α2, respectively. The composites exhibit more sensitive effect of precipitates on the room temperature embrittlement than the monolithic Ti60 alloy.

Microstructure evolution and properties of Al/Al–Mg–Si alloy clad wire during heat treatment

In this paper, heat treatment was carried out on Al/Al–Mg–Si alloy clad wire, and microstructure evolution and properties of Al/Al–Mg–Si alloy clad wire during heat treatment were investigated. During solution, contents of Mg and Si in inner matrix increased due to dissolution of primary Mg2Si, and they also increased in outer matrix because Mg and Si diffused across the interface. Tensile strength of the clad wire increased firstly and then decreased, and elongation continuously increased, while conductivity continuously decreased with the increase in solution time. In aging process, Mg2Si precipitated in both inner core and outer layer, and the content and average diameter of the precipitate increased with the increase in aging time. The content of precipitate was higher, and the average diameter was bigger in inner core. Tensile strength of the clad wire increased firstly and then decreased with the increase in aging time, and the elongation continuously decreased, while the conductivity continuously increased. The peak tensile strength of 202 MPa occurred at 8 h, when the corresponding elongation was 20 % and the conductivity reached 56.07 %IACS. Even tensile strength of the prepared clad wire approximately equaled to that of Al–0.5Mg–0.35Si alloy 203 MPa, the conductivity was obviously improved from 54.2 to 56.07 %IACS.

Effect of solution time on microstructure, texture and mechanical properties of Al–Mg–Si–Cu alloys

Effect of solution time on the microstructure, texture and mechanical properties of Al–Mg–Si–Cu alloy sheets with different contents of iron-rich phase was investigated systematically by microstructure characterization, texture measurement and tensile test. The results show that the recrystallization microstructure, texture and mechanical properties can be affected by the change of solution time, but the level depends on the content and distribution of iron-rich phase. With increasing solution time, the strengths and planar anisotropy Δr values of the sheets increase, but plasticity strain ratio r and strain-hardening exponent n values decrease, the change in values is much more significant in alloy with low volume fraction of iron-rich phase than those of alloy with high number of iron-rich phase. The same trend for the changes of recrystallization grain size of the two alloys can also be observed. Additionally, the texture of the sheet with low volume fraction of iron-rich phase particles transforms from Cube orientation to CubeND and P orientations firstly, and finally transforms to Goss orientation with further increasing solution time, whereas the texture of the sheet with a high number of iron-rich phase particles only transforms from Cube orientation to CubeND and P orientations even after long time solution treatment. Accordingly, the effect of texture on r value has been simulated and one recrystallization model is proposed to explain the recrystallization texture evolution.

Effects of Solution Heat Treatment on Microstructure and Mechanical Properties of the Mg-4.5Zn-4.5Sn-2Al-0.6Sr Alloy

Microstructure and mechanical properties of the Mg-4.5Zn-4.5Sn-2Al-0.6Sr alloy are investigated both in the as-cast condition and after the different three-step solution heat treatments (a solution heat treatment of 310 °C × 4 h + 340 °C × 28 h followed by a high-temperature solution treatment) to explore the optimal solution treatment cycle. The as-cast alloy contains a microstructure consisting of the α-Mg matrix, Mg2Sn, Mg51Zn20, Mg32(Al, Zn)49, and MgSnSr phases. After the solution heat treatment, all the Mg51Zn20, the Mg32(Al, Zn)49 phases, and most of the Mg2Sn phase are dissolved into the matrix, only the MgSnSr phase and a minority of the Mg2Sn phase are remained in the granular form or the fine dot-like. The volume fraction of the residual second phases decreases from 5.61 to 1.84% with the increasing solution time from 0 to 4 h at 420 °C and it decreases from 2.9 to 0.4% with the increasing solution temperature from 420 to 480 °C for 2 h. The alloy that experiences the solution treatment of 310 °C × 4 h + 340 °C × 28 h + 460 °C × 2 h exhibits the highest strength and the best plasticity among all the solution-treated alloys. Therefore, the optimal solution treatment is 310 °C × 4 h + 340 °C × 28 h + 460 °C × 2 h. The residual second phases in the alloy that experiences the optimal solution treatment are confirmed to be the Mg2Sn phase and the MgSnSr phase which are related to their relatively high thermal stability. The ultimate tensile strength and the elongation to rupture of the as-solutionized alloy are 238 MPa and 12%, respectively, about 25 MPa and 2.4% higher than the counterparts of the as-cast alloy.

Solution Treatment on Mechanical Properties and Microstructures of Al-Li-Cu Alloy

The mechanical properties and microstructures of Al-Li-Cu-Mg-Ag alloy after different solution treatments were investigated by means of Optical Microscopy (OM), tensile test, hardness and electrical conductivity tests, Differential Scanning Calorimetry (DSC), Energy Dispersive X-ray (EDX), Scanning Electron Microscopy (SEM) and Transmission Electron Microscopy (TEM). Results show that the tensile strength and hardness increase firstly and then decrease with elevating solution temperature when the holding time is kept for 30 min, and the maximum strength and hardness are reached when temperature is 520°C. The mechanical properties of alloy also display similar trend, which increase firstly and then decrease with increasing solution time when alloy is treated at 520°C. The tensile strength, hardness and elongation of the alloy solution treated at 520°C/30 min are 566 Mpa(σb),512 Mpa(σ0.2), 148HB and 8.23% (δ), respectively. TEM shows that an amount of T1 (Al2CuLi) phases are finely and dispersedly distributed in Al substrates, which can be an explanation of a mixed fracture mode of transgranular and intergranular delamination cracks observed by SEM.