On Time Fractional Partial Differential Equations and Their Solution by Certain Formable Transform Decomposition Method

This paper aims to investigate a new efficient method for solving time fractional partial differential equations.In this orientation,a reliable formable transform decomposition method has been designed and developed,which is a novel combination of the formable integral transform and the decomposition method.Basically,certain accurate solutions for time-fractional partial differential equations have been presented.Themethod under concern demandsmore simple calculations and fewer efforts compared to the existingmethods.Besides,the posed formable transformdecompositionmethod has been utilized to yield a series solution for given fractional partial differential equations.Moreover,several interesting formulas relevant to the formable integral transform are applied to fractional operators which are performed as an excellent application to the existing theory.Furthermore,the formable transform decomposition method has been employed for finding a series solution to a time-fractional Klein-Gordon equation.Over and above,some numerical simulations are also provided to ensure reliability and accuracy of the new approach.

Improvement of strength and ductility synergy in a room-temperature stretch-formable Mg-Al-Mn alloy sheet by twin-roll casting and low-temperature annealing

Strength and ductility synergy in an Mg-3mass%Al-Mn(AM30)alloy sheet was successfully improved via twin-roll casting and annealing at low-temperature.An AM30 alloy sheet produced by twin-roll casting,homogenization,hot-rolling,and subsequent annealing at 170℃ for 64 h exhibits a good 0.2%proof stress of 170 MPa and a large elongation to failure of 33.1%along the rolling direction.The sheet also shows in-plane isotropic tensile properties,and the 0.2%proof stress and elongation to failure along the transverse direction are 176 MPa and 35.5%,respectively.Though the sheet produced by direct-chill casting also shows moderate strengths if the annealing condition is same,the direct-chill casting leads to the deteriorated elongation to failure of 23.9%and 30.0%for the rolling and transverse directions,respectively.As well as such excellent tensile properties,a high room-temperature stretch formability with an Index Erichsen value of 8.3 mm could be obtained in the twin-roll cast sheet annealed at 170℃ for 64 h.The annealing at a higher temperature further improves the stretch formability;however,this results in the decrease of the tensile properties.Microstructure characterization reveals that the excellent combination of strengths,ductility,and stretch formability in the twin-roll cast sheet annealed at the low-temperature annealing is mainly attributed to the uniform recrystallized microstructure,fine grain size,and circular distribution of(0001)poles away from the normal direction of the sheet.

Optimisation of alloy composition for highly-formable magnesium sheet

The effectiveness of Ca or Gd addition on ductility and formability of Mg-Zn-Zr based dilute alloys in deep drawing has not been systematically compared previously.In this study,formable Mg-Zn-Gd-Zr and Mg-Zn-Ca-Zr sheet alloys are produced by hot rolling.These sheets have similarly weakened basal texture,but the sheet of the Mg-Zn-Gd-Zr alloys has higher ductility and formability than that of Mg-Zn-Ca-Zr alloys.The combined addition of 0.2wt%Ca and 0.4wt%Gd to the Mg-1Zn-0.5Zr(wt%)alloy leads to a Mg-1Zn-0.4Gd-0.2Ca-0.5Zr alloy that has even better ductility,and its formability during deep drawing is comparable to the benchmark Al6016 sheet.An increase in Ca content from 0.2wt%to 0.5wt%leads to decreased sheet ductility and formability,predominantly due to grain boundary embrittlement.

Formable porous biochar loaded with La-Fe(hydr)oxides/montmorillonite for efficient removal of phosphorus in wastewater:process and mechanisms

The development of biochar-based granule-like adsorbents suitable for scaled-up application has been attracting increasing attention in the field of water treatment.Herein,a new formable porous granulated biochar loaded with La-Fe(hydr)oxides/montmorillonite(LaFe/MB)was fabricated via a granulation and pyrolysis process for enhanced phosphorus(P)removal from wastewater.Montmorillonite acted as a binder that increased the size of the granulated biochar,while the use of Fe promoted the surface charge and facilitated the dispersion of La,which was responsible for selective phosphate removal.LaFe/MB exhibited rapid phosphate adsorption kinetics and a high maximum adsorption capacity(Langmuir model,52.12 mg P g^(−1)),which were better than those of many existing granulated materials.The desorption and recyclability experiments showed that LaFe/MB could be regenerated,and maintained 76.7%of its initial phosphate adsorption capacity after four adsorption cycles.The high hydraulic endurance strength retention rate of the developed material(91.6%)suggested high practical applicability in actual wastewater.Electro-static attraction,surface precipitation,and inner-sphere complexation via ligand exchange were found to be involved in selective P removal over a wide pH range of 3-9.The thermodynamic parameters were determined,which revealed the feasibility and spontaneity of adsorption.Based on approximate site energy distribution analyses,high distribution frequency contributed to efficient P removal.The research results provide a new insight that LaFe/MB shows great application prospects for advanced phosphate removal from wastewater.

Effect of pre-twinning and heat treatment on formability of AZX311 Mg alloy

In this study,the effects of pre-strain-induced tensile twins(TTWs)and controlled heat treatment on the formability behavior of AZX311 Mg alloy sheets were investigated.A 4%compressive strain was applied to pre-strain the sheets using the in-plane compression(IPC)technique along the rolling direction(RD)to introduce TTWs.The pre-strained(PS)samples were subsequently heat-treated at 250℃,350℃,and 400℃ independently for 1 hr,and are termed as PSA1,PSA2,and PSA3,respectively.Erichsen cupping tests were conducted to assess the formability of the sheet samples under different initial conditions.The results showed that the PS sample heat-treated at 250℃ for 1hr exhibited a decrease in the Erichsen index(IE)compared to the as-rolled sample,whereas PSA2 and PSA3 samples showed an increase in IE values.Microtexture analysis revealed that most of the TTWs generated through pre-twinning were stable at 250℃;however,the twin volume fraction reduced to 41%at 350℃ compared to the PS samples due to enhanced thermal activity at that temperature.Furthermore,PSA2 samples showed severe grain coarsening in some areas of the sample,and the fraction of such grains increased in the PSA3 samples.The stretch formability(IE value)of PSA2 samples showed a 32.3%increase compared to the as-rolled specimens.Additionally,the analysis of the deformed specimen at failure under the Erichsen test indicated that considerable detwinning occurs in the PS and PSA1 samples,whereas dislocation slip activity dominates in the PSA2 and PSA3 samples during stretch forming.Apart from detwinning and dislocation slip,deformation twins were also observed in all samples after the Erichsen test.Thus,this work highlights the importance of texture control and its underlying mechanisms via pre-twinning followed by heat treatment and their impact on the room temperature(RT)stretch formability of AZX311 Mg alloy sheets.

Towards designing high mechanical performance low-alloyed wrought magnesium alloys via grain boundary segregation strategy:A review

Low-alloyed magnesium(Mg)alloys have emerged as one of the most promising candidates for lightweight materials.However,their further application potential has been hampered by limitations such as low strength,poor plasticity at room temperature,and unsatisfactory formability.To address these challenges,grain refinement and grain structure control have been identified as crucial factors to achieving high performance in low-alloyed Mg alloys.An effective way for regulating grain structure is through grain boundary(GB)segregation.This review presents a comprehensive summary of the distribution criteria of segregated atoms and the effects of solute segregation on grain size and growth in Mg alloys.The analysis encompasses both single element segregation and multi-element co-segregation behavior,considering coherent interfaces and incoherent interfaces.Furthermore,we introduce the high mechanical performance low-alloyed wrought Mg alloys that utilize GB segregation and analyze the potential impact mechanisms through which GB segregation influences materials properties.Drawing upon these studies,we propose strategies for the design of high mechanical performance Mg alloys with desirable properties,including high strength,excellent ductility,and good formability,achieved through the implementation of GB segregation.The findings of this review contribute to advancing the understanding of grain boundary engineering in Mg alloys and provide valuable insights for future alloy design and optimization.

Synergistic effect of gradient Zn content and multiscale particles on the mechanical properties of Al-Zn-Mg-Cu alloys with coupling distribution of coarse-fine grains

This study investigated the influence of graded Zn content on the evolution of precipitated and iron-rich phases and grain struc-ture of the alloys,designed and developed the Al–8.0Zn–1.5Mg–1.5Cu–0.2Fe(wt%)alloy with high strength and formability.With the increase of Zn content,forming the coupling distribution of multiscale precipitates and iron-rich phases with a reasonable matching ratio and dispersion distribution characteristics is easy.This phenomenon induces the formation of cell-like structures with alternate distribu-tion of coarse and fine grains,and the average plasticity–strain ratio(characterizing the formability)of the pre-aged alloy with a high strength is up to 0.708.Results reveal the evolution and influence mechanisms of multiscale second-phase particles and the corresponding high formability mechanism of the alloys.The developed coupling control process exhibits considerable potential,revealing remarkable improvements in the room temperature formability of high-strength Al–Zn–Mg–Cu alloys.

Towards tailoring basal texture of rolled Mg alloy sheet by recrystallization for high room-temperature formability: A review

Room-temperature(RT) formability is a key factor to broaden the applications of rolled Mg alloy sheets in the industry. However, rolled Mg alloy sheets generally form strong basal texture, where the(0001) poles align parallel to the normal direction(ND). This hinders the activation of(0001) [1120] basal slip, limiting the RT formability. Therefore, texture weakening, i.e., the inclination of the(0001) poles from the ND, plays an important role to improve the RT formability. Recrystallization is crucial to control the textural development in Mg,and currently, the texture weakening is commonly achieved using static recrystallization(SRX). However, the type of slipping and twinning,which are activated during rolling, affect the textural features after SRX. It is also demonstrated that shear bands and preferential grain growth are important factors to tailor the texture during SRX. Indeed, dynamic recrystallization(DRX) easily occurs during rolling in Mg, which also affects the final rolling texture, while the effect of DRX on the textural formation is not extensively studied for the development of RT-formable Mg alloy sheets. Therefore, the effect of these factors on the textural development in rolled Mg is reviewed in this manuscript.Additionally, the ideal microstructure and texture for RT-formable Mg alloy sheets are still controversial. The RT-formability includes stretch forming(biaxial tension), bending(plane strain tension), and deep-drawing. In particular, the stretch forming is commonly used to evaluate the RT-formability of rolled Mg. Although the stretch formability has been improved by recent studies, the further improvement is necessary owing to the relatively low formability of rolled Mg compared with that of rolled Fe and Al. Based on the relationship between the microstructure/texture and stretch formability provided in the literature, the design guidance for high stretch formability is proposed in this review.

Recent advances in the in-plane shear testing of Mg alloy sheets

Sheet-metal products are integral parts of engineering industries and academia research. Various testing techniques have revealed the deformation behaviors of sheet metals under complex stress states. Information obtained from tensile and compression tests, however, are insufficient for the identification of material parameters relevant to modern constitutive laws, which require experimental setups capable of generating various loading conditions and applying great amounts of strain to sheet metals. In-plane shear testing has emerged as an important method to overcome the challenges associated with tension and compression tests and can provide additional information about deformation behaviors under large plastic strains. Materials such as Mg alloys with poor levels of both ductility and formability cannot accommodate large plastic strains. Therefore, tension and compression tests have limitations in explaining the material behaviors that occur during sheet metal forming where large plastic strains are introduced. Many studies have been conducted to explain the deformation behaviors of Mg alloys under shear deformation techniques. These include severe plastic deformation(SPD), especially the equal channel angular pressing(ECAP)and equal channel angular extrusion, rolling combined with shear deformation i.e. differential speed rolling(DSR), and also in-plane shear for sheet metals, particularly under large levels of plastic strain. These in-plane shear technique involves the Miyauchi shear test, ASTM shear test, and twin bridge shear tests. Moreover, many experimental results have revealed that the evolution of microstructure and texture during in-plane shear is closely related to the failure behavior of materials. Therefore, this review is focused on techniques for in-plane shear testing that have been reported thus far, on the effect of in-plane shear on the microstructure development of Mg alloy sheets, and on the usefulness of in-plane shear testing to evaluate the formability of Mg alloy sheets.

Influence of Ca addition on the dynamic and static recrystallization behavior of direct extruded flat profiles of Mg-Y-Zn alloy

This paper investigates the influence of addition of Ca in a Y-Zn-containing magnesium alloy on the dynamic and static recrystallization behaviors and reveals the formation mechanism of the quadrupole texture during thermomechanical processing. Direct extrusion of flat bands has been conducted at various process conditions to study the difference between the two alloys WZ10 and WZX100 in terms of microstructure and texture development. It can be shown that, Ca addition promotes the DRX of WZ10 alloy. During additional heat treatment,the absence of Y segregation at the grain boundaries and the associated lack of solute drag to the boundary mobility leads to a pronounced grain growth during SRX in WZX100 alloy. Furthermore, it is shown that the addition of Ca to Y-Zn is not beneficial in terms of formability.It is demonstrated that alloying elements can have different effects depending on the recrystallization mechanisms. Partially recrystallized microstructure is a prerequisite at the as-extruded status to form the quadrupole texture and during subsequent annealing, which stands for high formability.

Comparative research on the formability of several ultra-high-strength steels

Three kinds of ultra-high-strength steels are subjected to uniaxial tensile,forming limit,and hole expansion tests to characterize their material forming properties.Results show that the elongation of S1500 reaches 12.9%and is higher than that of MS1500 with the same strength grade but is lower than that of QP980.The forming limit of S1500 steel is higher than that of MS1500 but lower than that of QP980.The instantaneous n-value of the material changes with the volume fraction of retained austenite.The hole expansion ratios of S1500,MS1500,and QP980 steels are 31.3%,32.2%,and 28.3%,respectively.The hole expansion ratio of QP steel increases slightly with the increase in strength grade.This behavior is contrary to the change trend of elongation and forming limit.Among the three kinds of materials,QP980 steel has the best global formability,and S1500 steel has better global formability than martensitic steel with a similar strength grade.The local formability of the materials improves slightly with the decrease in the amount of retained austenite.MS1500 may have the best local formability in accordance with engineering practice.

Forming limit of textured AZ31B magnesium alloy sheet at different temperatures

Repeated unidirectional bending （RUB） was carried out to improve the texture of commercial AZ31B magnesium alloy sheets. All specimens were prepared in the rolling direction. The forming limit diagrams （FLDs） of AZ31B magnesium alloy sheet were determined experimentally by conducting stretch-forming tests at room temperature, 100, 200 and 300 ℃ Compared with the as-received sheet, the lowest limited strain of AZ31B magnesium alloy sheet with tilted texture in the FLD increased by 79% at room temperature and 104% at 100 ℃. The texture also affected the extension of the forming limit curves （FLC） in the FLD. However, the FLCs of two kinds of sheets almost overlapped at temperature above 200 ℃. It can be concluded that the reduction of （0002） texture intensity is effective to the improvement of formability not only at room temperature but also at low-and-medium temperature. The effect of texture on FLDs becomes weak with increasing temperature.

Analysis of bulging process of aluminum alloy by overlapping sheet metal and its formability

The influences of strength coefficient K, work hardening exponent n and thickness t of the overlapping sheet on bulging process are analyzed based on hardening material model. Also, bulging experiments are carried out by taking the aluminum alloy LF21 as formed sheet metal, and selecting overlapping sheet with different thicknesses and material properties, by which accuracy of the above analysis result is verified in the aspects of geometric shape, thickness distribution and limit bulging height. The results show that higher strength coefficient K, larger work hardening exponent n and proper thickness of the overlapping sheet are helpful to improve the formability and forming uniformity of formed sheet metal.

Influence of microstructure and texture on formability of AZ31B magnesium alloy sheets

The effect of the repeated unidirectional bending （RUB） process and annealing on the formability of magnesium alloy sheets was investigated. The RUB process and annealing treatments produce two effects on microstructure： grain coarsening and weakening of the texture. The sheet that underwent RUB and was annealed at 300 ℃exhibits the best formability owing to the reduction of the （0002） basal texture intensity, which results in low yield strength, large fracture elongation, small Lankford value （r-value） and large strain hardening exponent （n-value）. Compared with the as-received sheet, the coarse-grain sheet produced by RUB and annealing at 400 ℃ exhibits lower tensile properties but higher formability. The phenomenon is because the deformation twin enhanced by grain coarsening can accommodate the strain of thickness.

Influence of strain rate on microstructure and formability of AZ31B magnesium alloy sheets

The effects of strain rate on microstructure and formability of AZ31B magnesium alloy sheets were investigated through uniaxial tensile tests and hemispherical punch tests with strain rates of 10^-4, 10^-3, 10^-2, 10^-1 s^-1 at 200℃. The results show that the volume fraction of dynamic recrystallization grains increases and the original grains are gradually replaced by recrystallization grains with the strain rate decreasing. A larger elongation and a smaller r-value are obtained at a lower strain rate, moreover the erichsen values become larger with the strain rate reducing, so the formability improves. This problem arises in part from the enhanced softening and the coordination of recrystallization grains during deformation.

Influence of thermomechanical processing on microstructure,texture evolution and mechanical properties of Al-Mg-Si-Cu alloy sheets

Influence of thermomechanical processing on the microstructure, texture evolution and mechanical properties of A1-Mg-Si-Cu alloy sheets was studied systematically. The quite weak mechanical properties anisotropy was obtained in the alloy sheet through thermomechanical processing optimizing. The highly elongated microstmcture is the main structure for the hot or cold-rolled alloy sheets. H {001 } （110） and E { 111 } （110） are the main texture components in the surface layer of hot-rolled sheet, while ]/-fibre is dominant in quarter and center layers. Compared with the hot-rolled sheet, the intensities offl-fibre components are higher after the first cold rolling, but H {001 }（110） component in the surface layer decreases greatly. Almost no deformation texatre can be observed after intermediate annealing. And fl-fibre becomes the main texture again after the final cold rolling. With the reduction of the thickness, the through-thickness texture gradients become much weaker. The through-thickness recrystallization texture in the solution treated sample only has cubeyD {001 }（310） component. The relationship among thermomechanical processing, microstructure, texture and mechanical orouerties was analyzed.

Formability of aluminum-silicon coated boron steel in hot stamping process

Flow behavior of the Al-Si coated boron steel was investigated with Gleeble-3500,in comparison with the uncoated one.Effect of deformation conditions on the coating integrity was characterized by optical microscopy.Facture surfaces of the coated steels were inspected under SEM.Experimental results indicate that the ultimate tensile strength and ductility of the Al-Si coated boron steel are lower than those of the uncoated steel under test conditions.Extensive cracks occur in the coating after tensile tests;the width and density of cracks are sensitive to the deformation temperatures and strain rates.The bare substrate exposed between the separate coating segments is oxidized.Appearance of the oxide degrades the Al-Si coating adhesion.Remarkable difference between formability of the coating layer and the substrate is confirmed.The formability of the Al-Si coating could be optimized by controlling the phase transformation of the ductile Fe-rich intermetallic compounds within it during the austenization.

Formability determination of AZ31B tube for IHPF process at elevated temperature

Ring hoop tension test and tube bulging test were carried out at elevated temperatures up to 480 ℃to evaluate the formability of AZ31B extruded tube for internal high pressure forming （IHPF） process. The total elongation along hoop direction and the maximum expansion ratio （MER） of the tube were obtained. The fracture surface after bursting was also analyzed. The results show that the total elongation along hoop direction and the MER value have a similar changing tendency as the testing temperature increases, which is quite different from the total elongation along axial direction. Both the total elongation along hoop direction and the MER value increase to a peak value at about 160 ℃. After that, they begin to decrease quickly until a certain rebounding temperature is reached. From the rebounding temperature, they begin to increase rapidly again. Burnt structure appears on the fracture surface when tested at temperatures higher than 420 ℃. Therefore, the forming temperature of the tested tube should be lower than 420 ℃, even though bigger formability can be achieved at higher temperature.

Viscous warm pressure bulging process of AZ31B magnesium alloy with different ellipticity dies

Based on the bulging principle of different ellipticity dies, the methyl vinyl silicone rubber with excellent thermal stability and heat transfer performance was chosen as the viscous medium. The finite element analysis and experiments of viscous warm pressure bulging （VWPB） of AZ31B magnesium alloy were conducted to analyze the influence of different ellipticity dies on the formability of AZ31B magnesium alloy. At the same time, based on the grid strain rule, the forming limit diagram （FLD） of VWPB of AZ31B magnesium alloy was obtained through measuring the strain of bulging specimens. The results showed that at the temperature range of viscous medium thermal stability, the viscous medium can fit the geometry variation of sheet and generate non-uniform pressure field, and as the die ellipticity increases, the difference value of non-uniform pressure reduces. Meanwhile, according to the FLD, the relationship between part complexity and ultimate deformation was investigated.

Formability of AA5052/polyethylene/AA5052 sandwich sheets

The formability of AA5052/polyethylene/AA5052 sandwich sheets was experimentally studied. Three kinds of AA5052/polyethylene/AA5052 sandwich specimens with different thicknesses of core materials were prepared by the hot pressing adhesive method. Then, the uniaxial tensile tests were conducted to investigate the mechanical properties of AA5052/polyethylene/ AA5052 sandwich sheets, and the stretching tests were carried out to investigate the influences of polymer core thickness on the limit dome height of the sandwich sheet. The forming limit curves for three kinds of sandwich sheets were obtained. The experimental results show that the forming limit of the AA5052/polyethylene/AA5052 sandwich sheet is higher than that of the monolithic AA5052 sheet, and it increases with increasing the thickness of polyethylene core.