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.

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.

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.

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.

Enhancing plastic deformability of Mg and its alloys—A review of traditional and nascent developments

Mg and its alloys have continued to attract interest for several structural and super-sensitive applications because of their light weight and good combination of engineering properties.However for some of these applications,high plastic deformability is required to achieve desired component shapes and configurations;unfortunately,Mg and its alloys have low formability.Scientifically,the plastic behaviour of Mg and its alloys ranks among the most complex and difficult to reconcile in metallic material systems.But basically,the HCP crystal structure coupled with low stacking fault energies(SFE)are largely linked to the poor ductility exhibited by Mg alloys.These innate material characteristics have regrettably limited wide spread applicability of Mg and its alloys.Several research efforts aimed at exploring processing strategies to make these alloys more amenable for high formability–mediated engineering use have been reported and still ongoing.This paper reviews the structural metallurgy of Mg alloys and its influence on mechanical behaviour,specifically,plasticity characteristics.It also concisely presents various processing routes(Alloying,Traditional Forming and Severe Plastic Deformation(SPD))which have been explored to enhance plastic deformability in Mg and its alloys.Grain refinement and homogenising of phases,reducing CRSS between slip modes,twinning suppression to activate non-basal slip,and weakening and randomisation of the basal texture were observed as the formability enhancing strategies explored in the reviewed processes.While identifying the limitations of these strategies,further areas to be explored for enhancing plasticity of Mg alloys are highlighted.

Microstructure, mechanical properties and formability of friction stir welded dissimilar materials of IF-steel and 6061 Al alloy

AA 6061 alloy and interstitial-free(IF)steel plates were joined by the friction stir welding(FSW)method,and the microstructure,mechanical properties,and biaxial stretch formability of the friction stir welded(FSWed)parts were investigated.The results indicate that the FSWed parts showed optimum tensile strength during FSW with the 0.4-mm offset position of the tool.The Fe4Al13 intermetallic compound formed in the defect-free intersection of AA 6061 and IF-steel plates during FSW.The hardness of the IF-steel part of the FSWed region increased almost 90%relative to its initial hardness of HV0.2 105.The tensile and yield strengths of FSWed regions were approximately 170 MPa and 145 MPa,respectively.According to the formability tests,the Erichsen Index(EI)of the IF-steel,AA 6061,and the FSWed samples were determined to be 2.9 mm,1.9 mm,and 2.1 mm,respectively.The EI of the FSWed sample was almost the same as that of the AA 6061 alloy.However,it decreased compared with that of the IF-steel.The force at EI(FEI)was approximately 1180 N for the FSWed condition.This value is approximately 70%higher than that of AA 6061 alloy.

Enhanced mechanical properties and formability of 316L stainless steel materials 3D-printed using selective laser melting

This study is conducted to develop an innovative and attractive selective laser melting(SLM)method to produce 316 L stainless steel materials with excellent mechanical performance and complex part shape.In this work,the subregional manufacturing strategy,which separates the special parts from the components using an optimized process,was proposed.The results showed that produced 316 L materials exhibited superior strength of^755 MPa and good ductility.In the as-built parts,austenite with preferred orientation of the(220)plane,δ-ferrite,and a small amount of CrO phases were present.In addition,the crystal size was fine,which contributed to the enhancement of the parts’mechanical properties.The structural anisotropy mechanism of the materials was also investigated for a group of half-sized samples with variable inclination directions.This technique was used to fabricate a set of impellers with helical bevels and high-precision planetary gears,demonstrating its strong potential for use in practical applications.

Analytical and Experimental Studies on Critical Blank-holder Forces in Cylindrical cup deep drawing

Based on the plastic deformation theory and energy method, the critical blank-holder forces (BHF) of wrinkling and fracture in the cylindrical cup deep-drawing are analyzed. The verify experiments were performed and compared with the theory analysis results. The predictions agree well with the experiment results. Thus, the validated presenttheoretical analysis model may be applied to determinate the suitable BHF.

The effects of orientation control via tension-compression on microstructural evolution and mechanical behavior of AZ31 Mg alloy sheet

The grain orientation control via twinning activity on deformation features is of great significance to offer a key insight into understanding the deformation mechanism of Mg alloy sheets.The{10–12}twinning were performed by pre-strain paths,i.e.,tension(6%)and compression(5%)perpendicular to the c-axis along extrusion direction(ED),to investigate the microstructural evolution and mechanical properties of AZ31 Mg alloy sheets.The distinction in the texture evolution and strain hardening behavior was illustrated in connection with the pre-strain paths for the activities of twinning and slip.The result shows that the activation of the deformation mode was closely bound up with the grain orientation and the additional applied load direction.The{10–12}twin-texture components with c-axis//ED were generated by precompression,which can provide an appropriate alternative to accommodate the thin sheet thickness strain and enhance the room temperature formability of Mg alloy sheet.

Texture tailoring and bendability improvement of rolled AZ31 alloy using {10-12} twinning: The effect of precompression levels

In this study,the texture of a rolled Mg alloy is effectively modified through the application of precompression and subsequent annealing treatment,leading to a remarkable improvement in the bending formability of the alloy at room temperature.Precompression induces lattice reorientation through{10-12}twinning,and annealing treatment reduces the stored strain energy of the precompressed material,which results in the formation of a stable grain structure with two dominant texture components.With an increase in precompression,the tensile strain in the outer region of the bending samples is accommodated to a greater extent due to more pronounced{10-12}twinning and basal slip.As a result,the bending formability of the material at room temperature improves with greater precompression.The variation in microstructure,texture,and bending behavior in relation to the degree of precompression is discussed in detail.

Effect of Interface Friction on Overlapping Sheets Bulging Formability and Microstructure of 5A02 Aluminum Alloy

Aluminum alloy 5 A02 with low plasticity was used as target sheet, and stainless steel SUS304 with good plasticity was used as overlapping sheet to investigate the effect of interface friction on bulging formability and microstructure of target sheet in overlapping sheets bulging process. Sheet sliding experiment was performed to measure interface friction coefficient of 5 A02/SUS304 in different lubricating conditions and normal pressure. Overlapping sheets bulging experiment of 5 A02/SUS304 was carried out to investigate the influence of interface friction on limit bulging height, wall thickness distribution, microstructure and fracture morphology of 5 A02 bulging specimens. The results showed that increase of the interface friction coefficient of 5 A02/SUS304 could effectively improve the limit bulging height and deformation uniformity of 5 A02. And the fracture style of 5 A02 transformed from toughness fracture of dimples-micropores gathered to fault slip separation fracture. Therefore, target sheet bulging formability is improved with the increase of interface friction coefficient.

Formability of AZ31 Mg alloy sheets within medium temperatures

The stretching tests of the commercial AZ31 Mg alloy were conducted at 130 ℃, 170 ℃, 210 ℃, at the forming speeds of 10 mm/min and 50 mm/min, respectively. The formability of AZ31 sheets at high temperature was evaluated by forming limit diagrams (FLD). The fracture morphologies were analyzed using a scanning electron microscope. The results show that the FLD of AZ31 Mg alloy is affected by the forming temperature, in another word, the formability increases with the increasing of the forming temperature. That may be because the non-basal slip system starts to move by thermal activation at high forming temperature. It is also demonstrated that the formability of the AZ31 Mg alloy is on the decline with the increasing of the forming speed. The slipping performs thoroughly to release the stress during the deformation if the forming speed decreases. In addition, the higher the forming temperature is, the more obvious the effect of the forming speed is. The forming temperature is the main dominating factor on the formability of AZ31 Mg alloy.

HAZ Characterization and Mechanical Properties of QP980-DP980 Laser Welded Joints

The QP980-DP980 dissimilar steel joints were fabricated by fiber laser welding.The weld zone(WZ)was fully martensitic structure,and heat-affected zone(HAZ)contained newly-formed martensite and partially tempered martensite(TM)in both steels.The supercritical HAZ of the QP980 side had higher microhardness(~549.5 Hv)than that of the WZ due to the finer martensite.A softened zone was present in HAZ of QP980 and DP980,the dropped microhardness of softened zone of the QP980 and DP980 wasΔ21.8 Hv andΔ40.9 Hv,respectively.Dislocation walls and slip bands were likely formed at the grain boundaries with the increase of strain,leading to the formation of low angle grain boundaries(LAGBs).Dislocation accumulation more easily occurred in the LAGBs than that of the HAGBs,which led to significant dislocation interaction and formation of cracks.The electron back-scattered diffraction(EBSD)results showed the fraction of LAGBs in sub-critical HAZ of DP980 side was the highest under different deformation conditions during tensile testing,resulting in the failure of joints located at the sub-critical HAZ of DP980 side.The QP980-DP980 dissimilar steel joints presented higher elongation(~11.21%)and ultimate tensile strength(~1011.53 MPa)than that of DP980-DP980 similar steel joints,because during the tensile process of the QP980-DP980 dissimilar steel joint(~8.2%and 991.38 MPa),the strain concentration firstly occurred on the excellent QP980 BM.Moreover,Erichsen cupping tests showed that the dissimilar welded joints had the lowest Erichsen value(~5.92 mm)and the peak punch force(~28.4 kN)due to the presence of large amount of brittle martensite in WZ and inhomogeneous deformation.

Strong strain path dependence of strain localizations and fracture in magnesium AZ31 sheet

This study compares the deformation and fracture behavior of a basal-textured Mg AZ31 alloy sheet under uniaxial tension and biaxial stretching by using an in-plane biaxial test setup capable of observing and measuring the deformation at both meso(millimeter)and microstructure scales.Strain distributions at the mesoscale and accompanying fracture surfaces indicate a significant dependence on strain path.At the microscale,limited slip activity in biaxial case promotes contraction twins,where severe strain localizations(εmax/εmean≈220)to the twins and their boundaries cause mainly transgranular fracture.This leads to a brittle,and a more pronounced shear-type fracture under biaxial stretching.In uniaxial case,considerable tensile twinning activity reorients the initial texture for slip activity.Strain localizations(εmax/εmean≈2)to the grain interiors and boundaries initiate mainly intergranular fracture.Samples fail by displaying both brittle and ductile fracture structures,with smaller shear lips compared to the biaxial case.

Bending properties of extruded AZ91–0.9Ca–0.6Y alloy and their improvement through precompression and annealing

In this study,an extruded Mg–9Al–1Zn–0.3Mn–0.9Ca–0.6Y(AZXW9110)alloy is subjected to precompression and subsequent annealing(PCA)treatment for improving its bending formability,and the three-point bending properties of the as-extruded material and the precompressed and subsequently annealed(PCAed)material at room temperature are compared.During bending,microcracks formed in undissolved Al2Ca,Al2Y,and Al8Mn4Y particles propagate along the grain boundaries or twin boundaries and consequently form a macrocrack in the tension zones of the bending samples of both the materials.However,the bending formability of the PCAed material is 75%higher than that of the as-extruded material owing to the promoted twinning and slip behaviors in the former.The as-extruded material has a strong normal direction(ND)texture and a weak transverse direction(TD)texture,and the ND-and TD-oriented grains are unfavorable for both{10–12}twinning and basal slip in the tension zone of the bending sample of this material,which eventually results in its low bending formability.The PCAed material has a strong extrusion direction(ED)texture,weak TD texture,and spread ND texture.During bending,{10–12}twins are fully formed in the ED-oriented grains,and this{10–12}twinning effectively accommodates the plastic strain in the tension zone.In addition,the activation of basal slip in the ND-oriented grains of the PCAed material is promoted owing to the spread ND texture of this material.Consequently,this material exhibits substantially superior bending formability because of the vigorous{10–12}twinning in its ED-oriented grains and promoted basal slip in its ND-oriented grains.