Zn Zr Research Articles

Effects of annealing on mechanical properties and degradation behavior of biodegradable JDBM magnesium alloy wires

Mg–Nd–Zn–Zr magnesium alloy (JDBM) has been studied widely as biodegradable medical material. To process high quality JDBM wires, effects of annealing on the mechanical properties and degradation behavior after drawing were studied by microscopic observations, tensile and immersion tests. The as-extruded wires with a diameter of 3 mm could be drawn up to 9 passes without annealing until 125% cumulative drawing deformation. Complete recrystallization occurred after annealing at 325 °C for 30 min, 350 °C for 5 min or 450 °C for 3 min, respectively. Room temperature tensile tests and simulated body fluid immersion tests showed that annealing at slightly elevated temperature for short time could obtain better properties due to the finer grain size and more dispersive distribution of precipitates. For this study, annealing at 350 °C for 5 min is the best parameters which can be utilized to further fabricate fine wires.

Microstructure evolution and corrosion resistance improvement of Mg–Gd–Y–Zn–Zr alloys via surface hydrogen treatment

A surface hydrogen treatment is proposed to improve the corrosion resistance of a long-period stacking ordered (LPSO) phase-enhanced Mg–Gd–Y–Zn–Zr alloy. After hydrogen treatment, the block-like LPSO phases are replaced by novel strip-shaped Gd0.5Y0.5H1.96 aggregates in the surface hydrogenated layer with 260 ± 42 μm thickness. The results of immersion tests in a 3.5 % NaCl solution show that hydrogen treatment improves the corrosion resistance of the alloy. As the LPSO phase decomposes, the Zn enriched in the LPSO phase dissolves into a magnesium matrix, which increases the Volta potential of the surface hydrogenated layer.

Effect of subgrain and the associated DRX behaviour on the texture modification of Mg-6.63Zn-0.56Zr alloy during hot tensile deformation

The individual effect of DRXed grains, subgrains and deformed grains on the basal texture of Mg–Zn–Zr alloy during hot tensile deformation was systematically studied by extracting corresponding grains. The results show that the final texture was the result of compromise between the randomized texture of DRXed grains and preferred texture of subgrains and deformed grains. The texture attribute of subgrain did not change fundamentally compared with that of deformed grain, both of which dominated the final texture profile. Prismatic <a> dislocations exerted a profound effect on the compatible deformation of unDRXed grains, giving rise to a sharp [011‾0] fiber. Few basal <a> dislocations could be detected in the unDRXed grains due to the premature exhaustion of such slip operation and subsequent substitution by non-basal slips. Subgrains, in terms of DDRX, were caused by the interaction between basal and non-basal dislocations, resulting in the protrusions segmented by the subgrain boundaries (sub-GBs) whose misorientation increased gradually as trapping dislocation proceeded. As a result, these protrusions were segregated from the parent grains and transformed into DRXed grains. CDRX proceeded by high activity of profuse dislocations. In this case, sub-GBs came from the realignment and incorporation of the accumulated dislocations in the vicinity of dislocation forest, which subdivided one grain into several subgrains that could be converted into DRXed grains in situ via the transformation from LAGBs to HAGBs by consecutively absorbing dislocations. Besides, twinning deformation was an auxiliary way of compatible deformation, which could reorientate parent grains so as to reactivate the slip systems. The contribution of resulting {101‾2} twins to the final texture was not significant yet. Ultimately, the selection of {101‾2} twin variants was also discussed.

Susceptibility of Mg–REM–Zn–Zr Magnesium Alloys to Casting Unsoundness

Susceptibility of Mg–REM–Zn–Zr Magnesium Alloys to Casting Unsoundness

Neighboring Zn-Zr Sites in a Metal-Organic Framework for CO2 Hydrogenation.

ZrZnOx is active in catalyzing carbon dioxide (CO2) hydrogenation to methanol (MeOH) via a synergy between ZnOx and ZrOx. Here we report the construction of Zn2+-O-Zr4+ sites in a metal-organic framework (MOF) to reveal insights into the structural requirement for MeOH production. The Zn2+-O-Zr4+ sites are obtained by postsynthetic treatment of Zr6(μ3-O)4(μ3-OH)4 nodes of MOF-808 by ZnEt2 and a mild thermal treatment to remove capping ligands and afford exposed metal sites for catalysis. The resultant MOF-808-Zn catalyst exhibits >99% MeOH selectivity in CO2 hydrogenation at 250 °C and a high space-time yield of up to 190.7 mgMeOH gZn-1 h-1. The catalytic activity is stable for at least 100 h. X-ray absorption spectroscopy (XAS) analyses indicate the presence of Zn2+-O-Zr4+ centers instead of ZnmOn clusters. Temperature-programmed desorption (TPD) of hydrogen and H/D exchange tests show the activation of H2 by Zn2+ centers. Open Zr4+ sites are also critical, as Zn2+ centers supported on Zr-based nodes of other MOFs without open Zr4+ sites fail to produce MeOH. TPD of CO2 reveals the importance of bicarbonate decomposition under reaction conditions in generating open Zr4+ sites for CO2 activation. The well-defined local structures of metal-oxo nodes in MOFs provide a unique opportunity to elucidate structural details of bifunctional catalytic centers.

The development of a strong and ductile Mg–Zn–Zr thin sheet through nano precipitates and pre-induced dislocation

In this study, a strong and ductile thin sheet of Mg–Zn–Zr alloy was developed through nano precipitates and pre-induced dislocation. Our results displayed that the sheet was comprised of fiber basal texture and a small fraction of the grains having c-axes//TD of the sheet. Most specifically, profuse pre-induced dislocations and nano-size precipitates were witnessed in the grain interior. During deformation, twinning and <c+a> dislocations accommodated the strain. Therefore, these factors along with nano-precipitates, texture, and pre-induced dislocations lead to the high yield strength of ~290 MPa, ultimate tensile strength ~366 MPa, and fracture to elongation ~19%.

The role of Yb content on the microstructural evolution and mechanical characteristics of cast Mg-9Gd-0.5Zn-0.2Zr alloy

Inspections on microstructural design suggest that a high-strength Mg alloy can be achieved via the generation of co-precipitation of prismatic and basal precipitates with high number density and large aspect ratios. Currently, there is a lack of feasible approaches to generating such a microstructure. This work investigated the specific role of various Yb contents on the precipitation behavior, solute segregation and mechanical performance of cast Mg-9Gd-xYb-0.5Zn-0.2Zr alloys (x = 0, 0.5, 1 wt%). It was found that, the age hardening response of Mg-9Gd-0.5Zn-0.2Zr alloy could be significantly improved as the Yb addition increased, primarily ascribed to introduction of dense distribution of both prismatic and basal matrix precipitates involving γ′′, β′ and β1. Solute segregation of Yb had been examined utilizing high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM), revealing the evidence of strong Yb segregation in both prismatic β′, β1 and basal γ′′ precipitates. Quantitative TEM analysis indicated that the increasing Yb addition was found to improve the number density of γ′′, β′ and β1 during isothermal ageing at 225 °C. The substantial improvement on yield strength (~84 MPa) in peak-aged alloy was thereby achieved due to the co-precipitation of dense prismatic and basal strengthening phases associated with Yb addition (1 wt%). However, in addition to the promoted precipitation of these strengthening phases, Zn–Zr particles were confirmed to act as favorable nucleation sites for prismatic β1 phases in the under-aged condition. During prolonged ageing time, the addition of 1 wt% Yb was found to greatly accelerate the growth of these preferentially formed β1 phases and part of β1 transformed in situ into β phases, accompanied by the gradual developments of matrix precipitate-free zones (PFZs). The greatly improved uneven distribution of these coarse β-type phases concomitant with widened PFZs primarily led to the significant reduction in ductility as the Yb content increased up to 1%.

Enhanced ductility of Mg–1Zn–0.2Zr alloy with dilute Ca addition achieved by activation of non-basal slip and twinning

Wrought Mg–Zn–Zr alloys with a strong basal texture usually exhibit highly anisotropic plastic behavior, resulting in premature fracture during deformation at room temperature. In the present study, we prepared a Mg–1Zn–0.2Zr (ZK10) alloy sheet by multi-pass hot rolling and annealing, tailoring the basal texture and reducing the plastic anisotropy with the addition of dilute Ca. Microstructural characterizations of the tensile-deformed alloys show that pyramidal <c+a> slip and 101¯2 twinning are more easily formed in the Ca-containing alloy compared with those in the ZK10 alloy. The weakened basal texture involving Ca addition leads to promoted activation of 101¯2 twinning, without significant impact on the Schmid factor distribution of pyramidal <c+a> slip. Simulation results of the visco-plasticity self-consistent model further indicate that Ca reduces the ratio of critical resolved shear stress for pyramidal <c+a> slip and 101¯2 twinning versus basal <a> slip, leading to a significant improvement in ductility. This work may provide a new strategy to develop wrought Mg alloys with enhanced ductility.

Optimizing the mechanical properties of a Mg–Y–Nd–Zn–Zr alloy via interrupted compression with an intermediate annealing

This work proposed a practical method, interrupted compression with an intermediate annealing, for optimizing the mechanical properties of Mg–4Y-2Nd-0.2Zn-0.5Zr alloy. This method contained the first compressive step for an interrupted strain of 0.25, the intermediate annealing for 5 min, and the second compressive step for a total true strain of 1.6. The temperatures for the two steps of hot compression and intermediate annealing were the same. The obtained sample was named IC sample. As a comparison, the continuous compression was also performed (CC sample). During hot compression, the work softening of the CC sample was dominated by the rotational dynamic recrystallization (rDRX) and the twin-assisted DRX (tDRX). With the strain increasing, the rDRX acted a more dominant role compared to the tDRX. In the IC sample, the intermediate annealing triggered the formation of deformation bands. During the second compressive step of the IC sample, the work softening was dominated by the DRX assisted by deformation bands besides the rDRX. As a result, the volume fraction of ultra-fine grains (V UFG ) was much higher in comparison to the CC sample. Compared to the grain size of UFGs (D UFG ) and the basal pole distribution, the V UFG had a more important role in the resultant mechanical properties. The higher V UFG of the IC sample led to the better combination of strength and ductility at each compressive temperature. Comparing the IC sample to the CC sample after compressing at temperatures from 420 °C to 510 °C, the increments of the UTS were 7.4%, 2.4%, 1.2% and 0.4%, and the increments of the FE were 4.0%, 13.9%, 22.8% and 21.3%. The interrupted compression with an intermediate annealing had a deep potential in applying to other Mg alloys despite the initial texture. • Both continuous compression (CC) and interrupted compression (IC) are performed. • In CC sample, work softening is controlled by both rDRX and tDRX. • Intermediate annealing triggers the formation of deformation bands in IC sample. • In IC sample, work softening is dominated by the DRX assisted by deformation bands. • Interrupted compression successfully improves DRX degree and mechanical properties.

High cycle fatigue behavior and mechanical performance of a novel sand-cast Mg-Nd-Gd alloy: Effect of heat treatment

Abstract This work was primarily aimed at evaluating the effect of heat treatment on the microstructure, high cycle fatigue behavior and mechanical properties of a novel sand-cast Mg-3Nd-2.6Gd-0.2Zn-0.5Zr alloy. Results indicated that the as-cast studied alloy consisted of non-dendritic α-Mg grains and considerable eutectic phases distributed along grain boundaries, most of which could been successfully dissolved into matrix accompanied by the appearance of rod-shaped Zn–Zr phases after subjected to the optimized solution treatment (535 °C × 10 h). Examinations of microstructure revealed a finely dense dispersion of predominant β′′ and minor β′ phases in the peak-aged studied alloy (isothermally aging at 200 °C for 14 h). Tensile properties were significantly improved, and the relatively best combination of strength and ductility was obtained in peak-aged condition (YS = 220 MPa, UTS = 303 MPa and EL = 4.1%). Heat treatment conditions were found to exert a pronounced influence on the high cycle fatigue properties, and the highest fatigue strength σf (approximately 121.5 MPa), was achieved in peak-aged studied alloy, which is about 24% higher than that of commercial NZ30K-T6 alloy. Owing to the specifically significant response to heat treatments, the fatigue strength of the studied alloy was confirmed to increase in a near linear relationship with the increasing yield strength and ultimate tensile strength. This is also well consistent with the characteristic fatigue life predicted by Weibull statistics in different heat treatment conditions.

Influence of Glucose on Corrosion Fatigue and Cytocompatibility of Mg–Zn–Zr–Y Alloy

This article mainly focuses on the effects of glucose on the mechanical safety and cytotoxicity of Mg alloys used as implant materials. Under the corrosive human body fluid and dynamic loading, especially in a high‐glucose environment, Mg alloys are inevitably subjected to the decrease of mechanical properties in the process of long‐time service and eventually faced with corrosion fatigue (CF) failure. Herein, a comparative study on the dynamic mechanical properties of the Mg–Zn–Zr–Y alloy is evaluated by carrying out fatigue tests in air and in Hank's solution. CF and cytocompatibility of Mg–Zn–Zr–Y alloys response to different glucose contents (1 and 3 g L−1) are also detected. The Mg–Zn–Zr–Y alloy exhibits an excellent fatigue limit of 119.43 MPa in air compared with 47.77 MPa in Hank's solution at 37 °C. The fatigue cracks initiate at the microstructural defects in air and nucleate at corrosion pits in Hank's solution. Better corrosion resistance and enhanced CF are obtained with the increasing glucose content in Hank's solution. The in vitro tests with MC3T3‐E1 cells demonstrate that the Mg–Zn–Zr–Y alloy shows excellent cytocompatibility under high‐glucose condition.

Influences of the Texture Characteristic and Interdendritic LPSO Phase Distribution on the Tensile Properties of Mg–Gd–Y–Zn–Zr Sheets Through Hot Rolling

The Mg–Gd–Y–Zn–Zr alloy sheets with different texture characteristics and distribution of the interdendritic long period-stacking ordered (LPSO) phases were fabricated through altering the final rolling reduction (FRR). The results showed that the texture characteristic was closely related to FRR and affected the tensile properties of the resulted sheets to some extent. The Schmid factor (SF) of the basal $$\left\langle a \right\rangle$$ slip improved with further FRR, which was ascribed to that the dynamic recrystallization (DRX) grains expand into the deformed grains with basal texture. However, the improvement of the tensile yield strength (TYS) with further FRR indicates that the strengthening effect from DRX grains surpasses the weakening effect from the elevated SF. The formation of the line-distributed interdendritic 14H-LPSO phases can also affect the tensile properties of the resulted sheets. The line-distributed interdendritic 14H-LPSO phases along rolling direction (RD) can act as reinforcing fiber and contribute to the higher TYS along RD and 45° to some extent, which resulted in the higher TYS along 45° compared with that along transverse direction (TD) for each resulted sheet under the circumstance of approximate basal $$\left\langle a \right\rangle$$ and pyramid $$\left\langle {c + a} \right\rangle$$ friction stress. Thus, the tensile yield strength is not only related to the texture, but also depends on the grain size and line-distributed interdendritic LPSO phases. The micro-cracks spread perpendicular to the tension direction, and thus, the larger cracks form within the line-distributed 14H-LPSO phases during tension along TD, which accounts for the lower fracture elongation along TD.

Effective Suppression of CO Selectivity for CO2 Hydrogenation to High-Quality Gasoline

CO2 hydrogenation to gasoline fuels remains a sticky problem of CO selectivity from reverse water-gas shift reactions over a metal oxide and zeolite bifunctional catalyst. Herein, we report an efficient catalyst combining a Fe–Zn–Zr–T oxide hydrothermally treated with TPABr solution and HZSM-5 zeolite for CO2 hydrogenation into high-quality gasoline. The hydrothermal treatment contributes to the obvious enrichment of the Zn component and the residual Br on the surface of Fe–Zn–Zr–T oxide, as compared to Fe–Zn–Zr oxide, as well as the increased number of oxygen vacancies. These surface properties not only induce the increase of the H2 adsorption and CO2 adsorption ratio but also enhance the adsorption strength of the HCOO* species and the desorption rate of CH3O* species (close intermediate of methanol) over Fe–Zn–Zr–T oxide, which are responsible for higher methanol selectivity and lower CO selectivity. Furthermore, the presence of the adsorbed CO* species and higher C2+ hydrocarbon selectivity on Fe–Zn–Zr oxide affirm the F–T route of CO2 hydrogenation except for the methanol route, while the F–T route is effectively restrained after the TPABr hydrothermal treatment of Fe–Zn–Zr–T oxide. As the Fe and Zn–Zr molar ratio decreases, more HCOO* and CH3O* species on Fe–Zn–Zr (0.1:1:1)–T–24 h can form, which is in good agreement with the much higher methanol selectivity on Fe–Zn–Zr (0.1:1:1)–T–24 h oxide and hydrocarbon selectivity on the Fe–Zn–Zr(0.1:1:1)–T–24 h@HZSM-5 core–shell catalyst. The CO selectivity and C5+ isoalkane selectivity in gasoline on Fe–Zn–Zr(0.1:1:1)–T–24 h@HZSM-5 are up to 24% and 93%, respectively, with a CO2 conversion of 18%. The good matching of the Fe–Zn–Zr–T oxide and HZSM-5 zeolite plays the crucial role in the C5+ isoalkanes selectivity in gasoline over the Fe–Zn–Zr–T@HZSM-5 core–shell catalyst.

Synthesis of amino alcohols, cyclic urea, urethanes, and cyclic carbonates and tandem one-pot conversion of an epoxide to urethanes using a Zn–Zr bimetallic oxide catalyst

The one-pot tandem synthesis of urethanes directly from an epoxide, with urea in solvent-free condition using Zn2ZrOx is demonstrated. The catalyst exhibits excellent activity in cyclic urea, urethane, and cyclic carbonate production in neat conditions.

Research on the formation process of selective laser melting Mg–Y–Sm–Zn–Zr alloy

Selective laser melting technology was proposed to form the multi-element mixed rare earth magnesium alloys of Mg–3.4Y–3.6Sm–2.6Zn–0.8Zr (wt-%). The formation process, relative density, evaporation, microstructure and microhardness of the deposited samples at different laser power and scanning speed were characterised. Under the experimental conditions with a laser power of 40 W and a scanning speed of 300 mm s−1, the maximum relative density of the sample is 98.6%. The evaporation of elements exists but is not serious under all process parameters. Compared with the as-cast process, the microstructure of the samples prepared by SLM is mainly composed of α-Mg matrix and (Mg, Zn)3(Y, Sm) eutectic phase, Mg12(Y, Sm)Zn eutectic phase and LPSO structure are not found.

Microstructural evolution and enhanced mechanical properties of Mg–Gd–Y–Zn–Zr alloy via centrifugal casting, ring-rolling and aging

A ring-shaped Mg–8.5Gd–4Y–1Zn–0.4Zr (wt%) alloy was manufactured via centrifugal casting and ring-rolling process. The effects of accumulative ring-rolling reduction amount on the microstructure, texture, and tensile properties of the alloy were investigated. The results indicate that the microstructure of centrifugal cast alloy consists of equiaxed grains and network-like eutectic structure present at grain boundaries. The ring-rolled alloy exhibits a characteristic bimodal microstructure composed of fine dynamic recrystallized (DRXed) grains with weak basal texture and coarse un-DRXed grains with strong basal texture, along with the presence of LPSO phase. With increasing amount of accumulative ring-rolling reduction, the coarse un-DRXed grains are refined via the formation of increasing amount of fine DRXed grains. Meanwhile, the dynamic precipitation of Mg 5 RE phase occurs, generating a dispersion strengthening effect. A superior combination of strength and ductility is achieved in the ring-rolled alloy after an accumulative rolling reduction of 80%. The tensile strength of this ring-rolled alloy after peak aging is further enhanced, reaching 511 MPa, while keeping a reasonable ductility. The salient strengthening mechanisms identified include the grain boundary strengthening of fine DRXed grains, dispersion strengthening of dynamic precipitated Mg 5 RE phase, short fiber strengthening of LPSO lamellae/rods, and precipitation strengthening of nano-sized prismatic β′ precipitates and basal γ′ precipitates.

Achieving an ultra-high strength and moderate ductility in Mg–Gd–Y–Zn–Zr alloy via a decreased-temperature multi-directional forging

In this study, an ultra-high yield strength (~417 MPa) and moderate ductility (~12.9%) was obtained in Mg–8.2Gd–3.8Y–1.0Zn–0.4Zr (wt%) alloy through a method of decreased-temperature multi-directional forging (MDF) processing followed by aging treatment. The ultra-fine grained structure with average grain size of ~0.9 μm was prepared after 6 passes of forging progress, which was ascribed to the occurrence of dynamic recrystallization (DRX). Both the decreased MDF temperature and precipitation of fine Mg5(Gd, Y) phase particles effectively hinder the DRX grain growth, so that the grain refinement can realize their full potential in strengthening effect. The formation of some DRX grains is also accompanied with the consumption of LPSO structures. Additionally, a weak fiber texture with c-axis perpendicular to normal direction was gradually formed during the reduplicative MDF process. As compared to the hot-extruded counterpart, the significant improvement in the yield strength of MDF-processed Mg-Gd-Y-Zn-Zr alloy can be attributed to the combined strengthening effects of the grain refinement, dynamic precipitation and broken secondary phase particles. Meanwhile, the homogenous microstructure induced by decreased-temperature MDF is also responsible for a resulting moderate ductility.

Deformation behavior of Mg–Zn–Zr magnesium alloy on the basis of macro-texture and fine-grain size under tension and compression loading along various directions

The deformation behavior of an extruded Mg–Zn–Zr alloy in the form of plate/sheet was investigated on the basis of fine-grained and initial macro-texture along various directions under uniaxial compression and tension test. The initial macro-texture revealed that 60.4% of grains have c-axes of hexagonal closed packed crystal structure along the normal direction and 17.4% grains have c-axes parallel to the transverse direction. The results showed that the flow stress and strain hardening rate under compression and tension were significantly affected by the loading directions and the initial texture. The ratio of tensile yield strength to the compressive yield strength along normal direction extruded direction, and transverse direction was found 0.85, 1.5, and 0.93, respectively. The practically symmetric yielding behavior along normal and transverse direction was caused by the fine-grained size, twinning dependencies on strain path loading, and texture. The anisotropy ∼1.5 along extrusion direction is the cause of the large fraction of {101¯2}<101¯1> extension twinning under compression and no twinning activity in tension along ED in the early stages of deformation in large grains. The strain hardening curves under tension and compression shows almost similar behavior in the normal direction. For extrusion direction and transverse direction, strain hardening curves exhibited three and two regimes under compressive loading which leads to a large difference in ultimate compressive and tensile strength. It is also revealed that {101¯2}<101¯1> extension twinning was favorable, while {101¯1}<101¯2> contraction twinning and {101¯1}−{101¯2} double twinning were unfavorable for strain hardening. The underlying deformation mechanisms under different loading paths were discussed on the basis of X-ray diffraction and optical microscopic analysis.

Effect of Zirconium on the Formation of the Structure, Phase Composition, and Properties of Mg–Zn–Zr–REM Alloys

Abstract—The effect of zirconium of the formation of the structure, phase composition, and properties of MA20 and MA22 wrought Mg–Zn–Zr–REM alloys is studied. Zirconium is confirmed to be not only an efficient modifier of the structure of magnesium alloys but also an active phase-forming alloying element. It participates in the formation of nanodispersive intermetallic phases, such as zinc zirconides and zirconium hydrides, which favor an increase in the main mechanical characteristics of magnesium alloys when favorable morphology of phase particles is formed.

Microstructure evolution, texture and mechanical properties of a Mg–Gd–Y–Zn–Zr alloy fabricated by cyclic expansion extrusion with an asymmetrical extrusion cavity: The influence of passes and processing route

In the present work, two processing routes (A and B) with 3 CEE-AEC passes are performed on Mg–13Gd–4Y–2Zn–0.4Zr alloys, and the resultant microstructure evolution, texture analysis and mechanical properties are investigated systematically. The core difference between the two processing routes is the orientation between the expansion and extrusion steps, i.e., they are parallel to each other for on route A and perpendicular to each other for route B. The results show that a remarkable grain refinement is achieved via both processing routes due to dynamic recrystallization (DRX). Fine equiaxed grains are observed in the samples processed with route B with a final size of 3.6 ± 0.4 µm compared to the grain size of 4.5 ± 0.5 µm with route A. With an increasing number of CEE-AEC passes, the overall texture intensity decreases, and the basal texture gradually changes to the mixed texture components. The shear deformation introduced by the asymmetrical extrusion cavity promotes a broad angular distribution of the basal planes on routes A and B, leading to an obvious increase in the Schmid factor for the activation of the basal 〈a〉 slip system. The tensile test at ambient temperature reveals that the comprehensive mechanical properties are improved, and the conventional mechanical anisotropy of as-received alloys is alleviated by successive CEE-AEC processing, which is mainly derived from the competitive balance relation between the grain refinement and texture modification.