Microstructure and mechanical properties of as-cast(CuNi)100-xCox medium-entropy alloys

Microstructure and mechanical properties of non-equiatomic(CuNi)_(100-x)Co_(x)(x=15,20,25 and 30,at.%)medium-entropy alloys(MEAs)prepared by vacuum arc-melting were investigated.Results show that all the as-cast MEAs exhibit dual face-centered cubic(fcc)solid-solution phases with identical lattice constant,showing typical dendrite structure consisting of(Ni,Co)-rich phase in dendrites and Cu-rich phase in inter-dendrites.The positive enthalpy of mixing among Cu and Ni-Co elements is responsible for the segregation of Cu.With the increase of Co content,the volume fraction of(Ni,Co)-rich phase increases while the Cu-rich phase decreases,resulting in an increment of yield strength and a decrement of elongation for the(CuNi)_(100-x)Co_(x) MEAs.Nano-indentation test results show a great difference of microhardness between the two fcc phases of the MEAs.The measured microhardness value of the(Ni,Co)-rich phase is almost twofold as compared to that of the Cu-rich phase in all the(CuNi)_(100-x)Co_(x) MEAs.During the deformation of the MEAs,the Cu-rich phase bears the main plastic strain,whereas the(Ni,Co)-rich phase provides more pronounced strengthening.

Effects of Si Addition on Microstructure,Properties and Serration Behaviors of Lightweight Al-Mg-Zn-Cu Medium-entropy Alloys

A series of as-cast lightweight multicomponent alloys Al(86-x)Mg10Zn2Cu2Six(x=0,0.3,0.6,0.9,1.2 at.%)were prepared by a vacuum induction furnace with a steel die.With the addition of Si,the reticular white Al-Cu phase deposited were gradually replaced by the gray eutectic Mg-Si phase,while the compressive strength of the alloys increases first and then decreases slowly.It is particularly noteworthy that the compression plasticity also exhibits this trend.When the Si content is 0.9 at.%,the compressive strength reaches its maximum at 779.11 MPa and the compressive plasticity reaches 20.91%.The effect of the addition of Si on the serration behavior of alloy was also studied;we found that the addition of Si introduces a new MgSi phase,and with the change of Si is significantly affects the morphology of the precipitated phase,which affects the serration behavior of the alloys.The comprehensive mechanical properties of the alloy are optimal at the critical point where the serration behavior disappears.In this work,we have provided a method and a composition for the preparation of a low-cost,high-strength,lightweight medium-entropy alloys.

Prediction of chemical short-range order in high-/medium-entropy alloys

Chemical short-range orders(CSROs),as the built-in sub-nanoscale entities in a high-/medium-entropy alloy(H/MEA),have aroused an ever-increasing interest.With multi-principal elements in an H/MEA to form a complex concentrated solution,a variety of sub-systems of species exist to induce the metastable ordered compounds as candidates for ultimate CSROs.The issues remain pending on the origin of CSROs as to how to judge if CSRO will form in an H/MEA and particularly,what kind of CSROs would be stably produced if there were multiple possibilities.Here,the first-principles method,along with the proposed local formation energy calculation in allusion to the atomic-scale chemical heterogeneities,is used to predict the CSRO formation based on the mechanical stability,thermodynamic formation energy,and electronic characteristics.The simulations are detailed in an equiatomic ternary VCoNi MEA with three kinds of potential compounds,i.e.,L1_(1),L1_(2),and B2,in the face-centered cubic matrix.It turns out that L1_(1)is stable but hard to grow up so as to become the final CSRO.L1_(1)is further predicted as CSROs in CrCoNi,but unable to form in FeCoNi and CrMnFeCoNi alloys.These predictions are consistent with the experimental observations.Our findings shed light on understanding the formation of CSROs.This method is applicable to other H/MEAs to design and tailor CSROs by tuning chemical species/contents and thermal processing for high performance.

Ultrastrong and ductile(CoCrNi)_(94)Ti_(3)Al_(3)medium-entropy alloys via introducing multi-scale heterogeneous structures

The coarsening-grained single-phase face-centered cubic(fcc)medium-entropy alloys(MEAs)normally exhibit insufficient strength for some engineering applications.Here,superior mechanical properties with ultimate tensile strength of 1.6 GPa and fracture strain of 13.1%at ambient temperature have been achieved in a(CoCrNi)_(94)Ti_(3)Al_(3)MEA by carefully architecting the multi-scale heterogeneous structures.Electron microscopy characterization indicates that the superior mechanical properties mainly originated from the favorable heterogeneous fcc matrix(1-40μm)and the coherent sphericalγ’precipitates(10-100 nm),together with a high number density of crystalline defects(2-10 nm),including dislocations,small stacking faults,Lomer-Cottrell locks,and ultrafine deformation twins.

Design and optimization of the composition and mechanical properties for non-equiatomic CoCrNi medium-entropy alloys

The development of multi-principal element alloys(MPEAs,also called as high-or medium-entropy al-loys,HEAs/MEAs)provides tremendous possibilities for materials innovation.However,designing MPEAs with desirable mechanical properties confronts great challenges due to their vast composition space.In this work,we provide an essential criterion to efficiently screen the CoCrNi MEAs with outstanding strength-ductility combinations.The negative Gibbs free energy difference△E_(FCC-BCC)between the face-centered cubic(FCC)and body-centered cubic(BCC)phases,the enhancement of shear modulus G and the decline of stacking fault energy(SFE)γ_(isf)are combined as three requisites to improve the FCC phase stability,yield strength,deformation mechanisms,work-hardening ability and ductility in the criterion.The effects of chemical composition on△E_(FCC-BCC),G andγisf were investigated with the first principles calculations for Co_(x)Cr_(33)Ni_(67-x),Co_(33)Cr_(y)Ni_(67-y)and Co_(z)Cr_(66-z)Ni_(34)(0≤x,y≤67 and 0≤z≤66)alloys.Based on the essential criterion and the calculation results,the composition space that displays the neg-ative Gibbs free energy difference△E_(FCC-BCC),highest shear modulus G and lowest SFEγ_(isf)was screened with the target on the combination of high strength and excellent ductility.In this context,the optimal composition space of Co-Cr-Ni alloys was predicted as 60 at.%-67 at.%Co,30 at.%-35 at.%Cr and 0 at.%-6 at.%Ni,which coincides well with the previous experimental evidence for Co_(55)Cr_(40)Ni_(5)alloys.The valid-ity of essential criterion is further proved after systematic comparison with numerous experimental data,which demonstrates that the essential criterion can provide significant guidance for the quick exploitation of strong and ductile MEAs and promote the development and application of MPEAs.

Chemical short-range orders in high-/medium-entropy alloys

High(or medium)-entropy alloys(H/MEAs)are complex concentrated solid solutions prone to develop the chemical short-range orders(CSROs),as an indispensable structural constituent to make H/MEAs essentially different from the traditional alloys.The CSROs are predicted to play roles in dislocation behaviors and mechanical properties.So far,the image of CSROs is built up by the theoretical modeling and computational simulations in terms of the conventional concept,i.e.,the preference/avoidance of elemental species to satisfy the short-ranged ordering in the first and the next couple of nearest-neighbor atomic shells.In these simulated CSROs,however,the structural image is missing on the atomic scale,even though the lattice periodicity does not exist in the CSROs.Further,it is pending as to the issues if and what kind of CSRO may be formed in a specific H/MEA.All these are ascribed to the challenge of experimentally seeing the CSROs.Until recently,the breakthrough does not appear to convincingly identify the CSROs in the H/MEAs by using the state-of-the-art transmission electron microscope.To be specific,the electron diffractions provide solid evidence to doubtlessly ascertain CSROs.The structure motif of CSROs is then constructed,showing both the lattice structure and species ordering occupation,along with the stereoscopic topography of the CSRO.It is suggested that the CSROs,as the first landscape along the path of development of the local chemical ordering,offer one more route to substantially develop the ordered structure on the atomic scale in the H/MEAs,parallel to the existing grain-leveled microstructure.The findings of CSROs make a step forward to understand the CSROs-oriented relationship between the microstructure and mechanical properties.This review focuses on the recent progress mainly in the experimental aspects of the identification,structure motif,and mechanical stability in CSROs,along with the chemical medium-range orders as the growing CSROs。

Microstructure Evolution and Tensile Properties of the Alx(CoCrNi)100-x Medium-Entropy Alloys

A series of Alx(CoCrNi)100-x(x=0-21 at.%)medium-entropy alloys(MEAs)were designed and prepared to investigate the effects of Al addition on the microstructures and tensile properties.The results reveal that the lattice structure changes from the initial single FCC structure(x<10 at.%),to the FCC and disordered BCC structures(x=10 and 11 at.%),then to the FCC and BCC/B2 structures(11<x<21 at.%),finally to the duplex BCC/B2 structures(x≥21 at.%)with increasing Al addition.Consistent with microstructures,significant changes also occur in the corresponding tensile properties with Al addition,showing that the strength increases and the ductility decreases with increasing Al addition.Especially,the Al-15 MEA exhibits an acceptable balance of strength and ductility.Furthermore,the mechanism of microstructure evolution and the correlation between microstructures and tensile properties were also discussed and clarified.

Effect of hafnium and molybdenum addition on inclusion characteristics in Co-based dual-phase high-entropy alloys

Specific grades of high-entropy alloys(HEAs)can provide opportunities for optimizing properties toward high-temperature applications.In this work,the Co-based HEA with a chemical composition of Co_(47.5)Cr_(30)Fe_(7.5)Mn_(7.5)Ni_(7.5)(at%)was chosen.The refractory metallic elements hafnium(Hf)and molybdenum(Mo)were added in small amounts(1.5at%)because of their well-known positive effects on high-temperature properties.Inclusion characteristics were comprehensively explored by using a two-dimensional cross-sectional method and extracted by using a three-dimensional electrolytic extraction method.The results revealed that the addition of Hf can reduce Al_(2)O_(3)inclusions and lead to the formation of more stable Hf-rich inclusions as the main phase.Mo addition cannot influence the inclusion type but could influence the inclusion characteristics by affecting the physical parameters of the HEA melt.The calculated coagulation coefficient and collision rate of Al_(2)O_(3)inclusions were higher than those of HfO_(2)inclusions,but the inclusion amount played a larger role in the agglomeration behavior of HfO_(2)and Al_(2)O_(3)inclusions.The impurity level and active elements in HEAs were the crucial factors affecting inclusion formation.

Microstructure and mechanical properties stability of pre-hardening treatment in Al-Cu alloys for pre-hardening forming process

The stability of the microstructure and mechanical properties of the pre-hardened sheets during the pre-hardening forming(PHF)process directly determines the quality of the formed components.The microstructure stability of the pre-hardened sheets was in-vestigated by differential scanning calorimetry(DSC),transmission electron microscopy(TEM),and small angle X-ray scattering(SAXS),while the mechanical properties and formability were analyzed through uniaxial tensile tests and formability tests.The results in-dicate that the mechanical properties of the pre-hardened alloys exhibited negligible changes after experiencing 1-month natural aging(NA).The deviations of ultimate tensile strength(UTS),yield strength(YS),and sheet formability(Erichsen value)are all less than 2%.Also,after different NA time(from 48 h to 1 month)is applied to alloys before pre-hardening treatment,the pre-hardened alloys possess stable microstructure and mechanical properties as well.Interestingly,with the extension of NA time before pre-hardening treatment from 48 h to 1 month,the contribution of NA to the pre-hardening treatment is limited.Only a yield strength increment of 20 MPa is achieved,with no loss in elongation.The limited enhancement is mainly attributed to the fact that only a limited number of clusters are transformed into Guinier-Preston(GP)zones at the early stage of pre-hardening treatment,and the formation ofθ''phase inhibits the nucleation and growth of GP zones as the precipitated phase evolves.

Relationship between the unique microstructures and behaviors of high-entropy alloys

High-entropy alloys(HEAs),which were introduced as a pioneering concept in 2004,have captured the keen interest of nu-merous researchers.Entropy,in this context,can be perceived as representing disorder and randomness.By contrast,elemental composi-tions within alloy systems occupy specific structural sites in space,a concept referred to as structure.In accordance with Shannon entropy,structure is analogous to information.Generally,the arrangement of atoms within a material,termed its structure,plays a pivotal role in dictating its properties.In addition to expanding the array of options for alloy composites,HEAs afford ample opportunities for diverse structural designs.The profound influence of distinct structural features on the exceptional behaviors of alloys is underscored by numer-ous examples.These features include remarkably high fracture strength with excellent ductility,antiballistic capability,exceptional radi-ation resistance,and corrosion resistance.In this paper,we delve into various unique material structures and properties while elucidating the intricate relationship between structure and performance.

Accelerated design of high-performance Mg-Mn-based magnesium alloys based on novel bayesian optimization

Magnesium(Mg),being the lightest structural metal,holds immense potential for widespread applications in various fields.The development of high-performance and cost-effective Mg alloys is crucial to further advancing their commercial utilization.With the rapid advancement of machine learning(ML)technology in recent years,the“data-driven''approach for alloy design has provided new perspectives and opportunities for enhancing the performance of Mg alloys.This paper introduces a novel regression-based Bayesian optimization active learning model(RBOALM)for the development of high-performance Mg-Mn-based wrought alloys.RBOALM employs active learning to automatically explore optimal alloy compositions and process parameters within predefined ranges,facilitating the discovery of superior alloy combinations.This model further integrates pre-established regression models as surrogate functions in Bayesian optimization,significantly enhancing the precision of the design process.Leveraging RBOALM,several new high-performance alloys have been successfully designed and prepared.Notably,after mechanical property testing of the designed alloys,the Mg-2.1Zn-2.0Mn-0.5Sn-0.1Ca alloy demonstrates exceptional mechanical properties,including an ultimate tensile strength of 406 MPa,a yield strength of 287 MPa,and a 23%fracture elongation.Furthermore,the Mg-2.7Mn-0.5Al-0.1Ca alloy exhibits an ultimate tensile strength of 211 MPa,coupled with a remarkable 41%fracture elongation.

Microstructure and damping properties of LPSO phase dominant Mg-Ni-Y and Mg-Zn-Ni-Y alloys

This work studied the microstructure,mechanical properties and damping properties of Mg_(95.34)Ni_(2)Y_(2.66) and Mg_(95.34)Zn_(1)Ni_(1)Y_(2.66)alloys systematically.The difference in the evolution of the long-period stacked ordered(LPSO)phase in the two alloys during heat treatment was the focus.The morphology of the as-cast Mg_(95.34)Ni_(2)Y_(2.66)presented a disordered network.After heat treatment at 773 K for 2 hours,the eutectic phase was integrated into the matrix,and the LPSO phase maintained the 18R structure.As Zn partially replaced Ni,the crystal grains became rounded in the cast alloy,and lamellar LPSO phases and more solid solution atoms were contained in the matrix after heat treatment of the Mg_(95.34)Zn_(1)Ni_(1)Y_(2.66)alloy.Both Zn and the heat treatment had a significant effect on damping.Obvious dislocation internal friction peaks and grain boundary internal friction peaks were found after temperature-dependent damping of the Mg_(95.34)Ni_(2)Y_(2.66)and Mg_(95.34)Zn_(1)Ni_(1)Y_(2.66)alloys.After heat treatment,the dislocation peak was significantly increased,especially in the alloy Mg_(95.34)Ni_(2)Y_(2).66.The annealed Mg_(95.34)Ni_(2)Y_(2.66)alloy with a rod-shaped LPSO phase exhibited a good damping performance of 0.14 atε=10^(−3),which was due to the difference between the second phase and solid solution atom content.These factors also affected the dynamic modulus of the alloy.The results of this study will help in further development of high-damping magnesium alloys.

High-entropy alloys in thermoelectric application:A selective review

Since the superior mechanical,chemical and physical properties of high-entropy alloys(HEAs)were discovered,they have gradually become new emerging candidates for renewable energy applications.This review presents the novel applications of HEAs in thermoelectric energy conversion.Firstly,the basic concepts and structural properties of HEAs are introduced.Then,we discuss a number of promising thermoelectric materials based on HEAs.Finally,the conclusion and outlook are presented.This article presents an advanced understanding of the thermoelectric properties of HEAs,which provides new opportunities for promoting their applications in renewable energy.

Enhancing the mechanical properties of casting eutectic high -entropy alloys via W addition

The effect of W element on the microstructure evolution and mechanical properties of Al_(1.25)CoCrFeNi3 eutectic high-entropy alloy and Al_(1.25)CoCrFeNi_(3-x)W_(x)(x=0,0.05,0.1,0.3,and 0.5;atomic ratio)high-entropy alloys(HEAs)were explored.Results show that the Al_(1.25)CoCrFeNi_(3-x)W_(x) HEAs are composed of face-centered cubic and body-centered cubic(BCC)phases.As W content increases,the microstructure changes from eutectic to dendritic.The addition of W lowers the nucleation barrier of the BCC phase,decreases the valence electron concentration of the HEAs,and replaces Al in the BCC phase,thus facilitating the nucleation of the BCC phase.Tensile results show that the addition of W greatly improves the mechanical properties,and solid-solution,heterogeneous-interface,and second-phase strengthening are the main strengthening mechanisms.The yield strength,tensile strength,and elongation of the Al_(1.25)CoCrFeNi2.95W0.05 HEA are 601.44 MPa,1132.26 MPa,and 15.94%,respectively,realizing a balance between strength and plasti-city.The fracture mode of the Al_(1.25)CoCrFeNi_(3-x)W_(x) HEAs is ductile–brittle mixed fracture,and the crack propagates and initiates in the BCC phase.The eutectic lamellar structure impedes crack propagation and maintains plasticity.

Enhanced superelasticity and reversible elastocaloric effect in nano-grained NiTi alloys with low stress hysteresis

Solid-state cooling technologies have been considered as potential alternatives for vapor compression cooling systems.The search for refrigeration materials displaying a unique combination of pronounced caloric effect,low hysteresis,and high reversibility on phase transformation was very active in recent years.Here,we achieved increase in the elastocaloric reversibility and decrease in the friction dissipation of martensite transformations in the superelastic nano-grained NiTi alloys obtained by cold rolling and annealing treatment,with very low stress hysteresis(6.3 MPa)under a large applied strain(5%).Large adiabatic temperature changes(△T_(max)=16.3 K atε=5%)and moderate COP_(mater)values(maximum COP_(mater)=11.8 atε=2%)were achieved.The present nano-grained NiTi alloys exhibited great potential for applications as a highly efficient elastocaloric material.

Microstructures and Properties of Biomedical Mg-Zn-Sn-Zr Rolled Alloys

The as-cast Mg-2.0Zn-1.5Sn-xZr(x=0,0.4,0.6,0.8,1.0 wt%)alloy was rolled with the pressure less than 5%each time.The microstructure,mechanical properties,corrosion properties and biocompatibility of the alloy were investigated.The microstructure of the alloy was observed and analyzed by scanning electron microscope,and the tensile test was carried out by universal tensile machine.The corrosion resistance of the alloy in Hank's solution was studied by hydrogen evolution experiment and electrochemical test,and the biocompatibility of the alloy was tested by L929 cells.The results show that Mg-2Zn-1.5Sn-xZr alloy has excellent mechanical properties.The elongation of Mg-2Zn-1.5Sn-xZr alloy decreases with the increase of Zr content,but the tensile strength first increases and then decreases with the increase of Zr concentration.When the Zr content is 0.8 wt%,the maximum tensile strength of the alloy is 235 MPa.The results of hydrogen evolution experiment and electrochemical analysis show that the corrosion resistance of the alloy is the best when the Zr content is 0.8 wt%,and all the five alloys have high biocompatibility.In conclusion,the rolled alloy has good properties and has broad application prospects in the field of biomaterials.

Microstructures,corrosion behavior and mechanical properties of as-cast Mg-6Zn-2X(Fe/Cu/Ni)alloys for plugging tool applications

Mg-6Zn-2X(Fe/Cu/Ni)alloys were prepared through semi-continuous casting,with the aim of identifying a degradable magnesium(Mg)alloy suitable for use in fracturing balls.A comparative analysis was conducted to assess the impacts of adding Cu and Ni,which result in finer grains and the formation of galvanic corrosion sites.Scanner electronic microscopy examination revealed that precipitated phases concentrated at grain boundaries,forming a semi-continuous network structure that facilitated corrosion penetration in Mg-6Zn-2Cu and Mg-6Zn-2Ni alloys.Pitting corrosion was observed in Mg-6Zn-2Fe,while galvanic corrosion was identified as the primary mechanism in Mg-6Zn-2Cu and Mg-6Zn-2Ni alloys.Among the tests,the Mg-6Zn-2Ni alloy exhibited the highest corrosion rate(approximately 932.9 mm/a)due to its significant potential difference.Mechanical testing showed that Mg-6Zn-2Ni alloy possessed suitable ultimate compressive strength,making it a potential candidate material for degradable fracturing balls,effectively addressing the challenges of balancing strength and degradation rate in fracturing applications.

Predict the evolution of mechanical property of Al-Li alloys in a marine environment

The ocean is one of the essential fields of national defense in the future,and more and more attention is paid to the lightweight research of Marine equipment and materials.This study it is to develop a Machine learning(ML)-based prediction method to study the evolution of the mechanical properties of Al-Li alloys in the marine environment.We obtained the mechanical properties of Al-Li alloy samples under uniaxial tensile deformation at different exposure times through Marine exposure experiments.We obtained the strain evolution by digital image correlation(DIC).The strain field images are voxelized using 2D-Convolutional Neural Networks(CNN)autoencoders as input data for Long Short-Term Memory(LSTM)neural networks.Then,the output data of LSTM neural networks combined with corrosion features were input into the Back Propagation(BP)neural network to predict the mechanical properties of Al-Li alloys.The main conclusions are as follows:1.The variation law of mechanical properties of2297-T8 in the Marine atmosphere is revealed.With the increase in outdoor exposure test time,the tensile elastic model of 2297-T8 changes slowly,within 10%,and the tensile yield stress changes significantly,with a maximum attenuation of 23.6%.2.The prediction model can predict the strain evolution and mechanical response simultaneously with an error of less than 5%.3.This study shows that a CNN/LSTM system based on machine learning can be built to capture the corrosion characteristics of Marine exposure experiments.The results show that the relationship between corrosion characteristics and mechanical response can be predicted without considering the microstructure evolution of metal materials.

Investigation of Microstructure, Microhardness and Thermal Properties of Ag-In Intermetallic Alloys Prepared by Vacuum Arc Meltings

Ag-In intermetallic alloys were produced by using vacuum arc furnace. Differential Scanning Calorimetry(DSC) and Energy Dispersive X-Ray Spectrometry(EDX) were used to determine the thermal properties and chemical composition of the phases respectively. Microhardness values of Ag-In intermetallics were calculated with Vickers hardness measurement method. According to the experimental results, Ag-34 wt%In intermetallic system generated the best results of energy saving and storage compared to other intermetallic systems. Also from the microhardness results, it was observed that intermetallic alloys were harder than pure silver and Ag-26 wt%In system had the highest microhardness value with 143.45 kg/mm^(2).

Effect of characteristics and distribution of Mg_(17)Al_(12)precipitates on tensile and bending properties of high-Al-containing Mg alloys

This study investigates the effect of characteristics and distribution of Mg_(17)Al_(12)precipitates on the uniaxial tensile and three-point bending properties of extruded Mg alloys containing high Al contents.The extruded Mg–9Al–1Zn–0.3Mn(AZ91)alloy contains lamellar-structured Mg_(17)Al_(12)discontinuous precipitates along the grain boundaries,which are formed via static precipitation during natural air cooling.The extruded Mg–11Al–1Zn–0.3Mn(AZ111)alloy contains spherical Mg_(17)Al_(12)precipitates at the grain boundaries and inside the grains,which are formed via dynamic precipitation during extrusion.Due to inhomogeneous distribution of precipitates,the AZ111 alloy consists of two different precipitate regions:precipitate-rich region with numerous precipitates and finer grains and precipitate-scarce region with a few precipitates and coarser grains.The AZ111 alloy exhibits a higher tensile strength than the AZ91 alloy because its smaller grain size and more abundant precipitates result in stronger grain-boundary hardening and precipitation hardening effects,respectively.However,the tensile elongation of the AZ111 alloy is lower than that of the AZ91 alloy because the weak cohesion between the dynamic precipitates and the matrix facilitates the crack initiation and propagation.During bending,a macrocrack initiates on the outer surface of bending specimen in both alloys.The AZ111 alloy exhibits higher bending yield strength and lower failure bending strain than the AZ91 alloy.The bending specimens of the AZ91 alloy have similar bending formability,whereas those of the AZ111 alloy exhibit considerable differences in bending formability and crack propagation behavior,depending on the distribution and number density of precipitates in the specimen.In bending specimens of the AZ111 alloy,it is found that the failure bending strain(ε_(f,bending))is inversely proportional to the area fraction of precipitates in the outer zone of bending specimen(A_(ppt)),with a relationship ofε_(f,bending)=–0.1A_(ppt)+5.86.