Quantifying Solid Solution Strengthening in Nickel-Based Superalloys via High-Throughput Experiment and Machine Learning

Solid solution strengthening(SSS)is one of the main contributions to the desired tensile properties of nickel-based superalloys for turbine blades and disks.The value of SSS can be calculated by using Fleischer’s and Labusch’s theories,while the model parameters are incorporated without fitting to experimental data of complex alloys.In thiswork,four diffusionmultiples consisting of multicomponent alloys and pure Niare prepared and characterized.The composition and microhardness of singleγphase regions in samples are used to quantify the SSS.Then,Fleischer’s and Labusch’s theories are examined based on high-throughput experiments,respectively.The fitted solid solution coefficients are obtained based on Labusch’s theory and experimental data,indicating higher accuracy.Furthermore,six machine learning algorithms are established,providing a more accurate prediction compared with traditional physical models and fitted physical models.The results show that the coupling of highthroughput experiments and machine learning has great potential in the field of performance prediction and alloy design.

Design of low-alloying and high-performance solid solution-strengthened copper alloys with element substitution for sustainable development

Solid solution-strengthened copper alloys have the advantages of a simple composition and manufacturing process,high mechanical and electrical comprehensive performances,and low cost;thus,they are widely used in high-speed rail contact wires,electronic component connectors,and other devices.Overcoming the contradiction between low alloying and high performance is an important challenge in the development of solid solution-strengthened copper alloys.Taking the typical solid solution-strengthened alloy Cu-4Zn-1Sn as the research object,we proposed using the element In to replace Zn and Sn to achieve low alloying in this work.Two new alloys,Cu-1.5Zn-1Sn-0.4In and Cu-1.5Zn-0.9Sn-0.6In,were designed and prepared.The total weight percentage content of alloying elements decreased by 43%and 41%,respectively,while the product of ultimate tensile strength(UTS)and electrical conductivity(EC)of the annealed state increased by 14%and 15%.After cold rolling with a 90%reduction,the UTS of the two new alloys reached 576 and 627MPa,respectively,the EC was 44.9%IACS and 42.0%IACS,and the product of UTS and EC(UTS×EC)was 97%and 99%higher than that of the annealed state alloy.The dislocations proliferated greatly in cold-rolled alloys,and the strengthening effects of dislocations reached 332 and 356 MPa,respectively,which is the main reason for the considerable improvement in mechanical properties.

Origin of strong solid solution strengthening in the CrCoNi-W medium entropy alloy

Solid solution strengthening is one of the most conventional strategies for optimizing alloys strength,while the corresponding mechanisms can be more complicated than we traditionally thought specifically as heterogeneity of microstructure is involved.In this work,by comparing the change of chemical distribution,dislocation behaviors and mechanical properties after doping equivalent amount of tungsten(W)atoms in CrCoNi alloy and pure Ni,respectively,it is found that the alloying element W in CrCoNi alloy resulted in much stronger strengthening effect due to the significant increase of heterogeneity in chemical distribution after doping trace amount of W.The large atomic scale concentration fluctuation of all elements in CrCoNi-3W causes dislocation motion via strong nanoscale segment detrapping and severe dislocation pile up which is not the case in Ni-3W.The results revealed the high sensitivity of elements distribution in multi-principle element alloys to composition and the significant consequent influence in tuning the mechanical properties,giving insight for complex alloy design.

Tailoring grain growth and solid solution strengthening of single-phase CrCoNi medium-entropy alloys by solute selection

In the present study,we selected solutes to be added to the Cr Co Ni medium-entropy alloy(MEA)based on the mismatch of self-diffusion activation energy(SDQ)between the alloying elements and constituent elements of the matrix,and then investigated their grain growth behavior and mechanical properties.Mo and Al were selected as the solutes for investigation primarily because they have higher and lower SDQ,respectively,than those of the matrix elements;a secondary factor was their higher and lower shear modulus.Their concentrations were fixed at 3 at.%each because previous work had shown these compositions to be single-phase solid solutions with the face-centered cubic structure.Three alloys were produced by arc melting,casting,homogenizing,cold rolling and annealing at various temperatures and times to produce samples with different grain sizes.They were(a)the base alloy Cr Co Ni,(b)the base alloy plus 3 at.%Mo,and(c)the base alloy plus 3 at.%Al.The activation energies for grain growth of the Cr Co Ni,Cr Co Ni-3Mo and CrCo Ni-3Al MEAs were found to be^251,~368 and^219 k J/mol,respectively,consistent with the notion that elements with higher SDQ(in this study Mo)retard grain growth(likely by a solute-drag effect),whereas those with lower values(Al)accelerate grain growth.The roomtemperature tensile properties show that Mo increases the yield strength by^40%but Al addition has a smaller strengthening effect consistent with their relative shear moduli.The yield strength as a function of grain size for the three single-phase MEAs follows the classical Hall-Petch relationship with much higher slopes(>600 MPaμm-0.5)than traditional solid solutions.This work shows that the grain growth kinetics and solid solution strengthening of the Cr Co Ni MEA can be tuned by selecting solute elements that have appropriate diffusion and physical properties.

Effect of lattice distortion on solid solution strengthening of BCC high-entropy alloys

An analytical model is established to study the influence of lattice distortion and fraction of Hf on the yield strength of the BCC TiNbTaZrHfx multi-component high entropy alloys （HEAs）. Meanwhile, the mechanism of solid solution strengthening caused by lattice distortion is also discussed in the HEA. The distorted unit cell is introduced to indicate the lattice distortion effects induced by the differences of the atomic size and shear modulus by doping other elements in Ti-based metal. The results show that the calculated values of the alloying yield strength considering the path of least resistance are obtained with regard to various grain sizes for the equiatomic TiNbTaZrHf HEA, which is well in line with the experimental results. Furthermore, it is predicted that the alloying yield strength is the largest value in the case of the same grain size for the Hf atomic fraction of 0.122. The meaningful modeling could provide a theoretical method to investigate the yield strength and alloying design of other BCC HEAs in the future.

Solid solution strengthening of high-entropy alloys from first-principles study

Solid solution strengthening(SSS)is one kind of strengthening mechanisms and plays an important role in alloy design,in particular for single-phase alloys including high-entropy alloys(HEAs).The classical Labusch–Nabarro model and its expansions are most widely applicable to treating SSS of solid solution alloys including both conventional alloys(CAs)and HEAs.In this study,the SSS effects in a series of Febased CAs and HEAs are investigated by using the classical Labusch–Nabarro model and its expansions.The size misfit and shear modulus misfit parameters are derived from first-principles calculations.Based on available experimental data in combination with empirical SSS model,we propose fitting constants(i.e.,the ratio between experimental hardness and predicted SSS effect)for these two families of alloys.The predicted host/alloy family-dependent fitting constants can be used to estimate the hardness of these SSS alloys.General agreement between predicted and measured hardness values is satisfactory for both CAs and HEAs,implying that the proposed approach is reliable and successful.

Ultrafine Grain Tungsten Heavy Alloys with Excellent Performance Prepared by Spark Plasma Sintering

Ultrafine grain tungsten heavy alloys (WHAs) were successfully produced from the nano-crystalline powders using spark plasma sintering.The present study mainly discussed the effects of sintering temperature on the density,microstructure and mechanical properties of the alloys.The relative density of 98.12% was obtained at 1 050 ℃,and the tungsten grain size is about 871 nm.At 1 000 ℃-1 200 ℃,the mechanical properties of the alloys tend to first rise and then goes down.After SPS,the alloy exhibits improved hardness (84.3 HRA at 1 050 ℃) and bending strength (987.16 MPa at 1 100 ℃),due to the ultrafine-grained microstructure.The fracture mode after bending tests is mainly characterized as intergranular or intragranular fracture of W grains,interfacial debonding of W grains-binding phase and ductile tearing of binding phase.The EDS analysis reveals a certain proportion of solid solution between W and Ni-Fe binding phase.The good mechanical properties of the alloys can be attributed to grain refinement and solid solution strengthening.

Distribution,evolution and the effects of rare earths Ce and Y on the mechanical properties of ZK60 alloys

Eight kinds of Mg-RE alloys were prepared. The distribution, evolution, and effects of RE Ce and Y in the investigated alloys were studied by examining the mechanical properties of Mg alloys using X-ray diffraction and scan electron analysis, and by TEM observation. The results show that among the investigated alloys, ZK60-1.5%Ce and ZK60-1.0%Y possessed the optimal mechanical properties. Ce and Y were distributed on the grain boundary during casting. After extrusion and T5 （150℃/0-24 h） heattreatment, Ce and Y were distributed along the extrusion direction and they existed in compound form for both as-casting and asextrusion specimens. The mechanical properties of the investigated alloys were better than those of ZK60 because of the solid solution strengthening of RE and the dispersion strengthening of Mg-RE or Mg-Zn-RE compounds.

Strengthening in Al-,Mo-or Ti-doped CoCrFeNi high entropy alloys:A parallel comparison

In the current work,a parallel comparison of the influence of Al,Mo and Ti,on the microstructure and strengthening of the CoCrFeNi alloy was conducted.To achieve this,inconsistencies on variables including the extent of alloying,thermomechanical processing and property-evaluation method were avoided.Microstructurally,following cold-rolling,annealing of the 4 at.%Al-doped alloys at 800-1000℃ did not result in phase separation;nevertheless,that of the 4 at.%Mo-and Ti-doped alloys led to the respective formation ofσandηphase and,consequently,caused extra strengthening through the Orowan dislocation bypassing mechanism.Our systematic qualitative analysis and DFT calculations showed that Al and Ti are more effective than Mo in reducing the stacking fault energy(SFE)of the CoCrFeNi alloy,because they can induce more considerable deformation of electronic density,making the gliding of atomic layers easier.Following identical thermomechnical processing,Al-,Mo-,and Ti-doping causes different extent of solid solution strengthening and grain boundary strengthening.Mo causes the most pronounced solid solution strengthening but does not benefit the grain boundary strengthening;in contrast,the effectiveness of grain boundary strengthening is boosted by the doping Al and Ti.Current analyses support that Labusch instead of Fleischer mechanism is applicable to explain the differences in solid solution strengthening,and the observed differences in grain boundary strengthening arise from the different tendency of Al,Mo and Ti to reduce the SFE of CoCrFeNi.In addition,we determined the value of the dimensionless parameter f in the Labusch model for CoCrFeNi-based alloys and observed a close relation between Hall-Petch slope and SFE.Although more in-depth studies are needed to provide full and mechanistic understandings,both these findings in fact presents significant values toward designing novel singlephase high-strength CoCrFeNi-based alloys through manipulating the solid solution and grain boundary strengthening by compositional tuning.

Elaborating strengthen mechanism of Pt-Ir solid solution superalloy at finite temperature

Pt-Ir alloy is potential superalloys used above 1300℃because of their high strength and creep resistance.However,the ductility of Pt-Ir alloy has rapidly deteriorated with the increase of Ir,resulting in poor machinability.This work quantitatively evaluated the solid solution strengthening(SSS)and grain refinement strengthening(GRS)of Pt-Ir alloy using first-principles calculations combined with experimental characterization.Here,the stretching force constants in the second nearest neighbor region(SFC^(2nd))of pure Ir(193.7 eV·nm^(-2))are 3.40 times that of pure Pt(57.0 eV·nm^(-2)),i.e.,the interatomic interaction is greatly enhanced with the increase of Ir content,which leads to the decrease of ductility,and modulus misfit plays a dominant role in SSS.Then,the physical mechanisms responsible for the hardness(H_(V))of Pt-Ir alloy,using the power-law-scaled function of electron work function coupled SSS and GRS,are attributed to the electron redistribution caused by different Ir content.Furthermore,a thorough assessment of the thermodynamic characteristics of Pt-Ir binary alloy was conducted,culminating in development of a mapping model that effectively relates enmposition,temperature and strength.The results revealed that the compressive strength incrcases with the Ir content,and the highest strength was observed in Pt_(0.25)Ir_(0.75).This study provides valuable insights into the Pt-Ir alloy system.

Ultra-high strength Mg-Li alloy with B2 particles and spinodal decomposition zones

The bcc-structured Mg-Li alloy is currently the engineering metallic material with the lowest density,but it has not been widely used due to its low strength.In this paper,alloying Zn effectively improves the strength of the bcc-structured Mg-Li alloy.Due to the semi-coherent B2 structured nanoparticles,the compressive yield strength of the as-cast Mg-13Li-9Zn alloy reaches higher than 300 MPa.Due to the solid solution strengthening of Zn and the spinodal zone,the compressive yield strength of the as-quenched Mg-13Li-15Zn(LZ1315)alloy immediately increases to 400 MPa.In addition,the as-quenched LZ1315 alloy exhibits natural aging strengthening behavior.Due to the precipitation of B2 nanoparticles,the yield strength of the peak aged alloy is up to 495 MPa.

A revisit to the role of Mo in an MP35N superalloy:An experimental and theoretical study

Molybdenum(Mo)has been recognized as an essential alloying element of the MP35N(Co_(35.4)Cr_(22.9)Ni_(35.5)Mo_(6.2),at.%)superalloy for enhancing strength and corrosion resistance.However,a full understanding of the addition of Mo on microstructure and mechanical properties of the Mo-free parent alloy is lacking.In this work,we consider five(Co_(37.7)Cr_(24.4)Ni_(37.9))_(100-x)Mo_(x)(x=0,0.7,2.0,3.2,and 6.2)alloys,and reveal that yield/tensile strength and ductility are continuously increased for these alloys with increasing Mo content while a single-phase face-centered cubic structure remains unchanged.It is found that strong solid solution strengthening(SSS)is a main domain to the improved yield strength,whereas grain boundaries are found to soften by the Mo addition.The first-principles calculations demonstrate that a severe local lattice distortion contributes to the enhanced SSS,and the grain boundary softening effect is mostly associated with the decreased shear modulus.Both first-principles calculations and scanning transmission electron microscopy observations reveal that the stacking fault energy(SFE)reduces by the Mo addition.The calculated SFE value decreases from 0.4 mJ/m^(2) to-11.8 mJ/m^(2) at 0 K as Mo content increases from 0 at.%to 6.2 at.%,and experimentally measured values of SFE at room temperature for both samples are about 18 mJ/m^(2) and 9 mJ/m^(2),respectively.The reduction of SFE promoted the generation of stacking faults and deformation twins,which sustain a high strain hardening rate,thus postponing necking instability and enhancing tensile strength and elongation.

Effects of V Addition on Microstructural Evolution and Mechanical Properties of AlCrFe_(2)Ni_(2) High‑Entropy Alloys

The effects of vanadium addition on the microstructural evolution and mechanical properties of AlCrFe_(2)Ni_(2) high-entropy alloy(HEA)were investigated.The results showed that the AlCrFe_(2)Ni_(2)V_(0.2) HEA was composed of FCC phase,disordered BCC phase,and ordered BCC(B2)phase.With the increase in vanadium content,the formation of FCC phase was inhibited,and a transition from FCC phase to BCC phase occurred.The FCC phase disappeared completely when the value of x exceeds 0.4 in AlCrFe_(2)Ni_(2)V_(x) HEAs.Besides,the amplitude-modulated microstructure morphology transformed from a B2 phase matrix with dispersed BCC nano-phase into an alternating interconnected B2 and BCC phases.Vanadium element has the function of stabilizing BCC phase and B2 phase in AlCrFe_(2)Ni_(2)V_(x) alloys.The hardness of AlCrFe_(2)Ni_(2)V_(x) alloys increased from HV 332.4 to HV 590.7,while the yield strength increased from 765 to 1744.6 MPa with increasing vanadium content,which was mainly due to the decreasing content of FCC phase and the solid solution strengthening of vanadium element.At the same time,the compression ratio of the alloys decreased with the disappearance of the FCC phase.Among the alloys,the AlCrFe_(2)Ni_(2)V_(0.2) alloy possessed the most excellent comprehensive mechanical properties with yield strength,fracture strength,and compressive ratio 1231.1,2861.9 MPa,and 44.5%,respectively.

The intrinsic strength prediction by machine learning for refractory high entropy alloys

Herein,we trained machine learning(ML)model to quickly and accurately conduct the strength prediction of refractory high entropy alloys(RHEAs)matrix.Gradient Boosting(GB)regression model shows an outstanding performance against other ML models.In addition,the heat of fusion and atomic size difference is shown to be paramount to the strength of the high entropy alloys(HEAs)matrix.In addition,we discussed the contribution of each feature to the solid solution strengthening(SSS)of HE As.The excellent predictive accuracy shows that the GB model can be efficient and reliable for the design of RHEAs with desired strength.

A novel HfNbTaTiV high-entropy alloy of superior mechanical properties designed on the principle of maximum lattice distortion

This paper reports a synergistic design of high-performance BCC high-entropy alloy based on the combined consideration of the principles of intrinsic ductility of elements,maximum atomic size difference for solid solution strengthening and the valence electron concentration criterion for ductility.The single-phase BCC HfNbTaTiV alloy thus designed exhibited a high compressive yield strength of 1350 MPa and a high compressive ductility of>45%at the room temperature.This represents a 50%increase in yield strength relative to a HfNbTaTiZr alloy.This is attributed to the maximized solid solution strengthening effect caused by lattice distortion,which is estimated to be 1094 MPa.The alloy was also able to retain 53%of its yield strength and 77%of its ductility at 700℃.These properties are superior to those of most refractory BCC high-entropy alloys reported in the literature.

A novel non-stoichiometric medium-entropy carbide stabilized by anion vacancies

Recently,high-entropy ceramics have attracted considerable attentions because of comprehensive physical and chemical properties of high hardness,fracture toughness,and conductivity.However,as a newly emerging class of materials,the synthesis,performance and applications of high-entropy ceramics are subject to further development.Here,we reported a new non-stoichiometric TiC0.4/WC/0.5Mo2C medium-entropy carbide(MEC)with a rock-salt structure.Attributed to the solid solution strengthening and twinning strengthening,the TiCO0.4/WC/0.5Mo2C sintered at 1900℃by spark plasma sintering(SPS)shows superior mechanical behaviors of microhardness(21.7 GPa),which exceeds that expected from the rule of mixture(ROM)of three individual metal carbides(19.1 GPa)and good fracture toughness(5.3 MPa m1/2).Significantly,the bulk synthesized via high-pressure and high-temperature(HPHT)sintering possesses smaller grain size and shows better comprehensive mechanical properties of microhardness(23.7 GPa)and fracture toughness(6.2 MPa m1/2).In addition,the effect of anion vacancies on the thermodynamic stability and synthesizability of TiC0.4/WC/0.5Mo2C was analyzed via quantitatively calculated entropy.Vacancies could significantly enhance the configuratio nal entropy of mixing of the solid phase.The introduction of vacancy defects may expand synthetic path for entropy-stabilized ceramics,especially for multi-component high tempe rature refractory ceramics.

Charting the ‘composition–strength’ space for novel austenitic,martensitic and ferritic creep resistant steels

We report results of a large computational ＇alloy by design＇ study, in which the ＇chemical composition-mechanical strength＇ space is explored for austenitic, ferritic and martensitic creep resistant steels. The approach used allows simultaneously optimization of alloy composition and processing parameters based on the integration of thermodynamic, thermo-kinetics and a genetic algorithm optimization route. The nature of the optimisation depends on both the intended matrix（ferritic, martensitic or austenitic） and the desired precipitation family. The models are validated by analysing reported strengths of existing steels. All newly designed alloys are predicted to outperform existing high end reference grades.

Theoretical analysis for self-sharpening penetration of tungsten high-entropy alloy into steel target with elevated impact velocities

The“self-sharpening”effect has been observed experimentally in the penetration of tungsten high-entropy alloy(WHEA)into steel targets in previous study.From the microscopic observation of the residual WHEA long-rod projectile(LRP),the multiphase structure at micro-scale of WHEA is the key effects on self-sharpening penetration process.In order to describe the distinctive penetration behavior,the interaction between micro phases is introduced to modify the hydrodynamic penetration model.The yield strengths of WHEA phases are determined based on the solid solution strengthening methods.Combined with the elbow-streamline model,the self-sharpening mechanism is revealed in view of the multi-phase flow dynamics and the flow field in the deformation area of the LRP nose is characterized to depict the shear layer evolution and the shape of the LRP’s nose as well as the determination of the penetration channel.The self-sharpening coefficient considering the reduction of nose radius is proposed and introduced into the penetration model to calculate the depth of penetration and the penetration channel.Results show that the multi-phase interaction at the microscopic level contributes to the inhomogeneous distribution of the WHEA phases.The shear layer evolution separates part of the LRP material from the nose and makes the nose radius decrease more quickly.It is also the reason that WHEA LRPs have a pointed nose compared with the mushroom nose of WHA heavy alloy(WHA)LRPs.The calculated results agree well with the corresponding experimental data of WHA and WHEA LRPs penetrating into semi-infinite medium carbon steel targets with elevated impact velocities.