Plastic Deformation of Al
Plastic Deformation of Al 0.3CoCrFeNi and AlCoCrFeNi
High-Entropy Alloys Under Nanoindentation
Zhi-Ming Jiao,Sheng-Guo Ma,Guo-Zheng Yuan,Zhi-Hua Wang,Hui-Jun Yang,and Jun-Wei Qiao (Submitted January 24,2015;in revised form June 4,2015;published online June 23,2015)
The mechanical properties of Al 0.3CoCrFeNi and AlCoCrFeNi high-entropy alloys (HEAs)were investi-gated by instrumented nanoindentation over a broad range of loading rates.It was found that the loading portion of the two HEAs exhibited apparent discontinuities at low loading rates.However,the discontinuity became less pronounced with increasing the loading rate.The experimental results that the hardness,elastic modulus,and yield strength of AlCoCrFeNi HEAs are larger than those of Al 0.3CoCrFeNi HEAs can be elucidated in terms of thermodynamic and topological parameters of the constituent elements and solid solution strengthening,respectively.In situ scanning images displayed a signi?cant pile-up around the indents,demonstrating that a highly localized plastic deformation occurred under nanoindentation.Fur-thermore,the resistance for creep behavior increases as the Al concentration is increased due to the enlarged lattice distortion related to a solution strengthening effect.
Keywords
high-entropy alloys,mechanical properties,nanoin-dentation,serration behaviors
1.Introduction
Recently,the emerging high-entropy alloys (HEAs)have attracted increasing attention because of their unusual properties and potential applications in industries (Ref 1-5).Unlike the traditional alloys,which are typically based on one or two principal elements,HEAs are multi-principle component alloys with at least ?ve equiatomic or near-equiatomic alloying elements (Ref 6).However,it is of particular interest to note that,despite containing a large number of components,HEAs actually exhibit a signi?cant degree of mutual solubility and tend to form face-centered cubic (FCC)and/or body-centered cubic (BCC)solid solutions rather than intermetallic compounds or other complex ordered phases,which is often attributed to a high mixing entropy (Ref 7).Several studies showed that additions of Al element into HEAs could have strong effect on the crystalline structure,microstructural morphology,and the subsequent mechanical properties (Ref 8-11).In the Al x CoCrFeNi system (Ref 8),for example,the crystalline structure changed from the initial single FCC structure (0 BCC structure (0.5 In the present work,the mechanical properties of Al 0.3-CoCrFeNi and AlCoCrFeNi HEAs are investigated at room temperature through instrumental nanoindentation.The purpose of this study is to elucidate the experimental results of the two alloys on the basis of thermodynamic and topological param-eters of the constituent elements and characterize the effect of Al element on the microstructural evolution and mechanical behavior.This is a comparative study of the mechanical properties of the two types of HEAs,with the aim of achieving a better understanding of the fundamental mechanisms that dominate the mechanical properties of high-entropy alloys. 2.Experimental Alloy ingots with a nominal composition of Al 0.3CoCrFeNi and AlCoCrFeNi HEAs were synthesized by arc-melting a mixture of pure metals (purity >99mass%)in a Ti-gettered high-purity argon atmosphere.The alloys were remelted at least four times in order to obtain chemical homogeneity.The rods of Zhi-Ming Jiao,Sheng-Guo Ma,Guo-Zheng Yuan,and Zhi-Hua Wang ,Institute of Applied Mechanics and Biomedical Engineering,Taiyuan University of Technology,Taiyuan 030024,China;Hui-Jun Yang ,Laboratory of Applied Physics and Mechanics of Advanced Materials,College of Materials Science and Engineering,Taiyuan University of Technology,Taiyuan 030024,China;and Jun-Wei Qiao ,Institute of Applied Mechanics and Biomedical Engineering,Taiyuan University of Technology,Taiyuan 030024,China and Laboratory of Applied Physics and Mechanics of Advanced Materials,College of Materials Science and Engineering,Taiyuan University of Technology,Taiyuan 030024,China.Contact e-mails:wangzh@https://www.wendangku.net/doc/9b7803492.html, and qiaojunwei @https://www.wendangku.net/doc/9b7803492.html,. JMEPEG (2015)24:3077–3083óASM International DOI:10.1007/s11665-015-1576-01059-9495/$19.00 3mm in diameter were produced using the copper-mold suction-casting method.The phase structures of the two as-cast alloys were identi?ed by x-ray diffraction and transmission electron microscopy. Nanoindentation experiments were performed in a load-control mode conducted with a maximum load of30mN and at the loading rates of0.5,2,and10mN/s on MTS Nano Indenter XP system with a Berkovich diamond tip at room temperature. Initial machine calibration was conducted on a fused silica standard to ensure the validity of testing data.In order to remove the thermal effect,thermal drift was maintained below 0.05nm/s during each test.The load holding time was settled as10s to determine whether a creep behavior occurred.The 20-l m interval was chosen to avoid any overlap of plastic zones created by neighboring indentations.At least three indents at each loading rate were performed to verify the accuracy and scatter of the indentation data.After nanoinden-tation,the images around the indents were immediately examined using in situ scanning system,which is a part of nanoindentation method.Finally,cylindrical samples of two alloys with an aspect ratio of2:1were prepared for quasi-static compression with a strain rate of1910à3sà1at room temperature. 3.Results and Discussion Figure1shows the SEM images of the as-cast Al0.3CoCrFeNi (Al0.3)and AlCoCrFeNi(Al1.0)HEAs in(a)and(b),respectively. In order to clearly compare the morphology of two alloys,the magni?cation of SEM images are different.With the addition of Al atoms into the CoCrFeNi base alloy,the solidi?cation structure varies from columnar cell to equiaxed dendritic grain. The Al0.3CoCrFeNi alloy with single FCC phase has columnar grains with cellular structure.As the amount of Al atoms increases,the AlCoCrFeNi alloy with single BCC phase presents an equiaxed dendritic grain structure(Ref8,10). Figure2(a)and(b)shows the load-displacement(P-h) curves of the nanoindentation for Al0.3CoCrFeNi and AlCoCr FeNi HEAs,respectively,under different loading rates.It is noted that the loading portion of the P-h curves exhibits interesting discontinuities in the inset of Fig.2,and these are characteristic of energy-absorbing or energy-releasing events occurring beneath the indenter tip,where dislocation activity is detected during a shallow indentation into the two alloys (Ref19,20).Actually,the P-h curves for both HEAs show strong loading rate dependence.At low loading rates,the P-h curves are punctuated by a number of discrete bursts of displacement,as indicated by arrows in each case.Signi?cant discontinuities can only be observed for the AlCoCrFeNi at a loading rate of0.5mN/s.As the loading rate is increased,the discontinuities became less prominent for both alloys,espe-cially for AlCoCrFeNi,whose P-h curves became quite smooth when the loading rate is higher than 2.0mN/s.During indentation at a constant loading rate,the indentation strain rate,which is de?ned as1 2 _P P (Ref21),is non-linearly dimin-ishing with the indentation depth.Hence,a constant loading rate can be converted to a representative strain rate that might be a more useful parameter than the loading rate for analyzing the inhomogeneous deformation(Ref17).It can be seen from Fig.3that the strain rate during nanoindentation covers a broad range of values from low rates of below10à2sà1to as high as 104sà1.In addition,it is interesting to note that signi?cant discontinuities could be only observed in P-h curves recorded during nanoindentation when the strain rate is lower than a critical value for both alloys,demonstrating that the disconti-nuity behavior of the two alloys is both loading rate and strain rate dependent,which is similar to the serrated?ow in bulk metallic glasses(Ref22). Table1summarizes some important mechanical properties derived from the P-h curves of nanoindentations at different loading rates,including the maximum depth(H max),stiffness(S), elastic modulus(E),and hardness(H),based on the Oliver and Pharr method(Ref12,13).Although the discontinuity behavior is strongly dependent on the loading rate,the mechanical properties obtained at different loading rates do not appear to be much different,indicating that the mechanical properties are less loading rate dependent.However,the elastic modulus and hardness for AlCoCrFeNi are larger than those for Al0.3CoCrFe Ni HEAs,suggesting that the underlying fundamental mecha-nism is required to be elucidated based on the composition-structure-property relationship using thermodynamic and topological parameters of the constituent elements(Ref23 ). Fig.1SEM micrographs of etched as-cast Al0.3CoCrFeNi and AlCoCrFeNi HEAs,showing columnar grains with cellular structure(a)and an equiaxed dendritic grain structure(b),respectively For a solution phase,its Gibbs free energy of mixing (D G mix )can be determined by D G mix ?D H mix àT D S mix ; eEq 1T where D H mix is the enthalpy of mixing,D S mix is the entropy of mixing,and T is the absolute temperature. In this study,a regular solution model has been adopted in order to simplify the calculation of free energy of multi-component HEAs (Ref 24).From a thermodynamic point of view,and in particular derived from Hume-Rothery rules,Zhang et al.(Ref 25)proposed a criterion for achieving solid solution phases in HEAs using two parameters,d (atomic radius difference)and D H mix (enthalpy of mixing),as described below: d ???????????????????????????????????????????????????????X n i ?1 c i 1àr i =X n i ?1 c i r i !"#2v u u t eEq 2 T Fig.2Load-displacement (P-h)curves under different loading rates with a maximum load of 30mN for Al 0.3CoCrFeNi HEAs (a)and AlCoCrFeNi HEAs (b).Inset is an enlarged portion of loading stage Fig.3The conversion from loading rates to strain rates for Al 0.3CoCrFeNi HEAs (a)and AlCoCrFeNi HEAs (b) Table 1Mechanical properties of Al 0.3CoCrFeNi and AlCoCrFeNi HEAs Loading rate,mN/s Al 0.3CoCrFeNi AlCoCrFeNi H max ,nm S ,l N/nm E ,GPa H ,GPa H max ,nm S ,l N/nm E ,GPa H ,GPa 0.5612.88640.07217.95 3.41393.71433.32252.449.462614.50623.77210.98 3.39369.80386.58243.9211.0810 611.31642.86218.74 3.18376.43420.90257.999.86Average 612.90 635.57 215.89 3.33 379.98 413.60 251.45 10.14 D H mix ? X n i ?1;i ?j X ij c i c j ;eEq 3T where n is the total number of components in a system,r i is the Goldschmidt atomic radius of the i th element,c i is the molar ratio of the i th component,X ij (=4D H ij mix )is the regular solution interaction parameter between the i th and j th ele-ments,and D H ij mix is the enthalpy of mixing of binary liquid alloys.The parameter d characterizes the atomic size mis-match,which produces the local elastic strain and determines the system topological instability (Ref 26),while the parame-ter D H mix re?ects the tendency of forming stable intermetallic compounds. The entropy of mixing of the alloy system,D S mix ,for a solution phase can be calculated,according to Boltzmann ?s hypothesis using a regular solution approach:D S mix ?àR X n i ?1 ec i ln c i T;eEq 4T where R (=8.314J/K mol)is the gas constant. Furthermore,in order to include the mixing entropy effect,an additional parameter X was also proposed for predicting the solid solution formation for various multi-component alloys as in Ref 24:X ? T m D S mix D H mix j j ; eEq 5T where T m is the average melting temperature,which is calcu-lated using the rule of mixtures:T m ? X n i ?1 c i eT m Ti ; eEq 6T where (T m )i stands for the melting point of the i th element.From the available data,it is noted that solid solutions are mostly concentrated in the region with X ?1.1and d ￡6.6%(Ref 24). Table 2presents the values of d ,D H mix ,D S mix ,T m ,and X ,as calculated from Eqs 2-6,respectively,for the reported Al 0.25CoCrFeNi,Al 0.375CoCrFeNi,and AlCoCrFeNi HEAs (Ref 24).From Eq 1,the combination of a low absolute of D H mix and high D S mix results in the low free energy and,thus,stabilizes the solution phase (Ref 25).Actually,it is speculated that if solid solution phase possesses the lowest D G mix among all possible formed phases,it will be most possible to form and the most stable during the solidi?cation.As listed in Table 2,the enthalpy of mixing of AlCoCrFeNi HEAs is lowest,while its entropy of mixing is highest among the three alloys,giving rise to its lowest D G mix and the most stable solid solution phase.Moreover,the more negative D H mix means the larger binding force between elements (Ref 24),which macroscopi-cally dominates the elastic modulus of the materials.It is noted from above that the absolute value of enthalpy of mixing increases as Al concentration is increased,indicating that the elastic modulus of the three alloys increases with the increase of Al content,and the thermodynamic and topological parameters of Al 0.3CoCrFeNi are reasonably between them of Al 0.25CoCr FeNi and Al 0.375CoCrFeNi HEAs,leading to the fact that the absolute value of enthalpy of mixing of Al 0.3CoCrFeNi HEAs is less than that of AlCoCrFeNi HEAs.Accordingly,the elastic modulus of the former is less than that of the latter,which was Table 2The microstructure and parameters,d ,D H mix ,D S mix ,T m ,and X for Al 0.25CoCrFeNi,Al 0.375CoCrFeNi,and AlCoCrFeNi HEAs (Ref 24) Alloys Structure d ,%D H mix ,KJ/mol D S mix ,J/K mol T m ,K X Al 0.25CoCrFeNi FCC 3.25à6.7512.711805.97 3.40Al 0.375CoCrFeNi FCC 3.80à7.9912.971781.04 2.89AlCoCrFeNi BCC 5.25 à12.32 13.38 1675.10 1.83 Fig.4The relationship between parameter d and X for Al 0.25CoCr FeNi,Al 0.375CoCrFeNi,and AlCoCrFeNi HEAs Fig.5The engineering stress-strain curves of the present Al 0.3CoCrFeNi and AlCoCrFeNi HEAs upon quasi-static compression essentially in agreement with the experimental results as listed in Table 1. Figure 4presents the relationship between d and X for the Al 0.25CoCrFeNi,Al 0.375CoCrFeNi,and AlCoCrFeNi HEAs,as listed in Table 2(Ref 24).Clearly,it is noted that the descending tendency occurs with an increase in Al concentra-tions,demonstrating that there is a transition from the solid solution to intermetallic compounds.Due to the special feature in the bonding of intermetallics,the arrangement of atoms is highly ordered.As the formation of ordered phases in the Al x CoCrFeNi alloy system (Ref 8),the extent of ordering for multi-component alloys increases until the ordering is complete (Ref 24).Therefore,the ordered phase degree of solid solutions in AlCoCrFeNi HEAs is the highest among the three alloys,leading to its strength higher than that of Al 0.25CoCrFeNi and Al 0.375CoCrFeNi HEAs due to ordered strengthening effect.Based on this analysis,it can be concluded that the hardness of AlCoCrFeNi HEAs is higher than that of Al 0.3CoCrFeNi HEAs as the Al concentration increases,which is proved by this nanoindentation test. In order to elaborate the effect of Al concentration on yielding strength in the two alloys,the corresponding com-pression tests are required.Figure 5displays the engineering stress-strain curves of the present Al 0.3CoCrFeNi and AlCoCr FeNi HEAs upon quasi-static compression with a strain rate of 10à3s à1.It can be found that the yielding strength of AlCoCrFeNi HEAs is obviously greater than that of Al 0.3CoCrFeNi HEAs,which agrees well with the previous work (Ref 27,28).Actually,the fact that yielding strength increases with Al concentration in multi-component alloys is attributed to the solid solution strengthening,which is a type of alloying that can be used to improve the strength of metallic materials (Ref 29).It is well known that the strength of a material depends on how easily dislocations in its crystal lattice can be propagated,and these dislocations create stress ?elds within the materials depending on their character.When solution atoms Al are introduced,local stress ?elds are formed that interact with those of the dislocation,impeding their motion and causing an increase in the yielding strength of the materials due to the lattice distortion,and it becomes intensive with increasing Al element,which is in accordance with the higher yielding strength of AlCoCrFeNi HEAs. Figure 6(a)and (b)shows a typical example of in situ scanning images of the indents for Al 0.3CoCrFeNi and AlCoCrFeNi HEAs at a loading rate of 0.5mN/s in order to elucidate the deformation morphologies for the two alloy compositions,respectively.The surface uplift due to the pile-up of materials can be clearly observed around the indents, as Fig.6In situ scanning images with a loading rate of 0.5mN/s and a corresponding cross-sectional pro?les of the indent along the line of X and Y made with a Berkovich indenter for Al 0.3CoCrFeNi HEAs (a)and AlCoCrFeNi HEAs (b),respectively demonstrated in the insets of Fig.6.The cross-sectional pro?les of the indents along the directions of X and Y for the two HEAs are also shown in Fig.6.On the basis of the pro?les,the height of the pile-up is measured to be about 80nm for Al 0.3CoCrFeNi HEAs and 60nm for AlCoCrFeNi HEAs.A signi?cant pile-up around the indenter suggests that a highly localized plastic deformation occurred during nanoindentation (Ref 30). Empirically,the shape of the creep curves for all investi-gated materials can be described with the well-known loga-rithmic creep formula that was developed for metals (Ref 31):D h ?A áln B át t1eT; eEq 7T where A and B are ?tting parameters and D h and t are the displacement and time at the starting of holding time,respec-tively.Figure 7exhibits this for the examples of a 30mN in-dent into Al 0.3CoCrFeNi and AlCoCrFeNi HEAs with a holding time of 10s at a loading rate of 0.5mN/s,respec-tively.For metals,the parameters A and B depend among others on temperature,dislocation density,Burgers vector,and yielding strength (Ref 31).The maximum difference between ?t results and measured data is less than 0.5nm.Table 3shows the ?tting parameters and coef?cient of deter-mination (Adj.R 2)for Al 0.3CoCrFeNi and AlCoCrFeNi HEAs.For the coef?cient of determination,the extreme of 1occurs when all the points are exactly on a ?tted line,indicat-ing that the creep behavior of the two alloys is quantitatively described by the logarithmic creep formula.It should be noted that the depth change of Al 0.3CoCrFeNi HEAs is apparently more than that of AlCoCrFeNi HEAs,suggesting that the resistance for depth change increases with the in-crease of Al concentrations due to a highly distorted lattice structure responsible for the solid solution strengthening (Ref 29).However,the equations with the distinct physical foun-dation to elucidate the creep behavior in multi-component al-loys related to the dislocation dynamics are very dif?cult to be derived and solved.Furthermore,there are also two simple empirical equations to describe the creep behavior in multi-component alloys (Ref 15).Fischer proposed that the tran-sient creep stage was considered as viscous behavior related to the dislocation dynamics (Ref 32).The observed creep behaviors in the current Al 0.3CoCrFeNi and AlCoCrFeNi HEAs cannot be fully elucidated using the existing theories,suggesting that additional work is necessary for the under-standing of creep mechanism. 4.Conclusions Instrumented nanoindentation has been used to explore the mechanical properties of Al 0.3CoCrFeNi and AlCoCrFeNi high-entropy alloys.Both HEAs exhibited signi?cant discon-tinuity at low loading rate.However,the discontinuities became less prominent for both alloys as the loading rate is increased.Considering thermodynamic and topological parameters of the constituent elements,the AlCoCrFeNi HEAs has a higher elastic modulus and hardness due to its higher negative enthalpy of mixing related to the atomic binding force and the accumulation of ordered phase,respectively.The yielding strength of AlCoCrFeNi HEAs is apparently higher than that of Al 0.3CoCrFeNi HEAs as a result of solid solution strengthening induced by the lattice distortion.A signi?cant pile-up around the indents suggests that a highly localized plastic deformation occurs during nanoindentation.In addition,the creep behavior,considered as viscous behavior related to the dislocation dynamics in Al 0.3CoCrFeNi and AlCoCrFeNi HEAs,is char-acterized by nanoindentation tests. Acknowledgments J.W.Q.would like to acknowledge the ?nancial support of National Natural Science Foundation of China (No.51101110and No.51371122)and the Program for the Outstanding Innovative Teams of Higher Learning Institutions of Shanxi (2013).H.J.Y .would like to acknowledge the ?nancial support from State Key Lab of Advanced Metals and Materials (No.2013-Z03)and the Youth Science Foundation of Shanxi Province,China (No.2014021017-3).Z.H.W.would like to acknowledge the ?nancial support of the National Natural Science Foundation of China (No.11390362),the Top Young Academic Leaders of Shanxi,and the Outstanding Innovative Teams of Higher Learning Institutions of Shanxi.The ?nancial contributions were gratefully acknowledged. 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