<<

Article Investigation of Structural-Phase States and Features of Plastic Deformation of the Austenitic Precipitation-Hardening Co-Ni-Nb

Aidyn Tussupzhanov 1,2,3,*, Dosym Yerbolatuly 1, Ludmila I. Kveglis 1,3 and Aleksander Filarowski 2,4,5 ID 1 S. Amanzholov East Kazakhstan State University, Department of Physics and Technology, 30 Gvardeiskoi Divisii Str. 34, 070020 Ust-Kamenogorsk, Kazakhstan; [email protected] (D.Y.); [email protected] (L.I.K.) 2 Faculty of Chemistry, Wroclaw University, F. Joliot-Curie Str. 14, 50-383 Wroclaw, Poland; aleksander.fi[email protected] 3 Polytechnical Institute of Siberian Federal University, Svobodny Ave 79, 660041 Krasnoyarsk, Russia 4 Frank Laboratory of Neutron Physics, JINR, 141-980 Dubna, Russia 5 Department of Physics, Industrial University of Tyumen, 625-000 Tyumen, Russia * Correspondence: [email protected]; Tel.: +7-777-4775878

Received: 6 November 2017; Accepted: 23 December 2017; Published: 30 December 2017

Abstract: This article presents the results of investigation of the influence of holding during the quenching process on the microstructure and superplasticity of the Co-Ni-Nb alloy. Temperature-strain rate intervals of the deformation of the superplasticity effects are stated. The optimal regimes of the preliminary treatment by quenching and rolling as well as the routine of the superplastic deformation of the Co-Ni-Nb alloy are defined. The interval of the of the precipitation, morphology, composition, type and parameters of the lattice of the secondary phase, which appears after the annealing + rolling (to 90%) Co-Ni-Nb alloy, are determined.

Keywords: superplasticity; superplastic deformation; Co-Ni-Nb alloy; microstructure; precipitation; secondary phase; shear transformation zone

1. Introduction The application of the superplasticity (SP) effect in the technology of treatment under enables the production of metallic parts of complex configuration in a single operation. This approach reduces energy consumption and cost of the items and increases labor productivity [1–3]. Therefore, of specific interest are high-strength disperse-hardening alloys with the base of cobalt and nickel, which are highly resistant to treatment and become fragile after standard methods of treatment [4]. The paper [5] presents phase diagrams of the triple Co-Ni-Nb systems, where there were performed identification of phases that may form at the micro level, to predict how the microstructure changes upon the heat treatment used. Most effort has been focused on mechanisms of superplasticity [6]. A practical application of the SP of alloys poses important problems to be solved: the features of the precipitation and parameters of particles of the secondary phases, as well as the detection of basic and accommodative mechanisms of superplastic deformation (SPD). The understanding of these phenomena will allow for a deeper insight into the nature of superplasticity of alloys, and form the basis for the development of new methods of treatment for the design of structures with optimal technological properties. So far the literature has presented no data on the influence of holding temperature before quenching on superplastic properties of the Co-Ni-Nb alloy and the contradictory information about the secondary phases, defined in the given alloy. Such types of alloys are employed as a conducting spring in dental lighting devices [7]. Therefore, this suggests the following tasks:

Metals 2018, 8, 19; doi:10.3390/met8010019 www.mdpi.com/journal/metals Metals 2018, 8, 19 2 of 11

• The influence of quenching temperature on the structure and superplastic properties of the Co-Ni-Nb alloys; • The study of peculiarities of the formation of fine-grained superplastic structures at the annealing temperature of the rolled samples; • The influence of structure and phase composition on the superplasticity of an alloy; • The definition of optimal deformation regime.

2. Materials and Methods The Co-Ni-Nb alloy samples were prepared in accordance with GOST-9651-84 and had chemical composition: base—Co, wt. 28%-Ni, wt. 5%-Nb, wt. 0.2%-Si. The quenching was performed in room temperature water. The deformation treatment was performed on a standard rolling mill. The thermal treatment of the samples was carried out in a tube-type furnace “SUOL-4” (Tula-Therm, Tula, USSR) in quartz tubes, where vacuum was maintained with a residual pressure less than 10−3 MPa. The superplastic deformation was completed on the 1246R device in vacuum with a residual pressure 10−5 MPa. The study of a microstructure was made on “HITACHI S-3400N” (HITACHI, Japan) in the scanning electron microscope by the regime of secondary electrons under the accelerating tension of 25 kV voltage. The analysis of a phase state of the samples was performed on the X-ray diffractometer “DRON-3” with using Co Kα and Cu Kα X-rays (Burevestnik inc, St. Petersburg, Russia). The elemental analysis was performed by the energy dispersive X-ray fluorescence spectrometer SRV-1 (TechnoAnalit, Ust-Kamenogorsk, Kazahstan). The tube with a molybdenum anode BS-1 (U = 25 kV, I = 30 mA) and the energy resolution semiconductor detector were used (170 eV). The exposure time was 180 s. The Scanning Electron Microscopy (SEM) images were prepared using Hitachi S-3400N equipped with detector EDS Thermo Scientific Ultra Dry operating at 5 kV/10 kV. Microhardness measurements of the samples were performed on a PMT-3 microhardener (GEO-NDT, Moscow, Russia), with an indentor load P = 100 and a holding time of 10 s. As an indenter, a regular tetrahedral diamond pyramid with a vertex angle of 136◦ was used to measure the microhardness, similar to the method for determining the Vickers hardness.

3. Results and Discussion

3.1. Structural-Phase State of Co-Ni-Nb Alloy after the Quenching The metallographic (Figure1a) and X-ray diffraction (Figure2a (2)) studies show that quenching of the Co-Ni-Nb alloy at 1423 K for 10 min creates a one phase state with the formation of homogeneous solution Nb in Co-Ni matrix, having face-centered cubic lattice with a parameter a = 0.356 nm. The microstructure of the initial state sample of the Co-Ni-Nb alloy is characterized by equigranular grains and the presence of twins, which are traced in almost every grain (Figure1a,b). The average size of grains determined by the intercept method is about 30 µm (Figure2a). However, according to the data presented in paper [8], which revealed the quenching temperature and the influence of the regime of the consequent ageing on the service properties of the Co-Ni-Nb alloy, the most optimal combination of the durability properties (the relaxation stability and low electric resistance) is reached as a result of quenching at 1223 K (10 min) and ageing at 873 K (5 h). Metals 2018, 8, 19 3 of 11 MetalsMetals 20182018,, 88,, 1199 33 ofof 1010

Figure 1. Structural-phase state of the Co-Ni-Nb alloy: (left side) initial sample microstructure and FigureFigure 1. 1.Structural-phase Structural-phase state state of of the the Co-Ni-Nb Co-Ni-Nb alloy: alloy: ( left(left side side)) initial initial sample sample microstructure microstructure and and (right side) fragment microstructure with twins (black arrows). (right(right side side) fragment) fragment microstructure microstructure with with twins twins (black (black arrows). arrows).

TheTheThe data datadata obtained obtainedobtained by byby the thethe methods methodsmethods of ofof optic opticoptic microscopy microscopymicroscopy (Figure (Figure(Figure1 b) 1b)1b) and andand X-ray XX--rayray diffraction diffractiondiffraction analysis analysisanalysis γ (Figure(Figure(Figure2 a) 2a)2a) also alsoalso establish estestablishablish that thatthat the thethe Co-Ni-Nb CoCo--NiNi--NbNb alloy alloyalloy takes takestakes the thethe state statestate of ofof only onlyonly one oneone γγ-phase--phasephase in inin solid solidsolid solution solutionsolution bothbothboth after afterafter quenching quenchingquenching at atat 1223 12231223 K KK (10 (10(10 min) min)min) and andand after afterafter quenching quenchingquenching at at aat much aa muchmuch higher higherhigher temperature temperaturetemperature than thanthan 1423 14231423 K. µ TheK.K. TheThe structure structurestructure of the ofof alloy thethe alloyalloy quenched quenchedquenched at 1223 atat 1223 K1223 features KK featuresfeatures grains grainsgrains of less ofof size lessless (d sizesize= 18 ((dd m) == 1818 and µm)µm) much andand fewer muchmuch twinsfewerfewer (Figure twinstwins (Figure1(Figureb). 1b).1b).

FigureFigureFigure 2. 2.2.Fragments FragmentsFragments of ofof diffractograms diffractogramsdiffractograms of ofof Co-Ni-Nb CoCo--NiNi--NbNb alloy: alloy:alloy: ( (a(aa))) after afterafter quenching quenchingquenching at atat 1223 12231223 K KK (10 (10(10 min) min)min) ( (1(1)1)) andandand at atat 1423 14231423 K KK (10 (10(10 min) min)min) ( 2 ((2);2);); ( b ((b)b) after) afterafter annealing annealingannealing at atat 773 773773 K KK (1 (1(1 h) hh) () 1 ((1),1),), 973 973973 K KK (1 (1(1 h) hh) () 2 (()22) and) andand at atat 1173 11731173 (1 (1(1 h) h)h) ( 3 (().33).).

3.2.3.23.2..The TheThe Results ResultsResults of ofof the thethe Studies StudiesStudies of ofof the thethe Secondary SecondarySecondary Phase PhasePhase of ofof Co-Ni-Al CoCo--NiNi--AlAl Alloy AlloyAlloy AnnealingAnnealingAnnealing at atat 773 773773 KKK (1(1 h)hh)) ++ roll rollingrollinging (90(90 (90%)%)%) thethe the CoCo Co-Ni-Nb--NiNi--NbNb alloyalloy alloy diddid did notnot not evokeevoke evoke decompositiondecomposition decomposition ofof of γγ-- γphasephase-phase ofof of solidsolid solid solutionsolution solution (Figure(Figure (Figure 2b).2b).2b). TheThe The XX--rayray X-ray diffractiondiffraction diffraction ofof annealingannealing of annealing atat 973973 at KK 973 ofof alloyalloy K of showsshows alloy shows reflexesreflexes reflexesofof the the secondaryof secondary the secondary phase phase phase with with with the the hexagonalthe hexagonal hexagonal close close close-packed--packedpacked (HCP) (HCP) (HCP) lattice lattice lattice (Figure (Figure (Figure 2 2b). 2b).b). The The The electron electron electron microscopymicroscopymicroscopy (Figures (Figures(Figures3 3and3 andand4) 4)4) and andand metallographic metallographicmetallographic methods methodsmethods confirm confirmconfirm the thethe appearance appearanceappearance of ofof the thethe secondary secondarysecondary phasephasephase of ofof spherical spsphericalherical shape shapeshape after afterafter rolling rollingrolling (90%) (90(90%)%) and andand annealing annealingannealing of ofof the thethe Co-Ni-Nb CoCo--NiNi--NbNb alloy. alloy.alloy. TheTheThe analysis analysis analysis of of of the the the structure structure structure of of of the the the surface surface surface of of of the the the Co-Ni-Nb Co Co--NiNi--NbNb alloy alloy alloy by by by the the the scanning scanning scanning electron electron electron microscopymicroscopymicroscopy makes makes makes it possible it it possible possible to state to to state thatstate particles that that particles particles of the secondary of of the the secondary secondary phase at tempering phase phase at at cantempering tempering precipitate can can notprecipitateprecipitate only on not thenot edgesonlyonly onon of thethe grains edgesedges (Figure ofof grainsgrains3a) but (Figure(Figure also inside3a)3a) butbut in alsoalso their insideinside volume. inin theirtheir As volume. avolume. result, As atAs the aa result,result, initial atat stagethethe initialinitial of decomposition stagestage ofof decompositiondecomposition of the alloy ofof athethe matrix alloyalloy structureaa matrixmatrix structurestructure with finer withwith particles finerfiner particlesparticles of the secondary ofof thethe secondarysecondary phase isphasephase formed isis formedformed (Figure (Figure(Figure3b). The 3b).3b). size TheThe of sizesize the matrixofof thethe matrixmatrix grains grainsgrains equals equalsequals = <

> == 2µ2––m33 µm afterµm afterafter annealing annealingannealing at 1153 atat 11531153 K (25KK (25(25 min), min),min), and andand the thethe size sizesize of particles ofof particlesparticles of the ofof thethe precipitation precipitationprecipitation is isis <<=dd>> 0.2–0.4 == 0.20.2––0.40.4µm. µm.µm.

Metals 2018, 8, 19 4 of 10

Metals 2018, 8, 19 4 of 11 Metals 2018, 8, 19 4 of 10

Figure 3. Scanning electron microscopy of the Co-Ni-Nb alloy structure after annealing at 773 K (1 h) + 90% rolling at room temperature and the annealing at 1153 K (25 min) (picture (a) with 6000

magnificationFigure 3. Scanning Scanningand picture electron electron (b) withmicroscopy microscopy 15,000 of magnification) ofthe the Co Co-Ni-Nb-Ni-Nb alloyand alloy grainstructure structure size after histogram after annealing annealing (c )at obtained 773 at K 773 (1 hby K) the intercept(1+ 90 h)% +method. 90% rolling rolling at room at room temperature temperature and and the the annealing annealing at at 1153 1153 K K (25 (25 min) min) (picture (picture ( (aa)) with 6000 magnificationmagnification and picture (b)) with 15,00015,000 magnification)magnification) andand grain size histogram (c)) obtainedobtained byby the Withinterceptintercept the elongation method.method. of the annealing time up to 1 h, earlier precipitated particles inside new grains quicklyWith the dissolve. elongation As a of result, the annealing particles time merge up toat 1the h, earlierboundary precipitated of the grains particles due inside to the new inflow With the elongation of the annealing time up to 1 h, earlier precipitated particles inside new of releasedgrains quickly atoms.dissolve. As a result, particles merge at the boundary of the grains due to the inflow of grains quickly dissolve. As a result, particles merge at the boundary of the grains due to the inflow releasedHCP phase atoms. of precipitation starts from the ageing temperature at 923–973 K. After 4 h of of released atoms. annealingHCP at 1073 phase K of the precipitation size of particles starts from of thethe ageing secondary temperature η-phase at 923–973begin growing K. After 4 and h of annealingthe alloy has HCP phase of precipitation starts from the ageing temperature at 923–973 K. After 4 h of at 1073 K the size of particles of the secondary η-phase begin growing and the alloy has two-phase two-phaseannealing micro at 1073 duplex K the structure size of particles of grains of with the secondary the equiaxed η-phase grain begin (Figure growing 4). The and body the alloyof the has grains micro duplex structure of grains with the equiaxed grain (Figure4). The body of the grains is almost is almosttwo- phasefree from micro dislocation, duplex structure and the of grains size of with sec ondarythe equiaxed phases grain grains (Figure is smaller 4). The body than of1 µm.the grains A similar free from dislocation, and the size of secondary phases grains is smaller than 1 µm. A similar type of type isof almost structure free fromof grains dislocation, with the and non the- coherentsize of sec highondary angle phases grain grains boundaries is smaller isthan considered 1 µm. A similar favorable structure of grains with the non-coherent high angle grain boundaries is considered favorable for the for thetype realization of structure of of the grains superplasticity with the non -effect.coherent high angle grain boundaries is considered favorable realization of the superplasticity effect. forIn thisthe realizationpaper, the of parameters the superplasticity of the lattice, effect. the composition of dark particles in hexagonal close- In this paper, the parameters of the lattice, the composition of dark particles in hexagonal In this paper, the parameters of the lattice, the composition of dark particles in hexagonal close- packedclose-packed (HCP) phase (HCP) (Figure phase (Figure4) are established4) are established by the by X the-ray X-ray and andelectron electron-microscopic-microscopic analysis. analysis. HCP packed (HCP) phase (Figure 4) are established by the X-ray and electron-microscopic analysis. HCP phaseHCP have phase lattice have parameters lattice parameters a = 5.62a = Å 5.62 and Å andc = c7.90= 7.90 Å .Å. It Itis is noteworthy noteworthy that that under under the the annealing annealing of of phase have lattice parameters a = 5.62 Å and c = 7.90 Å . It is noteworthy that under the annealing of the rolledthe rolled (90 (90%)%) Co Co-Ni-Nb-Ni-Nb alloy alloy particlesparticles of of HCP HCP phase phase precipitating precipitating within within the interval the ofinterval 973 K–1153 of 973 K K– the rolled (90%) Co-Ni-Nb alloy particles of HCP phase precipitating within the interval of 973 K– 1153take K take a spherical a spherical shape. shape. This result This differs result from dif thatfers presented from that in referenncepresented [8 in,9 ], referennce where particles [8,9] had, where 1153 K take a spherical shape. This result differs from that presented in referennce [8,9], where particlesa plate had shape. a plate Paper shape. [9] Pap stateder [9] that stated the ageing that the of ageing the Co-Ni-Nb of the Co alloy-Ni- evokesNb alloy precipitation evokes precipitation of the particles had a plate shape. Paper [9] stated that the ageing of the Co-Ni-Nb alloy evokes precipitation equiaxed particles of the high-temperature stable phase within the interval of 1123–1223 K. of theof equiaxed the equiaxed particles particles of ofthe the high high-temperature-temperature stable phasephase within within the the interval interval of 1123of 1123–1223–1223 K. K.

Figure 4. Pictures of secondary phase precipitations after rolling-mill (90%) and annealing for 5 min FigureFigureat 11434. Pictures 4.K Picturesobtained of ofsecondary with secondary the Scanning phase phase precip precipitationsElectronitations Microscope. after after rolling-mill rolling -mill (90%) (90 and%) annealingand annealing for 5 min for at5 min at 11431143 K Kobtained obtained with with the ScanningScanning Electron Electron Microscope. Microscope. Rolling and annealing of the Co-Ni-Nb alloy, preliminary quenched from the temperature higher than 1223 K (10 min), results in the formation of two-phase micro duplex structure under a RollingRolling and and annealing annealing of of the the Co-Ni-Nb Co-Ni-Nb alloy, alloy, preliminary preliminary quenched quenched from the from temperature the temperature higher continuous recrystallization and precipitation of the secondary phase. However, it is stated that the higherthan than 1223 1223 K (10 K min), (10 min), results result in thes formation in the formation of two-phase of two micro-phase duplex micro structure duplex under structure a continuous under a temperature interval of HCP-phase precipitation is expanding significantly and covers the range of continuousrecrystallization recrystallization and precipitation and precipitation of the secondary of the phase. secondary However, phase. it is statedHowever, that theit is temperature stated that the 873–1213 K, which is 90 K larger than after the annealing at 1423 K (10 min). This fact explains the temperatureinterval ofinterval HCP-phase of HCP precipitation-phase precipitation is expanding is significantly expanding andsignificantly covers the and range covers of 873–1213 the range K, of temperature decrease of the annealing of the Co-Ni-Nb alloy from 1423 K to 1223 K, because the 873–which1213 K, is which 90 K larger is 90 than K larger after thethan annealing after the at annealing 1423 K (10 min).at 1423 This K fact(10 explainsmin). This the fact temperature explains the thermal processing of similar hetero-phase alloys usually brings about the expanding of the temperaturetemperature decrease interval of ofthe precipitation annealing andof the stabilization Co-Ni-Nb of alloy secondary from phases,1423 K whichto 1223 improves K, because the the thermalexploitin processingg properties. of similar hetero-phase alloys usually brings about the expanding of the temperature interval of precipitation and stabilization of secondary phases, which improves the exploiting properties.

Metals 2018, 8, 19 5 of 11 decrease of the annealing of the Co-Ni-Nb alloy from 1423 K to 1223 K, because the thermal processing of similar hetero-phase alloys usually brings about the expanding of the temperature interval of precipitation and stabilization of secondary phases, which improves the exploiting properties. The character of the dependence of both volume faction of HCP-phase and grain size of the matrix Metals 2018, 8, 19 5 of 10 on the annealing temperature has been defined. A visible precipitation of the HCP-phase starts at 873 K and, under furtherThe character temperature of the dependence increase, grows,of both volume reaching faction the maximumof HCP-phase value and grain at 1073–1123 size of the K (Figure5 curve-a).matrix Dissolution on the annealing of the particlestemperature of has HCP-phase been defined. inA visibl the matrixe precipitation above of the 1123 HCP K-phase and thestarts consequent at 873 K and, under further temperature increase, grows, reaching the maximum value at 1073–1123 reductionMetalsK of(Figure 2018 its, volume8 , 519 curve -a faction). Dissolution evoke of the the particles dramatic of HCP growth-phase ofin the the matrix matrix above grains 1123 K (Figure and5 of the10 5 curve- b). The obtainedconsequent results reduction show thatof its thevolume particles faction ofevoke HCP-phase the dramatic precipitated growth of the undermatrix grains the annealing (Figure 5 of rolled The character of the dependence of both volume faction of HCP-phase and grain size of the curve-b). The obtained results show that the particles of HCP-phase precipitated under the annealing (90%) Co-Ni-Nbmatrix on alloythe annealing hinder temperature the growth has of been matrix defined. grains A visible and, precipitation therefore, of stabilize the HCP-phase the microstructure starts in of rolled (90%) Co-Ni-Nb alloy hinder the growth of matrix grains and, therefore, stabilize the the wideat temperature 873 K and, under interval. further temperature increase, grows, reaching the maximum value at 1073–1123 microstructure in the wide temperature interval. K (Figure 5 curve-a). Dissolution of the particles of HCP-phase in the matrix above 1123 K and the consequent reduction of its volume faction evoke the dramatic growth of the matrix grains (Figure 5 curve-b). The obtained results show that the particles of HCP-phase precipitated under the annealing of rolled (90%) Co-Ni-Nb alloy hinder the growth of matrix grains and, therefore, stabilize the microstructure in the wide temperature interval.

a

b

a

b Figure 5. FigureDependences 5. Dependences of the of volumethe volume faction factionof of HCP-phaseHCP-phase (fHCP (f,HCP curve, curve--a) and graina) and size grain of γ-matrix size of γ-matrix (dγ, curve-(dbγ, )curve of the-b) Co-Ni-Nbof the Co-Ni- alloyNb alloy (preliminary (preliminary quench quenchinging from from 1223 1223K (10 min) K (10 and min) 90% androlling) 90% on rolling) on the annealingthe annealing temperature temperature (T). (T).

The dependence of microhardness (Hμ) on the annealing temperature of the studied alloy Figure 5. Dependences of the volume faction of HCP-phase (fHCP, curve-a) and grain size of γ-matrix The dependencepresents the decrease of microhardness of the microhardness (Hµ) onvalue the at annealing 973–1023 K temperature(Figure 6). It is most of the likely studied related alloy to presents the (begidγ, curvenning-b )of of the Corecrystallization-Ni-Nb alloy (preliminary process and quench removaling from of 1223hardening K (10 min) caused and 90by% therolling) preliminary on the decreasethe of annealing the microhardness temperature (T). value at 973–1023 K (Figure6). It is most likely related to the rolling. The rectilinear part on the graph (about 1100 K), observed under further temperature beginning of the recrystallization process and removal of hardening caused by the preliminary increase, is explained by the precipitation and growth of the HCP-phase particles, which stabilize the The dependence of microhardness (Hμ) on the annealing temperature of the studied alloy rolling. Thematrix rectilinear structure and part the alloy on thehardness graph to some (about extent. 1100 Above K), 1193 observed–1213 K a underdramatic further decrease temperaturein presents the decrease of the microhardness value at 973–1023 K (Figure 6). It is most likely related to micro-hardness occurs because of the reverse process of the dissolution of the phase particles in the increase,the is beginning explained of the by recrystallization the precipitation process and and growth removal ofof hardening the HCP-phase caused by particles, the preliminary which stabilize matrix and transition of the alloy into the one-phase state. Thereof, the HCP-phase particles the matrixrolling. structure The rectilinear and the part alloy on hardness the graph to (about some 1100 extent. K), observed Above under 1193–1213 further K temperature a dramatic decrease precipitation at the annealing of the 90% rolled alloy not only stabilize the microstructure but also in micro-hardnessincrease, is explained occurs by because the precipitation of thereverse and growth process of the HCP of the-phase dissolution particles, which of thestabilize phase the particles in promote the stability of micro-hardness. the matrixmatrix and structure transition and the of alloy the hardness alloy into to some the extent. one-phase Above state.1193–1213 Thereof, K a dramatic the HCP-phasedecrease in particles micro-hardness occurs because of6000 the reverse process of the dissolution of20 the phase particles in the precipitationmatrix at and the transition annealing of the of thealloy 90% into rolled the one alloy-phase not state. only Thereof, stabilize the HCP the-phase microstructure particles but also promoteprecipita the stabilitytion at ofthe micro-hardness.annealing of the 90% rolled alloy not only stabilize the microstructure but also 15 promote the stability of micro-hardness.4000

6000 20 m

10 

, MPa ,

, ,

d H 2000 15

4000 5 m

10 

, MPa ,

, , 

 0 0

d H 2000 700 900 1100 1300 Annealing temperature (T), K 5

Figure 6. The dependence of the microhardness (Hμ) on the annealing temperature (T) of the studied alloy after the quenching at 12230 K (10 min) and 90% rolling. 0 700 900 1100 1300 Annealing temperature (T), K

Figure 6. The dependence of the microhardness (Hμ) on the annealing temperature (T) of the studied Figure 6. The dependence of the microhardness (Hµ) on the annealing temperature (T) of the studied alloy after the quenching at 1223 K (10 min) and 90% rolling. alloy after the quenching at 1223 K (10 min) and 90% rolling.

Metals 2018, 8, 19 6 of 11

MetalsTo 2018 define, 8, 19 the element composition of HCP phase and analyze the changes in the element6 of 10 concentration in the matrix, X-ray fluorescence analysis of the samples has been made. The studies of the compositionTo define the of element the samples composition have been of performed HCP phase after and quenching analyze the at 1223 changes K, 90% in rolling the element and annealingconcentration at 1153 in Kthe (25 matrix, min), becauseX-ray fluorescence such procedure analysis oftreatment of the samples contributes has been to themade. improvement The studies ofof superplasticity the composition properties of the samples and a large have amount been performe of HCP-phase.d after quenching After electrochemical at 1223 K, 90 etching% rolling of the and obtainedannealing samples at 1153 at K 1153 (25 Kmin), (25 min), because the concentrationsuch procedure of cobaltof treatment decreases, contributes but the amountto the improvement of niobium, reversely,of superplasti increasescity comparedproperties toand the a polishedlarge amount sample of (TableHCP-phase.1). After electrochemical etching of the obtainedThe results samples of the at 1153 X-ray K fluorescent (25 min), the analysis concentration of the chemical of cobalt composition decreases, of but the the HCP-phase amount of particles,niobium, obtained reversely, by increases the precipitation compared on anodeto the polished and mounted sample on (Table the replica 1). are presented in Table1. They areThe clearly results different of the from X-ray the fluorescent matrix with analysis the small of concentration the chemical of composition cobalt and saturated of the HCP niobium-phase withparticles, the concentration obtained by up the to precipitation 17%. on anode and mounted on the replica are presented in Table 1. They are clearly different from the matrix with the small concentration of cobalt and saturated niobiumTable 1.withData the of concentration the chemical compositionup to 17%. of the samples of the Co-Ni-Nb alloy obtained on an X-ray-fluorescent energy-dispersion spectrometer. Table 1. Data of the chemical composition of the samples of the Co-Ni-Nb alloy obtained on an X-ray- Amount in wt. % (in Mass) fluorescentTreatment energy of-dispersion the Studied spectrometer. Sample Mn Co Ni Nb Amount in wt. % (in Mass) quenching at 1223 K, 90%Treatment rolling and of annealingthe Studied at 1153Sample K (25 min) after polishing <0.5Mn 67.8 ±Co0.9 28.5 Ni± 0.95 3.2Nb± 0.8 after etchingquenching at 1223 К, 90% rolling and annealing at 1153 К (25 min) <0.5 67.0 ± 0.9 28.7 ± 0.96 3.8 ± 0.81 participlesafter ofpolishing HCP-phase on the coal replica<0.5 53.367.8± 0.95± 0.9 29.928.5± ± 0.980.95 16.83.2 ±± 0.80.85 after etching <0.5 67.0 ± 0.9 28.7 ± 0.96 3.8 ± 0.81 participles of HCP-phase on the coal replica 53.3 ± 0.95 29.9 ± 0.98 16.8 ± 0.85 The analysis of the chemical composition of microzones of the studied alloy (Table2) performed on theThe scanning analysis electron of the chemical microscope composition equipped of with microzones the microanalyzer of the studied (Figure alloy7), (Table presents 2) performed a good agreementon the scanning with the electron X-ray-fluorescent microscope analysis. equipped with the microanalyzer (Figure 7), presents a good agreement with the X-ray-fluorescent analysis. Table 2. Data on the elements composition of the samples of the Co-Ni-Nb alloy obtained on the electron microscope with the microanalyzer. Table 2. Data on the elements composition of the samples of the Co-Ni-Nb alloy obtained on the electron microscope with the microanalyzer. Amount in wt. % (in Mass) Treatment of the Studied Sample MnAmount Co in wt. % Ni (in Mass) Nb Treatment of the Studied Sample quenching at 1223 K, 90% rolling and annealing at 1153 K (25 min) Mn Co Ni Nb quenching at 1223 К, 90% rolling and annealing at 1153 К (25 min) Matrix - 65.0 ± 0.7 29.9 ± 0.8 5.1 ± 0.6 Matrix - 65.0 ± 0.7 29.9 ± 0.8 5.1 ± 0.6 ± ± ± HCP–phaseHCP–phase -- 54.054.00.6 ± 0.6 30.230.2 ± 0.8 15.8 15.8 ± 0.60.6

FigureFigure 7. 7.X-ray X-ray fluorescence fluorescence spectra spectra of of the the Co-Ni-Nb Co-Ni-Nb alloy alloy measured measured in in matrix matrix (a ()a and) and particle particle (b ()b of) of secondarysecondary phase. phase.

According to obtained results, the samples in HCP phase consist of 52–55% Co, 29–31% Ni and According to obtained results, the samples in HCP phase consist of 52–55% Co, 29–31% Ni and 15–18% Nb (Tables 1 and 2). 15–18% Nb (Tables1 and2). 3.3. The Results of the Analysis of the Influence of Quenching Regime and Temperature—Strain rate Conditions Deformation on the Superplasticity of the Co-Ni-Nb Alloy In paper [10] superplasticity of the Co-Ni-Nb alloy is detected in the samples quenched at 1423 K (10 min) and 87% rolled at the deformation temperature 1143 K and the strain rate equals 0.7 × 10−3 s−1. Therefore, the oversaturated solid solution of the Co-Ni-Nb alloy was obtained at 1423 K (10 min).

Metals 2018, 8, 19 7 of 11

3.3. The Results of the Analysis of the Influence of Quenching Regime and Temperature—Strain Rate Conditions Deformation on the Superplasticity of the Co-Ni-Nb Alloy In paper [10] superplasticity of the Co-Ni-Nb alloy is detected in the samples quenched at Metals1423 K2018 (10, 8, min)19 and 87% rolled at the deformation temperature 1143 K and the strain rate equals7 of 10 0.7 × 10−3 s−1. Therefore, the oversaturated solid solution of the Co-Ni-Nb alloy was obtained at 142367CoNi5Nb K (10 min). alloy, rolled to 60% at high temperature strain, reveals the signs of superplasticity. The highest67CoNi5Nb ductility alloy, value rolled δ = to 158% 60% atand high the temperature index m = 0.41, strain, which reveals describes the signs the ofsensitivity superplasticity. of the flowThehighest rate of stress ductility to strain, value δ are= 158% achieved and theat 1203 index K mand= 0.41,ε = which 1.2 × 10 describes−4 s−1, correspondingly. the sensitivity of the flow . −4 −1 rate ofAfter stress quen to strain,ching atare 1423 achieved K (10 at min) 1203 and K and 90%ε = rolling 1.2 × 10 the Cos -Ni, correspondingly.-Nb alloy shows the effect of superplasticityAfter quenching in the deformation at 1423 K (10 range min) of and 1053 90%–1243 rolling K. Maximum the Co-Ni-Nb values alloy of the shows relative the residual effect of elongationsuperplasticity (δ) and in the the deformation m index reach range 780% of and 1053–1243 0.44, respectively, K. Maximum at valuesthe deformation of the relative temperature residual 1143elongation K and (velocityδ) and the0.72m ×index 10−3 s− reach1 (Figure 780% 8a). and The 0.44, experimentally respectively, defined at the deformationdependence of temperature the tensile 1143 K and velocity 0.72 × 10−3 s−1 (Figure8a). The experimentally defined dependence of the tensile strength (σ) of the Co-Ni-Nb alloy on the deformation velocity. ( ε ) at 1143 K for optimal strength (σ) of the Co-Ni-Nb alloy on the deformation velocity (ε) at 1143 K for optimal superplasticity superplasticity is precisely (R2 = 0.9994) described by .the σ = 1111.7 × 0,4644 function (Figure 8b). is precisely (R2 = 0.9994) described by the σ = 1111.7 × ε0,4644 function (Figure8b). Conformity of this . Conformitydependence of with this the dependence common empirical with the σcommon= k × εm empiricalequation σ verifies = k × a viscosem equation state verifies of the Co-Ni-Nba viscose statealloy of after the being Co-Ni treated.-Nb alloy This after empirical being equation treated. was This used empirical to calculate equation the value was ofused coefficient to calculatek (1111.7) the valueand the of valuecoefficie ofnt the k index(1111.7) of and the strainthe value rate of sensitivity the index of of the the flow strain tension rate sensitivity (m) ≈ 0.46, of thethe latterflow tension is close (tom) 0.44 ≈ 0.46, obtained the latter with is Hedworth-Stowell close to 0.44 obtained method with [ 11Hedworth]. The decrease-Stowell of method the alloy [11]. quenching The decrease temperature of the . alloy quenching temperature from 1423 K to 1223 K leads (at superplastic deformation −T3SPD− =1 1143 K from 1423 K to 1223 K leads (at superplastic deformation TSPD = 1143 K and ε = 1 × 10 s ) to the andimprovement = 1 × 10 of−3 the s−1) ductilityto the improv fromement 780 to 1140%.of the ductility from 780 to 1140%

100 (b) 2 (a) 160 800 80 120

600 60

MPa , MPa ,

, % , 80

, 

400 σ 40 1 

200 40 20

0 0 0 1000 1100 1200 1300 0 0.002 0.004 0.006 −1 T, K , s

Figure 8. TheThe mechanical mechanical properties properties of of the the Co Co-Ni-Nb-Ni-Nb alloy alloy at at the the superplastic superplastic deformation. deformation. Dependencies of the relative residual elongation ( δ) (curve 1) and the tensile tensile strength strength ( σ) (curve (curve 2)) on on thethe superplastic deformationdeformation temperaturetemperature ( T(T)) obtained obtained at at velocity velocity = 0.72= 0.72× ×10 10−−33 ss−−11 ((aa)) and and dependence dependence . of the tensile strength ( σ) on the stretching speed (ε) at) atT T= = 1143K 1143K (b (b).).

There are two reasons for the plasticity strengthening for the Co-Ni-NbCo-Ni-Nb alloy aft afterer quenching fromfrom 1223 K and 90 90%% rolling. The The first first reason reason is is that that the the grain grain size size ( (d)) after quenching from from 1223 1223 K K equals 18 µm.µm. This is 3.5 to 4 times less than after quenching from from 1423 K. The second reason is that after quenching from from 1223 1223 K K (10 (10 min) min) the the twin twin quantity quantity is is much much smaller smaller (compare (compare Figure Figuress 1 and9 9a).a). The twins are known to worsen superplastic properties of alloys [[2,32,3]. Therefore, the quenching of thethe Co Co-Ni-Nb-Ni-Nb alloy from 1423 K proves to be inefficient inefficient due to insufficientinsufficient plasticity at superplastic deformation, since since relative relative elongation af afterter the the break is 1.6 times smaller than after quenching from 1223 K. The experimental results can find find their practical practical application application in the the improvement improvement of of technological technological plasticity of the CoCo-Ni-Nb-Ni-Nb alloy. Therefore, Therefore, the the following following regime regime of of treatment treatment can can be be sug suggested:gested: quenching from 1223 K (10 min) + 90% rolling and superplastic deformation at 1143 K and  = 1 × 10−3 s−1. Such a regime makes it possible to obtain a structure with good technological characteristics and optimal combination of exploiting features. Next, for the further studies of the alloy, processing was employed—quenching at 1223 K (10 min) + 90% rolling and annealing at 1153 K (20 min). This processing helped produce a fine-grain superplastic structure with an average grain size (d) of the matrix ≈ 2.7 µm. The metallographic pictures show the precipitation of spherical particles on the borders of the matrix with the average

Metals 2018, 8, 19 8 of 11 quenching from 1223 K (10 min) + 90% rolling and superplastic deformation at 1143 K and . ε = 1 × 10−3 s−1. Such a regime makes it possible to obtain a structure with good technological characteristics and optimal combination of exploiting features. Next, for the further studies of the alloy, processing was employed—quenching at 1223 K (10 min) + 90% rolling and annealing at 1153 K (20 min). This processing helped produce a fine-grain superplastic structure with an average grain size (d) of the matrix ≈ 2.7 µm. The metallographic pictures show Metals 2018, 8, 19 8 of 10 the precipitation of spherical particles on the borders of the matrix with the average size of grains size(d) equal of grains from (d 1) equal to 1.5 fromµm (Figure 1 to 1.54 µmb). This(Figure fact 4b). is in This agreement fact is in withagreement the above-presented with the above- resultspresented for resultssuperplastic for superplas deformation.tic deformation. This phenomenon This was phenomenon verified by X-ray was verified diffraction by and X-ray electron-microscopy diffraction and electronmeasurements-microscopy which measurements show that optimal which superplastic show that properties optimal superplastic are typical for properties the alloy with are typical two-phase for thefine-grain alloy with structure two-phase (d = fine 4 µ-grainm), consisting structure ( ofd = grains4 µm), ofconsistingγ-matrix of andgrains particles of γ-matr ofix the and secondary particles f ofHCP-phase. the secondary The volume HCP-phase. part of TheHCP-phase volume particles part of (< HCPη>)-phase defined particles with the ( methods) defined of quantitative with the methodsmetallography of quanti istative 17–20%. metallography The samples is 17 of– the20%. Co-Ni-Nb The samples alloy of the were Co subjected-Ni-Nb alloy to deformationwere subjected at . −3 −1 Tto= deformation 1143 K and atε T= = 1 1143× 10 K ands ε. The= 1 × determined10−3 s−1. The determined degree of deformation degree of deformation at the relative at the residual relative residualelongation elongation (δ) equals (δ 26%.) equals 26%.

(a) (b)

Figure 9. The structures of the Co-Ni-NbCo-Ni-Nb alloys before ( a) and after (b) superplasticsuperplastic deformation at . temperature 1143 K and ε = 1 × 10−−3 s−−1 1(d0 = 2.7 µm). temperature 1143 K and ε = 1 × 10 s (d0 = 2.7 µm).

In the course of experiments on the deformation of the studied alloy it was stated that In the course of experiments on the deformation of the studied alloy it was stated that superplastic superplastic deformation provokes the growth of the grain size. This growth is much faster in the deformation provokes the growth of the grain size. This growth is much faster in the working part of working part of sample than in the non-deformed zones. After 26% deformation an average size of sample than in the non-deformed zones. After 26% deformation an average size of grains increased, grains increased, twice reaching = 5.4 µm. Moreover, the grains are expanding in all directions twice reaching = 5.4 µm. Moreover, the grains are expanding in all directions and their number and their number is decreasing. is decreasing. The obtained characteristics of microstructure features and results of mechanical tests are The obtained characteristics of microstructure features and results of mechanical tests are presented in Table 3. presented in Table3. Table 3. Characteristics of microstructure features and results of mechanical tests depending on the conditions for sampleTable preparation. 3. Characteristics of microstructure features and results of mechanical tests depending on the conditions for sample preparation. Treatment of the Studied Sample Grain Size, μm Phase Composition Microhardness, MPa preliminary quenching from 1223 K (10 µ Treatment of the Studied Sample Grain Size,18 m PhaseFCC Composition Microhardness,4405 MPa min) and 90% rolling preliminary quenching from 1223 K preliminary quenching from 1223 K (10 18 FCC 4405 (10 min) and 90% rolling min) and 90% rolling and TSPD = 1143 K -* FCC + HCP 2860 preliminaryand quenching ε = 1 × 10− from3 s−1 1223 K (10 min) and 90% rolling and -* FCC + HCP 2860 * The. track of− the3 − grain1 size of the matrix is not possible to define after SPD. TSPD = 1143 K and ε = 1 × 10 s * The track of the grain size of the matrix is not possible to define after SPD. After the superplastic deformation of the samples with the initial grain size d0 = 2.7 µm (at T = 1143 K and ε = 1 × 10−3 s−1) no significant formation of intergranular voids and cracks is observed as it was for the alloy with a large initial size. It means that superplastic deformation triggers After the superplastic deformation of the samples with the initial grain size d0 = 2.7 µm accommodative processes.. Using the metallographic and X-ray methods it was shown that during (at T = 1143 K and ε = 1 × 10−3 s−1) no significant formation of intergranular voids and cracks is superplastic deformation the dissolution of HCP-phase particles occur under optimal conditions. The pictures of the structure (Figure 9) clearly present the dissolution of spherical particles of HCP-phase, which is accompanied by the formation of shear transformation zones [12–16] near the boundaries of the matrix. The growth of grains and their consequent decrease in number is observed in the zones of the structure lacking particles of the secondary phase (Figure 9), since the temperature of the beginning of the reverse dissolution of the HCP-phase particles coincides with the optimal temperature of the superplastic deformation. This phenomenon supports the fact that the directed mass-transfer on grain boundary is an accommodative process, initiated by the dissolution of the secondary phase particles, which causes the grain growth and removal of the defects arising from the grain boundary sliding. The authors of the papers [17,18] suggest considering the process of the re-

Metals 2018, 8, 19 9 of 11 observed as it was for the alloy with a large initial size. It means that superplastic deformation triggers accommodative processes. Using the metallographic and X-ray methods it was shown that during superplastic deformation the dissolution of HCP-phase particles occur under optimal conditions. The pictures of the structure (Figure9) clearly present the dissolution of spherical particles of HCP-phase, which is accompanied by the formation of shear transformation zones [12–16] near the boundaries of the matrix. The growth of grains and their consequent decrease in number is observed in the zones of the structure lacking particles of the secondary phase (Figure9), since the temperature of the beginning of the reverse dissolution of the HCP-phase particles coincides with the optimal temperature of the superplastic deformation. This phenomenon supports the fact that the directed mass-transfer on grain boundary is an accommodative process, initiated by the dissolution of the secondary phase particles, which causes the grain growth and removal of the defects arising from the grain boundary sliding. The authors of the papers [17,18] suggest considering the process of the re-orientation and the growth of the grains under super-plastic deformation as a result of transformation of part of the material into the liquid state. The liquid component facilitates the sliding of the grains’ boundaries and acts as a soft sliding. However, this liquid oiling is not a liquid as it is. Such a state is called liquid-like and it is considered a shifting transformation zone where the switching of chemical bonds takes place fully or to some extent [11]. Such switching is obviously a solid phase phenomenon, bringing about a decrease of Gibbs energy and is non-reversible as a mechanical-chemical reaction, which causes the formation of new products and gives off heat [19]. In the SPD process, the material is in the state of intense dynamic loading; in such a case the Stokes-Einstein equation can be used to describe the behavior of the alloy. The Stokes-Einstein Equation (1) as well as the dynamic viscosity Equation (2) are used for calculation of the energy:

Eη η = η0 exp RT (1)

η ∼ τµ (2) where η0 is a coefficient independent from temperature, Eη is the activation of relaxation energy of a viscous flow and τ—structural relaxation time. According to Landau and Lifshitz [20], under extreme conditions, viscosity can be equated for the product of the relaxation time by the shear modulus. According to [4], the time of structural relaxation for the 67CoNi5Nb alloy is 4 h at 400 ◦C and it equals 5 h at 450 ◦C. On the basis of Equations (1) and (2) one can obtain the equation for the activation of relaxation energy:

τ1 Eη = RTSPDln (3) τ2

The estimated value of the activation of relaxation energy is 120 kJ/mol for non-superplastic materials [21], and for a superplastic material it is 2.1 kJ/mol.

4. Conclusions The studies have shown an impact of temperature on microstructure (a grain size of the matrix, the presence of twins, and a phase composition) and superplastic properties of the Co-Ni-Nb alloy. Metallographic and X-ray diffraction methods have proved that the quenching temperature decrease from 1423 K (10 min) to 1223 K (10 min) does not change the phase composition. A significant reduction of the number of twins was observed after the quenching of the studied alloy at 1223 K (10 min) compared to the procedure at 1423 K (10 min). The decrease of the alloy quenching temperature from 1423 K to 1223 K leads to the improvement of the ductility from 780% to 1140%. This phenomenon is conditioned by the following processes: firstly, a grain size is decreasing by 3.5–4 times with the quenching temperature decrease to 1223 K (10 min), and secondly, the twins number is also reducing. The Co-Ni-Nb alloy after quenching from 1223 K (10 min) and rolling by 90% demonstrates the superplasticity effect in the deformation temperature range of 1053–1243 K. Metals 2018, 8, 19 10 of 11

The transformation of the HCP-phase particles during the superplastic deformation under optimal conditions was found. Moreover, alongside the dissolution of the spherical particles of HCP-phase the formation of “shear transformation” zones take place nearby the matrix boundaries. The growth of the grain size and the decrease of the number of grains were observed in the zones without the secondary phase. Since the temperature of the beginning of the reverse transformation of the HCP-phase particles coincides with the optimal temperature of superplastic deformation, it is assumed that the accommodative process in the shear transformation zones under the deformation influences the transformation of the secondary phase. This shear transformation zone is characterized by the repaired defects arising from the grain boundary sliding.

Acknowledgments: A.T. acknowledges the financial support Bolashak International Scholarship Program of Kazakhstan. Authors gratefully acknowledge the financial support of Polish Government Plenipotentiary for JINR in Dubna (Grant No. 389/07.06.2017, p. 20). Author Contributions: The development of the experiments was carried out by D. Yerbolatuly and A. Tussupzhanov. The images design and the experiments were completed by A. Tussupzhanov. The X-ray results were analyzed by D. Yerbolatuly. L.I. Kveglis accomplished the analysis and consolidation of all experimental studies. A. Filarowski made a research of the microstructure and took part in the data analysis. Conflicts of Interest: The authors declare no conflict of interest.

References

1. Hosford, W.F. Mechanical Behavior of Materials; Cambridge University Press: Cambridge, UK, 2005. 2. Kaibyshev, O.A. Superplasticity of Alloys, Intermetallics and ; Springer-Verlag: Berlin, Germany, 1992. 3. Pilling, J.; Ridley, N. Superplasticity in Crystalline ; Institute of Metals: London, UK; Brookfield, VT, USA, 1989. 4. Molotilov, B.V. Precision Alloys, Handbook; Metallurgy: Moscow, Russia, 1974. 5. Wang, Y.M.; Liu, H.S.; Zheng, F.; Jin, Z.P. The isothermal section of the Co–Ni–Nb ternary system at 1123 K determined by triple technique. J. Alloys Compd. 2008, 454, 501–505. [CrossRef] 6. Nieh, T.G.; Wadsworth, J. Microstructural characteristics and deformation properties in superplastic intermetallics. Mater. Sci. Eng. A 1997, 88, 239–240. [CrossRef] 7. Xhunga, I.K. Recessible Task Lighting. U.S. Patent 20110103075 A1, 5 May 2011. 8. Borisov, A.K.; Goryushkina, N.M. Properties of current-conducting spring alloy 67KN5B in relation to degree of deformation and heat treatment. Met. Sci. Heat Treat. 1972, 14, 950–954. [CrossRef] 9. Tushinskii, L.I. New Methods of Hardening and Metal Processing; Novosibirsk State Technical University: Novosibirsk, Russia, 1980; pp. 71–79. 10. Radashin, M.V.; Nazarov, U.K.; Abrosov, V.N. The Superplasticity of Precipitation-Hardening Alloy 67KN5B. In Proceedings of the Evolution of Defect Structures in Metals and Alloys, Barnaul, Russia, 1992; p. 178. 11. Hedworth, J.; Stowell, M.J. The measurement of strain-rate sensitivity in superplastic alloys. J. Mater. Sci. 1971, 6, 1061–1069. [CrossRef] 12. Langer, J.S. Instabilities and pattern formation in crystal growth. Rev. Mod. Phys. 1980, 52, 1–28. [CrossRef] 13. Falk, M.L.; Langer, J.S. Shear transformation zone theory elasto-plastic transition in amorphous solids. Phys. Rev. 1998, E57, 7192–7204. 14. Lemaitre, A.; Carlson, J. Boundary lubrication with a glassy interface. Phys. Rev. E 2004, 69.[CrossRef] [PubMed] 15. Maloney, C.; Lemaitre, A. Universal breakdown of elastisity at the onset of material failure. Phys. Rev. Lett. 2004, 93.[CrossRef][PubMed] 16. Lemaitre, A. Origin of a repose angle: Kinetics of rearrangement for granular materials. Phys. Rev. Lett. 2002, 89.[CrossRef][PubMed] 17. Straumal, B.B.; Sauvage, X.; Baretzky, B.; Mazilkin, A.A.; Valiev, R.Z. Grain boundary films in Al–Zn alloys after high pressure torsion. Scr. Mater. 2014, 70, 59–62. [CrossRef] 18. Protasova, S.G.; Kogtenkova, O.A.; Straumal, B.B.; Zi˛eba,P.; Baretzky, B. Inversed solid-phase grain boundary wetting in the Al–Zn system. J. Mater. Sci. 2011, 46, 4349–4353. [CrossRef] 19. Zel’dovich, Ya.B.; Rayzer, Yu.P. Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena; Nauka: Moscow, Russia, 2008. Metals 2018, 8, 19 11 of 11

20. Landau, L.D.; Lifshitz, E.M. Theory of Elasticity, 3rd ed.; Butterworth-Heinemann: Oxford, UK, 1986; Volume 7. 21. Noskova, N.I. Physics of Deformation of Nanocrystalline Metals and Alloys. In Proceedings of the 1X International Seminar Dislocation structure and mechanical properties of metals and alloys, Yekaterinburg, Russia, 2002; pp. 91–92.

© 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).