evaluating a new core-sheath procedure for processing hard metals by equal-channel angular pressing

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DOI: 10.1002/adem.201300474
LLPAPER

Evaluating a New Core-Sheath Procedure for ProcessingHard Metals by Equal-Channel Angular Pressing**

By Hamed Shahmir, Mahmoud Nili-Ahmadabadi,* Mojtaba Mansouri-Arani, Ali Khajezadeand Terence G. Langdon

A new design of billet, based on a core–sheath configuration, was used for the processing of Ni, Fe, and aNiTi alloy by equal-channel angular pressing (ECAP) at room temperature. This configuration involvesinserting metal cores within Fe sheaths prior to processing and it is designed especially for use withhard-to-deform materials. Billets were processed through one or two ECAP passes at room temperatureand the microhardness values were recorded across the transverse directions within the cores to evaluatethe flow process. As in conventional ECAP, the hardness increased significantly after the first pass andthere were regions of lower hardness along the bottom surfaces of each core. The gradient of hardnessdecreased with increasing core diameter but the average microhardness values remained unchanged.Three-dimensional finite element simulations were used to evaluate the flow behavior after one pass ofECAP using different core metals. These simulations show the lower areas of the cores undergo lessdeformation than the upper areas and the homogeneity increases with increasing levels of friction at thecore–sheath interface.

1. Introduction

The process of equal-channel angular pressing (ECAP) isnow one of themost important techniques for the processing ofmetals through the application of severe plastic deformation(SPD) and thereby producing materials having ultrafine grainsizes in the submicrometer range.[1–3] In practice, ECAP is aprocessing procedure in which a sample, generally in the form

[*] Prof. M. Nili-Ahmadabadi, H. Shahmir, M. Mansouri-Arani,A. KhajezadeSchool of Metallurgy and Materials, College of Engineering,University of Tehran, Tehran, IranCenter of Excellence for High Performance Materials, School ofMetallurgy and Materials, University of Tehran, Tehran, IranE-mail: [email protected]. T. G. LangdonMaterials Research Group, Faculty of Engineering and theEnvironment, University of Southampton, SouthamptonSO17 1BJ, UKDepartments of Aerospace and Mechanical Engineeringand Materials Science, University of Southern California,Los Angeles, CA 90089-1453, USA

[**] The authors are indebted to Mr. Mahdi Naderi for usefuldiscussions of simulations. The work of one of us (TGL) wassupported by the European Research Council under ERC GrantAgreement No. 267464-SPDMETALS.

DOI: 10.1002/adem.201300474 © 2014 WILEY-VCH VerlADVANCED ENGINEERING MATERIALS 2014,

of a rod or bar, is forced through a die constrained within achannel, which is bent through a sharp angle near the center ofthe die. Since the two parts of the channel are equal in cross-section on either side of the bend, the sample emerges from thedie having experienced a high-shearing strain but withoutany change in the cross-sectional dimensions. Therefore, thesample can be pressed repetitively through the die in orderto attain exceptionally high strains.

Processing by ECAP is generally considered superior tomost other SPD techniques because it uses relatively large bulksamples and develops near uniform structures. In addition, it isa simple processing technique that has the capability, byadding a step of conform processing, of being developed into acontinuous processing procedure.[4,5] Furthermore, althoughthe samples generally used in laboratory investigations havediameters of only �10mm, the process is easily scaled-up foruse with larger billets[6,7] and this provides an opportunity forusing the technology in commercial applications.[8] The mostimportant parameter in ECAP is the magnitude of the imposedstrain, which was calculated in an early analysis through anequation incorporating the channel angle, w, and the outer arcof curvature, c, where the two parts of the channel intersect.[9]

It is important to recognize that the shear strain imposed onthe billet during ECAP is generally homogeneous[10,11] butin practice the strain may be affected by several factorsthat produce inhomogeneities in the internal microstructure.Possible sources of these inhomogeneities include the frictional

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H. Shahmir et al./A New Core-Sheath Procedure for ECAP

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forces between the billet and the die walls[12–14] and the
presence of a “dead zone” or corner gap, which may occur ifthe billet loses contact with the die wall at the outer corner as itpasses through the shear zone.[15,16] A high degree ofhomogeneity is usually achieved when conducting multiplepasses in ECAP although there may remain a small region oflower hardness adjacent to the bottom surface of the billet.[17]

It is relatively easy to press soft pure face-centered cubicmetals by ECAP but processing is difficult in some materialssuch as hexagonal close-packed metals where the number ofindependent slip systems is limited. An added difficulty is therequirement to conduct the ECAP at a relatively lowtemperature in order to avoid significant grain growth. Thisdifficulty led to an early conclusion, in experiments conductedon commercial purity (CP) titanium and NiTi shape memoryalloys using an ECAP die with an angle of w¼ 90°, that it wasnot possible to process these materials at room temperaturebecause of the occurrence of significant segmentation in whichthe billets become sheared into discrete but inter-connectedsegments during the pressing operation.[18–21] Detailed finiteelement calculations showed these so-called “hard-to-deform”

alloys may be processed more easily by using an ECAP diehaving an increased channel angle[22] and this approachwas subsequently confirmed in experiments on a two-phaseMg–8% Li alloy[23] and CP Ti.[24]

Recently, a new billet design was introduced, which wasused successfully to process NiTi shape memory alloys byECAP through two passes at room temperature using aconventional die design with a channel angle of w¼ 90°.[25] Inthis procedure, the hard-to-deform material was inserted as acore within an Fe sheath to give a core–sheath billet. Inaddition, the ECAP processing of different specimens as a corewith different cross-sections is obtainable by using this designin a single ECAP die. Based on this initial success, the presentinvestigation was initiated to more fully evaluate, usinghardness measurements and finite element modeling (FEM),the deformation behavior occurring within core–sheath billetsof three different materials processed by ECAP. In order toprovide a direct comparison between the experiments andFEM, each sample was pressed for only one or two passes togive information on the general feasibility of this newprocessing technique.

Fig. 1. Schematic cross-section of a billet showing the Fe sheath (30mm in diameter and50mm in length) and the Fe, Ni, and NiTi cores (3 or 5mm in diameter and 40mm inlength).

2. Experimental Materials and Procedures

The experiments were conducted using three materials:a commercial nickel of 99.7% purity, an electrolitic iron, and aNi-50.2 at% Ti alloy, where these materials are henceforthdenoted by Ni, Fe, and NiTi, respectively. The Ni and Fe weresupplied in the form of bars having diameters of 30mmand these bars were annealed at 873K for 60min priorto processing by ECAP. The NiTi alloy was prepared using anon-consumable vacuum arc melting technique in a water-cooled copper crucible and with melted pure titanium usedas a getter in the chamber. After several remeltings forhomogenization, the NiTi ingot was hot forged and then

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homogenized at 1273K for 720min. Thereafter, it was hotrolled at 1273K into rods with cross-sections of 7� 7 mm2 andthese rods were solution annealed at 1123K for 60min andquenched into ice-water. Samples for ECAP were cut usingwire electro-discharge machining with lengths of 40mm anddiameters of 3 or 5mm to serve as the cores of the core–sheathbillets. Samples of similar dimensions were also prepared fromthe Ni and Fe bars. All core samples were fitted in Fe sheathswith diameters of 30mm and lengths of 50mm as depictedschematically in Figure 1. It is apparent from Figure 1 that theFe sheath is in direct contact with the die walls throughoutthe ECAP processing. In addition, some ECAP billets of thesame overall dimensions were fabricated only from Ni or Fein order to provide a direct comparison with the core–sheathconfiguration.

The processing by ECAP was conducted at room tempera-ture using a hydraulic press with a capacity of 50 tons and asolid die with an internal channel angle, w, of 90° and an outerarc of curvature,c, of 20°. The pressing speedwas 0.05mms�1,molybdenum disulfide (MoS2) was used as a lubricant and allbillets were processed for one pass. Following ECAP, micro-hardness measurements were taken along vertical traverses atthe center points of longitudinal sections of the as-pressedbillets cut parallel to the pressing direction, where the pressingis along the X direction in the conventional notation forECAP.[26] These measurements were taken at intervals of0.3mmusing a load of 100 gf applied for 10 s and at every pointthe local value of Hv was taken as the average of sevenseparate hardness values taken around the selected point afterremoving the highest and lowest values.

Three-dimensional (3D) finite element simulations ofmaterial plastic flow and the strain condition were conductedusing ABAQUS V.6.12 software. A material model withisotropic hardening was applied together with tensile datafrom a plot of true stress versus true strain as shown in Figure 2where the stress–strain curves of NiTi and the Fe sheath arecompared using wire-shaped samples of the two materials.

& Co. KGaA, Weinheim DOI: 10.1002/adem.201300474ADVANCED ENGINEERING MATERIALS 2014,

Fig. 2. Stress–strain curves for NiTi and Fe obtained at a strain rate of 1.0� 10�3 s�1.

Fig. 3. Longitudinal section of a billet after ECAP: Fe sheath 30mm in diameter� 50mm length and NiTi core 3mm in diameter� 40mm in length. The white arrow andwhite line show the point and path for measuring the microhardness.


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Thesewireswere prepared by hot rolling of the ingots followedby cold rolling to a cross-section of 1�1 mm2 with an inter-pass annealing at 973K for 10min. The stress–strain curveswere recorded by tensile testing wires with lengths of 100mmusing a Santam universal testing machine with a load capacityof 2 kN and spindle-type jaws. The cross-head speed was set at0.12mms�1 to give a true constant strain rate of 1.0� 10�3 s�1

and the strain distributions were measured along thelongitudinal directions. The die and the punch consideredfor the experimental and numerical analyses were made ofhigh-strength steel and, as the strength and rigidity of the steelare very high compared to the billet materials, the die andpunchweremodeled as rigid surfaces. The inside surface of thedie and the outer surface of the billet may be in close contactdepending on the local flow behavior. Accordingly, a nominalvalue of 0.2 was assumed for the coefficient of friction betweenthese two contacting surfaces using MoS2 as a lubricant.

Different boundary conditions were applied to the modelfor the core–sheath configuration. Thus, the core and sheathwere modeled with friction coefficients, K, of 0.3 and 0.6 andwith the condition that all nodes on the surface of the corecontact directly to all nodes on the surface of the sheathwithout any sliding so that K is 1. A constant punch speed of0.05mms�1 was imposed on the rigid punch in agreementwith the experimental conditions and any possible heatgeneration due to friction and/or deformation was ignored.The core and sheath volumes were meshed to �110 000 and42 000 four-node elements, respectively.

3. Experimental Results

3.1. Fundamentals of ECAP Using a Core–Sheath BilletFigure 3 shows a longitudinal section of a billet after one

pass with a NiTi core (3mm in diameter and 40mm in length)in an Fe sheath (30mm in diameter and 50mm in length). Thisresult demonstrates the capability of successfully processingthe NiTi alloy by ECAP at room temperature using a NiTi

DOI: 10.1002/adem.201300474 © 2014 WILEY-VCH VerlagADVANCED ENGINEERING MATERIALS 2014,

sample contained within an Fe sheath. Processing wasperformed successfully up to two passes of ECAP bycontrolling the processing variables. Inspection of the proc-essed billet in Figure 3 reveals the development of a significantfillet radius at the outer intersection of the channels but with nocorresponding fillet radius at the inner point of intersection.The equivalent strain imposed on the billet may be calculatedfrom the expression[9]

e ¼ 1ffiffiffi3

p 2 cotw

2þ c

2

� �þ c cosec

w

2þ c

2

� �� ð1Þ

where the angles w and c are marked in Figure 3. Carefulmeasurements from Figure 3 show that these angles increasefor the core material so that w � 92° and c� 24° and therefore,using Equation 1, the strain for the NiTi core is �1, which isslightly smaller than the strain of �1.05 for the billet.

Close inspection of Figure 3 shows also that, for the core andunlike the sheath, there are arcs of curvature at both the innerand outer points of intersection of the channels. These twodiscrete configurations are depicted schematically in Figure 4,where the channel in a conventional ECAP die is shown in (a)[9]

and (b) depicts a channel, where there are arcs of curvature atboth the inner and outer surfaces.[27] It was suggested earlierthat the absence of a fillet radius in a conventional die at theinner point of intersection of the channels may produce a stressconcentration in the billet but nevertheless it was demonstrat-ed, in experiments using a special die with equal fillet radii atthe outer and inner points of intersection, that this die is lesseffective than a conventional die in producing a homogeneousstructure.[28]

3.2. Values of the MicrohardnessThe results of the Vickers microhardness measurements are

summarized in Table 1 for the central areas of cores havingdiameters of 3mm, where the measurements were taken at thelongitudinal section illustrated by the white arrow in Figure 3.

GmbH & Co. KGaA, Weinheim http://www.aem-journal.com 3

Fig. 4. The channel within an ECAP die: (a) with an intermediate outer of arc of curvature of c[9] and (b) withtwo equal arcs of curvature of radius R at the intersection.[27]

Table 1. Microhardness measurements of Ni, Fe, and NiTi before and after one passprocessing by ECAP.

Material Condition Microhardness

Ni Fully annealed 101� 3ECAP (fully Ni billet) 227� 6ECAP (3mm Ni core–Fe sheath) 195� 10

Fe Fully annealed 110� 5ECAP (fully Fe billet) 210� 5ECAP (3mm Fe core–Fe sheath) 201� 12

NiTi Solution annealed 201� 5ECAP (3mm NiTi core–Fe sheath) 332� 24

80

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-3 -2.4 -1.8 -1.2 -0.6 0 0.6 1.2 1.8 2.4 3

Vic

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v)

Distance from center (mm)

5 mm

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Bottom Top

Fe core - Fe sheath

Core

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v)


5 mm

3 mm

Core

Fully anneal

poTmottoB

Ni core - Fe sheath

a)

b)

Fig. 5. Variation of the Vickers microhardness along vertical traverses at the centers ofthe longitudinal section of (a) Ni and (b) Fe cores (3 and 5mm in diameter) in Fe sheathsafter one pass of ECAP.


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Results are given for three different cores contained within Fesheaths after pressing through one ECAP pass. In addition,microhardness measurements are tabulated for the same areasfor conventional Ni and Fe billets processed by ECAP withoutusing a core–sheath configuration and for samples in the initialannealed conditions without processing by ECAP.

Inspection of Table 1 shows that the hardness increasessignificantly after one pass both in the core–sheath conditionand in the conventional billets for all materials such that, byreference to the fully annealed condition, there is an increase bya factor of �2 for Ni and Fe and �1.5 for the NiTi alloy. Thehardness values of Ni and Fe in the core–sheath condition arelower than in the conventional Ni and Fe billets and thisdifference in hardness,DHv, is higher for Ni (DHv� 30) than Fe(DHv� 10). In addition, the magnitudes of the error bars showthat the variations in hardness values are larger for the core–sheath condition than for the conventional Ni and Fe billets.

Figure 5 shows the variation of the Vickers microhardnesswith the associated error bars along vertical traverses at thecenters of the longitudinal sections of processed billets for Niand Fe cores of 3 and 5mm diameter contained within Fesheaths: the path for recording these hardness values is shownby the vertical white line in Figure 3. The individual points areplotted as a function of the measured distance from the center

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of the billet with the lower surface on the leftand the upper surface on the right. In terms ofthe distributions of hardness values, afterone pass for Ni cores having 3 and 5mmdiameters it is apparent from Figure 5a thatthe average hardness values at the centers ofthe cores are the same at Hv � 195. Thesemeasurements also provide a visual displayof the level of hardness homogeneity alongvertical traverses at the centers of thelongitudinal sections. Thus, there is a gradientin hardness values from higher values at thetop surfaces to lower values at the bottomsurfaces thereby revealing a general inhomo-geneity in the cores. The difference inhardness values between the top and bottomsurfaces for the Ni cores is given by DHv� 58for the cores with both 3 and 5mm diameters.

m DOI: 10.1002/adem.201300474ADVANCED ENGINEERING MATERIALS 2014,

80

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-1.5 -1.2 -0.9 -0.6 -0.3 0 0.3 0.6 0.9 1.2 1.5

Vic

kers

mic

roha

rdne

ss (H

v)


Fe billet

Core-sheath

poTmottoB

Fully anneal

Fig. 6. Variation of the Vickers microhardness along vertical traverses at the centers ofthe longitudinal section of an Fe billet and an Fe core (3mm) and Fe sheath combinationafter processing through one pass of ECAP.

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Hv)


Fe

Ni Core- Fe Sheath

poTmottoB

Interface

htaehShtaehS

Core

Fig. 7. Variation of the Vickers microhardness along vertical traverses at the centers ofthe longitudinal section of an Fe billet and an Ni core (3mm) and Fe sheath combinationafter processing through one pass of ECAP: the vertical dashed lines show the positions ofthe upper and lower interfaces in the core–sheath configuration.

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-1.5 -1.2 -0.9 -0.6 -0.3 0 0.3 0.6 0.9 1.2 1.5

Vic

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roha

rdne

ss (H

v)


NiTiFeNi

Bottom Top

3mm core - Fe sheath

Fig. 8. Variation of the Vickers microhardness along vertical traverses at the centers ofthe longitudinal section for Ni, Fe, and NiTi cores after one pass of ECAP.


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There are also similar trends for the Fe cores shown in Figure 5balthough the hardness values for the Fe cores are generallyhigher than for the Ni core.

The distribution of hardness values for the Fe core with3mm diameter is shown in Figure 6 together with measure-ments taken on a vertical traverse at the center of thelongitudinal section of a conventional Fe billet. These resultsdemonstrate that the average values of hardness at the centersof the billets are approximately identical but nevertheless theconventional billet exhibits a higher degree of homogeneity.

Inspection of these results suggests that the interfacebetween the core and sheath may have an important effect onthe degree of inhomogeneity within the billet. Accordingly,the hardness values were measured at points on the Fesheath corresponding to the upper and lower positions on theNi core with a diameter of 3mm. The results are plotted inFigure 7 and it is apparent that the hardness values of the Fesheath in the vicinity of the interfaces are approximately equalbut generally lower than the values for the conventional Febillet.

After one pass of ECAP, Figure 8 shows the hardness valuesalong vertical traverses at the centers on longitudinal sectionsof the processed billets for 3mm diameter Ni, Fe, and NiTicores contained within Fe sheaths. Close inspection shows thehardness values and the gradient in the hardness values aresignificantly higher in NiTi than in Ni and Fe. These resultssuggest there is a band of lower hardness near the lowersurface for all materials. The hardness values at the top arehigher by comparison with the values at the bottom by factorsof �1.4, �1.3, and �1.2 for NiTi, Ni, and Fe, respectively.

3.3. An FEM Analysis of the Principles of the Core–SheathBillet in ECAP

Figure 9 shows the effective strain distributions for a 3mmdiameter Fe core contained within an Fe sheath billet and


pressed through one pass under different boundary conditionscorresponding to different values of the friction coefficient, K,of (a) 0.3, (b) 0.6, and (c) 1.0, respectively. These distributionscorrespond to the longitudinal planes on the central verticalplanes of the billets. It is apparent from these calculations thatthe value of the strain along the upper surface of the core ishigher than at the bottom surface. The analysis also indicatesthat, by increasing the friction coefficient between the core andthe sheath, it is possible to achieve a higher level of strainhomogeneity. In Figure 9a and b, the sheared lattice is hardlyvisible in the lower section and this leads to a non-uniformshear deformation. In practice, it appears that the lower part ofthe core experiences bending instead of shearing. However, asthe friction coefficient increases, the magnitude of the sheardeformation also increases so that there is a consequent


Fig. 9. Effective plastic strain distribution of a 3mm Fe core along the longitudinal planefor different boundary conditions of (a) K¼ 0.3, (b) K¼ 0.6, and (c) K¼ 1 after one passof ECAP.

Fig. 10. Effective plastic strain distribution of a 3mm Fe core–Fe sheath in the traverseplane for a boundary condition of K¼ 0.6 after one pass of ECAP: the core is shown by thewhite circle.

Fig. 11. Effective plastic strain distribution of a 3mm NiTi core along the longitudinalplane for different boundary conditions of (a) K¼ 0.3, (b) K¼ 0.6, and (c) K¼ 1 after onepass of ECAP.


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reduction in the strain difference between the upper and lowerparts of the core. In Figure 9c where K¼ 1.0, there is a uniformshear deformation throughout the core.

The effective strain distribution for the condition of K¼ 0.6is illustrated in Figure 10 for the core and sheath on thetransverse plane corresponding to the YZ plane in ECAP,where the core is represented by the central white circle and itis apparent that the effective strain of an area in the sheathbelow the core is higher than in other areas of the sheath. Thesame general trend in the strain distribution is also visible for a3mm diameter NiTi core in an Fe sheath processed throughone pass as shown on the longitudinal planes in Figure 11 fordifferent values of K and in Figure 12 on a transverse plane forK¼ 0.6. A comparison of the FEM analyses for NiTi and Feshows that the effective strain is lower in NiTi. Furthermore, itis apparent from Figures 10 and 12 that the effective strain isdifferent in the core and the sheath such that the area of thesheath immediately beneath the core undergoes a high strain

6 http://www.aem-journal.com © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim DOI: 10.1002/adem.201300474ADVANCED ENGINEERING MATERIALS 2014,

Fig. 12. Effective plastic strain distribution of a 3mm NiTi core–Fe sheath in thetraverse plane for a boundary condition of K¼ 0.6 after one pass of ECAP: the core isshown by the white circle.

0.4

0.6

0.8

1

1.2

1.4

Equ

ival

ent s

train

K=1

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ival

ent s

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K=1

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K=0.3

oTmottoB p

Eq.2

Eq.1

0

0.2

0.4

0.6

0.8

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1.2

1.4

-1.5 -1.2 -0.9 -0.6 -0.31.3E-150.3 0.6 0.9 1.2 1.5

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ent s

train


K=1

K=0.6

K=0.3

oTmottoB p

Eq.2

Eq.1

a)

b)


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due to the core deformation that occurs when the billet passesthrough the fan zone.

Considering cores of 3mm diameter, Figure 13 shows theeffective plastic strain distributions for (a) Fe, (b) Ni, and (c)NiTi cores in an Fe sheath for different boundary conditionsalong vertical traverses at the centers of the longitudinalsections after one pass of ECAP: in practice, this corresponds tothe same positions selected for recording the microhardnessdistributions. The FEM results demonstrate that in all corematerials there is a gradient from a higher effective strain at thetop of the core to a lower effective strain at the bottom and thisis consistent with the hardness measurements in Figures 5and 8. This gradient decreases when the friction coefficient ofthe core and sheath interface is increased and a homogenousdistribution of plastic strain is achieved when K¼ 1 for Fe andNi. In practice, it is reasonable to assume there is no effectiveinterface between the core and the sheath when K¼ 1 andtherefore a homogeneous strain distribution is attained as inthe hardness measurements in Figure 6 for a conventional Febillet without any interface. A direct comparison of the FEMcalculations and the microhardness results is summarized inTable 2 and inspection shows the strain distributions at K¼ 0.6are in good agreement with the hardness measurements forFe and Ni.

0

0.2

-1.5 -1.2 -0.9 -0.6 -0.3 0 0.3 0.6 0.9 1.2 1.5


K=0.6

K=0.3

oTmottoB pc)

Fig. 13. Effective plastic strain distributions of 3mm (a) Fe, (b) Ni, and (c) NiTi core–Fesheath along vertical traverses at the centers of the longitudinal sections after one passof ECAP.

4. Discussion

4.1. Advantages of the Core–Sheath Configuration for HardMetals

This investigation was conducted with the objective ofexamining the potential for processing hard-to-deformmaterialsby ECAP at room temperature by enclosing these materialswithin an Fe sheath and then studying the deformationevolution of the core–sheath billets after processing by ECAP.The experimental results provide direct confirmation of thefeasibility of using a core–sheath configuration for processing byECAP and they demonstrate this is an excellent procedure for theprocessing of “hard-to-deform”materials such as the NiTi alloy.


Considering Figure 3, it is apparent that the Fe sheath actsin a manner analogous to a movable die wall[29] so that theassociated rigidity is lower than for a conventional ECAP dieconstructed from tool steel. In practice, the shear is imposed


Table 2. The factor increase in the microhardness and effective plastic strain at thetop and bottom surfaces of Ni, Fe, and NiTi.

Material Microhardness

Effective plastic strain

K¼ 0.3 K¼ 0.6 K¼ 1

Fe 1.2 4.7 1.2 1Ni 1.3 5.5 1.3 1NiTi 1.4 8 6 2


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through a fan zone associated with the core and therefore it isreasonable to assume the values of the two angles w and c

change for the core according to the lower rigidity of thesheath. The variation of dw and dc, the variation of the innerand outer angle, respectively, is a function of the mechanicalproperties of both the core and the sheath. For the exampleof the NiTi core, it has a higher strain hardening, higherstrength, and higher hardness than the sheath as demon-strated in Figure 2 and Table 1. It has been proposed thatif dw¼ 0 then the plastic zone and flow are stable so that, asa consequence of the geometrical limitations imposed bythe tool, only the case of dw< 0 is possible.[30] Nevertheless,the results for the present investigation show dw> 0 andalso dc> 0 and this is attributed to the very high strengthof the NiTi core. Therefore, by increasing these angles andusing the standard relationship for the equivalent straingiven in Equation 1, the strain for the core decreases from�1.05 to �1.

The FEM calculations predict an essentially homogeneousequivalent strain across the cross-section of the sample exceptonly for very small differences immediately adjacent to theinner and outer arcs of curvature.[27] As noted earlier, this typeof configuration is less effective than conventional dies inproducing homogeneity[28] and therefore it is reasonable toanticipate therewill be less homogeneity in theNi and Fe coreswhen using the core–sheath configuration by comparisonwith the conventional Ni and Fe billets. This prediction isconfirmed by the hardness measurements that reveal inFigure 8 the development of inhomogeneities in all cores forNi, Fe, and NiTi. Specifically, the hardness and FEM analysesshow that the value of strain at the top of the core is higherthan at the bottom. Earlier reports suggested that the lowerstrain at the bottom surface is associated with the develop-ment of a “dead zone” or corner gap at the outer corner of thedie[31–34] and in the present experiments there is evidence inFigure 3 for the development of a gap at the outer surfacebetween the core and the Fe sheath. The formation of a cornergap is also clearly visible at the outer edge of the sheath inFigure 3.

4.2. Analyzing the Core–Sheath Configuration as a CompositeMaterial

An alternative procedure is to investigate the core–sheathconfiguration as a composite with a higher strength core (NiTi)

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contained within a lower strength sheath (Fe). Earlier experi-ments were reported in which an aluminum matrix compositewas processed by ECAP with a high-strength nickel-basedwire reinforcement and an isostrain model was assumed inwhich the shear strains of the wires were equivalent to the Aland in turn the exerted stress on the wire at the onset ofplastic flowwas higher than on the matrix.[35] This assumptionwas related to the low volume fraction of the wires and theability of the wires to pass through the fan zone withoutany deviation in the flow pattern within the matrix. However,close inspection of Figures 10 and 12 shows that theisostrain model for the core–sheath configuration is not validand this is probably due to the occurrence of a slight slidingat the core–sheath interface, the increasing values of w and c

in the core and the higher volume fraction of the core bycomparison with the use of thin embedded wires. It seems anassumption of isostress is reasonable in the core–sheathbillets so that the stress is the same in the core and thesheath. According to Figure 2 at high stress levels, and as aresult of the low level stress in Fe compared with NiTi, the Feyields to the imposed shear strain during passage through thefan zone and in NiTi this causes bending as the main mode ofdeformation. By contrast, there are similar strengths for Fe andNi between the core and the sheath and therefore the coreundergoes shear as the main mode of deformation. By thisassumption, the shear strain exerted on the core at the onset ofplastic flow is lower than on the sheath as supported byFigures 10 and 12.

5. Summary and Conclusions

1)

& C

A new form of billet, based on a core and sheathconfiguration, was designed for the processing of hard-to-deform materials by ECAP. Experiments were conductedusing an Fe sheath with NiTi, Fe, and Ni as core materials.

2)
The results show the new procedure may be used for thesuccessful processing of all selected materials. The designalso provides an opportunity for processing core materialshaving different cross-sectional areas.
3)
Materials were processed by ECAP and then investigatedusing microhardness measurements and FEM. The hard-ness measurements reveal the presence of a zone of lowerstrain along the lower part of the core and these results aresupported by the FEM analyses, which indicate that thelower part of the core undergoes bending instead ofshearing when passing through the fan zone. It is alsoshown that greater homogeneity may be attained byincreasing the friction between the core and the sheath.
4)
The results demonstrate that an increase in the core sizeincreases both the imposed strain and the gradient ofhomogeneity. Also, a comparison of different corematerialsshows that inhomogeneity is increased when the harden-ability of the core material is increased.
Received: October 5, 2013Final Version: December 4, 2013

o. KGaA, Weinheim DOI: 10.1002/adem.201300474ADVANCED ENGINEERING MATERIALS 2014,

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evaluating a new core-sheath procedure for processing hard metals by equal-channel angular pressing

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