Revue de Métallurgie 110, 341–348 (2013)c© EDP Sciences, 2013DOI: 10.1051/metal/2013077www.revue-metallurgie.org

Revue deMétallurgie

Numerical prediction of the effects of materialproperties on strain behavior during equalchannel angular pressing

M. Ebrahimi1, F. Djavanroodi1,2, C. Gode3 and K.M. Nikbin2

1 Department of Mechanical Engineering, Iran University of Science and Technology, Tehran, Irane-mail: mebrahimi@iust.ac.ir

2 Department of Mechanical Engineering, Imperial College, London, SW7, UK3 School of Denizli Vocational Technology, Program of Machine, Pamukkale University, 20100 Denizli,

Turkey

Key words:Equal channel angular pressing;finite element modeling; materialproperties; strain behavior

Received 16 April 2013Accepted 22 October 2013

Abstract – Equal channel angular pressing is both a novel and an industrialized processamong severe plastic deformation methods to fabricate ultra-fine-grained metals and al-loys. Verification of a three-dimensional finite element model which compares variousstrength coefficients and strain-hardening exponents (virtual materials) defined for theplastic deformation behavior of materials was performed with experimental tests. The vir-tual process numerically analyzed the effects of the strain behavior and pressing force.The results show that strength coefficient enhancement leads to decreased effective strainvalue, heterogeneous strain distribution and higher pressing force, and an increment in thestrain-hardening exponent results in lower pressing force. However, this parameter doesnot have an obvious effect on the effective strain magnitude and strain dispersal unifor-mity. Furthermore, the highest imposed effective strain, the best strain distribution homo-geneity and the lowest required punch load were achieved for the deformed material withthe lowest strength coefficient and highest strain-hardening exponent.

D uring the last decade, severe plas-tic deformation (SPD) methodshave been widely developed by

researchers in the materials science fieldbecause of the principal benefits and ad-vantages of these techniques in military, air-space, and especially medical applicationsand industries. In other words, encourag-ing economic forecasts for ultra-fine-grain(UFG) materials have led to much atten-tion being paid to the generation and de-velopment of SPD processes with mass-production scale-up capacities [1–6]. Amongall the SPD techniques such as accumulativeroll bonding (ARB) [7], high pressure tor-sion (HPT) [8], constrained groove pressing(CGP) [9], etc., equal channel angular press-ing (ECAP) [1] has attracted the most atten-tion because of its low cost and feasibility ofset-up.

The ECAP process includes imposinglarge shear strain on the specimen by push-ing it through a die that consists of two chan-nels with the same cross-sectional shape

meeting at an angle to each other (die chan-nel angle, Φ) [1]. Since the cross-section ofthe two channels is the same, the ECAPedsample can be reinserted into the entrancechannel and pushed through the die again.Repeated pressing through the die accumu-lates sufficient strain to obtain materials withUFG structures [1, 10].

Effective strain magnitude, strain distri-bution uniformity at the cross-section andin the whole of the deformed sample, andpressing force are affected by several factorssuch as die channel angle and outer cornerangle [11,12], friction coefficient [11,13], pro-cessing routes [14,15], back pressure [16, 17],billet diameter [18], strain rate sensitiv-ity [14, 16], processing temperature [19],pass number [20,21], material response [22],kind of solution treatment [23], etc. Effectivestrain (ES) is defined as the total true strainminus the recoverable strain for the over-all elements. In other words, it can be saidthat ES is related to the residual true strainafter unloading the elastic part. Previous

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M. Ebrahimi et al.: Revue de Métallurgie 110, 341–348 (2013)

studies [11, 12] showed that the level of theimposed plastic strain was increased by us-ing an acute die channel angle or adding afriction coefficient value. Also, a lower diechannel angle or higher friction coefficientleads to completely filling the outer corner ofthe die. In addition, although lower effectivestrain magnitude was obtained for a largerdie channel angle, a better strain distribu-tion uniformity was attained. The researchby Oruganti et al. [13] showed an ECAPedsample with higher shear strain and betterdistribution was achieved by applying highback pressure with low friction. The inves-tigation of the effect of routes on strain be-havior indicated that route BC gives betterstrain dispersal homogeneity as comparedwith the other ones for a die channel angleof 90◦ [14,15]. The study by Kim [24] showedthat the strain rate was decreased by the diechannel and outer corner angles. Further-more, the effect of the outer corner angle onthe strain rate is much greater than that of thedie channel angle due to the expanded maindeformation zone and decreased deformingtime.

There are several empirical equationsto describe experimental stress – straincurves such as Hollomon (Eq. (1)), Ludwik(Eq. (2)), Swift (Eq. (3)) and Voce (Eq. (4))relationships:

σ = Kεn (1)

σ = σ0 + Kεn (2)

σ = K(ε + ε0)n (3)

σ = B − (B − A) exp(−nε) (4)

where σ and ε are the true stress and truestrain, respectively, and the other parame-ters are constants. Previous studies indicatedthat the Hollomon equation is the best for an-nealed metals with a cubic lattice, and alsogives a less accurate result for pre-workedmaterials. In this research, the Hollomon re-lationship was applied to define the plas-tic behavior of material by considering thatannealed pure aluminum was utilized forthe ECAP process. In addition, K and n arethe strength coefficient and strain-hardeningexponent, respectively. This equation canbe linearized by taking logarithms on bothsides, and then a linear regression line canbe determined and the parameters (K and n)will be easily calculated [25].

Up to now, several numerical studieshave investigated the influence of mate-rial properties on the strain behavior. Fi-nite element modeling (FEM), which is themost suitable procedure to direct explo-rations similar to the real circumstances, re-moves the need for experimental complexi-ties. The result of investigations on the ECAPprocess by Dumoulin et al. [26] showedthat the strain-hardening exponent has themost significant effect on the strain uni-formity. The influences of material prop-erties on the strain behavior and requiredpunch force were studied by Djavanroodiand Ebrahimi [27] during equal channel an-gular pressing with parallel channels. Theyshowed that various magnitudes of strain-hardening exponents do not have mucheffect on the pressing force value, but an in-crease in the magnitude of the strength coef-ficient causes a higher magnitude of pressingforce. The results of the study on aluminumalloys by Karpuz et al. [28] indicated thatstrain-hardening constants affect the forma-tion of the corner gap angle due to variationsin the material flow and plastic deforma-tion homogeneity in the deformation zoneof an ECAP die. The findings showed thatany increase in these parameters results inan increase in the angle of the corner gap.Although several studies have been carriedout on the effects of these two parameters (Kand n) on the strain responses and requiredpressing load, there is a lack of informationregarding material properties’ influences onthe strain behavior and required force value.

In this research, numerical investiga-tions using representative virtual materialproperties were carried out on the effectivestrain magnitude, strain distribution uni-formity and required pressing force afterthe first pass of the ECAP process at roomtemperature.

1 Finite element modeling

The commercial finite element code,ABAQUS/Explicit software, was utilized inorder to investigate the effects of materialproperties on the strain behavior and re-quired force magnitude during the ECAPprocess at an ambient temperature. The dieand punch were assumed to be discretely

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Fig. 1. True stress – strain curve of an an-nealed CP billet Al before the ECAP processobtained by a tensile test and curve fitting bythe Hollomon model.

rigid, meaning that there is no deformation.The ECAP die characteristics are the sameas in the experimental work. The constantpunch speed was equal to 1 mm/s, similarto the experimental procedure. The magni-tude of the friction coefficient was taken tobe 0.1 [27]. This value was obtained by usingthe ring compression test for the ring 6:3:2(outer diameter: inner diameter: height) andcalibrated with the curves recommended byMale and Cockcroft [29]. Figure 1 displaysthe true stress – true strain curves of an-nealed commercial-purity (CP) aluminumobtained by a tensile test according to ASTMB557M (2010) and also, curve fitting with theHollomon relationship, which was importedto the software. Furthermore, the stress –strain equation can be written as σ = 137 ε0.2.The length and diameter of the simulatedsample were 50 mm and 19 mm, respectively.Adaptive meshing, mass scaling and auto-matic re-meshing were used and justified forall simulations to prevent failure of the meshduring large deformation and to reducecomputation time. The mesh sensitivity di-agram was attained, and then the optimumelement size was found to be 0.7 mm. Also,the type of element was a three-dimensionalhexahedral element (C3D8R). In addition,the number of elements for the CP billetaluminum was 19.750.

Verification of the numerical work wasbased on the required pressing force valueto press CP billet aluminum after onepass of the ECAP process. After valida-tion, various strength coefficients (K) and

strain-hardening exponents (n) were numer-ically analyzed to investigate and comparethe influences of material properties on thestrain behavior, including effective strainmagnitude and strain distribution unifor-mity, and required pressing load. Figure 2displays the effective strain contour of thesample after one pass of the ECAP process.

2 Experimental procedure

A commercial-purity aluminum specimen(diameter of 19 mm and length of 50 mm) asa test material was prepared for this study.Before operation, the Al sample was an-nealed at 350 ◦C for 1 h and slowly cooled inthe furnace. An ECAP die with a die channelangle of 90◦, outer corner angle of 17◦ andchannel diameter of 19 mm was designedand manufactured. The hydraulic press, dieset-up and billet after one pass of the pro-cess are shown in Figure 3. All experimentalwork was done in the Research and Technol-ogy center at the Department of MechanicalEngineering of IUST. Molybdenum disulfide(MoS2) was used as a lubricant to reduce fric-tional effects between the outer surface of thebillet and the inner surface of the die chan-nels. The ECAP process was performed atroom temperature using a hydraulic presswith a ram speed of 1 mm s−1.

3 Results and discussion

3.1 Verification of FEM work

The ECAP die set-up in the experimentalwork was utilized to validate the simula-tion results. The magnitude of the requiredpressing force was measured in the labora-tory and compared with the FEM results.After one pass, the pressing force magni-tudes obtained by the experimental workand the simulation results are 51 KN and47 KN, respectively. This represents about8% discrepancy between the experimentaland the numerical results, which for all prac-tical purposes is acceptable.

3.2 Effect of material propertieson the strain behavior

As is known, K and n are two importantparameters for defining materials’ plastic

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Fig. 2. Effective strain contour of billet Al after the first pass of the ECAP process.

Fig. 3. Hydraulic press, ECAP die set-up and CP billet Al after the first pass of pressing.

deformation behavior influencing the strainbehavior of ECAPed samples, including theeffective strain (ES) magnitude and straindistribution homogeneity. A numerical anal-ysis was performed with materials of vari-ous strength coefficients (50, 100, 150, 150,200, 250, 300 and 350 MPa) and strain-hardening exponents (0.20, 0.215, 0.230,0.245, 0.260, 0.275, 0.290 and 0.305). Thesewere numerically analyzed (56 different vir-tual materials), following which the influ-ences of these two parameters on the strainbehavior were investigated.

Figure 4 represents a contour plot of theimposed effective strain magnitude for 56different K and n values during one passof the ECAP process. It is apparent that ahigher magnitude of effective strain was at-tained for the lower strength coefficient forthe range of various strain-hardening ex-ponents (0.2 < n < 0.3). Also, Figure 5

shows the effective strain magnitude for var-ious strength coefficients, irrespective of thestrain-hardening exponent. As can be seen,a low magnitude for the strength coefficientresults in a high value for the effective strainmagnitude. As an example, a 3% increasein the ES value can be obtained by apply-ing material with K = 50 MPa instead of350 MPa.

On the other hand, the effective strainmagnitude for different strain-hardening ex-ponents is represented in Figure 6, irrespec-tive of the strength coefficient. It can be saidthat the magnitude of the strain-hardeningexponent does not have any obvious effecton the ES value. As a result, the magnitudeof K has more influence than n on the ESvalue during the ECAP process.

In general, two factors have been utilizedto investigate strain distribution uniformityin order to demonstrate it quantitatively.

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Fig. 4. Effects of various strength coefficients (K)and strain-hardening exponents (n) on the effec-tive strain contour (ES) during one pass of theECAP process.

Fig. 5. Effective strain (ES) magnitude for differ-ent strength coefficients (K) after the first pass ofthe process, irrespective of the strain-hardeningexponent.

One is the inhomogeneity index (Ci), definedas [30]:

Ci = (εmax − εmin)/εave (5)

where εmax, εmin and εave denote the maxi-mum, minimum and average magnitude ofeffective plastic strain, respectively. A highvalue for the inhomogeneity index leadsto heterogeneity for strain distribution. Theother one is the inhomogeneity factor (IF),based on a statistical parameter which hasbeen applied as follows [31]:

IF =√⎛⎜⎜⎜⎜⎜⎝

n∑

i=1

(εi−ε)2

⎞⎟⎟⎟⎟⎟⎠ /(n − 1) (6)

where εi, ε and n are the strain value at theith element, mean strain value and number

Fig. 6. Effective strain (ES) magnitude for dif-ferent strain-hardening exponents (n) after thefirst pass of the process, irrespective of strengthcoefficients.

Fig. 7. Effects of various strength coefficients (K)and strain-hardening exponents (n) on the inho-mogeneity factor (IF) contour during one pass ofthe ECAP process.

of elements, respectively. A lower magni-tude for the IF leads to better uniformity forstrain distribution. Therefore, the IF is a bet-ter factor to measure strain dispersal unifor-mity because it is based on the magnitudeat all the nodes in the sample, where Ci isbased on only two extreme magnitudes.

Figure 7 exhibits the inhomogeneity fac-tor of strain distribution uniformity af-ter 1 pass of the ECAP process usinga contour plot. The graphical analysisshows that a deformed sample with bet-ter strain distribution homogeneity canbe achieved for a lower strength co-efficient when different strain-hardeningexponents of 0.2 to 0.3 are examined.Furthermore, the effect of material proper-ties (K and n) on the inhomogeneity factor

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Fig. 8. Inhomogeneity factor (IF) values for var-ious strength coefficients (K) after 1 pass ofthe ECAP process, irrespective of the strain-hardening exponent.

Fig. 9. Inhomogeneity factor (IF) values for var-ious strain-hardening exponents (n) after 1 passof the ECAP process, irrespective of the strengthcoefficient.

is investigated individually. Figure 8 showsIF values for various strength coefficients(K), irrespective of the strain-hardening ex-ponent (n). As can be observed, strain distri-bution uniformity decreases by adding thestrength coefficient. It means that a lowermagnitude for k leads to producing mate-rial with better strain distribution homo-geneity. For example, about 3% improve-ment in the uniformity of strain dispersalcan be achieved by applying material withK = 50 MPa instead of 350 MPa.

On the other hand, various strain-hardening exponents (n) have a negligibleeffect on the IF value, irrespective of thestrength coefficient (K); see Figure 9. As aresult, K has more impression than n on theIF value during the ECAP process.

As a summary of this section, the mag-nitude of the strength coefficient has moreinfluence than the strain-hardening expo-nent from the effective strain value andstrain distribution uniformity points of view.Also, higher imposed effective strain with

Fig. 10. Effects of various strength coefficients(K) and strain-hardening exponents (n) on thepressing force contour (RF) during one pass ofthe ECAP process.

better strain dispersal uniformity was at-tained for the material with a lower strengthcoefficient.

3.3 Effect of material propertieson the pressing force

The influence of the strength coefficient andstrain-hardening exponent on the requiredpunch load is shown in Figure 10 as a con-tour plot form. The figure depicts that thelowest and highest required pressing forceduring the ECAP process were acquired forthe samples with (lower K and higher n) and(higher K and lower n), respectively. Also,this finding can be shown using ultimatetensile strength (UTS). The UTS value can beobtained using the strength coefficient andstrain-hardening exponent as follows:

UTS = K(n/e)n (7)

where e is the base of the natural loga-rithm. According to the above relationship,the lowest RF value is related to the UTS =26 MPa (K = 50 MPa and n = 0.305) andthe highest RF magnitude is assigned tothe UTS = 208 MPa (K = 350 MPa andn = 0.2), which is consistent with the aboveexplanation.

The required force (RF) magnitude topress materials with various strength coef-ficients and strain-hardening exponents isalso represented in Figures 11 and 12.

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Fig. 11. Required pressing force values (RF)for materials with different strength coeffi-cients (K), irrespective of the strain-hardeningexponent.

Fig. 12. Required pressing force values (RF) formaterials with different strain-hardening expo-nents (n), irrespective of the strength coefficient.

As can be seen in Figure 11, an increas-ing strength coefficient leads to a higherrequired pressing force. For example, usingK = 50 MPa instead of 350 MPa results in a440% increase in the RF magnitude. On theother hand, it is noted from Figure 12 that anincrement in the strain-hardening exponentresults in a decrease in the pressing load. Asan example, about 40% reduction can be ob-tained by using material with n = 0.2 insteadof 0.305. On the whole, K has much more ef-fect than n on the RF value during the ECAPprocess.

4 Conclusion

In this work, a detailed numerical analysisof the influences of material properties onthe strain behavior and required force wasperformed using FEM. To validate the sim-ulated results, an ECAP die with Φ = 90◦,Ψ = 17◦ and channel diameter of 19 mmwas designed and manufactured. The in-

fluence of various strength coefficients andstrain-hardening exponents, defined for theplastic behavior of materials, was numeri-cally simulated on the effective strain mag-nitude, strain distribution uniformity usingan inhomogeneity factor and the requiredpressing force. Increasing the strength coef-ficient results in a lower effective strain mag-nitude, strain dispersal heterogeneity andhigher punch load value. On the other hand,an increment in the strain-hardening expo-nent has a negligible effect on the ES andIF values, but leads to a lower RF magni-tude. It clearly means that the K value hasmore influence than the n value on the ES,IF and even RF magnitude during the ECAPprocess. Furthermore, the highest imposedeffective strain, the best strain distributionhomogeneity and lowest required punchload were attained for the ECAPed pro-cessed material with the lowest strengthcoefficient and highest strain-hardeningexponent.

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