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Journal of Materials Processing Technology 243 (2017) 465–473

Contents lists available at ScienceDirect

Journal of Materials Processing Technology

jo ur nal ho me page: www.elsev ier .com/ locate / jmatprotec

nverse finite element modeling of the barreling effect onxperimental stress-strain curve for high temperature steelompression test

. Wang a, H. Li a, K. Chandrashekhara a,∗, S.A. Rummel b, S. Lekakh b, D.C. Van Aken b,

.J. O’Malley b

Department of Mechanical and Aerospace Engineering, United StatesDepartment of Materials Science and Engineering, Missouri University of Science and Technology, Rolla, MO 65409, United States

r t i c l e i n f o

rticle history:eceived 20 February 2016eceived in revised form5 November 2016ccepted 14 January 2017vailable online 16 January 2017

eywords:arreling effecttress-strain curve

a b s t r a c t

Thermomechanical properties used in the modeling of steel forming processes that are determined usinghigh temperature cylindrical coupon compression testing are subject to errors due to barreling of the testspecimen. Barreling caused by the friction between specimen and platens reduces the accuracy of themechanical property determination. In this study, Gleeble hot compression testing was conducted toinvestigate material behavior for a low carbon structural steel over a range of temperatures (from 900 ◦Cto 1200 ◦C) and strain rates (from 1 s−1 to 30 s−1). An inverse method combined with finite elementanalysis was developed to correct the experimental stress-strain curves for the observed barreling effectto obtain the actual stress-strain curves for the material. In deformation simulations, the revised stress-strain curves produced barreling shape predictions that agreed well with the barrel shapes observed in

nverse methodinite element analysisot compression

experiments. A comprehensive parametric study based on the revised stress-strain curves was performedto study barreling for a range of friction coefficients, temperatures, and strain rates. Results showed thatthe magnitude of barreling increases with increasing friction coefficient. For a specific friction coefficient,the magnitude of the barreling decreases with increasing temperature and varies non-linearly with strainrate.

© 2017 Elsevier B.V. All rights reserved.

. Introduction

Compression tests are widely used to obtain elevated temper-ture mechanical properties for metals. Metal mechanics in theot rolling process are complicated by high temperatures (up to300 ◦C), strain rate, recrystallization and chemical compositionensitivity. Any change in these factors causes variations in massow behavior. Building a successful cylindrical compression testhat accounts for these factors is critical, as it is a requirementor accurate simulation of comprehensive hot forming processes.mong these factors, barreling during cylinder compression poses

significant challenge to acquire the accurate material modelseeded for subsequent finite element analysis. Traditional methods

sed in calculating material properties from Gleeble compressionests do not account for the effects of non-uniform deformation.xperimental stress-strain data obtained from a barrel shaped

∗ Corresponding author.E-mail address: chandra@mst.edu (K. Chandrashekhara).

ttp://dx.doi.org/10.1016/j.jmatprotec.2017.01.012924-0136/© 2017 Elsevier B.V. All rights reserved.

specimen differs from the actual stress-strain curve obtained undera frictionless situation without barreling.

Initial dimensions of the compression specimen are representedby height (H), and diameter (D) (Fig. 1a). Barreling (Fig. 1b) occursduring uniaxial compression testing. The barreling shape parame-ters include top and bottom surface diameter (dmin), the maximumdiameter in barreling area (dmax), and specimen height after com-pression (h).

Barreling occurs due to friction between platens and specimen,causing a triaxial stress state, which differs from the ideal uniaxialstress condition. The experimental stress-strain curve calculatedfrom a barreling specimen deviates from the actual stress-straincurve (Fig. 1c), which is based on ideal uniaxial stress conditions.Therefore, it is necessary to study the barreling effect on experi-mental stress-strain curves and correct these experiment results forthe barreling condition. Unfortunately, friction between the platens

and the specimen cannot be eliminated during hot compressiontesting to obtain the actual material properties. Finite element anal-ysis (FEA) is necessary to correct for the barreling effect observedin high temperature compression testing.

466 X. Wang et al. / Journal of Materials Processing Technology 243 (2017) 465–473

Fc

cstbr(drrammsttaecrtbcewcsacrrbtosshstrasm

sice

ig. 1. (a) Dimension of cylinder before compression, (b) dimension of cylinder afterompression, and (c) barreling effect on stress-strain curve.

Many researchers have investigated the barreling effect inompression tests using cylindrical specimens. Deviation of stress-train curves under different barreling conditions is a prevalentopic in this research area. Martínez et al. (2006) studied thearreling effect during compression test of alloy 2117-T4 atoom temperatures (20 ◦C–40 ◦C) and quasi-static strain rates10−3 s−1–10−2 s−1). Load-displacement curves under differenteformation conditions were compared and concluded that mate-ial is not sensitive to studied range of temperature and strainate. However, they did not study barreling at high temperaturesnd higher strain rates. Charkas et al. (2008) proposed an inverseethod to correct the local material response during finite ele-ent analysis, effectively increasing simulation accuracy of highly

tressed element. Rasti et al. (2011) used a finite element methodo study the relationship between barreling shape and the parame-ers of their material model based on AISI 304 stainless steel. Chennd Chen (2000) proposed a mathematical method to calculateffective stress and effective strain of barreled specimen during hotompression process. However, effects of temperature and strainate on barreled specimens were not considered in these litera-ures. Narayanasamy and Murthy (1988) developed a relationshipetween barreling radius and applied load using solid cylinderompression of AISI 5120. In a more recent study (Narayanasamyt al., 2000), barreling effects on stress and strain distributionsere studied by cold upset forming of magnesium alloy ZM-21

ylinders. Malayappan and Esakkimuthu (2006) studied barrelinghape during compression testing of pure aluminum and proposed

mathematical expression of barreling radius in an aluminumompression test. However, these literatures emphasized on bar-eling shape, lack of study of barreling effect on experimentalesults. Hervas et al. (2013) investigated complex strain distri-utions in ductile cast iron compression testing, which includedhe effects of barreling. Their results show that the aspect ratiof graphite nodules in the iron could be used to predict localtrains. Bao and Wierzbicki (2004) conducted cylinder compres-ion tests using Aluminum alloy 2024-T351 specimens of differenteight/diameter ratios. With increasing height/diameter ratio, thetress-strain curves converged to a stable state, which is assumedo be the actual stress-strain curve. In the previous studies, fewesearchers performed barreling effect on actual experimental datat high temperature and varying strain rate, at which high barrelinghape is involved and has significant influence on experimentallyeasured stress-strain curves.

Friction between the specimen and platens is another widely

tudied topic by researchers. Ebrahimi and Najafizadeh (2004)nvestigated the effect of friction on barreling shape during bothold and hot compression tests of Ti-IF steel, and proposed a math-matical relationship between barreling shape and the average

Fig. 2. Test profile for Gleeble hot compression test.

friction factor. They concluded that the maximum difference in flowstress under different friction conditions was approximately 8%. Liet al. (2010a) studied the barreling effect of IHS38MSV steel in anequivalent strain range, 0–1.8 using both experimental and finiteelement methods. Results showed that upper bound analysis of thefriction condition during compression test is not accurate for largestrains (>0.55). Yao et al. (2013) developed an empirical model topredict the relationship between barreling factor and friction coef-ficient based on CuZn40 brass. A convenient expression relatingthe effect of friction to barreling shape for room temperature com-pression was proposed. On the other hand, Li et al. (2010b) studiedthe effect of friction in a hot compression test (800 ◦C–1200 ◦C) andconcluded that the top radius of specimen after compression wasaffected significantly by friction. Based on these studies, Ebrahimi’sequation is widely adopted and verified by researchers, providingan effective method to predict friction coefficient.

In the current study, a methodology to correct experimen-tal stress-strain curves for the barreling effect is presented. Theeffect of increased temperatures as well as varying strain rates isalso examined. Material testing was performed using Gleeble hotcompression test at various strain rates and temperatures. Exper-imental stress-strain curves obtained from Gleeble testing wereevaluated and revised stress-strain curves were obtained. A com-prehensive parametric study was performed to study the effects ofvarying friction coefficients, temperatures, and strain rates on thebarreling observed during compression testing.

2. Experiments

A low carbon structural steel (C 0.075%, Mn 0.9%, Nb 0.016%, V0.005%, Si 0.26%, Cr 0.11%) was used in the current study. Specimens(15 mm height and 10 mm diameter) for compression testing weremachined from as-casted steel product. To investigate the effectsof varying temperatures and strain rates on barreling and materialproperties, hot compression tests were performed at different tem-peratures (900 ◦C, 1000 ◦C, 1100 ◦C and 1200 ◦C) and strain rates(1 s−1, 5 s−1, 15 s−1, and 30 s−1). Each combination was replicatedthree times, and a total of 48 specimens were tested. Compres-sion tests at elevated temperatures were performed using a Gleeblethermo-mechanical tester. The experimental plan for hot compres-sion test is shown and Fig. 2.

Specimens were first heated up to 1300 ◦C at a rate of260 ◦C/min, and held for 3 min for austenitizing. The temperature

of specimens was then lowered to the desired test temperature.After a brief holding period of 2 min, the compression test wasperformed. Tantalum foil with nickel paste was used to minimizethe friction between platens and specimen. After compression, the

X. Wang et al. / Journal of Materials Processing Technology 243 (2017) 465–473 467

under varying temperatures and strain rates.

swpp

3

totyb[w

atGi[w

mac1mme

iG

Fig. 3. Experimental stress-strain curves

pecimen is cooled by water cooling. The raw Gleeble test resultsith experimental noise are plotted in Fig. 3. Smooth process was

erformed on these raw stress-strain curves to remove noise androvide material model for finite element analysis.

. Finite element modeling and inverse method

A nonlinear thermo-mechanical finite element model was builto investigate the effect of barreling. Triaxial stress distributionccurs due to friction between platen and specimen, and generalhree-dimensional analysis is used instead of axi-symmetric anal-sis. The governing equation for thermo-mechanical analysis cane written as:

Me]{�̈e}

+[Ke

] {�e

}=

{FeM

}+

{FeT

}(1)

here [Me] is mass matrix, [Ke] is the stiffness matrix, and{FeM

}nd

{FeT

}are mechanical and thermal loadings respectively. Heat

ransfer during compression was also considered to simulate theleeble hot compression process. The formulation for heat transfer

s expressed as:

CeT]{�̇e

}+

[KeT

] {�e

}=

{Qe

}(2)

here[CeT

]is specific heat capacity matrix,

[KeT

]is conductivity

atrix, and{Qe

}is the external flux vector. The software pack-

ge, ABAQUS 6.12, was used to build this finite element model. Aylindrical specimen model was built as a 3D isotropic cylinder with5 mm height and 10 mm diameter. Two compression platens wereodeled as 2D rigid plates. Eight-node deformable hexahedron ele-ent, C3D8R, was used to mesh the cylinder and the discrete rigid

lement, R3D4 was used to mesh the platens (Fig. 4).Friction between each platen and the specimen was developed

n the finite element model. Because of large deformation duringleeble hot compression test, both of sliding and sticking occurred

Fig. 4. Finite element model for Gleeble hot compression test.

between platen and specimen. A Coulomb’s friction law used incurrent finite element model is defined as:

� ={� ∗ p

�yield

when � < �yield

when � > �yield(3)

where � is critical shear stress, �yield is yield shear stress, � is fric-tion coefficient, and p is contact pressure. During high temperaturecompression test, it is very difficult to measure friction coefficientor friction force. The empirical friction coefficient at high temper-ature is around 0.3–0.6. To more accurately model the friction, ananalytical method based on barreling shape is used to calculate thefriction coefficient (Ebrahimi and Najafizadeh, 2004):

√

� = m/ 3 (4)

m =(r/h

)b(

4/√

3)

−(

2b/3√

3) (5)

468 X. Wang et al. / Journal of Materials Processing Technology 243 (2017) 465–473

Fig. 5. Schematic of inverse method combined with FEA.

F fore ca nd 15

waibmfrf

ec(s

ε

�

wiaficfb

ig. 6. Barreling shape after Gleeble hot compression tests of (a) initial specimen bend 15 s−1 (d) specimen 3 under 1100 ◦C and 30 s−1 (e) specimen 4 under 1200 ◦C a

here m is average friction factor, r is average radius of cylinderfter compression, r = r0

√Hh , r0 is initial radius of cylinder, H is

nitial height of cylinder, h is height of cylinder after compression, = 4�rr

h�H , �H is reduction in height, and �r is difference between

aximum radius and minimum radius. The friction coefficients ofour specimens were calculated as 0.374, 0.365, 0.366, and 0.386espectively. Average friction coefficient was set as 0.375 for theseour specimens in finite element model.

The Gleeble hot compression test was simulated using a finitelement model. For each specimen, both friction and frictionlessonditions were simulated. Reaction force (P) and displacement�l) of platen were recorded in the finite element simulation. Truetrain, ε, and true stress, �, were obtained by Eqs. (6) and (7):

= ln(

1 + �l/H)

(6)

= 4P/�d2(

1 + �l/H)

(7)

here d is initial diameter, and H is initial height of cylinder. Annverse method combined with finite element analysis (FEA) waspplied to modify the experimental stress-strain curves. An initial

nite element model was built using the experimental stress-strainurves obtained from Gleeble tests and the hot compression processor each cylindrical specimen was simulated. Due to the effect ofarreling, the simulated stress-strain curve differs from the exper-

ompression (b) specimen 1 under 1000 ◦C and 15 s−1 (c) specimen 2 under 1100 ◦C s−1.

imental stress-strain curve. The initial error was determined fromdifference between the simulated stress-strain curve and experi-mental stress-strain curve. The error refined the input for the nextrun of finite element simulation. The material model is then mod-ified to minimize the difference between simulated results andexperimental results. This process was iterated until the coeffi-cient of determination (R2) between simulated stress-strain curveand experimental stress-strain curve was greater than 0.99. Theschematic of this process is shown in Fig. 5.

4. Results and discussion

4.1. Inverse finite element analysis

Four tested specimens showing the typical barreled shape andone untested specimen are shown in Fig. 6. Since the analyzedmaterial properties in this study are used for simulation of hotrolling process, the hot rolling conditions become research focus.The hot rolling temperature is 1000 ◦C–1200 ◦C, and strain rate is upto 50 s−1. Selected specimens are at temperature 1000 ◦C–1200 ◦C

and relatively high strain rate 15 s−1–30 s−1 to avoid significantdynamic recrystallization. Due to the friction between platens andspecimen, barreling is visible on the tested specimens. The shapeof each specimen after hot compression testing was recorded,

X. Wang et al. / Journal of Materials Processing Technology 243 (2017) 465–473 469

Table 1Barreling shapes and compression condition of specimens.

Specimen number Height (mm) dmax (mm) dmin (mm) Temperature Strain rate

1 7.826 14.887 12.527 1000 ◦C 15 s−1

2 7.226 15.415 12.886 1100 ◦C 15 s−1

3 8.550 14.239 12.198 1100 ◦C 30 s−1

4 7.389 15.327 12.730 1200 ◦C 15 s−1

Fig. 7. (a) Simulation results of specimen 1 at frictionless condition, (b) friction coefficient 0.375, and (c) corresponding simulated stress-strain curves.

d barr

idcm0is

sdcbtts

Fig. 8. (a) Inverse finite element analysis results of specimen 1, (b) simulate

ncluding top and bottom surface diameter (dmin), the maximumiameter in barreling area (dmax), and specimen height (h) afterompression. Dimensions, dmax and h, of these specimens wereeasured five times using a micrometer with a resolution of

.001 in. (0.0254 mm). Dimension dmin was measured from spec-men photographs using ImageJ software package. Dimensions ofpecimens 1–4 are shown in Table 1.

Ebrahimi and Najafizadeh (Ebrahimi and Najafizadeh, 2004)howed similar deformed specimen with different friction con-itions and concluded that the difference between stress-strainurves with different friction conditions is approximately 8%ased on theoretical analysis. However, it is difficult to represent

his complex triaxial compression using pure analytical calcula-ion with assumption and simplification. Finite element methodhows advantage and can perform the barreling effect study under

eling shape using revised stress-strain curve, and (c) actual barreling shape.

different friction conditions. Simulated equivalent plastic straindistributions of specimen 1 are plotted in Fig. 7. The frictionlesssituation shown in Fig. 7a, specimen 1 was deformed uniformly,showing ideal uniaxial strain distribution. On the other hand, forthe friction condition shown in Fig. 7b, barreling is visible and a tri-axial strain state is observed. Simulated stress-strain curves werecalculated and compared in Fig. 7(c). In the frictionless condition,the simulated stress-strain curve was similar to the input mate-rial properties of FEA, which means that if friction is eliminated inpractical hot compression test, the experimental stress-strain curvebased on platen reacting force and displacement will be similar toactual stress-strain curve. For condition with friction, the simulated

stress-strain curve deviates from the input material properties ofFEA, proving that experimental stress-strain curve with barrelingeffect differs from actual stress-strain curve.

470 X. Wang et al. / Journal of Materials Processing Technology 243 (2017) 465–473

s usin

tdBmfiAimtrrltlt

4

fircisprat

Fig. 9. Revised stress-strain curve

Charkas et al. (2008) proposed inverse finite element methodo effectively recover local material behavior by correcting load-isplacement response of nodes during single simulation process.ased on this method, inverse analysis was extended to revise inputaterial properties during multiple simulation processes. Inverse

nite element analysis results for specimen 1 are shown in Fig. 8(a). revised stress-strain curve was calculated by iteration of the

nverse method. Using this stress-strain curve as input of finite ele-ent model, the simulated stress-strain curve is shown to be close

o the experimental stress-strain curve (R2 > 0.99). Therefore, thisevised stress-strain curve of FEA input is expected to accuratelyepresent the actual stress-strain curve of the material. The simu-ated barreling shape based on the revised stress-strain curve andhe actual barreling shape are shown in Fig. 8b and 8c. The simu-ated dmax (14.542 mm) based on revised stress-strain curve is closeo actual dmax (14.887 mm).

.2. Revised stress-strain curves

Experimental stress-strain curves were revised based on inversenite element analyses (Fig. 9). The solid lines and dashed lines rep-esent experimental stress-strain curves and revised stress-strainurves respectively. All dashed lines are lower than correspond-ng solid lines, due to friction between platen and specimen. Thetress deviation between solid lines and dashed lines at low tem-

erature is larger than at high temperature, and strain rate haselatively small effect on stress deviation. Inverse finite elementnalysis provides an effective method to revise experimental datao determine the actual material properties, which describes mate-

g inverse finite element analysis.

rial flow behavior more accurately. Comparing to 8% difference inEbrahimi’s study (Ebrahimi and Najafizadeh, 2004), the differencesbetween experimental and revised stress-strain curves in the cur-rent study vary from 2.5% to 7.5% at different temperature and strainrate.

4.3. Parametric study results

A comprehensive parametric study was performed usinginverse finite element analysis to investigate barreling effect ondeviation between experimental stress-strain curve and actualstress-strain curve. The input material properties of the finite ele-ment model are the revised stress-strain curves plotted in Fig. 9.The parameters include friction coefficient (0, 0.125, 0.25, 0.375,and 0.5), temperature (900 ◦C, 1000 ◦C, 1100 ◦C, and 1200 ◦C), andstrain rate (1 s−1, 5 s−1, 15 s−1, and 30 s−1). Eighty hot compressionsimulation cases were performed. The flow stress is recorded atstrain 0.15 (Fig. 10) where the stress deviation is visible and dis-tinguishable among different parametric conditions. In the currentstudy, material is sensitive to strain rate range 1 s−1–30 s−1 andhigh temperature range 900 ◦C–1200 ◦C, comparing to the state-ment (Martínez et al., 2006) that material is insensitive to lowstrain rate range 10−3 s−1–10−1 s−1 and room temperature range20 ◦C–40 ◦C.

4.3.1. Friction effectFriction is the main factor resulting in barreling during hot com-

pression test. Flow stress at 0 friction coefficient in Fig. 10 is theactual material property and serves as the baseline for comparison.

X. Wang et al. / Journal of Materials Processing Technology 243 (2017) 465–473 471

Fig. 10. Flow stress at different friction coefficients, temperatures and strain rates.

Fig. 11. Temperature effect on barreling effect.

472 X. Wang et al. / Journal of Materials Processing Technology 243 (2017) 465–473

effect

Atre

B

wεfo

4

sasfobvp

4

Uecioasr

Fig. 12. Strain rate

s friction coefficient increases, the flow stress increases propor-ionally with friction coefficient at constant temperature and strainate, and reaches maximum at friction coefficient 0.5. Barrelingffect can be represented by the differences of the flow stresses:

arreling effect = � (�i, Ti, ε̇i) − � (�0, Ti, ε̇i) (8)

here � is the flow stress, �i is friction coefficient, Ti is temperature,˙ i is strain rate, and �0 is frictionless condition. � (�0, Ti, ε̇i) standsor actual material properties. Barreling was then calculated basedn Fig. 10, and discussed in following sections.

.3.2. Temperature effectThe effect of temperature on barreling is shown in Fig. 11. At con-

tant strain rate and friction coefficient, barreling effect decreasess temperature increases from 900 ◦C to 1200 ◦C. Temperaturehows a uniformly negative relationship with barreling effect at allriction coefficients and strain rates. This can be due to the softeningf material at elevated temperatures, which increases material flowehavior. Also, the effect of friction on barreling is smaller at ele-ated temperature. The effects of friction on material flow betweenlaten and specimen is reduced by material softening.

.3.3. Strain rate effectThe influence of strain rate on barreling is shown in Fig. 12.

nlike the temperature softening effect, the strain rate hardeningffects on stress-strain curve is not uniform. At constant frictionoefficient and temperature, barreling increases when strain rate isncreased from 1 s−1 to 5 s−1 due to strain hardening. The softening

f stress-strain curves mainly occurs from strain rate 5 s−1–15 s−1

nd 15 s−1–30 s−1. The difference between experimental stress-train curves and actual stress-strain curve is maximum at strainates of 5 s−1 and 15 s−1.

on barreling effect.

5. Conclusion

In this paper, Gleeble hot compression tests were conductedto obtain experimental stress-strain curves under varying tem-peratures and strain rates. Barreling of the specimen during hotcompression testing results in an experimental stress-strain curvethat differs from actual stress-strain curve. An inverse methodcombined with finite element analysis was used to correct theexperimental stress-strain curves for the barreling, and a compre-hensive parametric study was performed to study the barrelingeffect. Revised stress-strain curves were calculated based oninverse finite element analysis. It was found that inverse finite ele-ment analysis is an effective method to modify the experimentalstress-strain curve to minimize errors from barreling on materialproperties. A parametric study was performed in order to investi-gate the effect of varying friction coefficient, temperature and strainrates. It was found that the friction coefficient has a significanteffect on barreling effect. Barreling effect increases as friction coef-ficient increases. However, an increase in temperature reduces thedeviation of experimental results from actual stress-strain curvedue to the temperature softening effect. Strain rate has a complexinfluence on barreling effect. The barreling effect increases whenstrain rate is increased from 1 s−1 to 5 s−1 due to strain harden-ing. When strain rates are increased beyond 15 s−1, barreling effectdecreases. This study of the barreling effect on experimental stress-strain curves can be used to develop accurate material models forhot working simulation.

Acknowledgements

This work was supported by the Peaslee Steel ManufacturingResearch Center (PSMRC) at Missouri University of Science and

rocess

TS

R

B

C

C

E

H

L

Rasti, J., Najafizadeh, A., Meratian, M., 2011. Correcting the stress-strain curve inhot compression test using finite element analysis and Taguchi method. Int. J.

X. Wang et al. / Journal of Materials P

echnology. The authors would like to thank Todd Link from USteel Corporation for Gleeble testing.

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