T

Ae

MD

a

ARRA

KZFLSSA

1

dtzncirrw(tlfItsatct

h1

Journal of Manufacturing Processes 23 (2016) 122–129

Contents lists available at ScienceDirect

Journal of Manufacturing Processes

j ourna l ho me pa g e: www.elsev ier .com/ locate /manpro

echnical Paper

nalytical determination of forming limit curve for zirlo and itsxperimental validation

insoo Kim, Felix Rickhey, Hyungyil Lee ∗, Naksoo Kimepartment of Mechanical Engineering, Sogang University, Seoul 04107, Republic of Korea

r t i c l e i n f o

rticle history:eceived 28 January 2016eceived in revised form 10 June 2016ccepted 13 June 2016

a b s t r a c t

Zirconium alloy sheets used in the nuclear fuel assembly are subject to high temperature and stress,a corrosive and radiation environment and their performance has thus been of big concern. However,knowledge regarding the properties and the formability of zirconium alloys is still lacking. In this paper,strain-based forming limit diagrams (FLDs) are established for the zirconium alloy Zr1Sn1Nb0.1Fe (alsocalled zirlo). The analytical forming limit curve (FLC) varies with forming limit model and yield criterion.

eywords:irconium alloyorming limit curveimit dome height testtress–strain relationtrain hardening exponent

To obtain the right hand side of the FLD, we apply the Swift’s diffuse necking model, and for the left handside, Hill’s local necking model. Solutions from the analytical method are compared with experimentalFLD established based on limit dome height (LDH) tests. Using the strain hardening exponent of a modifiedstress–strain relation, we could find excellent agreement of the analytical FLC with the LDH-based FLC.

© 2016 The Society of Manufacturing Engineers. Published by Elsevier Ltd. All rights reserved.

nisotropy coefficient

. Introduction

Zirconium alloys are used in the power plants for their strength,uctility, resistance to corrosion and neutron irradiation embrit-lement. A typical composition of them is more than 95 wt.%irconium and less than 2% of tin, niobium, iron, chromium,ickel and other metals, which are added to improve mechani-al properties and corrosion resistance. One of zirconium alloyss zircaloy-4; it is employed as fuel cladding in pressurized watereactor (PWR), spacer grid structural material in light watereactor (LWR), and channel box structural material in boilingater reactor (BWR). For extended burnup, new zirconium alloy

Zr1Sn1Nb0.1Fe, which is called ‘zirlo’) was developed by Wes-inghouse. ‘zirlo’ stands for ‘zir’conium ‘l’ow ‘o’xidation. Due to theower Sn content in zirlo compared with that in zircaloy-4, theormer alloy has a lower irradiation-induced dimensional change.rradiation-induced dimensional change is one of the most impor-ant phenomena which should be avoided in order to maintaintructural integrity. Further, zirlo exhibits a lower irradiation creepnd hardening, as well as better corrosion resistance, comparedo that of zircaloy-4 [1,2]. Zirlo is used today as material for fuel

ladding as well as fuel assembly structural parts such as guideubes and spacer grids in several PWRs.

∗ Corresponding author. Tel.: +82 2 705 8636.E-mail address: hylee@sogang.ac.kr (H. Lee).

ttp://dx.doi.org/10.1016/j.jmapro.2016.06.006526-6125/© 2016 The Society of Manufacturing Engineers. Published by Elsevier Ltd. Al

Formability is the material’s capability to plastically deformwithout necking and tearing. The forming limit curve (FLC) is theplot of critical major strain vs. minor strain [3,4]. The onset of localnecking is given by the forming limit strain (FLS). The FLC providesthe forming limit strain (FLS), which is the strain that a sheet canwithstand before local necking. A deformation condition below theFLC is safe from fracture, whereas deformation condition above theFLC can cause a risk of failure. As the strain-based FLC is loadingpath-dependent, the strain-based forming limit diagram (FLD) isvalid only for the case of proportional loading. Multi-step stamp-ing, tool geometry and interfacial friction will induce changes inthe loading path. For this reason, strains far below the conven-tional FLC are sometimes found to neck while strains far above thecurve are safe from necking. The strain path varies throughout thestamping process due to the non-proportional increments of strain.Hence, to assess the formability in multi-step stamping process,FLD for specific strain paths are necessary. However, considerationof strain paths in actual stamping process is unrealistic. Althoughsome experimental works were done on the FLD, as specimen shapeand test equipment may differ from study to study [5–7], standardssuch as ISO 12004 [8] or ASTM E2218-2 [9] were provided for thedetermination of the forming limit of metal sheets. Yet anotherdrawback of experimental FLD is that specimen manufacturing iscostly and time consuming and that results may differ depending

on the point where strains are measured.

Assuming homogeneous sheet metals, Swift [10] and Hill [11]established theoretical FLC for diffuse and local necking, respec-tively. The Swift model was further refined later by Hora and Tong

l rights reserved.

cturin

[ciofdod

sdouraacca[zda

zaafttscd

2

yddfa[

2

s[

f

F

H

wNF

�

of diffuse necking, whereupon the metal sheet becomes uniformlythinner and eventually fractures. Region II comprises those caseswhere local necking occurs after diffuse necking. The resulting sud-den local decrease in thickness leads to more or less immediate

M. Kim et al. / Journal of Manufa

12] and Hora et al. [13]. Marciniak and Kuczynski (M-K model) [14]onsidered geometrical as well as microstructural inhomogeneitiesn their approach. Stören and Rice [15] contrived a model basedn the bifurcation theory. Stoughton [16] suggested a generalizedailure criterion by considering how failure is affected by the stressistribution normal to the sheet plane. To reduce the complexityf these models and to facilitate analysis, alternative models wereeveloped recently [17–19].

Methods for establishing FLC have been the focus of numeroustudies on diverse metals, yet for zirconium alloys information oneformability is scarce. Moreover, zirconium alloys are HCP (hexag-nal close packed) metals, for which yield conditions are not fullynderstood. For zirconium alloys, Seo et al. [20] established theo-etical FLC for zirconium alloy. However, the hardening law theypplied does not accurately reflect the real behavior. Further, bypplying diverse yield criteria for zirlo and zircaloy-4, it was con-luded that zirlo shows better agreement with the Stören–Rice inombination with the Hosford yield criterion while for zircaloy-4

better match was reached with the Swift–Hill model. Kim et al.21] thus proposed FE models which serve to determine FLSs forircaloy-4. Their numerical FLSs agree well with the experimentalata. However, numerical approach is also time-demanding tasknd quite complicated.

This work aims to investigate the validity of analytical FLCs forirlo. FLCs are derived for zirlo (Zr1Sn1Nb0.1Fe, wt.%) using annalytical method that combines the necking theory of Swift [10]nd Hill [11], the anisotropic yield criterion of Hill [22] and Hos-ord [23], and a modified Rice–Rosengren hardening law. Uniaxialensile tests and finite element analyses are carried out to obtainhe anisotropic coefficients and the constitutive behavior of zirloheets. Finally, limit dome height (LDH) tests are conducted foromparison with the numerical results. The paper ends with a briefiscussion of the validity of analytical FLC.

. Yield criteria for anisotropic materials

The theoretical FLC varies with the applied forming limit model,ield condition and hardening model. Various yield criteria areeveloped over the past decades [22–24]. An accurate materialescription and an appropriate choice of yield condition are there-ore crucial for obtaining accurate theoretical FLC. Among manynisotropy yield criteria, in this study, we use the criteria of Hill 4822] and Hosford 79 [23].

.1. Hill 48 yield criterion

The material is anisotropic with respect to the three orthogonalymmetry planes. In terms of principal stresses �1, �2 and �3, Hill’s22] yield criterion can be written as

(�) = F(�2 − �3)2 + G(�3 − �1)2 + H(�1 − �2)2 = 1 (1)

= 12

(1

�2y2

+ 1

�2y3

− 1

�2y1

); G = 1

2

(1

�2y3

+ 1

�2y1

− 1

�2y2

);

= 12

(1

�2y1

+ 1

�2y2

− 1

�2y3

)(2)

here F, G and H are constants which characterize the anisotropy.

ote that if F = G = H = 1, Eq. (2) is equal to von Mises yield criterion.or plane stress conditions, the Hill 48 yield criterion reduces to

e ≡[f�2

1 + g�22 + h(�1 − �2)2]1/2

(3)

g Processes 23 (2016) 122–129 123

The coefficients f, g and h can be expressed in terms of theanisotropy coefficients r0 and r90.

f = 11 + r0

; g = r0

r90(1 + r0); h = r0

1 + r0(4)

Note that the Hill 48 yield criterion does not account for theBauschinger effect, which has been observed in zirconium alloy[25]. However, it has the advantage that it requires only a fewmechanical parameters. Although Hill’s yield criterion cannotdescribe the Bauschinger effect, it is widely used due to its sim-plicity.

2.2. Hosford 79 yield criterion

Under the plane stress state, Hosford [23] suggested a yield con-dition in the form of Eq. (5)

f (�) = F |�2 − �3|a + G|�3 − �1|a + H|�1 − �2|a = 1 (5)

where F, G, H are the same as in Eq. (2) and a is the parameterwhich characterizes the shape of yield surface. The Hosford yieldcriterion is similar to Hill’s yield criterion. The main advantage ofthis yield criterion is that suitable choice of a ensures a good fit-ting of experimental data. The parameter a can be determined fromthe crystallographic theory. Plastic deformation is generated by theslip. The slip occurs along the slip system having the greatest planardensity. Metals with face-centered cubic (FCC) or body-centeredcubic (BCC) or hexagonal close-packed (HCP) crystal structureshave a number of slip systems, 12 or 48 or 3, respectively. Metalswith FCC or BCC are quite ductile because extensive plastic defor-mation is normally possible along the various systems. Conversely,formability of HCP metals, having few active slip systems, is rela-tively poor compared to other metal structures. Mostly a = 6 is usedfor the BCC metals, a = 8 for the FCC metals. If a = 2 and F = G = H = 1,Eq. (5) is equal to von Mises yield condition for isotropic mate-rial. In plane stress, the equivalent stress becomes according to theHosford yield criterion

�e ≡[f |�1|a + g|�2|a + h|�1 − �2|a

]1/a(6)

where f, g and h are given in Eq. (4).

3. Analytical FLCs based on the necking theory

According to the minor-to-major strain ratio, the FLD consistsof the three regions shown in Fig. 1. Note that the major strain isalways positive. Region I refers to the case where the material isunder biaxial tension. The maximum load point denotes the onset

Fig. 1. Schematic figure of forming limit diagram.

1 cturin

ft

sdrdcb

3

SiictS

ε

ε

Hat(m

3

ε

ε

Ay

3(

ei

F

wl

yield strength for LARD = 90◦ is higher than that for 0◦ and 45◦.When the plate is rolled through the press, most of the change indimension is in the direction of rolling. Therefore, there is a lotof work hardening in that direction. The grains of material get long

24 M. Kim et al. / Journal of Manufa

racture. The minor-to-major strain ratio � (≡ε2/ε1) = −1 denoteshe case of pure shear.

Theoretical forming limit models are available for each minortrain region of the FLD [10–15]. Swift [10] suggested a method toetermine the sheet’s forming limit for ε2 ≥ 0 based on the crite-ion for diffuse necking whereas Hill [11] proposed a formula toetermine the forming limit for ε2 < 0 based on the local neckingondition. Here, theoretical FLCs for Regions I and II are establishedased on the models by Swift and Hill.

.1. Swift model

For estimation of the limit strains in the biaxial tensile case,wift [8] referred to an early criterion by Considere [26]. When thenstability occurs in biaxial stretching of sheet metal, the local areas decreased evenly, which is called the diffuse necking. Theoreti-ally, local necking is ruled out in the positive ε2 region. Assuminghe strain-hardening law as suggested by Hollomon (� = Kε n) [27],wift [10] obtained the following expressions for the limit strains

1 =�1

(∂f

∂�1

)2+ �2

(∂f

∂�2

)(∂f

∂�1

)

�1

(∂f

∂�1

)2+ �2

(∂f

∂�2

)2n;

2 =�2

(∂f

∂�1

)2+ �1

(∂f

∂�1

)(∂f

∂�2

)

�1

(∂f

∂�1

)2+ �2

(∂f

∂�2

)2n (7)

ere f is the yield surface function, �1 and �2 stand for major stressnd minor stress, and n is the strain hardening exponent, respec-ively. The FLS depends on the yield criteria. Using the Hill 48 of Eq.1) and the Hosford yield potentials of Eq. (5) for f in Eq. (7), we get

ajor and minor strains for FLS

ε1 = A(A + ˛B)D

n, ε2 = A(˛A + B)D

n

Hill 48; A = 1 + r(1 − ˛); B = ̨ − r(1 − ˛); D = A2 + ˛B2

Hosford 79; A = k[

1r

+ (1 − ˛)a−1]

; B = k[

˛

r− (1 − ˛)a−1

];

D = A2 + ˛B2; k = ar

1 + r(8)

.2. Hill model

Hill [11] proposed a formula to determine the forming limit for2 < 0 based on the local necking condition. Principal strains are

1 =∂f

∂�1

∂f∂�1

+ ∂f∂�2

n; ε2 =∂f

∂�2

∂f∂�1

+ ∂f∂�2

n (9)

s ε1 + ε2 = n, the FLC based on Hill’s model is independent of theield criteria, but only on the strain hardening coefficient.

.3. Model of North American Deep Drawing Research GroupNADDRG)

The NADDRG proposed an empirical method for obtainingxperimental and theoretical FLD [28] that is easier to implementn the press workshop

LDo (%) = n(23.3 + 14.13t)0.21

(10)

here t is the sheet thickness. The FLC is here composed of twoines through the point FLDo in the plane-strain state. The slope of

g Processes 23 (2016) 122–129

the lines located on the left and right sides of FLC are about 45◦ and20◦, respectively. Since Eqs. (8)–(10) are function of n, formabilityincreases due to right-upwards shift of FLC with increasing n.

4. Mechanical properties of zirlo

4.1. Tensile test

The tensile tests were carried out to obtain the material proper-ties and anisotropy coefficient for zirlo. The anisotropy coefficientsr� is defined as

r� ≡ εw

εt(11)

where εw and εt refer to the strain in the width and thicknessdirections, and subscript � is the loading angle to rolling direction(LARD). The anisotropy coefficients are obtained from the final griddeformation. For strain measurement, a grid of marks is printed onthe specimen, with (initial) gaps of ll = 50 mm in length directionand lw = 20 mm in width direction. Specimens (in accordance withKS B5) of thickness 0.67 mm were used for tensile tests (Fig. 2).Tensile tests were carried out on an Instron 5882 machine witha constant cross-head speed of 4.8 mm/min. A video extensome-ter was used to measure the grid deformations (Fig. 3). The strainin thickness direction εt is calculated based on the assumption ofplastic incompressibility

εl + εw + εt = 0 (12)

Anisotropy coefficients were measured before necking (elonga-tion = 9%) from the grid deformation (Fig. 4). In this work, normalanisotropy is assumed. For each specimen cut with (loading) angleto rolling direction (LARD = 0◦, 45◦, 90◦), we perform 5 tests and cal-culate mean average values of r0, r45 and r90. The normal anisotropycoefficient r is then calculated by

r = r0 + 2r45 + r90

4(13)

For zirlo we get r0 = 3.38, r45 = 4.15, r90 = 3.61 and r = 3.82.For obtaining Young’s modulus E and yield strength �o we use

the same specimens as for getting r. �e–εe curves of the zirlo sheetcut along the three orientations are shown in Fig. 5. Note that the

Fig. 2. Grid shape and reference point marking for measurement of displacement(tensile specimen, KS B5).

M. Kim et al. / Journal of Manufacturing Processes 23 (2016) 122–129 125

Fig. 3. Tensile testing equipment (Instron 5882) and specimens.

at

d[r

�

wrlws

Fig. 4. Scan image of tensile specimen for measurement of grid deformation.

nd hard in the rolling direction, but in directions normal to rolling,hey are relatively undeformed and remain soft.

The drop in the cross sectional area following necking makes theetermination of uniaxial true stress–strain data problematic. Ling29] proposed the post-diffuse necking true stress–strain (�t–εt)elation for flat specimens

t = �d

[w(1 + εt − εd) + (1 − w)

(ε

εdt

εεdd

)](14)

here �d is the true stress at diffuse necking and εd the cor-

esponding strain. w = [0, 1] is a weight factor. w = 1 means ainear stress–strain relation (after the onset of diffuse necking),

hile w = 0 refers to the power law function. Eq. (14) is theo-called weight-average method (wam). For various materials

Fig. 5. �e–εe curves for three different ARD.

Fig. 6. Specimen for tensile test and FE model.

including zircaloy-4, Hyun et al. [30] expressed the relation of truestress–strain using Eq. (14).

Finite element (FE) simulations are performed in Abaqus [31].The shape of the tensile specimen is in accordance with above men-tioned standard (KS B5, Fig. 2). The employed quarter model (Fig. 6)comprises approximately 16,000 8-node brick elements. Varyingthe weight factor w, we fit the FE �e–εe curve to the experimen-tal data for LARD � = 0◦ [Fig. 7(a)]. The fracture strain εf – the ε1value corresponding to the fracture displacement (Hyun et al. [30])– is evaluated to 0.8 (w = 0.43). The circumstance that w is muchlarger than zero shows that the material deviates significantly fromthe power-law function. Experimental and numerical �e–εe curvesshown in Fig. 7(a) are in good agreement. Corresponding �t–εt

curve is depicted in Fig. 7(b). E, �o, εf and � obtained from tensiletests are given in Table 1.

4.2. Stress–strain relation

Since the establishment of theoretical FLC requires n [Eqs.

(8)–(10)], accurate determination of n is essential. However, thetheoretical FLC cannot be established based on Eqs. (8)–(10)together with Eq. (14) because n does not appear in Eq. (14)

Table 1Material property for zirlo.

Material E (GPa) �o (MPa) εf �

Zirlo 82.3 415.7 0.8 0.37

126 M. Kim et al. / Journal of Manufacturing Processes 23 (2016) 122–129

Fb

em

Hs6Ynfdp(∣∣Fc

TC

Many researchers have been actively involved in the devel-opment of experimental methods for accurate and objectivedetermination of limit strains. To consider the forming limit

ig. 7. (a) Comparison of �e–εe curves for zirlo. (b) �t–εt curves for zirlo obtainedy weight average method (wam).

xplicitly. Following the suggestion by Rice and Rosengren [32], theaterial data is therefore fit to the piecewise power law function

�

�o=

⎧⎪⎨⎪⎩

ε

εo� ≤ �o

(ε

εo

)n

� > �o

(15)

owever, the fitting of plastic stress–strain data to Eq. (15) revealsensitivity of n to the regression range. Kim et al. [21] suggested

ranges for investigating the sensitivity of n: (1) from yield point to diffuse necking point D (Y–D), (2) from yield point Y to localecking point L (Y–L), (3) from yield point Y to failure F (Y–F), (4)

rom diffuse necking point D to local necking point L (D–L), (5) fromiffuse necking point D to failure F (D–F), and (6) from local neckingoint L to failure F (L–F). Local necking is assumed to set in whenHyun et al. [30])∣ ∣ ∣

�local

∣ = ∣�Pmax∣ (1 − 0.1 ε1|Pmax) (16)

or each regression range, n is listed in Table 2. However, the �t–εt

urves obtained with the values in Table 2 do not agree well with

able 2oefficients of power law with various regression ranges.

Regression range Y–D Y–L Y–F D–L D–F L–F

n 0.113 0.127 0.137 0.171 0.245 0.275

Fig. 8. Comparison of �t–εt curves with various regression ranges.

those from the tensile test (Fig. 8). The �t–εt curves from Eq. (15)shows poor agreement with wam (reference) data (average devia-tion of 18% in all cases). Further, since the range of n values is quitelarge (0.113 ≤ n ≤ 0.275), we cannot find a representative value ofn for zirlo.

For mathematical description of this behavior, we modify Eq.(15) as suggested by Hyun et al. [33]

�

�o=

⎧⎪⎨⎪⎩

ε

εo� ≤ �o

(ε + εs

εo + εs

)n

� > �o

(17)

where an additional regression parameter εs is introduced (Fig. 9).Eq. (17) is the so-called modified piecewise power law (mppl). Forεs = 0.028 and n = 0.211, the corresponding graph for zirlo (Fig. 10)is in a good agreement with Eq. (17). The �t–εt curves from Eq.(17) shows good agreement with wam (reference) data (maximumdeviation of 4%). Applying the material properties as defined in Eqs.(14) and (17), we find an excellent agreement between the P–ıcurves from FE analysis and tensile test (Fig. 11). The stress–strainrelation of zirlo can thus be accurately described by the mppl [Eq.(17)].

5. Experimental validation

5.1. Limit dome height test

Fig. 9. Schematic of stress–strain curve for modified piecewise power law regres-sion.

M. Kim et al. / Journal of Manufacturing Processes 23 (2016) 122–129 127

Fig. 10. �t–εt curves for zirlo (modified piecewise power law).

F

oHic

Table 3Experimental conditions for LDH test.

Material Zirlo

Specimen

Thickness (t) 0.67 ± 0.01 mmWidth (w LDH) 25, 50, 75, 100, 125, 150,

200 mm

Length (l LDH) 200 mmDirection (�) (= angle torolling direction)

0◦

ig. 11. Comparison of �e–εe curves with different relation of �–ε [cf. Fig. 7(a)].

f sheets and the uniform deformation of contact surface, theecker test can be adopted. In Hecker’s method [34], the exper-

mental procedure mainly involves three stages as follows: (1)ircle-marking the specimens, (2) stretching the circle-marked

Fig. 12. Formability testing equipmen

Punch speed (v) 0.1 mm/sBinder force (PBF) 300 kN

specimens to failure, and (3) measurement of strains. Duringdeformation the circles in the fracture region turn into ellipses,the aspect-ratios of which are used to deduce the major/minorstrains.

The Nakajima workgroup suggested a more robust method forthe establishment of experimental FLC [35]. Here, the strain evolu-tion from necking to fracture is analyzed from the recorded formingprocess. To mitigate the problems inherent in the Hotz method –namely, the sensitivities to specimen shape, LARD, grid size andpattern as well as strain measurement method – the workgroupfurther proposed a revision, which eventually became ISO 12004standard [8]. This procedure is followed here. Test conditions are asin Kim et al. [21] and are reproduced in Table 3. The LDH test equip-ment and associated dimensions are provided in Fig. 12 and Fig. 13,respectively. The deformed grid is imaged by an ATOSTM scannerand major/minor strains are computed from the grid images usingthe software ARGUSTM (Fig. 14). The standardized method has themerit that micro necking and fractured length do not significantlyaffect results. However, the FLS is here a presumed strain some-where between local necking and ductile fracture and is obtainedby Gaussian regression of the strains measured on the fracturedspecimen. The experimental FLS for diverse wLDH are provided inFig. 15.

5.2. Comparison of analytical and experimental FLC

The FLC obtained with the corresponding n value and Eqs.(8)–(10), nearly coincides with the FLS from the LDH test,

t and specimens after LDH test.

128 M. Kim et al. / Journal of Manufacturing Processes 23 (2016) 122–129

F

wAitcFl

ig. 13. Schematic figure of limit dome height test for test tool and drawbead detail.

hereas the NADDRG shows rather poor agreement (Fig. 16).ssuming isotropic material behavior, we find that the theoret-

cal FLC also agrees with the experimental FLS; however, since

he stress–strain relation varies significantly with the r-value,onsideration of material anisotropy is mandatory in obtainingLC. As the strain path for uniaxial tensile test is a straightine with the slope of −(1 + r)/r in the ε1–ε2 plane, increasing

Fig. 14. (a) 3D white light scanning systems. (b) Major

Fig. 15. Experimental forming limit strains by LDT test.

r shifts the loading-path to the left, which results in higherε1 for a given ε2. Higher r value thus has favorable effect onformability for ε2 < 0. On the other hand, formability decreaseswith increasing r value for ε2 > 0, and are independent of the

r value at plane strain conditions (ε2 = 0) [36]. It has alsobeen shown in Section 3 that the formability increases withincreasing n.

strain distributions with various values of wLDH.

M. Kim et al. / Journal of Manufacturin

6

ozeoflbstirblt

A

DEtK

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[[

[[

[[

[

[

Fig. 16. Comparison of theoretical FLCs with experimental data.

. Conclusions

Little is known about the property of zirlo due to the scarcityf the material. In this study, we present an analytical FLC forirlo sheets. Material properties and anisotropy coefficients werevaluated from tensile test, and the experimental FLSs werebtained by LDH test. Applying two different yield criteria to theorming limit models by Swift and Hill, we obtained the ana-ytical FLC. For the material ‘zirlo’ used in this work, n coulde determined accurately by using the modified Rice–Rosengrentress–strain relation. The analytical FLC is in good agreement withhe experimental data of zirlo. Hence, the Swift and Hill models,n combination with the modified Rice–Rosengren stress–strainelation are appropriate for predicting the FLC for zirlo. Inrief, with the values of n and r from tensile tests, the ana-

ytical FLC can substitute the cost- and time-demanding LDHests.

cknowledgments

This work was supported by the Nuclear Power Core Technology

evelopment Program of the Korea Institute of Energy Technologyvaluation and Planning (KETEP), granted financial resource fromhe Ministry of Trade, Industry & Energy, Republic of Korea. (No.ETEP-2013 85400 40010).

[

[

g Processes 23 (2016) 122–129 129

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