Journal of Nuclear Materials 446 (2014) 134–141

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Journal of Nuclear Materials

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Tensile deformation behaviors of Zircaloy-4 alloy at ambient andelevated temperatures: In situ neutron diffraction and simulation study

0022-3115/$ - see front matter � 2013 Elsevier B.V. All rights reserved.http://dx.doi.org/10.1016/j.jnucmat.2013.12.006

⇑ Corresponding author. Tel.: +86 816 2496846.E-mail address: lihongjia_caep@126.com (H. Li).

Hongjia Li a,⇑, Guangai Sun a, Wanchuck Woo b, Jian Gong a, Bo Chen a, Yandong Wang c,Yong Qing Fu d, Chaoqiang Huang a, Lei Xie a, Shuming Peng a

a Institute of Nuclear Physics and Chemistry, China Academy of Engineering Physics, Mianyang 621999, People’s Republic of Chinab Neutron Science Division, Korea Atomic Energy Research Institute, Daejeon 305-353, South Koreac Department of Materials Science and Engineering, University of Science and Technology Beijing, Beijing 100083, People’s Republic of Chinad Thin Film Centre, Scottish Universities Physics Alliance (SUPA), University of the West of Scotland, Paisley PA1 2BE, UK

a r t i c l e i n f o

Article history:Received 10 June 2013Accepted 6 December 2013Available online 12 December 2013

a b s t r a c t

Tensile stress–strain relationship of a rolled Zircaloy-4 (Zr-4) plate was examined in situ using a neutrondiffraction method at room temperature (RT, 25 �C) and an elevated temperature (250 �C). Variations oflattice strains were obtained as a function of macroscopic bulk strains along prismatic (1 0 �10), basal(0002) and pyramidal (10 �11) planes in the hexagonal close-packed structure of the Zr-4. The mecha-nisms of strain responses in these three major planes were simulated using elastic–plastic self-consistent(EPSC) model based on Hill–Hutchinson method, thus the inter-granular stresses and deformation sys-tems of each individual grain under loading were obtained. Results show that there is a good agreementbetween the EPSC modeling and neutron diffraction measurements in terms of macroscopic stress–strainrelationship and lattice strain evolutions of the planes at RT. However, there is a slight discrepancy in thelattice strains obtained from the EPSC modeling and neutron diffraction when the specimen wasdeformed at 250 �C. Analysis of grain structure and texture obtained using electron back-scattereddiffraction suggests that dynamic recovery process is significant during the tensile deformation at theelevated temperature, which was not considered in the simulation.

� 2013 Elsevier B.V. All rights reserved.

1. Introduction

Zirconium (Zr) alloy is one of the core structural materialsextensively used in nuclear power industries because of its excel-lent corrosion resistance in the radioactive environments, goodthermal conductivity and low absorption for thermal neutrons[1]. Since the Zr alloys have a hexagonal close-packed (hcp) crystal-line structure, they show significant anisotropic thermal and elas-tic/plastic properties at liquid nitrogen (LN) temperature (76 K),room temperature (RT), and moderately high temperatures (gener-ally less than 500 �C) [2–5]. Beyerlein et al. [5] studied the plasticflow of pure Zr at four different temperatures ranging from LN to177 �C, and concluded that the yield strength and hardening ratesare quite different under different loading directions (parallel orperpendicular to c-axis), loading modes (tension or compression)and temperatures. It is well known that the thermal anisotropyof the Zr alloy is mainly caused by the constraints imposed bythe neighboring grains in the polycrystalline aggregates and in-ter-granular stresses generated after the rolling process [6,7].Therefore, residual stresses can be easily generated due to

incompatibility of the neighboring grains during the subsequentplastic deformation processes. Therefore, it is critical to evaluateand control the inter-granular stresses inside the polycrystallineZr alloy materials.

In situ neutron diffraction is a non-destructive technique, whichhas been used to monitor the development of strains of variouslattice planes as functions of applied loads or macroscopic strains[8–14]. The changes of lattice strains among different (hki l) planesunder the applied loads can be also predicted effectively using anelastic–plastic self-consistent (EPSC) Hill-Hutchinson polycrystal-line model [13–16]. This method accounts for the mechanicalanisotropy, hardening and crystallographic deformation mecha-nisms of both the aggregate and single crystal [3,5,8,17–21]. There-fore, a combination of neutron diffraction measurements and EPSCsimulation is a unique methodology to characterize the inter-gran-ular stress/strain in various polycrystalline structures, e.g., cubic[8,13,18,20], hcp [3,5,17,21,22] and dual-phase (hcp and body-cen-tered cubic) [14,23], etc. Deformation behaviors of Zr and Zr alloysunder loading at ambient and/or LN temperatures have been stud-ied based on experiments and EPSC simulations [3–5,10,12,17,21].Recently, Tome et al. [3] systematically studied deformation mech-anisms of pure Zr at LN temperature and 20 �C using self-consis-tent simulation. McCabe et al. [4] have experimentally studied

H. Li et al. / Journal of Nuclear Materials 446 (2014) 134–141 135

the texture evolution and twin/slip systems of pure Zr using micro-scopic method. However, the mechanical properties of the Zr alloysat an elevated temperature (generally larger than 200 �C) have notbeen studied, although the application temperature for many Zralloys is within the range of 200–300 �C [1]. It is critical to under-stand the relationship between microscopic stress/strain and crys-tallography in the deformation systems for the Zircaloy-4 (Zr-4)alloy because it has been widely used in the form of rolled sheetto fabricate various tubes for the nuclear power plant applications.

The objective of this paper is to compare the deformationbehavior of Zr-4 rolled plate at RT and 250 �C under uniaxial tensileloading. The relationship between bulk stress and lattice strainobtained from in situ neutron diffraction was applied into EPSCsimulation to understand the crystal deformation behavior attwo different temperatures.

2. Experimental

2.1. Sample preparation

Tensile specimens were wire-cut from commercial Zr-4 rolledplate (ASTM-B352, purchased from General Research Institute forNonferrous Metals, China) with their dimensions shown in Fig. 1.The chemical composition of the specimen is 1.38 Sn, 0.24 Fe,0.11 Cr and balance Zr, in wt% with other minor elements suchas Hf, C, Al, N, and Nb. less than 0.05 wt%. The directions alonglength, width and thickness of the samples correspond to the roll-ing direction (RD), transverse direction (TD) and normal direction(ND) of the initial plate, respectively.

Two types of samples were prepared from the original and de-formed tensile specimens and used for analysis using electronback-scattered diffraction (EBSD). They were mechanically groundto an 1200 grit SiC finish and then electropolished using an electro-lyte consisting of 90% C2H5OH and 10% HClO4 at 15 V DC for 40 s atRT. The EBSD observation was performed using a TESCAN MIRA 3LMH field emission gun scanning electron microscope (SEM)equipped with an Oxford/HKL system. A step size of 0.6 lm wasused for EBSD scans and the acquired EBSD data were processedusing software packages of HKL Project Manager and AZTEC.

2.2. Neutron diffraction measurements

The diffraction measurements were carried out using astraining scanner, called Residual Stress Instrument (RSI) at KoreaAtomic Energy Research Institute. The neutron diffraction was per-

Fig. 1. Dimensions of the specimen (the unit is mm) and orientation of thespecimen with respect to the neutron beam for the in situ measurements.

formed from the gauge volume of the sample defined by a cad-mium slit of 5 mm wide and 3 mm high for the incident beamand another cadmium slit of 2 mm wide for the diffracted beam.The gauge length direction of the specimen (longitudinal direction)was located between the incident beam and the detector to mea-sure the longitudinal component (Q vector which is parallel tothe loading direction) during tensile loading, as shown in Fig. 1.The bent perfect crystal monochromator Si (111) at the take-offangle of 45� was adopted to provide a wavelength of 2.39 Å ofthe neutron beam. The neutron measurements were performedat diffraction angles (2h) of 50.0�, 54.8�, and 57.6� for the prismatic(10 �10), basal (0002) and pyramidal (10 �11) diffraction peaks,respectively. The diffraction conditions provided the reflectionsfrom each set of grains in the gauge volume of the Zr-4 specimens.

Neutron diffraction peaks were measured at a total of 7 staticloading stages in the sample. It should be noted that the loadingstages during the neutron diffraction measurements include theinitial stage (0), 0.4%, 0.8%, 3.2%, 5.5%, 8.2%, and 10.8% of strainsat RT, and 0, 0.2%, 0.4%, 1.2%, 2.2%, 3.8%, and 4.4% of strains at250 �C. The measurements at the initial stage and 3.8% of strainswere repeated to verify the accuracy of the experiments. The mea-surement steps were controlled by the displacement of the speci-men in a step of 0.01 mm/s, which corresponded to a strain rateof 10�4 s�1, and simultaneously the load was recorded by the loadcell attached. In situ lattice strains were measured at different load-ing stages as shown in the macroscopic stress–strain curves inFig. 2. It should be noted that the stress relaxation is obvious rightafter stop of the loading, Fig. 2, we start to measure the neutrondiffraction peak constantly 1 min after the loading step when theabrupt stress relaxation occurred. The inter-planar spacing (dhkil)was determined using the Bragg’s law: k = 2dhkilsinh. The diffrac-tion peak was analyzed using the least-square Gaussian fittingmethod and the RSI data analysis program. Once the peak positionwas determined, the elastic lattice strains (ehkil) were calculatedusing the formula:

ehkil ¼ ðdhkil � d0Þ=d0 ¼ �cothðh� h0Þ ð1Þ

where d0 is the inter-planar spacing of the spelled (hki l) plane inthe initial state (0% of strain), and h0 and h are the diffraction anglesfor the initial state and loading state of the specimen, respectively.

3. Elastic–plastic self-consistent model and single crystalparameters

The elastic–plastic properties of a polycrystalline aggregate aregenerally described based on the Hill-Hutchinson self-consistentapproach [15,16]. A population of various grains (2025 and 2450grains at RT and 250 �C, respectively) were chosen with a distribu-tion of orientations and weight fractions in this simulation. It wasobtained experimentally from the texture measurement using the

Fig. 2. (a) Experimental (Exp.) and calculated (Cal.) true stress–strain curves forrolled Zr-4 deformed at RT and 250 �C under RD tension, (b) hardening ratecalculated from the simulated stress strain curves shown in (a) at the twotemperature cases.

Fig. 3. Work-hardening curves of individual slip systems adjusted to fit the truestress–strain curves at (a) RT and (b) 250 �C, and the relaxed stress curves at (c) RTand (d) 250 �C.

136 H. Li et al. / Journal of Nuclear Materials 446 (2014) 134–141

EBSD. The initial textures derived from the experimental orienta-tion distribution functions, which illustrate the orientation andweight proportion of each grain, were used as the input parametersfor the EPSC simulation for the cases of RT and 250 �C, respectively.Each grain in the model was treated as an ellipsoidal inclusionembedded inside a homogeneous effective medium (HEM), havinganisotropic elastic constants and deformation characteristic of asingle crystal of the material. Interactions between individualgrains and their surrounding HEM were simulated using an elas-tic–plastic Eshelby-type self-consistent formula [24]. The proper-ties of the HEM were derived from the average response of allthe grains. The numerical code employed in this work was theone developed by Tomé et al. [17], and the version used was Ver-sion 4 (February 2010) written in FORTRAN-77. It should be notedthat all the formula were based on the work of Hutchinson [16].

The elastic constants of Zr single crystal used in the model wasobtained by fitting the curves obtained by Fisher [2], and thecorresponding coefficients were C11 = 143.5, C12 = 72.5, C13 = 65.4,C33 = 164.9, C44 = 32.1 GPa at RT and C11 = 132.3, C12 = 77.8,C13 = 65.6, C33 = 157.4, C44 = 28.8 GPa at 250 �C. According to thedata obtained from the EBSD (Fig. 4), from Refs. [4,5] and fromthe deformation theory of Zr and Zr alloys [25], twinning doesnot happen when the uniaxial tensile loading direction is alongthe RD at RT and above. According to the transmission electronmicroscope (TEM) observations by Holt et al. [26] and the EPSCsimulation results [3–5,27], basal slip activity in Zr alloys isnot conclusive, which is not included in our calculations. Therefore,slip modes considered as potential systems for accommodatingthe imposed plastic strain in this work include prismatic{10 �10}h11 �20i(hai type), pyramidal {10 �11}h11 �20i(hai type),pyramidal {10 �12}h11 �20i(hai type), and pyramidal{10 �11}h11 �2 �3i (hc+ai type) which are summarized in Table 1.The implemented work-hardening law, i.e. an extended Vocehardening law, was described by an evolution of the thresholdstress with accumulated shear strain C in each grain based onthe following equation [3]:

ss ¼ ss0 þ ðss

1 þ hs1CÞð1� exp�ðhs

0C=ss1ÞÞ ð2Þ

where ss0, hs

0, hs1, ss

0 þ ss1 are the initial critical resolved shear stress

(CRSS), the initial hardening rate, the asymptotic hardening rate,and the back-extrapolated CRSS, respectively. The critical resolvedshear stress and exponential hardening coefficients used in Eq. (2)were fitted to give an optimum agreement with the measured mac-roscopic stress–strain curves and lattice strains, which are listed inTable 1. We have fitted both the unrelaxed and relaxed stress curvesfor each temperature. The unrelaxed stress curve is the same as thatmeasured by drawing mill without stops, and the yield point isaccurate. However, the lattice strains are measured during therelaxation process. Therefore, we use the hardening coefficients thatwell fit the relaxed stress curve for lattice strain fitting. The

Table 1Parameters describing the evolution of threshold stress with deformation [Eq. (2)] for the slstress (CRSS), the initial hardening rate, the asymptotic hardening rate, and the back-extrap

T Slip systems ss0 (MPa)

RT (25 �C) Prismatic {10 �1 0} h11 �20i 155/132

Pyramidal {10 �1 1} h11 �20i 161/141

Pyramidal {10 �1 2} h11 �20i 155/135

Pyramidal {10 �1 1} h11 �2 �3i 179/159

250 �C prismatic {10 �10} h11 �20i 60/52

pyramidal {10 �11}h11 �2 0i 67/55

pyramidal {10 �12}h11 �2 0i 66/58

pyramidal {10 �11} h1 1 �2 �3i 85/77

corresponding work-hardening curves of the individual slip systemsare shown in Fig. 3.

4. Results

4.1. Tensile behavior and texture changes

True stress–strain curves of the polycrystalline Zr-4 were ob-tained under uniaxial tensile loading along RD at RT and 250 �C,and the results are shown in Fig. 2(a). There are several stressrelaxations among the sequences of the several loading stages dur-ing in situ neutron diffraction measurements. Compared to theyield strength (360 MPa) and elongation (over 10%) at RT, the cor-responding readings at 250 �C were significantly decreased toabout 150 MPa and about 4%, respectively. Furthermore, there isa difference in the work-hardening rates for the two different tem-perature cases (Fig. 2b). It should be noted that the work-harden-ing rates were calculated from the fitted true stress–straincurves, as shown in Fig. 2(a), by removing the ‘downward tips’on the measured stress–strain curves. The platforms at thebeginning of the hardening rate curves correspond to the lineardeformation stage for the two temperature cases, and the elasticmoduli (E) of 98.2 and 81.6 GPa for RT and 250 �C, respectively,were labeled in Fig. 2(b). It is interesting to mention that the hard-ening rate changes to minus sign (or so-called negative hardeningeffect) when the true strain is larger than 2% at 250 �C. A similaryielding peak has also been reported in the macroscopic stress–strain curves of ultrafine-grained aluminum at RT and LN [28,29]and magnesium alloy AZ31 [30] at 280–350 �C, which is due tothe increased grain boundaries which act as sinks for dislocations,and recrystallization occurred at higher temperatures.

ip modes at RT and 250 �C, where ss0, hs

0, hs1, ss

0 þ ss1 are the initial critical resolved shear

olated CRSS, respectively. Note for the value: for unrelaxed/relaxed stress curve fitting.

ss1 (MPa) hs

0 (MPa) hs1 (MPa)

80/80 100/78 25/1077/77 35/35 15/1570/70 35/35 5/593/93 380/380 15/15

45/45 280/280 0/025/25 670/670 �440/�44015/15 570/570 �350/�35045/45 1580/1580 �115/�155

Fig. 4. EBSD inverse pole figures (IPFs) for initial and deformed Zr-4 at RT and 250 �C. The orientations in each IPF correspond to the ND. Labels refer to% strain.

H. Li et al. / Journal of Nuclear Materials 446 (2014) 134–141 137

Fig. 4 shows EBSD inverse pole figures (IPFs) for the original anddeformed Zr-4 at the two temperatures. Different colors (or colorcontrast) in the EBSD results stand for the orientation of the origi-nal plate along ND with respect to the hcp reference frame asindicated by the orientation triangle in the index of Fig. 4. It showsclearly that the (0002) basal plane significantly decreases asdeformation increases at both RT and 250 �C. Fig. 5 shows thecorresponding pole figures (PFs). It shows that the texture of theoriginal and deformed Zr-4 specimens has a c-axis component inthe vicinity of the ND of the plate with a tendency to spread by±20� to 40� toward TD. It also shows that the component is aniso-tropic within the plane of the plate specimen. Interestingly, it hasbeen found that the (10 �10) planes along RD and (0002) planesalong ND rotate around the c-axis of the hcp crystal lattice in clock-wise direction at both temperatures. Similar results have been re-ported by Tome for the pure Zr [3]. Fig. 6 shows quantitativestatistics on the proportion of large angle grain boundary (LAGB,

Fig. 5. EBSD pole figures (PFs) for original and deform

generally larger than 15�) and small angle grain boundaries (SAGB,2–15�) as the plastic deformation increases. It was analyzed basedon the EBSD IPFs results shown in Fig. 4. The EBSD results con-firmed that the SAGB continuously increases as the deformationincreases.

4.2. Lattice strains by neutron diffraction measurements

Fig. 7 shows neutron diffraction patterns at various stages un-der uniaxial tensile loading at RT and 250 �C. At both temperatures,the intensity of prismatic (10 �10) peak is higher than that of basal(0002) peak. It is consistent when comparing the orientations be-tween the neutron beam (RD, Fig. 1) and EBSD IPFs (ND, Fig. 4) ofthe samples, which has 90� difference in direction. At RT, the inten-sities of (10 �10), (0002) and (10 �11) reflections do not changeapparently as the plastic deformation increases (Fig. 7a). On theother hand, at 250 �C, when the true strain is less than 2%, the

ed Zr-4 at RT and 250 �C. Labels refer to% strain.

Fig. 6. Statistics of grain boundary types and their proportions for various stages of deformation at (a) RT and (b) 250 �C based on EBSD data. Labels refer to the grainboundary types as large angle grain boundary (LAGB, generally larger than 15�) and small angle grain boundary (SAGB, 2–15�).

138 H. Li et al. / Journal of Nuclear Materials 446 (2014) 134–141

intensities of the three main (hkil) reflections also do not showapparent changes. When the true strain is larger than 2%, the inten-sity of (10 �10) reflection increases, while the (0002) and (10 �11)reflections decreases with the increased plastic deformation(Fig. 7b).

The variations of the diffraction peaks provide the changes oflattice strain in the (0002), (10 �11) and (10 �10) planes at RT and250 �C (see Fig. 8). The magnitude of lattice strains measured at250 �C (�2000 le) is about half of that at RT (�4000 le) as themacroscopic strain increases. It is interesting to note a distinct de-crease at the larger true strain (from 3.8% to 4.4%) for the 250 �Ccase (Fig. 8b). It could be attributed to the increases in defectsalong the SAGBs as shown in Fig. 6, and/or inhomogeneous distri-bution of inter-granular stresses at this temperature.

4.3. Lattice strains and deformation mechanism by EPSC simulation

The EPSC simulation was carried out to provide in-depth under-standing and quantitative analysis of the deformation mechanism.Based on the fitted macroscopic stress–strain curves and the dataof lattice strains, work-hardening processes and deformationmechanisms were obtained. Fig. 8 shows the EPSC simulation re-sults as solid lines. At RT, the calculated and measured latticestrains for the (10 �10) reflection agree well, and their magnitudesand change trends for the (0002) and (10 �11) reflections are alsoacceptable compared to the experimental results. At 250 �C, thepredicted results do not exactly fit the measured data, however,the magnitudes and the trend of three reflections as a function ofthe macroscopic strains agree well with the experimental results,especially for the ‘downward trend’ when the true strain is larger

Fig. 7. Neutron diffractograms acquired at various stages of deform

than 3.8% (Fig. 8b). It is worth to point out that the magnitude oflattice strains measured at 250 �C is about half of that at RT, whichagrees with the yield strength or the hardening stresses for the twotemperature cases. The apparent difference is that the lattice stainsat 250 �C tend to decrease at the relatively larger true strains(‘downward trend’ shown in Fig. 8b), and those will increase atthe RT.

Based on the macroscopic stress–strain curves and strains of themain lattice planes of Zr-4, the deformation mechanisms of theZr-4 at the two temperatures were simulated. Fig. 9 shows thepredicted results of evolution of the relative activity of multipleslip modes with deformation under tensile loading along RD fromthe EPSC simulation. Fig. 9a shows that the prismatic{10 �10}h11 �20i(hai type) slip is the dominant deformation mecha-nism at RT. It is consistent with results which the intensitiesamong the (10 �10), (0002) and (10 �11) reflections did not appar-ently change under deformation as shown in Fig. 7a. It is similarin the case of 250 �C when the true strain is less than 2% as shownin Figs. 7b and 9b. However, when the true strain is larger than 2%,the other three pyramidal slips become significant (Fig. 9b) and theintensity of (10 �11) reflection decreases. It could be attributed tothe significant increases of the pyramidal {10 �12}h11 �20i(hai type)slip as shown in Fig. 9b. In addition, the exchanges between inten-sities of (10 �10) and (0002) reflections can be related to pyramidal{10 �11}h11 �2 �3i (hc+ai type) slip. The grain rotation (EBSD datashown in Fig. 4 and Fig. 5) combined with prismatic slip does notchange the reflection intensities of the lattice planes, whereasthe combination with the pyramidal slips will change the intensi-ties of the (hkil) reflections differently for different reflectionplanes.

ation under tensile loading along RD at (a) RT and (b) 250 �C.

Fig. 8. Experimental (Exp.) and calculated (Cal.) lattice strains for the main reflections of Zr-4 as a function of true strain: (a) RT and (b) 250 �C.

Fig. 9. Predicted evolution of the relative activity of multiple slip modes with deformation under tensile loading along RD at (a) RT and (b) 250 �C.

H. Li et al. / Journal of Nuclear Materials 446 (2014) 134–141 139

5. Discussions

5.1. Comparison of macroscopic deformation behavior between RT and250 �C

Flow responses of Zr-4 at RT and 250 �C are quite different inyield phenomenon, hardening rate, and elongation. It can be ex-plained from a perspective of dislocation theory. At RT, upper yieldpoint (UYP) and lower yield point (LYP) are observed, i.e., thedashed line as shown in Fig. 2(a). When the velocity of the mobiledislocations is comparable with the diffusion velocity of the impu-rity atoms, the dislocations are pinned and a larger stress is neces-sary. The UYP level corresponds to this larger stress. As the stressrequired for motion of dislocations is much lower than the UYP,an abrupt multiplication of dislocations takes place, which can beverified from the increased SAGB with the deformation (a localstrain softening) as shown in Fig. 6. Therefore, the LYP level corre-sponds to the propagation of the band of freed dislocations at aconstant velocity [31]. On the other hand, at 250 �C, the velocityof the mobile dislocations is larger than the diffusion velocity ofthe impurity atoms [32], and pinning effect is significantly de-creased. As a result, the yield point at 250 �C reduces to 150 MPa,comparing to that of 360 MPa at RT, as shown in Fig. 2.

Significant difference in the work-hardening rates between thetwo temperature cases (Fig. 2b) can be related to the dislocationdensity [28,30]. The density of dislocation continuously increasesduring the deformation, thus forming dislocation locks or SAGBsacting as sinks for dislocations. Therefore, it is possible to enhancethe dynamic recovery rate and reducing hardening rate at 250 �C.The negative hardening effect observed at the earlier stage of thestrain (�2%) at 250 �C compared to that of RT (see Fig. 2(b)) canbe explained by the increases of the SAGBs (2–15�) as shown inFig. 5. Clearly, the EBSD results confirmed that the SAGBs wereformed and continuously increased with the deformation. Thegeneration of the SAGBs could act as the sinks for dislocations, en-

hance the dynamic recovery rate, and reduce the hardening rate at250 �C. This is a typical dynamic recovery process. A similar crystalrecovery, which was identified as a process of dislocation annihila-tion, has also been experimentally observed in body-centeredcubic (bcc) b-Zr [33] and stainless steel [34]. Such recovery pro-cesses can lead to a decrease of elongation (from over 10% to about4%) at 250 �C. The significant increases of the SAGBs act as veryeffective sinks for dislocations, which result in a lower probabilityfor inter-granular intersection of dislocations and a lower harden-ing rate, and hence lead to an early onset of necking and a reducedtensile elongation [29].

5.2. Influence of microscopic strain on macroscopic deformationbehavior

Influence of the inter-granular stresses on the macroscopicdeformation behavior can be discussed at various stages of defor-mation based on the experimental results and EPSC simulation.Fig. 10 shows the weighted variance, which is a description of graindeformation as a function of bulk macroscopic tensile stresses.Deformation stages labeled by A, B, C, D at RT (Fig. 10a) and A0,B0, C0, D0 at 250 �C (Fig. 10b) are corresponding to the labels onthe respective true stress–strain curves as shown in Fig. 2(a).Weighted variance was calculated using the formula:

XN

i¼1

ðri � �rÞ2wi ð3Þ

where N is the total number of grains, ri is the stress in Grain i, �r isthe average stress among all the grains or the macroscopic stress,and wi is the weight factor of Grain i. Grain number and the corre-sponding weight factors of the included grains are shown in thebottom of Fig. 10 (a) and (b) for the two temperature cases,respectively.

Fig. 10. Internal stresses at different stages of deformation: labeled by A, B, C, D at RT and A0 , B0 , C0 , D0 at 250 �C on the true stress strain curves (Fig. 2a). The red solid linesstand for the average stress (or the measured macroscopic stress), and the black solid lines indicate the stress in each grain, where the weight factor of each grain are shownbelow. The weighted variance at each deformation stage is labeled on the right. (For interpretation of the references to color in this figure legend, the reader is referred to theweb version of this article.)

140 H. Li et al. / Journal of Nuclear Materials 446 (2014) 134–141

Weighted variances of each deformation stage are marked inFig. 10, and plots of the weighted variance versus true stress areshown in Fig. 11. It is clear that the weighted variance of theinternal stress in grains increases as the true stress increases atboth temperatures. The major differences occur at the early stageand the final stage. It is obvious that the slope of line of A0-B0 is lessthan that of A–B (SA0–B0 < SA–B), and SB0–C0�SB–C, whereas the abso-lute value of SC0–D0 is much larger than that of SC–D as shown inFig. 11. Therefore, during the dynamic recovery process, from pointC0–D0 on the stress–strain curve of 250 �C case shown in Fig. 2 (a),although the macroscopic stress decreases, the inter-granularstresses increase significantly. Moreover, the phenomenon thatthe lattice strains decrease at relatively larger true strains (from3.8% to 4.4%) at 250 �C, Fig. 8(b), is most possibly caused by the sig-nificantly increased discrepancies of internal stresses in the grains(Fig. 11) combined with necking [29,35], where the localized neck-ing of the specimen was significant (not shown here).

5.3. Comparison of deformation behavior between neutron diffractionand EPSC simulation

In overall, the results from the EPSC polycrystal model are wellsuited to interpret the measurements provided by neutron diffrac-tion [13]. That is because the neutron diffraction technique mea-sures an average lattice spacing over many grains with acommon crystallographic plane normal surrounded by differentneighbors, and similarly, the EPSC model treats the polycrystallineaggregate as a homogeneous effective medium (HEM). Each grainembedded in the HEM as an ellipsoidal inclusion and the interac-

Fig. 11. Plots of the weighted variance versus true stresses at RT and 250 �C.

tion between a grain and its surrounding creates consistency withthe intrinsic statistical character of the neutron diffractionmeasurement. As a result, combining the fitted macroscopicstress–strain curves and lattice strains by the neutron diffraction,the deformation mechanisms and the inter-granular stresses canbe obtained for the Zr-4 at RT and 250 �C by using EPSC simulationas shown in Figs. 9 and 10.

In the EPSC model, the whole hardening process is controlled byan extended Voce hardening law, as shown in Eq. (2), which exhib-its an asymptotic hardening rate hs

1 [3]. However, the dislocationdensity, velocity, its production and annihilation, and pinningeffect have not been considered in the hardening law. For example,we set hs

1 of pyramidal slips with minus values for the 250 �C case(Table 1), in order to simulate the ‘softening’ at larger strains. Thediscrepancies of lattice strains are larger than those of true stress–strain curves, especially for the 250 �C case. It might be due to thelimited inputs of material properties e.g., vacancy, interstitialatoms, dislocations to simulate the proper anisotropic latticestrains in the modeling by a simplified hardening law. Thus, spe-cific hardening laws for particular orientations and slip systemsshould be introduced [18], or dislocation-based work-hardeninglaw with temperature effects should be used [5]. The downwardtrend of the true stress–strain curve of pure Zr under tensile loadalong RD at larger strains still could not be fitted well with exper-imental results at a moderately high temperature of 177 �C by EPSCsimulation with the dislocation-based work-hardening law [5]. Thegeneral conclusion from such comparisons is that model calcula-tions and experiments agree quite well although with somedifferences [36,37]. Our current result of the crystallographicdeformation mechanisms for the RT case is consistent with Gloag-uen et al.’s work on Zr-4 by combining X-ray diffraction and a self-consistent model [27]. For the 250 �C case, the dynamic recoveryprocess at a strain larger than 2% is quite complicated to model.Improved hardening law is needed to accurately describe the hard-ening process at elevated temperatures.

6. Conclusions

(1) In situ neutron diffraction measurements of the strainresponse of three main (hkil) lattice planes of rolled Zr-4under uniaxial tensile loading along RD were performed atRT and 250 �C. Combined with the results from the EBSDmeasurements and EPSC simulation, the mechanisms of dif-ferent responses of the rolled Zr-4 under uniaxial tension atthese two temperatures were observed.

H. Li et al. / Journal of Nuclear Materials 446 (2014) 134–141 141

(2) The yield strength of the Zr-4 sample at RT is approximatelytwice as much as that at 250 �C. A large difference of themacroscopic mechanical properties between these two casesis that the hardening rate turns to minus sign when the truestrain is larger than 2% at 250 �C, which is caused by theincreased SAGBs. This is because formation of sinks of dislo-cations enhances dynamic recovery rate and reduces hard-ening rate at 250 �C.

(3) Based on the fitted experimental macroscopic stress–straincurves and the lattice strains, inter-granular stresses of thegrains and the deformation mechanisms were obtainedusing the EPSC simulation.

(4) At RT, prismatic {10 �10}h11 �20i(hai type) slip dominates,and the intensities of (10 �10), (0002) and (10 �11) reflectionsdo not show much changes with the increased plastic defor-mation. At 250 �C, when the true strain is less than 2%, pris-matic {10 �10}h11 �20i(hai type) slip dominates, and theintensities of the three reflections show little changes. How-ever, when the true strain is larger than 2%, the other threepyramidal slips become dominant. The intensity of (10 �10)reflection increases and the intensity of (0002) reflectiondecreases, which could be due to pyramidal {10 �11}h11 �2 �3i(hc+ai type) slip. The intensity of (10 �11) reflection decreasesdue to pyramidal {10 �12}h11 �20i(hai type) slip.

(5) Weighted variance of the internal stress in the grainsincreases with the increased microscopic stress at both tem-peratures. The phenomenon that lattice strains decrease atrelatively larger true strains (>3.8%) at 250 �C is mainly causedby the significantly increased differences of the internal stres-ses in various oriented grains combined with necking.

Acknowledgements

The authors acknowledge all the experimental participants inKorea Atomic Energy Research Institute, and valuable discussionswith Dr. Guoming Le in Department of Materials Science and Engi-neering of Tsinghua University. This work is supported by the Na-tional Natural Science Foundation of China (Grants 11105128,91126001, 51231002) and the China Postdoctoral Science Founda-tion (Grant 2012M521715), as well as Royal Society of Edinburghand Carnegie Trust Funding.

References

[1] D.O. Northwood, Mater. Des. 6 (1985) 58–70.[2] E.S. Fisher, C.J. Renken, Phys. Rev. 135 (1964) A482–A494.[3] C.N. Tome, P.J. Maudlin, R.A. Lebensohn, G.C. Kaschner, Acta Mater. 49 (2001)

3085–3096.[4] R.J. McCabe, E.K. Cerreta, A. Misra, G.C. Kaschner, C.N. Tome, Philos Mag. 86

(2006) 3595–3611.[5] I.J. Beyerlein, C.N. Tome, Int. J. Plasticity 24 (2008) 867–895.[6] I.C. Noyan, J.B. Cohen, Residual Stress Measurement by Diffraction and

Interpretation, Springer, New York, 1987.[7] J.W.L. Pang, T.M. Holden, P.A. Turner, T.E. Mason, Acta Mater. 47 (1999) 373–

383.[8] N. Jia, R.L. Peng, D.W. Brown, B. Clausen, Y.D. Wang, Metall. Mater. Trans. A 39A

(2008) 3134–3140.[9] V. Davydov, P. Lukas, P. Strunz, R. Kuzel, J. Phys.-Condens. Mater. 21 (2009).

[10] G. Proust, G.C. Kaschner, I.J. Beyerlein, B. Clausen, D.W. Brown, R.J. McCabe,C.N. Tome, Exp. Mech. 50 (2010) 125–133.

[11] D. Ma, A.D. Stoica, K. An, L. Yang, H. Bei, R.A. Mills, H. Skorpenske, X.L. Wang,Metall. Mater. Trans. A 42A (2011) 1444–1448.

[12] S. Cai, M.R. Daymond, R.A. Holt, Acta Mater. 60 (2012) 3355–3369.[13] H. Wang, B. Clausen, C.N. Tome, P.D. Wu, Acta Mater. 61 (2013) 1179–1188.[14] O. Muransky, M.R. Daymond, O. Bhattacharyya, O. Zanellato, S.C. Vogel, L.

Edwards, Mater. Sci. Eng. A 564 (2013) 548–558.[15] R. Hill, J. Mech. Phys. Solids 13 (1965) 89–101.[16] J.W. Hutchinson, Proc. R. Soc. Lon. Ser. – A 319 (1970) 247–272.[17] P.A. Turner, N. Christodoulou, C.N. Tome, Int. J. Plasticity 11 (1995) 251–265.[18] B. Clausen, T. Lorentzen, Metall. Mater. Trans. A 28 (1997) 2537–2541.[19] C.N. Tome, Model Simul. Mater. Sci. 7 (1999) 723–738.[20] T. Lorentzen, M.R. Daymond, B. Clausen, C.N. Tome, Acta Mater. 50 (2002)

1627–1638.[21] G.C. Kaschner, C.N. Tome, I.J. Beyerlein, S.C. Vogel, D.W. Brown, R.J. McCabe,

Acta Mater. 54 (2006) 2887–2896.[22] S.R. Agnew, C.N. Tome, D.W. Brown, T.M. Holden, S.C. Vogel, Scripta Mater. 48

(2003) 1003–1008.[23] S. Cai, M.R. Daymond, R.A. Holt, E.C. Oliver, Acta Mater. 59 (2011) 5305–5319.[24] J.D. Eshelby, Proc. R. Soc. Lon. Ser. – A 241 (1957) 376–396.[25] E. Tenckhoff, Deformation Mechanisms, Texture, and Anisotropy in Zirconium

and Zircaloy, Special Technical Publication, Philadelphia, PA, 1988.[26] R.A. Holt, A.R. Causey, J. Nucl. Mater. 150 (1987) 306–318.[27] D. Gloaguen, T. Berchi, E. Girard, R. Guillen, Acta Mater. 55 (2007) 4369–4379.[28] C.Y. Yu, P.W. Kao, C.P. Chang, Acta Mater. 53 (2005) 4019–4028.[29] P.C. Hung, P.L. Sun, C.Y. Yu, P.W. Kao, C.P. Chang, Scripta Mater. 53 (2005) 647–

652.[30] T. Walde, H. Riedel, Mater. Sci. Eng. a – Struct. 443 (2007) 277–284.[31] G. Ananthakrishna, Phys. Rep. 440 (2007) 113–259.[32] W.G. Johnston, J.J. Gilman, J. Appl. Phys. 30 (1959) 129–144.[33] S. Kabra, K. Yan, D.G. Carr, R.P. Harrison, R.J. Dippenaar, M. Reid, K.D. Liss, J.

Appl. Phys. 113 (2013) 063513.[34] F. Christien, M.T.F. Telling, K.S. Knight, Scripta Mater. 68 (2013) 506–509.[35] C.Y. Yu, P.L. Sun, P.W. Kao, C.P. Chang, Scripta Mater. 52 (2005) 359–363.[36] B. Clausen, T. Lorentzen, T. Leffers, Acta Mater. 46 (1998) 3087–3098.[37] B. Clausen, T. Leffers, T. Lorentzen, Acta Mater. 51 (2003) 6181–6188.