Frank Laboratory of Neutron Physics   Joint Institute for Nuclear Research  

Determination of the residual stress tensor in Determination of the residual stress tensor in textured zirconium alloy by neutron diffractiontextured zirconium alloy by neutron diffraction

V.V.Sumin1,, I.V.Papushkin1, R.N.Vasin1, A.M. Venter2 , R.S.Wimpory3 andand A.M.Balagurov1

1 Frank Laboratory of Neutron Physics, Joint Institute for Nuclear Research, Dubna, Russia1 Frank Laboratory of Neutron Physics, Joint Institute for Nuclear Research, Dubna, Russia

2 Research and Development Division, NECSA Limited, Pretoria, South Africa2 Research and Development Division, NECSA Limited, Pretoria, South Africa

3 3 Helmholtz Centre Berlin for Materials and EnergyHelmholtz Centre Berlin for Materials and Energy

Introduction

FLNP has excellent conditions for the both measurements of the crystallographic textures and residual stresses in the materials by time-of-flight neutron scattering:

SKAT texture diffractometer allows to collect 1368 diffraction spectra and receive experimental pole figures of all the phases in the bulk sample (volume up to 125 cm3) in the regular 5x5° grid. Thus the orientation distribution functions for all the phases may be easily reconstructed with a great angular resolution.

FSD (The Fourier stress diffractometer) has rather high resolution of Δd/d ≈ 4x10-3 and is equipped with

HUBER a 5-axes goniometer, which makes it perfect device for the measurements of the strain tensor.

The combined use of those two instruments makes possible the evaluation of the residual stress tensor in textured materials (Y.D.Wang, et all (ICRS-6), MAUD-program,1999).

Two different cases were studied:

• 1) Textured Zr+1%Nb alloys with texture index F2 ≈ 3-4 and almost isotropic diffraction elastic constants (DEC);

• 2) Polycrystalline graphite with almost random texture and low F2 = 1.19, but with the strongest elastic anisotropy (C1111/C3333 ≈ 29),

Carbon, 2011.

• 3) All other polycrystal materials are between these two!!!

Detector Neutronguide

Zr – 1.0 Nb alloy RTOF-neutronography for vertical (900) and horizontal (00) sample positions

0,75 1,00 1,25 1,50 1,75 2,00 2,25 2,50 2,75 3,00

0

200

400

600

800

1000

1200

Inte

nsity

d, Å

00

900

The lattice preferred orientation of zirconium in samples

ODF min. value fmin = 0, ODF max. value fmax = 6.11, texture index F2 = 3.38.

The axis of fiber texture is close to the normal to the {1-40} planes.

ODF min. value fmin = 0, ODF max. value fmax = 7.70, texture index F2 = 4.04.

The axis of fiber texture is close to the normal to the {321} planes (12° rotation relative to Zr1).

Zr1 (hard-drawn) Zr0 (annealed, 600 С

Voigt’s and Reuss’s polycrystal models for calculation Zn, Zr, C and Fe diffraction modulus

After Z. Mathies

Averaging method Young’s modulus ,GPa

VP, km/s

Reuss 30.9 4.79

GEO 136.6 9.42

Voigt 561.2 16.37

Table 1. Calculated Young’s modulus and VP for textured graphite

Calculation of bulk elastic properties of the textured Zr+1%Nb samples

Table 2. Young’s modulus (GPa) of Zr1 (left) and Zr0 (rihgt) samples calculated by GEO-method end measured texture; linear scale contours, stereographic.

Zr1 Zr0 Averaging

method

.

Min. Young’s modulus,GPa

Max. Young’s modulus, GPa

Min. Young’s modulus, GPa

Max. Young’s modulus, GPa

Reuss 92.8 98.6 93.0 98.4GEO 93.3 99.9 93.5 99.7Voigt 93.8 101.2 94.0 101.1

Stress tension for Zircaloy-4 (E.Garlea, 2005)

Is a sense to continue the measurement?

Layout of t-of-flight neutron diffraction experiment

vs -position

0 20 40 60 80 10038,14

38,16

38,18

38,20

38,22

38,24

38,26

38,28

38,30

0 20 40 60 80 100

43,68

43,70

43,72

43,74

43,76

43,78

43,80

43,82

43,84

43,86

2th

eta

- angles

(100) reflex of Zr-1% Nb, annealed (100) reflex of Zr-1% Nb, cold forging (100) reflex of Zircoloy, annealed

(101) reflex of Zr-1% Nb, annealed (101) reflex of Zr-1% Nb, cold forging (101) reflex of Zircoloy, annealed

2th

eta

-angle

Residual stress tensor for textured sample

(1)

(2)

(3)

The angular dependence of dhkl for (100) – A, (101) – B, (103) – C, (110) – D, (002) – E planes in Zr1 sample, HRFD data. Experimental (■) and

calculated (○) data are shown. Solid line is the calculated do value.

0 10 20 30 40 50 602,797

2,798

2,799

2,800

2,801

2,802 Zr1 meas. HRFD d0 sig=(136, 0, -5) d calc. sig=(136, 0, -5)

d 100

, Å

, o0 10 20 30 40 50 60 70 80 90

2,456

2,457

2,458

2,459

2,460

2,461

2,462

2,463 Zr1 meas. HRFD d0 sig=(136, 0, -5) d calc. sig=(136, 0, -5)

d 101

, Å

, o40 50 60 70 80 90

1,4610

1,4615

1,4620

1,4625 Zr1 meas. HRFD d0 sig=(136, 0, -5) d calc. sig=(136, 0, -5)

d 103

, Å

, o

0 10 20 30 401,615

1,616

1,617

Zr1 meas. HRFD d0 sig=(136, 0, -5) d calc. sig=(136, 0, -5)

d 110

, Å

, o80 90

2,568

2,569

2,570

2,571

Zr1 meas. HRFD d0 sig=(136, 0, -5) d calc. sig=(136, 0, -5)d 0

02, Å

, o

The angular dependence of dhkl for (100) – A, (101) – B, (103) – C, (110) – D planes in Zr1 sample, E7 (Berlin) data. Experimental (■) and calculated (○)

data are shown. Solid line is the calculated do value.

0 10 20 30 40 502,793

2,794

2,795

2,796

2,797

2,798

2,799

2,800

2,801

2,802

2,803 Zr1 meas. d0 d calc. sigma=(166, 0, -43)

d 100

, Å

, o20 30 40 50 60 70 80 90

2,454

2,456

2,458

2,460

2,462

2,464

2,466 Zr1 meas. d0 d calc. sigma=(166, 0, -43)

d 101

, Å, o

The angular dependence of dhkl for (100) – A, (103) – B planes in Zr0 sample, E7 data. Experimental data (■) are shown. The calculated data

coincide (σI = 0) with the solid line, which is the calculated value.

0 10 20 302,794

2,795

2,796

2,797

2,798

2,799

Zr meas. d calc. sigma=(0, 0, 0)

d 100

, A

, o

50 60 70 80 90

1,4620

1,4625

1,4630

Zr meas. d calc. sigma=(0, 0, 0)

d 103

, A

, o

Table 3. Values of the type I residual stress tensor components σ, and cell parameters a0 and c0 for Zr1 and Zr0 samples measured on HRFD and Е7 diffractometers. The values of a0 and c0 estimated from the literature data and from the E-110 chip measurements on HRFD are also given. The mean relative discrepancy between measured and

calculated dhkl values is indicated Spectrometerjib

,rfSampl

e.σ1 σ3 σ4 ao co Δd/d

10-4

HRFD Zr1 136 0 5 3.2340 5.1367 0.8

Zr0 0 0 0 3.2295 5.1463 2.7

E7 Zr1 166 0 -43 3.2342 5.1386 4.13

Estimate from [Holden,

1999]

3.2326# 5.1395#

HRFD Strip Zr1%Nb 3.2323 5.1449

Intergranular stresses in Zr at elastoplastic deformation.( T. Holden,1999)

a) tension parallel Q along cylindrical axis

Intergranular stresses in Zr at elastoplastic deformation.( T. Holden,1999)

b) tension perpendicular Q

“Poisson’s coeff.” changes sighfor keeping continuity

Resume

• The grain preferred orientation was measured in cylindrical fuel element plugs made of Zr+1%Nb (E-110 ) alloy. In the sample made by swage machining, a fiber texture with texture index F2 = 3.38 is observed. The fiber axis is collinear with the cylinder axis and with the crystallographic direction normal to the {1-40} plane. The process of annealing changes the crystallographic texture of the material. The fiber texture remains, but texture index changes to 4.04 and the axis of texture tilts and becomes collinear to the direction normal to {321} plane.

• The use of the BulkPathGEO method for the determination of the type I residual stresses in the samples Zr+1%Nb (E-110 ) alloy gave satisfactory results. In the annealed sample the residual stresses are close to zero. In the cold-worked sample stresses are tensile (≈150 MPa) in the radial direction and zero in the axial direction.

• The residual stresses in the studied cold-worked plug seem to originate from the anisotropy of the elasto-plastic transition for grains of different orientation. Annealing leads to the recrystallization processes, which reduce residual stresses in the material. The calculated values of stress tensor components are almost independent on the micromechanical model used and account for the real ODF instead of random ODF.

Acknowledgments

We would like to thank Dr. V.N. Shishov (Bochvar VNIINM) for the provision of samples,

Prof. A.N. Nikitin and Dr. Ch. Scheffzuk (FLNP, JINR) for their help in conducting experiments on SKAT diffractometer,

Prof. S. Matthies (FLNP, JINR) for his interest in this work and help in calculations.