Frank Laboratory of Neutron Physics Joint Institute for Nuclear Research Determination of the residual stress tensor in textured zirconium alloy by neutron diffraction and V.V.Sumin 1,, I.V.Papushkin 1, R.N.Vasin 1, A.M. Venter 2, R.S.Wimpory 3 and A.M.Balagurov 1 1 Frank Laboratory of Neutron Physics, Joint Institute for Nuclear Research, Dubna, Russia 2 Research and Development Division, NECSA Limited, Pretoria, South Africa 3 Helmholtz Centre Berlin for Materials and Energy 3 Helmholtz 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, ) All other polycrystal materials are between these two!!!

Detector Neutronguide

Zr – 1.0 Nb alloy RTOF-neutronography for vertical (90 0 ) and horizontal (0 0 ) sample positions

The lattice preferred orientation of zirconium in samples ODF min. value fmin = 0, ODF max. value fmax = 6.11, texture index F2 = 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 = 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 methodYoung’s modulus,GPa VP, km/s Reuss GEO Voigt 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. Zr1Zr0 Averaging method. Min. Young’s modulus, GPa Max. Young’s modulus, GPa Min. Young’s modulus, GPa Max. Young’s modulus, GPa Reuss GEO Voigt

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  -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.

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.

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.

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,rf Sampl e. σ1σ1 σ3σ3 σ4σ4 aoao coco Δd/d HRFD Zr Zr E7E7Zr Estimate from [Holden, 1999] # # HRFD StripZr1%Nb

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 sigh for 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.