Fig. 2. Intersection between X-ray and diffracted beams. 2θ 1 (1) (2) (3) (4) method.

Transcription

1 2017A-E10 Program Title An attempt to measure strains of coarse grains and micro area using double exposure method 1), 2) 3) 3) 4) Username : K. Suzuki 1), T. Shobu 2) R. Yasuda 3) A. Shiro 3) Y. Kiso 4) 1), 2) 3) 4) Affiliation : 1) Niigata University, 2) Sector of Nuclear Science Research, JAEA, 3) Quantum Beam Science Research Directorate, NIQRST Strain, Coarse grains, X-ray stress measurement, Synchrotron, Double exposure method, 3D-XRD 1. (Summary) 0 (1) (DSTM: Diffraction Spot Trace Method) (2) 2 (DEM: Double Exposure Method) DEM 30 kev PILATUS-300K 3D-XRD 2. (Experimental) P 1 P 2 2 P 1 =(x 1,y 1,z 1 ), P 2 = (x 2,y 2,z 2 ) l X P 1 P 2 l 2 2 θ P C =(x C,y C,z C ) 3 (x, y, z) 2 Specimen X-Ray beam z O P C x 1 x2 Beam Area detector stopper PILATUS l y X y L 2 r y 2 1 z 2 l L0 r 1 z 1 P 2θ LD 2 P 1 P 2 =(x 2,y 2,z 2 ) P 1 =(x 1,y 1,z 1 ) x P C =(x C,y C,z C ) Fig. 1. Optics for double exposure method.

2 l P C l 1 e P 1 P 2 l X O e X l 0 OX Fig. 2. Intersection between X-ray and diffracted beams. (DEM) DEM 0 2θ 1 2 (PLATUS) P 1 P 2 2 l X 2θ 1 P 1, P 2 l 2 l X l 2 y l X 2 P C O X DEM l P C 2θ ( ) r2 r 1 2θ = arctan y 2 y 1 L = y 2 y 1, L 0 = y 1, L D = L cos 2θ P C P C = l 1 = x C y C z C = P 1 + l 1 e = x 1 + l 1 e x y 1 + l 1 e y z 1 + l 1 e z cos 2θ [ ] L sin 2 (x2 x 1 ) x 1 +(z 2 z 1 ) z 1 2θ e = 2.2 (1) (2) (3) (4) cos 2θ L (x 2 x 1,y 2 y 1,z 2 z 1 ) (5) DEM Al-Mg A5052 A1050 ( 99.8%) 5 mm 3mm 350 C, 1 hr Fig. 3. Jig for tensile test. 3 σ A 4 PILATUS-300K 2θ = 26 2θ = θ = θ = SPring-8 BL22XU λ = Å mm 2 PILATUS-300K pixel mm/pixel 2θ = Intensity, % Fig. 4. method Al by synchrotron with 30 kev Al Powder diffraction for aluminum using Rietveld 1 a 0 = Å S.G.= Fm 3m A-225 λ = Å

3 (a) Position at P 1 (b) Position at P 2 (c) Continuous image Fig. 5. Diffraction images using double exposure method with PILATUS-300K y 1 = L 0 = mm, y 2 = mm, L = mm, L D = mm PILATUS- 300K 10 s Kröner (3) 331 E 331 = GPa, ν 331 = E 420 = GPa, ν 420 =0.348 E m = GPa, ν m =0.347 Kröner c ij c 11 = , c 12 = 60.74, c 44 = GPa (4) Kröner (5) 3 (Results and Discussion) (a) P 1 (b) P 2 P 1 P 2 (c) (c) (a) P 2 (a) DEM P 1 P 2 P 1 P 2 (O x1,o y1 ) = ( , ) (O x2,o y2 ) = ( , ) P 2 (x 2,y 2 ) P 1 (x 1,y 1 ) P 1 P 2 α (mm) α = L 0 + L L 0 = L 0 = , L 0 + L = P 2 (x 2,y 2 ) P 1 (x 1,y 1 ) ( ) ( ) ( x 1 = α 1 x 2 O x2 + y 1 y 2 O y2 O x1 O y1 (O x2,o y2 ) (O x1,o y1 ) ) (6) bit (xxx.tiff) ImageJ ( 2.4Mbyte, xxx.txt) B(i 1,j 1) B(i+1,j+1) 9 5 B(i, j) ( + ) P 1 P (3 3) 2. (CCF: Cross-correlation function, 1, 10, 10 2 ) x, y 2 2

4 (a) Original (b) CCF (c) Binary (d) Outline Fig. 6. Image processing and detecting outline of spots 2 6 P 1 P 2 P 1 (x, y) P 2 (x, y) P 2 P 1 7 (1) 2θ (6) P C (x C,y C,z C ) 2θ, P C (x C,y C,z C ) 3.2 Al-Mg (A5052) DEM 0.5 mm 5 (a) Position at P 1 (b) Position at P 2 Fig. 7. Processed images. The pair of spots is indicated with a cross mark.

5 loading unloading Mean in loading Mean in unloading A5052, uniaxial tension Al 331 by keV Strain, μ Measured by DEM Theoretical A5052 Al 331, kev Fig. 8. Diffraction angle, deg , MPa A (a) All measured data A5052, uniaxial tension Loading Unloading (b) Mean of measured data Change in diffraction angles measured by DEM with applied stresses. DEM 8 (a) DEM 2θ θ 2 8(b) (a) Fig. 9. Strain measurement by DEM 2θ 9 σ A DEM ε ψ σ A 331 σ A σ A σ 1, σ 2 σ 3 (6) ε 1 = 1 E σ A ε 2 = ν E σ A (7) ε 3 = ν E σ A φψ ε φψ ε φψ = ε 1 cos 2 φ sin 2 ψ + ε 2 sin 2 φ sin 2 ψ + ε 3 cos 2 ψ (8) σ 1 φ =0 ε ψ = ε 1 sin 2 ψ + ε 3 cos 2 ψ (9) ψ = π/2 θ ε ψ = σ A E hkl (cos 2 θ ν hkl sin 2 θ) (10) θ ε ψ 9

6 1.0 Diffracted grain positions (x c,y c,z c ) DEM, Al 331, keV A5052, 0μ x c z c Loading Unloading Mean (loading) Mean (unloading) Position (x c,z c ), mm DEM Position y c, mm Fig. 10. Positions of crystal grains. 10 y y C = 0.15 mm y C =0.15 mm x C z C y C 0.5 mm x C (±0.1 mm) z C ±0.1 mm x y (A1050) A5052 DEM (A1050) 2θ 11 (a) 0.5 mm 5 DEM 2θ σ A (b) Al Al-Mg Al σ A 10 MPa (a), (b) (a) All measured data DEM (b) Mean of measured data Fig. 11. Change in diffraction angles measured by DEM in loading and unloading for A θ (10)

7 Measured strain,, μ DEM Measured strain Theoretical a, MPa DEM (DEM) (DEM) Fig. 12. Strain measurement by DEM for A MPa DEM 13 x ±0.1 mm x 2θ 0 z y 3.0 0mm 3mm 1.5mm DEM DEM 1.0 x c z c 4. (Others) (1) P.J. Withers, P.J. Webster, Neutron and Synchrotron X-ray Strain Scanning, Strain, Vol. 37, Issue 1, pp (2001). DOI: /j tb01216.x (2), 2,, Vol. 63, No. 7, pp (2014). (3) E. Kröner, Berechnung der elastischen Konstanten des Vierkristalls aus den Konstanten des Einkristalls, Zeitschrift Physik, Vol. 151, pp (1958). (4) G.N. Kamm and G.A. Alers Low-temperature elastic moduli of aluminum, J. Appl. Phys., Vol 35, pp (1964). (5) ( ) (6),,,, p. 101 (2006),. Position(x c,z c ), mm X-ray beam All data in loading Position y c, mm Fig. 13. loading. Positions of crystal grains for A1050 sample in