In polycrystalline materials, such as columnar grained austenitic weld metal, grain scattering occurs. The extent of the scattering depends on the elastic anisotropy of the grains and the geometric features of the grains and grain boundaries. Therefore these properties have to be incorporated in any theoretical modelling

Eberhard Neumann, A. W.

Munikoti, Cijayendra K.

English

In polycrystalline materials, such as columnar grained austenitic weld metal, grain scattering occurs. The extent of the scattering depends on the elastic anisotropy of the grains and the geometric features of the grains and grain boundaries. Therefore these properties have to be incorporated in any theoretical modelling.</p

Munikoti, Cijayendra

Eberhard Neumann, A.

Digital Repository @ Iowa State University (ISU)

EXTENSION OF AHMED & THOMPSON THEORY TO GENERAL ELASTIC PLANE QUASI-WAVE PROPAGATION IN TEXTURED POLYCRYSTALLINE MATERIAL Vijayendra K. Munikoti'I" and A. W. Eberhard Neumann" 'FORCE Institute DK-2605 Copenhagen / Brl?lndby, Denmark "Federal Institute for Materials Research and Testing (BAM) D-12200 Berlin, Germany POLYCRYSTALLINE AUSTENITIC WELD METAL In polycrystalline materials, such as columnar grained austenitic weld metal, grain scattering occurs. The extent of the scattering depends on the elastic anisotropy of the grains and the geometric features of the grains and grain boundaries. Therefore these properties have to be incorporated in any theoretical modelling. Some of these features (which have been measured on MMA austenitic weld metal X 6 CrNi 1811, which is equivalent to AISI 304 H ss) are as follows [6]: 1. Columnar grains are made up of dendrites and residual interdendritic melting areas. Both are characterized by the same crystallographic basis vectors. This feature can therefore be used to define a columnar grain as being an area of constant dendritic orientation. 2. Though the main dendritic growth orientation [001] depends on the temperature gradient during solidification, only a few grains within a bead are observed to have exactly equal orientation. Growth orientations of adjacent grains in a bead can differ by 30° and sometimes even more. However there seems to be no mechanism which controls the orientation of [100] and [OlD] axes of different grains in a certain direction. Rather it is more probable that during solidification the axes [100] and [010] of different grains distribute randomly. This enables the weld metal to be described (macroscopically) as transversely isotropic. 3. A verage values of columnar grain length up to 8 mm and columnar grain width up to 2 mm have been measured. Grains of adjacent beads are intergrown epitaxially, in a defined manner in most cases, all three crystallographic directions being unchanged. However dendritic configuration may be changed without changing the crystallographic Review of Progress in Quantitative Nondestructive Evaluation, Vol. 17 Edited by D.O. Thompson and D.E. Chimenti" Plenum Press. New York. 1998 1657 orientation. Depending on the direction of the maximum temperature gradient, the crystallization rate of the subsidiary dendrite branches may increase and one of these directions may become the main branch as the preferred growth direction. 4. In the direction of welding the grains may be tilted upto 20° (layback angle). Additional causes of ultrasound scattering may include different degrees of segregations within a bead and grain boundary precipitations. However, these are still under investigation and have been left out due to space considerations. The results discussed in this paper concern the Rayleigh-stochastic transition region. The results for other regions of interest, viz. stochastic and geometric regions, have been analyzed and could be a part of a future publication. THEORETICAL PROCEDURE The work of Stanke and Kino [1], who developed a unified theory for elastic wave propagation in polycrystalline materials based on second order Keller's approximation, considered wave propagation in textureless material. This work was extended by Hirsekorn [2, 3] and Ahmed and Thompson [4, 5]. They applied the theory to polyphased and textured material respectively. This theory is applied under the following conditions: - Sound propagation is not restricted to the meridian plane alone: The texture of the weld metal may exhibit lay back in the direction of welding and bending in the direction perpendicular to it. Therefore the grain axis Zl is generally not contained in the plane of ultrasound incidence, fig. l. - Polarization deviation is taken into account, fig. 2. - Phase velocity variation and attenuation coefficients are calculated for the range of wave vector angles (wave vector to z-direction of the laboratory system {x,y,z}) from 0° to 90°. The stochastic wave equation given by Stanke and Kino [1] for macroscopic texture can be manipulated into the more familiar Christoffel equation form [4]: where and where fik = [eii kl + t (!:::.iikl) - t 2{(!:::.ijmn!:::.opkl)-(!:::.ijmn) (!:::.opkl)} x 1 Gmo(r) {W(r) e-.. ·ff},np ] njn/ (1) (2) IThe crystallographic co-ordinates [100],[010],[001] are represented by X, Y, and Z respectively. The laboratory co-ordinates are represented by x, y, and z respectively. 1658 Figure 1. Orientation of orthogonal particle displacement polarizations (,trihedral') quasi longitudinal (qL), quasi transverse (qTl), and pure transverse (T2) with respect to k-vector, plane of propagation xz, weld direction y, and texture Z [7, 8, 9]. T.xturc angle 2f>O /2f>0 y Figure 2. Geometric loci of the trihedral when k-vector direction varies between -900 to 900 in the plane of propagation; texture direction Z after subsequent rotations in-plane and out-of-plane by 25° [7, 8, 9]. 1659 i1 = (3). I complex wave number (3). = k - ta I = unit wave vector subscript v denotes Voigt approximation subscript A denotes wave mode crikl Voigt averages Green's function, G(r), for isotropic media is given by Lifshits and Parkhomovski [10] and has subsequently been used by other authors [2,4]. Grain geometry is defined by the auto correlation function W(r). The quantities in angled brackets (~iikl) and (~iimn~opkl) are one and two point averages respectively. A general solution to the above equation (1) is quite complicated. Therefore, certain assumptions are essential to find a solution [2,4]: - The grains are equiaxed and of similar size. This assumption simplifies the derivative in the above integral replacing W(r) by W(r). - The [001] axes of the grains are all aligned but the other two axes [100] and [010] are randomly oriented. This assumption is supported by the afore mentioned metallurgical investigations. This enables one to describe the welded structure as a textured medium. - The grains have cubic symmetry. - The weld metal is assumed to be weakly anisotropic. Therefore Green's function for isotropic media, as given by Lifshits and Parkhomovski [10], can be used. RESULTS AND DISCUSSION Material elastic constants have been chosen for 18/12 stainless steel as given by [11]: Cll = 2.16, C12 = 1.45, and C44 = 1.29 [1011 :2]' Attenuation Coefficients Normalized attenuation coefficients alkol and a/k08 have been calculated as a function of wave vector to z-direction of the laboratory system {x,y,z} (incidence angle), normalized frequency (wave number), and grain (texture) tilt (in and out of plane of incidence). (kOl and kos are wave vectors of longitudinal and transverse waves respectively in the absence of scattering.) Frequency and grain tilt are parameters shown in figures 3 - 5. The maximum attenuation, observed at 900 incidence angle for quasi longitudinal and pure transverse waves and at at 45° for quasi transverse waves, shifts to lower incidence angles and flattens with increasing texture angle. Finally, at 900 texture angle the attenuation would be constant, i. e. independent of incidence angle. This means that attenuation as a polar plot would be rotationally symmetric, just like as the slowness surface. Certain observations, concerning coherence of wave vector and polarization on the one hand and attenuation on the other, are summarized in table 1. However, attenuation measurements are not in full agreement with the a. m. calculated figures: quasi longitudinal waves exhibit a maximum of attenuation [12, 9] 1660 o ~ ;0.02 c Q) '0 ~ Q) 8 c: .Q iii ::> ~.01 ~ "C Q) .~ "iii E o z /~.---........ I" F .... / , , ' . t " 25· .. / / ................. / / '" 10''; // //.: .... :. ~ / ., ' I I I I I ' . I ~< I I I I I I I \ \, ' . ""\ .. , " ' . ' . " Parameter: Texture angle -------------0.00 '-='-====---r--r-.----- - -----1 o 10 20 30 40 50 60 70 Incidence angle tel in degrees 80 90 Figure 3. Normalized attenuation coefficient of quasi longitudinal (qL) waves as a function of incidence angle; normalized frequency: 2.0; texture tilt 5° - 45° both in and out of plane of incidence. 0.05 r------ -------- -------, I I I I I I I c I .Q / m I ~0.02 .. /""'-r cv ....... " -g .. / I ~0.01 ./ ,' § ... ;.:~ ... : ..... / ~ _ ...... "" ;' 0.00 J -------.... . ...... . o 10 20 30 40 50 60 Incidence angle [0] in degrees Parameter: Texture angle ~/ 70 80 90 Figure 4. Normalized attenuation coefficient of quasi transverse (qTl) waves as a function of incidence angle; normalized frequency: 2.0; texture tilt 5° - 45° both in and out of plane of incidence. 1661 014 r----------------------------------------, -;;;-o 1012 II) 5;010 ·0 !E CD 8008 c: . 2 ~O.06 c: ~ '" -g0.04 .~ (ij EO.02 o z , . , . ,if",. .... / . ,. l"~' -- .. ,~/ , ' ,' ...... , , . , , -. , -, , -, J ~ .. 'I • .' I • , I .' , • I ... /,' Parameter: .' .. ' ,/ [Texture an~ .. .. ~ .. 25° ./ l.!.0:J./ 5" 0 ... 45- "," ~" -------" 10 20 30 40 50 60 70 Incidence angle [0] in degrees 80 90 Figure 5; Normalized attenuation coefficient of pure transverse (T2) waves as a function of incidence angle; normalized frequency : 2.0; texture tilt 5° - 45° both in and out of plane of incidence. Table 1. Dependence of attenuation on wave vector and polarization direction Attenuation Relative Wave mode to qL qT1 T2 texture kII p II Min -- ---kII p.L --- Min Min k.L p.L Max Min Max k.L p II -- Min ---kL pL Interm. Max Interm. when wave vector and polarization are parallel to the texture instead of a minimum as predicted by modelling. Investigations are underway to improve the model and find an explanation for this discrepancy. Slowness Surface Scattering only slightly influences the slowness compared to the values calculated for the transverse isotropic 'monocrystalline' medium, fig 6 - 7. Slowness is almost unaffected for quasi longitudinal waves, whereas it increases by about 5% for transverse waves , quasi transverse and pure transverse, at maximum scattering rates. ACKNOWLEDGEMENT This work is funded by the Commission of the European Communities under the Standards, Measurements & Testing Programme, 1996 - 1999, DG XII , Brussels under Project No. SMT4-CT95-2012. 1662 90 120 60 o 180 t-----------lHl--------lL,---iL.......----l 0 5 270 Figure 6. Slowness surface (one quadrant section); texture almost in the plane of incidence. 120 o. E O. E 0,; :::!. O. o. 90 180 t-----------l~------l.----l:--...!!:-...j 0 00 Slowness surface with scattering Slowness surface without scattering I Texture angle: 25°) 240 270 Figure 7. Slowness surface (one quadrant section); texture tilt in and out of plane of incidence 25°. 1663 REFERENCES 1. F.E. Stanke, G.S. Kino, A unified theory for elastic wave propagation in polycrystalline materials, J. Acoust. Soc. Am. 75 (1984) 665-681 2. S. Hirsekorn, Directional dependence of ultrasonic propagation in textured polycrystals, J. Acoust. Soc. Am. 79 (1986) 1269-1279 3. S. Hirsekorn, The scattering of ultrasonic waves by multiphase polycrystals, J. Acoust. Soc. Am. 83 (1988) 1231-1242 4. S. Ahmed, R. B. Thompson, Propagation of elastic waves in equiaxed stainless-steel polycrystals with aligned (001 J axes, J. Acoust. Soc. Am. 99 (1996) 2086-2096 5. S. Ahmed, R. B. Thompson, On the observation of elliptic polarization of quasi-P and quasi-SV waves propagating in highly oriented equiaxed stainless steel polycrystals, Proc. 1't USA-Japan Symp. Adv. in NDT (1996) 150-155, ASNT Columbus, ISBN 1-57117-021-9 6. S. Bauer, G. Nolze, Metallurgical investigations in the project SMT4-CT95-2012 "Effect of Ultrasonic Scattering on Inspection of Austenitic Welds" funded by the Commission of the European Communities under the Standards, Measurements & Testing Programme, 1996 - 1999, DG XII, Brussels; BAM, Lab. VIII.42, D-12200 Berlin 7. Vijayendra Munikoti, E. Neumann, R. Boehm, On the polarization of ultrasonic waves in textured anisotropic materials (in German), Proc. Ann. Conf. German Society for Non-destructive Testing 37.1 (1993) 225-240 8. Vijayendra Munikoti, E. Neumann, Polarization of ultrasound in textured materials; physical elements of ultrasonic inspection of austenitic weld joints (in German), Materialpriifung 35 (1993) 260-264 9. E. Neumann, S. Hirsekorn, G. Hiibschen, T. Just, R. Schmid, Ultrasonic inspection of austenitic claddings, transition welds, and austenitic welds, Theory - Practice - Regulations (in German), D-71272 Renningen - Malmsheim, Expert-Verlag, 1995, ISBN 3-8169-1078-5 10. E. M. Lifshits, G. D. Parkhomovski, Zh. Eksp. Teor. Fiz. 20 (1950) 176-182 11. G. Bradfield; Comparison of the elastic anisotropy of two austenitic steels, Journal of the Iron and steel Institute 202 (1964) 616 12. B. L. Baikie, A. R. Wagg, M. J. Whittle, D. Yapp; Ultrasonic inspection of austenitic welds, J. Bf. Nucl. Energy Soc. 15 (1976) 257-261 1664 

Extension of Ahmed & Thompson Theory to General Elastic Plane Quasi-Wave Propagation in Textured Polycrystalline Material

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Extension of Ahmed & Thompson Theory to General Elastic Plane Quasi-Wave Propagation in Textured Polycrystalline Material

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