NUMERICAL SIMULATION OF ULTRASONIC ATTENUATION BY A BIMODAL GRAIN SIZE POLYCRISTAL Xue Bai, Bing Tie, Denis Aubry, Jean-Hubert Schmitt

Transcription

1 BIM ODAL GRAIN SIZE ATTENUATION 1 UMR 8579 NUMERICAL SIMULATION OF ULTRASONIC ATTENUATION BY A BIMODAL GRAIN SIZE POLYCRISTAL Xue Bai, Bing Tie, Denis Aubry, Jean-Hubert Schmitt MSSMat, CNRS, CentraleSupélec, Université Paris Saclay, France September 21 th 2017

2 OUTLINE Introduction: Effect of grains on attenuation Numerical simulation of wave propagation Simulation of the grain size effect on attenuation Simulation of a bimodal grain size effect on attenuation Conclusions 2 BIMODAL GRAIN SIZE ATTENUATION

3 INTRODUCTION: EFFECT OF GRAINS ON ATTENUATION Attenuation due to scattering by grains depends on: grain disorientation incidence angle grain size Orientation 1 Emitter Orientation 2 Receiver 3 BIMODAL GRAIN SIZE ATTENUATION FE simulation of the effect of GB orientation Ni superalloy B. Tie et al. 2010

4 INTRODUCTION: EFFECT OF GRAINS ON ATTENUATION Sources of attenuation echo(i) echo(j) B. Tie et al Internal Friction/Gain Grain Scattering Beam divergence (sample geometry) 4 BIMODAL GRAIN SIZE ATTENUATION

5 INTRODUCTION: EFFECT OF GRAINS ON ATTENUATION Attenuation dependence on grain size : Rayleigh domain : stochastic domain : diffusion domain 5 BIMODAL GRAIN SIZE ATTENUATION (from F.E. Stanke & G. Kino 1984)

6 INTRODUCTION: EFFECT OF GRAINS ON ATTENUATION An example on C-Mn A36 steel: In-situ measurement of grain growth in austenite Good correlation with metallographic measurements (EQAD) abnormal grain growth with 6 BIMODAL GRAIN SIZE ATTENUATION M.Dubois et al. 2000

7 INTRODUCTION: EFFECT OF GRAINS ON ATTENUATION Heterogeneous grain growth in Inco 718 sample 7 BIMODAL GRAIN SIZE ATTENUATION T.Garcin et al. 2016

8 INTRODUCTION: EFFECT OF GRAINS ON ATTENUATION 3 different domains of grain growth kinetics After s normal grain growth (parabolic) 8 BIMODAL GRAIN SIZE ATTENUATION T.Garcin et al. 2016

9 INTRODUCTION: EFFECT OF GRAINS ON ATTENUATION 3 different domains of grain growth kinetics After s normal grain growth (parabolic) Intermediate domain: bimodal grain size Mixture law 9 BIMODAL GRAIN SIZE ATTENUATION T.Garcin et al. 2016

10 INTRODUCTION: EFFECT OF GRAINS ON ATTENUATION 3 different domains of grain growth kinetics After s normal grain growth (parabolic) Intermediate domain: bimodal grain size Mixture law Fast evolution of b between 30 and 200 s Quantification of the volume fraction of large grains 10 BIMODAL GRAIN SIZE ATTENUATION T.Garcin et al. 2016

11 OUTLINE Introduction: Effect of grains on attenuation Numerical simulation of wave propagation Simulation of the grain size effect on attenuation Simulation of a bimodal grain size effect on attenuation Conclusions 11 BIMODAL GRAIN SIZE ATTENUATION

12 NUMERICAL SIMULATION OF WAVE PROPAGATION 2D Finite Element model to investigate bimodal structure Hexagonal grains Pressure Loading T Emitters line Le Pressure Loading T e 2 e 1 free boundary outside the emitters Incident signal: Combined Ricker (representative of LUS) 2MHz 16MHz 12 BIMODAL GRAIN SIZE ATTENUATION

13 NUMERICAL SIMULATION OF WAVE PROPAGATION Time discontinuous space-time Galerkin method implicit solver (OOFE Object Oriented Finite Element program) B. Tie et al Mesh convergence (nb of elements per grain and per wavelength) 13 BIMODAL GRAIN SIZE ATTENUATION

14 NUMERICAL SIMULATION OF WAVE PROPAGATION Wave fronts of quasi-longitudinal and quasi-shear waves 14 BIMODAL GRAIN SIZE ATTENUATION Quasi-longitudinal wave Quasi-shear wave

15 NUMERICAL SIMULATION OF WAVE PROPAGATION Numerical calculation of the attenuation coefficient by grain scattering A r A r,refer In the time domain In the frequency domain 15 BIMODAL GRAIN SIZE ATTENUATION

16 NUMERICAL SIMULATION OF WAVE PROPAGATION Simulation with regular hexagonal grains A single grain size with no spreading 2 less regular microstructures to discard any artefact due to regular GB orientations of hexagonal grains Regular hexagons Voronoï Irregular hexagons 16 BIMODAL GRAIN SIZE ATTENUATION

17 NUMERICAL SIMULATION OF WAVE PROPAGATION Simulation with regular hexagonal grains A single grain size with no spreading 2 less regular microstructures to discard any artefact due to regular GB orientations of hexagonal grains Frequency Irregular hexagons Frequency Irregular hexagons Frequency Relative grain size Voronoï GB orientation 17 BIMODAL GRAIN SIZE ATTENUATION Relative grain size

18 NUMERICAL SIMULATION OF WAVE PROPAGATION Simulation with regular hexagonal grains Almost no effect of the GB orientation for a narrow grain size distribution 18 BIMODAL GRAIN SIZE ATTENUATION

19 OUTLINE Introduction: Effect of grains on attenuation Numerical simulation of wave propagation Simulation of the grain size effect on attenuation Simulation of a bimodal grain size effect on attenuation Conclusions 19 BIMODAL GRAIN SIZE ATTENUATION

20 SIMULATION OF THE GRAIN SIZE EFFECT ON ATTENUATION Grain size effect on the ultrasonic attenuation Strong dependence of the attenuation coefficient on the grain size Simulations agree with analytical predictions (Stanke-Kino) 20 BIMODAL GRAIN SIZE ATTENUATION

21 SIMULATION OF THE GRAIN SIZE EFFECT ON ATTENUATION Grain size effect 80 m 160 m 320 m Effect of the crystallographic orientation distribution on the attenuation Increase of the dispersion between samples with frequency for a given grain size 21 BIMODAL GRAIN SIZE ATTENUATION

22 SIMULATION OF THE GRAIN SIZE EFFECT ON BACKSCATTERING Strong dependence of the average backscattering coefficients on the grain size Simulated master curves lying between upper and lower theoretical limits 22 BIMODAL GRAIN SIZE ATTENUATION

23 OUTLINE Introduction: Effect of grains on attenuation Numerical simulation of wave propagation Simulation of the grain size effect on attenuation Simulation of a bimodal grain size effect on attenuation Conclusions 23 BIMODAL GRAIN SIZE ATTENUATION

24 SIMULATION OF A BIMODAL GRAIN SIZE EFFECT ON ATTENUATION Two grain sizes, regular hexagonal grain shape Attenuation is affected by the volume fraction of the larger grain 24 BIMODAL GRAIN SIZE ATTENUATION

25 SIMULATION OF A BIMODAL GRAIN SIZE EFFECT ON ATTENUATION Random distribution of LG Isolated distribution of LG N LG = 1 Forming the clusters of LG Banded microstructure N LG [1,10] or N LG = 10 Two-, three- and four-layer 25 BIMODAL GRAIN SIZE ATTENUATION

26 SIMULATION OF A BIMODAL GRAIN SIZE EFFECT ON ATTENUATION Large dispersions between individual samples Insignificant differences between different types of location distributions Random distribution of large grains Different spatial distribution 26 BIMODAL GRAIN SIZE ATTENUATION Volume fraction of the larger grains: F LG = 45%

27 SIMULATION OF A BIMODAL GRAIN SIZE EFFECT ON ATTENUATION How to express attenuation for a bimodal grain size: Attenuation is a function of: Assumptions: Elastic constants within a grain and its characteristic function vary independently Elastic constants vary independently from grain to grain Statistically isotropic media 27 BIMODAL GRAIN SIZE ATTENUATION

28 SIMULATION OF A BIMODAL GRAIN SIZE EFFECT ON ATTENUATION How to express attenuation for a bimodal grain size: 28 BIMODAL GRAIN SIZE ATTENUATION

29 SIMULATION OF A BIMODAL GRAIN SIZE EFFECT ON ATTENUATION Attenuation is determined by the volume fraction of the constituent grains: Bi (f ) F SG SG (f ) F LG LG (f ) 80 m and 160 m, F LG 45% 80 m and 20 m, F LG 45% 29 BIMODAL GRAIN SIZE ATTENUATION 80 m and 320 m, F LG 45%

30 SIMULATION OF A BIMODAL GRAIN SIZE EFFECT ON ATTENUATION Correlation with metallographic measurement is not straightforward as: Rayleigh domain: LS scattering grain volume Stochastic domain: LL scattering grain length // wave direction 30 BIMODAL GRAIN SIZE ATTENUATION

31 SIMULATION OF A BIMODAL GRAIN SIZE EFFECT ON ATTENUATION Non-existence of an equivalent grain size: Bi (f, d SG, d LG ) (f, d S / N G ) 80 m and 320 m, F LG 45% 80 m and 320 m, F LG 10% 31 BIMODAL GRAIN SIZE ATTENUATION 80 m and 320 m, F LG 80%

32 CONCLUSIONS Laser ultrasonics allow measurement of grain size and grain growth kinetics Absolute value if a reference state is possible (very small grains size) or relative grain size evolution with a metallographic reference What about bimodal microstructure (abnormal grain growth or heterogeneous grain size)? 32 BIMODAL GRAIN SIZE ATTENUATION

33 CONCLUSIONS Finite Element simulation of wave propagation in a polycrystalline medium Simulation of the grain size effect on the ultrasonic attenuation and scattering Agreement with former analytical studies Effect of a bimodal grain size Attenuation mainly due to the volume fraction of large grains No influence of the large grain spatial distribution If the scattering domains are different: the attenuation is not a function of a single equivalent grain size 33 BIMODAL GRAIN SIZE ATTENUATION

34 THANK YOU FOR YOUR ATTENTION This work was part of PhD work by BAI Xue Finite Element Modeling of Ultrasonic Wave Propagation in Polycrystalline Materials Université Paris-Saclay, Feb. 2 nd, BIMODAL GRAIN SIZE ATTENUATION