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SUMMARY:Statistical Moments of Coverage Maps of Ultrasonic Waves in Layere
 d Polycrystalline Solids - Tony Mulholland (University of Bristol)
DTSTART:20230323T113000Z
DTEND:20230323T120000Z
UID:TALK195712@talks.cam.ac.uk
DESCRIPTION:This talks considers the propagation of high frequency elastic
  waves (ultrasound waves) in a polycrystalline material (titanium alloys u
 sed in high value manufacturing such as the aerospace industry). &nbsp\;In
  this high frequency regime\, we assume that the wave &rsquo\;sees&rsquo\;
  the complex media as a series of locally anisotropic layers with varying 
 thicknesses\, where the distribution of layer thicknesses and orientations
  follow a stochastic (Markovian) process [1].&nbsp\; The reflected wave su
 bsequently has a complex structure and therefore a homogenisation or effec
 tive medium approach is not appropriate.&nbsp\; Indeed this complex wave h
 as encoded within it the journey that the wave has undertaken and hence op
 ens up tomography opportunities via full wave inversion.&nbsp\; In ultraso
 nic non-destructive testing it is of value to be able to model the attenua
 tion within such media and comment on the uncertainty in doing so.&nbsp\; 
 This motivates this study where a probabilistic framework is adopted and w
 herein a probability density function of the reflected/transmitted wave is
  determined [2].&nbsp\; At its heart is a set of stochastic differential e
 quations which describe the statistics of the energy in the system. &nbsp\
 ;The material properties are captured within this system by a correlation 
 integral which encapsulates the coupling of length-scales between the rand
 om media and the probing wave. Using experimentally obtained EBSD (electro
 n backscatter diffraction) data for an austenitic steel weld\, and subsequ
 ent processing of the data via a ray based probing technique\, we show to 
 calculate this correlation integral [3].&nbsp\; A diffusion approximation 
 was then used to obtain the statistical moments of the transmission/reflec
 tion coefficients. &nbsp\;A Ricatti equation for the reflection coefficien
 t was derived\, allowing a study into the frequency autocorrelation functi
 on for the reflected wave. &nbsp\;Using this solution to the transport equ
 ations an expression was obtained for the reflected intensity of the wave 
 at each element of an ultrasonic transducer array on the surface of the ma
 terial. &nbsp\;This was then used to create coverage maps via the Total Fo
 cusing Method.\n[1] J. P. Fouque\, J. Garnier\, G. Papanicolaou\, and K. S
 &oslash\;lna. Wave Propagation and Time Reversal in Randomly Layered Media
 . New York\, Springer\, (2007).\n[2] J. Garnier and K. S&oslash\;lna. &ldq
 uo\;Apparent Attenuation of ShearWaves Propagating through a Randomly Anis
 otropic Medium&rdquo\;. In: Stochastics and Dynamics\, No. 4. Vol. 16 (201
 5).\n[3] A. S. Ferguson\, K. M. M. Tant and A. J. Mulholland\, "Modelling 
 of Ultrasonic Waves in Layered Elastic Heterogeneous Materials\," 2021 IEE
 E International Ultrasonics Symposium (IUS)\, 2021\, pp. 1-4\, doi: 10.110
 9/IUS52206.2021.9593907.
LOCATION:Seminar Room 1\, Newton Institute
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