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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Statistical Moments of Coverage Maps of Ultrasonic
Waves in Layered Polycrystalline Solids - Tony Mu
lholland (University of Bristol)
DTSTART;TZID=Europe/London:20230323T113000
DTEND;TZID=Europe/London:20230323T120000
UID:TALK195712AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/195712
DESCRIPTION:This talks considers the propagation of high frequ
ency elastic waves (ultrasound waves) in a polycry
stalline material (titanium alloys used in high va
lue manufacturing such as the aerospace industry).
\;In this high frequency regime\, we assume
that the wave &rsquo\;sees&rsquo\; the complex med
ia as a series of locally anisotropic layers with
varying thicknesses\, where the distribution of la
yer thicknesses and orientations follow a stochast
ic (Markovian) process [1]. \; The reflected w
ave subsequently has a complex structure and there
fore a homogenisation or effective medium approach
is not appropriate. \; Indeed this complex wa
ve has encoded within it the journey that the wave
has undertaken and hence opens up tomography oppo
rtunities via full wave inversion. \; In ultra
sonic non-destructive testing it is of value to be
able to model the attenuation within such media a
nd comment on the uncertainty in doing so. \;
This motivates this study where a probabilistic fr
amework is adopted and wherein a probability densi
ty function of the reflected/transmitted wave is d
etermined [2]. \; At its heart is a set of sto
chastic differential equations which describe the
statistics of the energy in the system. \;The
material properties are captured within this syst
em by a correlation integral which encapsulates th
e coupling of length-scales between the random med
ia and the probing wave. Using experimentally obta
ined EBSD (electron backscatter diffraction) data
for an austenitic steel weld\, and subsequent proc
essing of the data via a ray based probing techniq
ue\, we show to calculate this correlation integra
l [3]. \; A diffusion approximation was then u
sed to obtain the statistical moments of the trans
mission/reflection coefficients. \;A Ricatti
equation for the reflection coefficient was derive
d\, allowing a study into the frequency autocorrel
ation function for the reflected wave. \;Usin
g this solution to the transport equations an expr
ession was obtained for the reflected intensity of
the wave at each element of an ultrasonic transdu
cer array on the surface of the material. \;T
his was then used to create coverage maps via the
Total Focusing Method.\n[1] J. P. Fouque\, J. Garn
ier\, G. Papanicolaou\, and K. Sø\;lna. Wave
Propagation and Time Reversal in Randomly Layered
Media. New York\, Springer\, (2007).\n[2] J. Garn
ier and K. Sø\;lna. &ldquo\;Apparent Attenua
tion of ShearWaves Propagating through a Randomly
Anisotropic Medium&rdquo\;. In: Stochastics and Dy
namics\, No. 4. Vol. 16 (2015).\n[3] A. S. Ferguso
n\, K. M. M. Tant and A. J. Mulholland\, "Modellin
g of Ultrasonic Waves in Layered Elastic Heterogen
eous Materials\," 2021 IEEE International Ultrason
ics Symposium (IUS)\, 2021\, pp. 1-4\, doi: 10.110
9/IUS52206.2021.9593907.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:
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