FIFTH CANADIAN CONFERENCE ON NONDESTRUCTIVE ... - IAEA

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These boundary conditions are constructed by assuming that the solution is
uniform in the direction parallel to the boundary, then applying the perfectly
absorbing conditions for the resulting one space dimension equation
perpendicular to the* boundary. For example, the equation is approximated at
the boundary x=0 (i.e. a vertical surface) by the one-dimensional equation
W_ = AW .
—t —x
The perfectly absorbing boundary conditions for this equation are
) - T XX = 0
/ET(pV ) - T xy = 0 .
7. CRACKS AND CAVITIES
We are primarily concerned with the detection of cracks and cavities in
metals. In an unbounded elastic material it is possible to model a wide
variety of cracks and cavities by fitting the coordinate system of the
simulation to the geometry of the flaw. If boundaries and flaws must all be
modelled, then it can be much more difficult to fit a coordinate system to the
geometry of the problem.
Planar cracks with stress-free surfaces have been successfully modelled.
Cracks with various orientations can be included in the approximation by using
a coordinate system which is skewed so that one axis is parallel to the crack.
The crack tips have so far been assumed to be stress free, but further investigation
of this is required. Some cavities with a simple parallelogram shape
have also been modelled, but more cojplicated geometries have not yet been
attempted.
8. TRANSDUCERS
The simulation of transducer generated ultrasonic pulses has two closelyrelated
purposes. It can simply be regarded as a way to send a pulse with
reasonable physical properties into the computational region to gain insight
into the physics of interactions with cracks and other features. Alternatively,
accurate modelling of the input can be used to study the properties of
specific transducers. We note that accurate models of transducers can be used
to predict both transmission and reception of signals.