FIFTH CANADIAN CONFERENCE ON NONDESTRUCTIVE ... - IAEA

10. EXAMPLE
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The following example demonstrates the application of our numerical model to a
simple test problem. It represents the generation, propagation and reflection
by a crack of a shear wave in steel. The computational region is a 10 mm by 10
mm square and all its edges are energy-absorbing except for a 1 mm crack along
the centre part of the right edge. The figures show the geometry of the region
and plot the energy density by contour levels which are graded to pick out the
low amplitude features.
The first two figures show the generation of the wave at the left edge uf the
region. It is generated by specifying a combination of stress and
displacement, and it has the form of an exponentially damped wave packet wir.h
frequency 3.5 MHz. Small amplitude compressional waves are generated at tho
edges of the input region due to the rapid variation in stress and displacement
there. There are no signs of spurious reflection by the absorbing boundaries.
Figures 3 and 4 show the shear wave after reflection by the crack. A large
amount of energy is lost through the absorbing boundary, but a significant
portion is reflected by the crack. Another important feature is the scattering
by the crack tips which shows itself mainly in the two compressional waves
emanating from the tips.
11. SUMMARY AND CONCLUSIONS
We have described the construction of numerical approximations of the Elastic
Wave Equation and outlined the particular advantages of using the first order
form of the equations. We have discussed the current and potential uses of
computer simulation in ultrasonic testing and also suggested that powerful
computers are required if codes are to be run reasonably quickly and
efficiently. The example given shows that the physical phenomena of reflection
and crack-tip scattering can be successfully modelled and we have been equally
successful in modelling other physical phenomena.
12. REFERENCES
1) R.J. CLIFTON, Quart. Appl. Math., V. 25, p.97 (1967).
2) P.D. SMITH, Int. J. Num. Meth. Eng. , V. 8, p.9x11 (1974).
3) Z. ALTERMAN and D. LOEWENTHAL, Methods in Computational Physics Vol. 12,
Ed. B.A. Bolt, pp.35-164, Academic Press (1972).
4) J. ABOUDI, Modern Problems in Elastic Wave Propagation, Eds. J. Miklowitz
and J.D. Achenbach, pp. 45-65, Wiley (1978).
5) L.J. BOND, Research Techniques in NDT Vol. 6, Ed. R.S. Sharpe,
pp. 106-150, Academic Press (1983).