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Mathematical modelling in non-destructive testing
Mathematical Modelling in Non-Destructive Testing IMA Conference Series (new series), Number 16 Edited by M. Blakemore and G.A. Georgiou Clarendon Press, Oxford, UK 1988,365 O-l 9-853622-4, f35
pp, ISBN
This volume contains the papers presented at the conference on Mathematical Modelling in Non-Destructive Testing held by the Institute of Mathematics and its Applications at Cambridge, UK, in September 1986. It provides a useful and reasonably self-contained description of the then current theoretical understanding of ultrasonic and electromagnetic NDT techniques. In his introductory remarks, F.A. Wedgwood of UKAEA Harwell comments: ‘About 70% of the papers in the conference are on ultrasound . . . perhaps in 10 years time 70% will be devoted to electromagnetic modelling’. The idea that ultrasonic NDT is a science approaching maturity is a seductive one. But that there is still a great deal of valuable work yet to be done before the interaction between an elastodynamic wave and a defect is fully understood is demonstrated in papers by Achenbach on the modelling of both direct and inverse problems; by Willis on scattering from rough cracks; by Bond, Punjani and Saffari on finite difference methods; by Langenberg et al. on combined analytical/numerical methods; and by Ogilvy on anisotropy. Nevertheless, electromagnetic NDT poses a tougher mathematical problem, with fields severely attenuated and wavelengths typically comparable to defect sizes. The conference would have benefitted from a wider selection of papers on eddy currents and related techniques, but the three presented span a wide range - on finite element modelling of eddy currents by French and Bond, on AC field (AC potential drop) methods by Collins and Michael
186
Ultrasonics
1989
Vol 27 May
and on magnetic flux leakage by Edwards and Palmer. The importance of system models, describing the entire NDT experiment rather than an idealized wave-defect interaction, is stressed in Wedgwood’s introduction and by many of the contributors. Silk, Bainton and Hillier give an analysis of an ultrasonic probe; Chapman an integrated model of ultrasonic NDT; and Blakemore and Firth an analysis of the scattering of ultrasonic wave packets rather than the usual fictitious sinusoidal excitation. The meeting of mathematically inclined researchers and practically oriented users of NDT was a strong point of the conference, underpinning the need to predict and interpret the outcome of real procedures, not abstractions. The first and second papers, by Coffey and Firth respectively, set out this agenda for mathematical modelling in NDT. Inevitably, some of the value and attraction of a conference is lost in the formal proceedings. A diverting, albeit erudite dinner-time address by J.A. Hudson entitled Evaluating the Earth non-destructively, a foray into geophysics where the scale may be larger but the principles are the same as in ultrasonic NDT, loses something by being printed without comment alongside the other papers. The congeniality of Jesus College, Cambridge, is not apparent. It is particularly disappointing to find that discussion sessions held immediately after a paper is read have not been recorded. The Institute of Mathematics and its Applications, also Topexpress Ltd (who provided the editors and much of the organization), deserve thanks for a timely conference which brought together practitioners and modellers, both of ultrasonics and of electromagnetics. It is an event worth repeating. The next conference should be larger, give more attention to electromagnetic techniques and bring its findings to light more quickly.
University
College
P. French 1 ondon, UK
pp, ISBN
This volume contains the papers presented at the conference on Mathematical Modelling in Non-Destructive Testing held by the Institute of Mathematics and its Applications at Cambridge, UK, in September 1986. It provides a useful and reasonably self-contained description of the then current theoretical understanding of ultrasonic and electromagnetic NDT techniques. In his introductory remarks, F.A. Wedgwood of UKAEA Harwell comments: ‘About 70% of the papers in the conference are on ultrasound . . . perhaps in 10 years time 70% will be devoted to electromagnetic modelling’. The idea that ultrasonic NDT is a science approaching maturity is a seductive one. But that there is still a great deal of valuable work yet to be done before the interaction between an elastodynamic wave and a defect is fully understood is demonstrated in papers by Achenbach on the modelling of both direct and inverse problems; by Willis on scattering from rough cracks; by Bond, Punjani and Saffari on finite difference methods; by Langenberg et al. on combined analytical/numerical methods; and by Ogilvy on anisotropy. Nevertheless, electromagnetic NDT poses a tougher mathematical problem, with fields severely attenuated and wavelengths typically comparable to defect sizes. The conference would have benefitted from a wider selection of papers on eddy currents and related techniques, but the three presented span a wide range - on finite element modelling of eddy currents by French and Bond, on AC field (AC potential drop) methods by Collins and Michael
186
Ultrasonics
1989
Vol 27 May
and on magnetic flux leakage by Edwards and Palmer. The importance of system models, describing the entire NDT experiment rather than an idealized wave-defect interaction, is stressed in Wedgwood’s introduction and by many of the contributors. Silk, Bainton and Hillier give an analysis of an ultrasonic probe; Chapman an integrated model of ultrasonic NDT; and Blakemore and Firth an analysis of the scattering of ultrasonic wave packets rather than the usual fictitious sinusoidal excitation. The meeting of mathematically inclined researchers and practically oriented users of NDT was a strong point of the conference, underpinning the need to predict and interpret the outcome of real procedures, not abstractions. The first and second papers, by Coffey and Firth respectively, set out this agenda for mathematical modelling in NDT. Inevitably, some of the value and attraction of a conference is lost in the formal proceedings. A diverting, albeit erudite dinner-time address by J.A. Hudson entitled Evaluating the Earth non-destructively, a foray into geophysics where the scale may be larger but the principles are the same as in ultrasonic NDT, loses something by being printed without comment alongside the other papers. The congeniality of Jesus College, Cambridge, is not apparent. It is particularly disappointing to find that discussion sessions held immediately after a paper is read have not been recorded. The Institute of Mathematics and its Applications, also Topexpress Ltd (who provided the editors and much of the organization), deserve thanks for a timely conference which brought together practitioners and modellers, both of ultrasonics and of electromagnetics. It is an event worth repeating. The next conference should be larger, give more attention to electromagnetic techniques and bring its findings to light more quickly.
University
College
P. French 1 ondon, UK