1. Pierre Gélat National Physical Laboratory 3 April 2003 Developments in Acoustic Emission at the UK’s National Physical Laboratory

2. The Finite Element Method  The FE method is a numerical method to solve arbitrary PDEs  The method consists of approximating the structure in small domain portions called finite elements  Each element has a set of material properties associated with it (Young’s modulus, material density, Poisson’s ratio, etc.)  A set of output quantities (e.g. displacement) can be obtained for given forcing/boundary conditions http://www.npl.co.uk/npl/acoustics

3. Axisymetric and Three Dimensional Transducer Modelling  Use of PAFEC 8.6 Vibroacoustics software (soon to be upgraded to 8.8) used for modelling the behaviour of ultrasonic and audio-range transducer, with fluid loading or in vacuum, for both continuous and transient excitation  Allows the coupling of vibrating structures to the modelling of finite and infinite regions of fluid (boundary elements, wave envelope elements)  Piezoelectric elements can be defined  PAFEC’s mathematicians are working with NPL both to extend the functionality of the software and to provide NPL with bespoke software to tackle specific modelling problems  Quantities routinely obtained from PAFEC include: acoustic pressure, structural displacement and electrical impedance  Sensitivity analysis and optimisation capabilities http://www.npl.co.uk/npl/acoustics

4. Sensor Modelling Using the Finite Element Method  Understanding the dynamics of piezoelectric sensor  Investigating the effect of variations in design on overall sensitivity  Designing novel sensor configurations  Sensitivity analysis and optimisation (sensitivity vs. bandwidth) http://www.npl.co.uk/npl/acoustics

5. AE sensor modelling  Sensor is assumed to be axisymmetric  Piezoelectric material is PZT5-A  Apply unit voltage across PZT5-A between 0.1 MHz and 1MHz  Obtain electrical impedance http://www.npl.co.uk/npl/acoustics

6. Electrical Impedance of AE sensor

7. Modelling of AE reference facility  Aim is to develop a methodology to model a simple AE system from the electrical excitation of the reference transducer to the electrical output of the sensor  Requires the combination of more than one technique - one to model the transducer and sensor - the other to model the stress wave propagation in the medium  NPL’s Finite Element (FE) method used to - predict displacement output of transducer for a given electrical input - predict electrical response of sensor for a given displacement at its face  Fraunhofer’s Finite Difference/Integral (EFIT) method used to - predict displacement as a function of time at a given point in an elastic medium http://www.npl.co.uk/npl/acoustics

8. Experimental arrangement The reflective coating is Aluminium or ChromiumThe reflective coating is Aluminium or Chromium The displacement equivalent noise floor of the interferometer is around 3.5 pm RMSThe displacement equivalent noise floor of the interferometer is around 3.5 pm RMS 1)Out-of-plane displacement history of surface measured using interferometer 2)Repeated with sensor coupled in place of interferometer

9. Modelling of AE reference facility Comparison of NPL’s FE and Fraunhofer’s EFIT method  Comparison performed using a simple problem for validation - point displacement excitation - small cylindrical glass block allows treatment as an axisymmetric problem - displacements compared at chosen points Peter D. Theobald:.. Force f = A sin (2  ft). B sin (  ft) excited at r = 0, z = 0 http://www.npl.co.uk/npl/acoustics

10. Reference source - Reference source - Finite Element modelling of conical transducer

12. Modelling of AE reference facility Comparison results at 200 kHz

15. Modelling of AE reference facility - Conclusions  Validation is complete and shows good comparison between techniques  Work is now progressing on the modelling of a complete system comprising of source transducer, glass cylinder and sensor  If successful this should produce a complete transfer function for the AE system for each wave mode received at the sensor  Next stage of work is to model the NPL test facility - would provide more information for the calibration of sensors - could be combined with a calibrated reference source to provide system calibration