Revisiting Piezoelectric Sensor Calibration Methods Using Elastodynamic Body Waves

Rui Wu,Omid Moradian,Paul A Selvadurai,Chaojian Chen

doi:10.1007/s10921-021-00799-1

Abstract

The application of absolutely calibrated piezoelectric (PZT) sensors is increasingly used to help interpret the information carried by radiated elastic waves of laboratory/in situs acoustic emissions (AEs) in nondestructive evaluation. In this paper, we present the methodology based on the finite element method (FEM) to characterize PZT sensors. The FEM-based modelling tool is used to numerically compute the true Green’s function between a ball impact source and an array of PZT sensors to map active source to theoretical ground motion. Physical-based boundary conditions are adopted to better constrain the problem of body wave propagation, reflection and transmission in/on the elastic medium. The modelling methodology is first validated against the reference approach (generalized ray theory) and is then extended down to 1 kHz where body wave reflection and transmission along different types of boundaries are explored. We find the Green’s functions calculated using physical-based boundaries have distinct differences between commonly employed idealized boundary conditions, especially around the anti-resonant and resonant frequencies. Unlike traditional methods that use singular ball drops, we find that each ball drop is only partially reliable over specific frequency bands. We demonstrate, by adding spectral constraints, that the individual instrumental responses are accurately cropped and linked together over 1 kHz to 1 MHz after which they overlap with little amplitude shift. This study finds that ball impacts with a broad range of diameters as well as the corresponding valid frequency bandwidth, are necessary to characterize broadband PZT sensors from 1 kHz to 1 MHz.

Highlights

As brittle materials are subjected to external stress in a laboratory setting, localized and rapid inelastic deformation events occur that are associated with the growth or appearance of small defects at the grain-scale, which can generate acoustic emissions (AEs) [1,2,3]
We characterize the performance of PZT sensors to measured kinematic motion excited by body wave propagation through an elastic isotropic, homogeneous steel transfer plate due to the active source produced by a steel ball impact
Since body waves caused by ball impact in the 3-direction are symmetric about the 1-3 and 2-3 planes, we have focused most of our PZT sensors converge to one quadrant of the sensors mounting plate

Summary

Introduction

As brittle materials are subjected to external stress in a laboratory setting, localized and rapid inelastic deformation events occur that are associated with the growth or appearance of small defects at the grain-scale (from micrometers to millimeters), which can generate acoustic emissions (AEs) [1,2,3] These emissions can cause high-frequency vibrations, at frequencies ranging from tens of kHz to several MHz, and are recorded by piezoelectric (PZT) sensors at known locations. Kwiatek et al [11] reported on picoseismic and nanoseismic events (Mw > −4.1) caused by aftershock sequence following the postblasting activity inside a volume of 300 × 300 × 300 m at Mponeng Deep Gold Mine, South Africa They installed PZT sensors that were relatively calibrated according to 3component accelerometers at frequency from 400 Hz to 17 kHz in boreholes along the tunnel and monitored the seis-

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