Calculation of ultrasonic fields radiated in a ferromagnetic medium by an EMAT of arbitrary bias field driven by a current of arbitrary intensity

ElectroMagnetic Acoustic Transducers (EMATs) are contactless transducers generating ultrasonic waves in conductive media, notably shear horizontal and torsional waves (in plates and pipes, respectively), possibly in hostile environments. In a ferromagnetic part, the elastic strain and the magnetic field couple through magnetostriction phenomena, so that a magnetostriction and magnetization forces add up to the Lorentz force created in any conductive medium. Here, a model is proposed to predict these forces for an arbitrary bias field due to the EMAT permanent magnet and whatever the current intensity in its electric circuit, whereas the usual assumption of high bias field and low intensity current leads to important model simplifications. To handle the nonlinear behavior of all the three forces when the usual assumption cannot be made, forces are expressed in the time domain. In particular, magnetostriction force generates waves at several harmonic frequencies of the driving current frequency. Forces are then transformed into equivalent surface stresses readily usable as source terms in existing models of ultrasonic radiation, under the assumption that ultrasonic wavelengths are much longer than force penetration depths, (which is generally true in NDT applications of EMATs). Force spectra computed in various EMAT configurations are compared for illustration