Journal of ELECTRICAL ENGINEERING, VOL 57. NO 8/S, 2006, 15-20  * LMT-Cachan (ENS-Cachan, CNRS UMR 8535, University Paris 6), 61, avenue du président Wilson, 94235, Cachan cedex, France, E-mail: lollioz@lmt.ens-cachan.fr ** same address, E-mail: pattofat@lmt.ens-cachan.fr *** same address, E-mail: hubert@lmt.ens-cachan.fr - corresponding author ISSN 1335-3632 © 2006 FEI STU APPLICATION OF PIEZO-MAGNETISM FOR THE MEASUREMENT OF STRESS DURING AN IMPACT Ludovic Lollioz*  Stéphane Pattofatto**  Olivier Hubert*** This paper presents the basic of a research program whose final aim is to propose of a new kind of stress sensor for Hopkinson bar apparatus. The measurement is an electromotive force-induced signal due to the piezo-magnetic property of the material constitutive of the Hopkinson bar. The calculation of stress requires the construction of an explicit model of the magneto-mechanical behavior, based on a microscopic description. Magnetostrictive quasi-static behavior is modeled first. Magnetization quasi-static behavior is then written thanks to a thermodynamic coupling relation. The stress is estimated from emf signal through an inverse identification procedure. Amplitudes are nevertheless too low because dynamic magnetic phenomena are neglected in the modeling at present. Keywords: piezo-magnetism, magneto-elastic coupling, dynamic tests, stress sensor 1 INTRODUCTION The Hopkinson bar apparatus (figure 1) is an usual way to identify the dynamic mechanical behavior of materials at high strain rates [1-3]. The impact energy is provided by a projectile launched at high velocity (typically 100 m/s) against an incident bar that crushes the specimen against the transmitted bar. The measurements are provided by strain gauges cemented on the bar. They allow us to determine the nominal strain rate dε/dt and nominal stress σ(t) into the specimen [4]. One strong drawback is that for very high impact velocities, experiments are often destructive for the gauges. Moreover, gauge measurement is a local measurement, giving stress value only on the surface, and the quality of the measurement is dependent on the gauge size. Consequently, the development of a new stress sensor for impact applications is relevant. Fig.1. Hopkinson bar apparatus (principle). 2 PURPOSE Some Hopkinson bar tests show a gauge signal V G (t) which is composed of the signal V m (t) 1 of the measured deformation and an additional signal V(t) (figure 2). This signal is especially occurring when non-demagnetized steel made bars are used. V(t) can be measured using a simple pick-up coil wounded around one of the bars. The existence of a variable remanent magnetization M r seems to be the source of this disturbance, following Lenz's law (equation 1). The link to the stress variation can be made 1 The measured signal is theoretically given by Vm=kV0σ/(4E) considering a Wheatstone quarter-bridge circuit, with k the gauge factor, V0 the voltage of the supply, σ the uniaxial stress and E the Young's modulus of the material. thanks to the magneto-mechanical coupling, leading to a modified Lenz's law expression (equation 2). V(t) Gauge signal - VG(t) t Vm(t) Fig. 2. Gauge signal VG (full line) with magnetized steel bar. Dashed line corresponds to the foreseen signal Vm (schematic). V (t ) = nS dB dt = nSμ 0 dM r dt (1) V (t ) = nSμ 0 dM r dσ dσ dt (2) B is the magnetic induction; μ 0 is the air permeability; n is the number of turns of the pick-up coil; S is the section of the coil. In equation (2), dσ/dt denotes the stress velocity and ∂M r /∂σ the magneto-mechanical coupling (piezo-magnetic part of the coupling [5]). Its general expression is given by dM(H, σ)/dσ (H: magnetic field strength) with dM r /dσ=dM(H=0, σ)/dσ. Assuming that the magneto-mechanical coupling can be evaluated, the stress can theoretically be derived from equation (3) after simple time integration. σ(t) = 1 nSμ 0 dM(H, σ ) dσ       -1 V(t )dt t ∫ (3) M(H, σ) behavior is obviously not simple, because its variations are most of the time non-constant and non- monotonous with stress variation. The study and mathematical modeling of M(H, σ) are thus required to get an accurate evaluation of stress thanks to equation (3). Another consequence is that iterative procedures will have to be constructed in order to implement this equation.