Nondestructive Measurement of Texture and Plastic Strain Ratio of Steel Sheets Using EMATs: Comparison of Two Approximations to Calculate CODFs

All the lowest order independent CODF coefficients, W400, W420 and W440 of a rolled metal sheet were satisfactorily measured using only EMATs by Kawashima(1990). In that method only the Voigt approximation was used to calculate CODF coefficients from measured ultrasonic velocities and known values of single crystal elastic constants. In this paper both the Voigt and Reuss approximations are used for the calculation, and the results are compared. Stress in a steel sheet was neglected because, in general, it has significant texture which gives the major contribution to elastic anisotropy. In the 1st section the basic equations for the CODF, elastic constants, Young’s modulus, polefigure diagrams and ultrasonic waves in a sheet are reviewed. In the theory of the 2nd section, it is shown that W400, W420 and W440 can be obtained as the solutions of three linear equations. Two sets of three linear equations are given by using the Voigt and Reuss approximation methods respectively. In the experiment, the through thickness resonance method is used with an EMAT that can simultaneously measure all three modes of ultrasonic waves propagating in the through thickness direction. A set of EMATs to measure precisely SHO (shear horizontal) plate wave velocity is also used. In the 3rd section, the CODF coeficients are calculated by the equations given in the 2nd section using the measured ultrasonic velocities. Further, X-ray polefigures and ultrasonic pole-figures obtained using the calculated CODF coefficients are compared. All nine elastic constants of the steel sheets and Young’s modulus in the sheet plane are also calculated and compared with plastic strain ratio. The paper is concluded in section 4.