Linear Versus Nonlinear Acoustic Probing of Plasticity in Metals: A Quantitative Assessment

Abstract

The relative dislocation density of aluminum and copper samples is quantitatively measured using linear Resonant Ultrasound Spectroscopy (RUS). For each metallic group, four samples were prepared with different thermomechanical treatments in order to induce changes in their dislocation densities. The RUS results are compared with Nonlinear Resonant Ultrasound Spectroscopy (NRUS) as well as Second Harmonic Generation (SHG) measurements. NRUS has a higher sensitivity by a factor of two to six and SHG by 14–62%. The latter technique is, however, faster and simpler. As a main result, we obtain a quantitative relation between the changes in the nonlinear parameters and the dislocation density variations, which in a first approximation is a linear relation between these differences. We also present a simple theoretical expression that explains the better sensitivity to dislocation content of the nonlinear parameters with respect to the linear ones. X-Ray diffraction measurements, although intrusive and less accurate, support the acoustics results.

The Scattering of Phonons by Infinitely Long Quantum Dislocations Segments and the Generation of Thermal Transport Anisotropy in a Solid Threaded by Many Parallel Dislocations

“…In recent years, it has been used to compute the scattering cross section of elastic waves by dislocation segments in a first Born approximation, a result that has been further employed to compute the change in propagation velocity and attenuation for said waves by many such dislocation segments [28][29][30]. These results, in turn, have led to novel ways of acoustically characterizing the plasticity of metals and alloys [31][32][33][34].…”

Scattering of phonons by quantum-dislocation segments in an elastic continuum

“…Given that we are interested in phonon-phonon amplitudes, in order to have a non-vanishing contribution from (25) we need to expand the time-ordered exponential up to quadratic order. Employing our definition for the string propagator and performing the relevant contractions, we see that…”

“…and G is an effective Green's function, resulting from performing the averages just described. By inspecting the time-ordered two-point function associated to the amplitude (25). If we define a reduced amplitudeT ij throughT…”

“…Use of the formalism developed therein, together with multiple scattering theory, has enabled the computation of an effective, complex, index of refraction for the propagation of coherent elastic waves in a medium filled with randomly distributed and oriented, pinned dislocation segments 21,22 . In turn, this has led to novel characterization tools to describe the plasticity of metals and alloys [23][24][25] .…”

Sensor to Monitor Localized Stresses on Steel Surfaces Using the Magnetostrictive Delay Line Technique

“…Sensing elements able to monitor surface stresses in steels can be those monitoring localized changes of sound velocity, including the use of non-linear acoustics [11], electromagnetic properties such as eddy currents for resistivity and impedance determination [12], optical properties using the Kerr effect [13], as well as magnetic properties like surface permeability in the magnetic stress calibration curve (MASC) technique [14] and the magnetic memory method (MMM) [15], or magnetic Barkhausen noise method [16]. The sensing elements used in acoustic techniques offer a spatial resolution in the order of cm and may be used in industrial conditions.…”