Martin Lott

Dynamic acousto-elastic test using continuous probe wave and transient vibration to investigate material nonlinearity

This study demonstrates the feasibility of the dynamic acousto-elastic effect of a continuous high frequency wave for investigating the material nonlinearity upon transient vibration. The approach is demonstrated on a concrete sample measuring 15×15×60cm(3). Two ultrasonic transducers (emitter and receiver) are placed at its middle span. A continuous high frequency wave of 500kHz propagates through the material and is modulated with a hammer blow. The position of the hammer blow on the sample is configured to promote the first bending mode of vibration. The use of a continuous wave allows discrete time extraction of the nonlinear behavior by a short-time Fourier transform approach, through the simultaneous comparison of a reference non-modulated signal and an impact-modulated signal. The hammer blow results in phase shifts and variations of signal amplitude between reference and perturbed signals, which are driven by the resonant frequency of the sample. Finally, a comprehensive analysis of the relaxation mechanisms (modulus and attenuation recovery) is conducted to untangle the coupled fast and slow hysteretic effects.

Three-dimensional treatment of nonequilibrium dynamics and higher order elasticity

This letter presents a three-dimensional model to describe the complex behavior of nonlinear mesoscopic elastic materials such as rocks and concrete. Assuming isotropy and geometric contraction of principal stress axes under dynamic loading, the expression of elastic wave velocity is derived, based on the second-order elastic constants (λ,μ), third-order elastic constants (l, m, n), and a parameter α of nonclassical nonlinear elasticity resulting from conditioning. We demonstrate that both softening and recovering of the elastic properties under dynamic loading is an isotropic effect related to the strain tensor. The measurement of the conditioning is achieved using three polarized waves. The model allows the evaluation of the third-order elastic constants uncoupled from conditioning and viscoelastic effects. The values obtained are similar to those reported in the literature using quasi-static loading.

From local to global measurements of nonclassical nonlinear elastic effects in geomaterials

In this letter, the equivalence between local and global measures of nonclassical nonlinear elasticity is established in a slender resonant bar. Nonlinear effects are first measured globally using nonlinear resonance ultrasound spectroscopy (NRUS), which monitors the relative shift of the resonance frequency as a function of the maximum dynamic strain in the sample. Subsequently, nonlinear effects are measured locally at various positions along the sample using dynamic acousto elasticity testing (DAET). After correcting analytically the DAET data for three-dimensional strain effects and integrating numerically these corrected data along the length of the sample, the NRUS global measures are retrieved almost exactly.

Non Destructive Evaluation of Containment Walls in Nuclear Power Plants

Two functions are regularly tested on containment walls in order to anticipate a possible accident. The first is mechanical to resist a possible internal over-pressure and the second is to prevent leakage. The AAPR reference accident is the rupture of a pipe in the primary circuit of a nuclear plant. In this case, the pressure and temperature can reach 5 bar and 180°C in 20 seconds. The national project ‘Non-destructive testing of the containment structures of nuclear plants’ aims at studying the non-destructive techniques capable to evaluate the concrete properties and its damaging and cracks. This 4-year-project is segmented into two parts. The first consists in developing and selecting the most relevant NDEs in the laboratory to reach these goals. These evaluations are developed in conditions representing the real conditions of the stresses generated during ten-yearly visits of the plants or those related to an accident. The second part consists in applying the selected techniques to two containment st...

Three-dimensional modeling and numerical predictions of multimodal nonlinear behavior in damaged concrete blocks

In this paper, the multimodal nonlinear elastic behavior of concrete, which is representative of a consolidated granular material, is modeled numerically. Starting from a local three-dimensional softening law, the initial stiffness properties are re-estimated according to the local strain field. The experiments deal with samples of thermally damaged concrete blocks successively excited around their first three modes of vibration. The geometry of these samples cannot be described by a one-dimensional approximation in these experiments where compressional and shear motions are strongly coupled. Despite this added complexity, the nonlinear behavior for the three modes of vibration of the samples is well captured by the simulations using a single scalar nonlinear parameter appropriately integrated into the elasticity equations. It is shown that without sufficient attention paid to the latter, the conclusions would have brought erroneous statements such as nonlinearity dispersion or strain type dependence.

Three-dimensional description of nonlinear elasticity in rocks: Modeling and experiments

We study theoretically and experimentally the mechanisms of nonlinear and nonequilibrium dynamics in geomaterials through dynamic acousto-elasticity testing. In the proposed theoretical formulation, the classical theory of nonlinear elasticity is extended to include the effects of conditioning. This formulation is adapted to the context of dynamic acousto-elasticity testing in which a low-frequency “pump”-wave induces a strain field in the sample and modulates the propagation of a high-frequency “probe”-wave. Experiments are conducted to validate the formulation in a long thin bar of Berea sandstone. Several configurations of the pump and probe are examined—the pump successively consists of the first longitudinal and first torsional mode of vibration of the sample while the probe is successively based on (pressure) P- and (shear) S-waves. The theoretical predictions reproduce many features of the elastic response observed experimentally, in particular, the coupling between nonlinear and nonequilibrium dyn...

Retreiving global nonclassical nonlinearity parameters from local measurements

We demonstrate the equivalence between local and global measures of nonclassical nonlinear elasticity in a slender resonant bar of Berea sandstone. Nonlinear effects are first measured globally using Nonlinear Resonance Ultrasound Spectroscopy (NRUS), which monitors the relative shift of the resonance frequency as a function of the maximum dynamic strain in the sample. Subsequently, nonlinear effects are measured locally at various positions along the sample using Dynamic Acousto-Elasticity Testing (DAET). After processing the DAET signals and correcting for three-dimensional strain effects, it is shown that by numerically integrating these corrected data along the length of the sample the NRUS global measures are retrieved almost exactly.

Nonlinear dynamic acousto-elasticity measurement by Rayleigh wave in concrete cover evaluation

This paper presents local non-destructive evaluation of concrete cover by using surface Rayleigh wave in nonlinear Dynamic Acousto-Elasticity (DAE) measurement. Dynamic non classical nonlinear elastic behavior like modulus decrease under applied stress and slow dynamic process has been observed in many varieties of solid, also in concrete. The measurements conducted in laboratory, consist in qualitative evaluation of concrete thermal damage. Nonlinear elastic parameters especially conditioning offset are analyzed for the cover concrete by Rayleigh wave. The results of DAE method show enhanced sensitivity when compared to velocity measurement. Afterward, this technique broadens measurements to the field.