Stress imaging by guided wave tomography based on analytical acoustoelastic model.

A nondestructive method ( M) for stress characterization in plate-like structures is proposed. In this method, the acoustoelastic effects (AEEs) on Lamb and shear horizontal guided waves are used to reconstruct a nonuniform multiaxial stress field. The development of M starts by deriving an analytical acoustoelastic model (An-AEM) to predict AEEs induced by a triaxial stress tensor as a function of the stress components, its orientation, the wave propagation direction, and three acoustoelastic coefficients (AECs). The AECs are independent of stress but specific to each mode. The An-AEM allows one to retrieve the three components of the stress tensor and its orientation from AEEs, assuming the stress to be uniform in the plane of the plate and through its thickness. To deal with stress that is nonuniform in the plane, the An-AEM is combined with time-of-flight straight ray tomography to enable stress field reconstruction. Numerical simulation is used to illustrate how such reconstruction can be performed. It is shown that in some cases, stress components can be reconstructed with arbitrary accuracy, and in other cases, the tensorial nature of stress renders the accuracy of its reconstruction dependent on spatial variations of the stress orientation.

Effects of multiaxial pre-stress on Lamb and shear horizontal guided waves.

A theoretical model is derived to extend existing work on the theory of acoustoelasticity in isotropic materials subjected to uniaxial or hydrostatic loadings, up to the case of arbitrary triaxial loading. The model is applied to study guided wave propagation in a plate. The semi-analytical finite element method is adapted to deal with the present theory. Effects of triaxial loading on velocities of Lamb and shear horizontal (SH) modes are studied. They are non-linearly dependent on stress, and this nonlinearity is both frequency-dependent and anisotropic. Velocity changes induced by the effect of stress on the plate thickness are shown to be non-negligible. When a stress is applied, both Lamb and SH modes lose their simple polarization characteristics when they propagate in directions different from the principal directions of stress. The assumption that effects induced by a multiaxial stress equal the sum of effects induced by each of its components independently is tested. Its validity is shown to depend on frequency and propagation direction. Finally, the model is validated by comparing its predictions to theoretical and experimental results of the literature. Its predictions agree very well with measurements and are significantly more accurate than those of existing theories.

Mechanisms of elastic wave generation by EMAT in ferromagnetic media.

The present paper deals with the problem of elastic wave generation mechanisms (WGMs) by an electromagnetic-acoustic transducer (EMAT) in ferromagnetic materials. The paper seeks to prove that taking into account all the WGMs must be a general rule to quantitatively predict the elastic waves generated by an EMAT in such materials. Existing models of the various physical phenomena involved, namely magnetic and magnetostrictive, electromagnetic, and ultrasonic, are combined to solve the multiphysics wave generation problem. The resulting model shows that WGMs (i.e., electromagnetic force, magnetostrictive strain, and magnetic traction) strongly depend on material properties and EMAT design and excitation. To illustrate this, four magnetic materials (nickel, AISI410, Z20C13, and low carbon steel) with similar elastic but contrasting electromagnetic properties are studied. A given EMAT of fixed excitation and geometry yields WGMs with highly different amplitudes in these materials, with a WGM dominant in one material being negligible in another. Experimental results make it possible to validate the accuracy of certain predictions of the model developed. In summary, the present work shows that considering all WGMs is the general rule when working with ferromagnetic materials. Furthermore, it offers a generic model that can be integrated into various numerical tools to help optimize EMAT design and give reliable data interpretation.

Transformation of body force localized near the surface of a half-space into equivalent surface stresses.

An electromagnetic acoustic transducer (EMAT) or a laser used to generate elastic waves in a component is often described as a source of body force confined in a layer close to the surface. On the other hand, models for elastic wave radiation more efficiently handle sources described as distributions of surface stresses. Equivalent surface stresses can be obtained by integrating the body force with respect to depth. They are assumed to generate the same field as the one that would be generated by the body force. Such an integration scheme can be applied to Lorentz force for conventional EMAT configuration. When applied to magnetostrictive force generated by an EMAT in a ferromagnetic material, the same scheme fails, predicting a null stress. Transforming body force into equivalent surface stresses therefore, requires taking into account higher order terms of the force moments, the zeroth order being the simple force integration over the depth. In this paper, such a transformation is derived up to the second order, assuming that body forces are localized at depths shorter than the ultrasonic wavelength. Two formulations are obtained, each having some advantages depending on the application sought. They apply regardless of the nature of the force considered.

Modal pencil method for the radiation of guided wave fields in finite isotropic plates validated by a transient spectral finite element method.

Elastic guided waves (GW) can be profitably used in non-destructive evaluation and in structural health monitoring of plate-like structures. Nevertheless, the multi-modal and dispersive behaviour of GW often leads to difficult interpretation of typically measured time-dependent signals. The development of efficient simulation tools appears necessary to better understand complex phenomena involved and to optimize testing configurations. Here, a semi-analytical modal method is proposed to compute GW displacement fields in finite plates radiated by an arbitrary finite-sized source of surface stresses. It takes into account GW reflections and mode conversions at plate boundaries. As far as computation efficiency is concerned, this method is independent of the length of propagation paths, allowing to efficiently address configurations involving long range propagation. Predicted results are given as sums of modal contributions to ease their interpretation. The model is validated by comparing its predictions to those computed by a transient finite-element code.

A model-based inverse method for positioning scatterers in a cladded component inspected by ultrasonic waves.

Nondestructive methods aim at detecting, locating and identifying defects. Inversion of ultrasonic measurements obtained by inspecting a steel component of regular geometry with an immersed transducer leads to accurate location of defects. When the component is cladded, the irregular geometry of the surface and the anisotropic nature of the cladding material lead to aberrations of the radiated field (e.g., beam distortions, splitting and defocusing, these varying with the transducer scanning position). As a consequence, defect location may be inaccurate and defects (e.g., cracks) sizing impossible. In the present paper, a model-based inverse method is developed to solve this problem. It relies on the time-dependent simulation of ultrasonic propagation in this material of complex geometry and structure, in order to determine a set of probable positions for the defect at the origin of the measured ultrasonic echo-structure. The most probable position is determined by minimizing a cost-function of likeness between the simulated and measured ultrasonic images. The overall scheme shall generally apply to inverse measured ultrasonic echo-structures as soon as the simulation of the forward problem is tractable. To validate the method, examples of application are given dealing with actual measurements obtained in the real configuration of pressure vessel inspection.

Modeling of ultrasonic fields radiated by contact transducer in a component of irregular surface.

The wedge of a contact transducer is imperfectly coupled to a component of irregular surface. A volume between the wedge and the component (filled by water or oil used as a coupling) is created that fundamentally modifies transducer radiation behavior. As a result, phenomena like beam spreading, skewing and splitting, generation of unwanted contributions that possibly lead to false alarms may occur. At first, the paper describes a model to account for the main effects observable in such a situation. The model is based on a matrix method which describes the behavior of transient elementary contributions as the variation of a pencil propagating into homogeneous regions (namely, the wedge, the coupling and the component) and through interfaces between them (refraction and reflection). The elementary contributions accounting for the finite size of the transducer are summed to predict transducer diffraction effects. In a second part, predicted fields are compared to measured results. The comparison concerns particle velocity fields measurements at the surface opposite to that (irregular) on which the transducer acts. The very good agreement obtained proves the validity of our approach.