Modeling for nonlinear acoustic imaging of an isolated crack via standing waves in a 2D solid.

This paper is concerned with numerical modeling for nondestructive imaging of defects in solids via standing waves excited by a periodic sinewave signal. The stationary solution, purely sinusoidal in an intact sample, contains higher harmonics when damage is present. These harmonics are generated by contact acoustic nonlinearity and form their own standing waves whose intensity maximum usually indicates the position of damage, in a way similar to resonant vibrometry experiments. The key point of the developed numerical tool that describes those wave phenomena is a model of planar damage (crack, delamination) considered here as an inner contact with rough surfaces and friction. The corresponding boundary conditions are given by the previously developed contact model based on the Method of Memory Diagrams (MMD) capable of automating the account for hysteretic frictional effects. Combination of the MMD for boundary conditions and a finite element formulation for waves in a volume (MMD-FEM model) provides a complete description which represents a numerical code applied here for nonlinear standing waves simulations. We present a number of examples obtained for idealized 2D geometry and reveal conditions in which both position and extent of damage are clearly seen as well as cases where only partial detection is possible.

Two dimensional modeling of elastic wave propagation in solids containing cracks with rough surfaces and friction - Part I: Theoretical background.

Our study aims at the creation of a numerical toolbox that describes wave propagation in samples containing internal contacts (e.g. cracks, delaminations, debondings, imperfect intergranular joints) of known geometry with postulated contact interaction laws including friction. The code consists of two entities: the contact model and the solid mechanics module. Part I of the paper concerns the modeling of internal contacts (called cracks for brevity), while part II is related to the integration of the developed contact model into a solid mechanics module that allows the description of wave propagation processes. The contact model is used to produce normal and tangential load-displacement relationships, which in turn are used by the solid mechanics module as boundary conditions at the internal contacts. Due to friction, the tangential reaction curve is hysteretic and memory-dependent. In addition, it depends on the normal reaction curve. An essential feature of the proposed contact model is that it takes into account the roughness of the contact faces. On one hand, accounting for roughness makes the contact model more complicated since it gives rise to a partial slip regime when some parts on the contact area experience slip and some do not. On the other hand, as we will show, the concept of contact surfaces covered by asperities receding under load makes it possible to formulate a consistent contact model that provides nonlinear load-displacement relationships for any value of the drive displacements and their histories. This is a strong advantage, since this way, the displacement-driven model allows for a simple explicit procedure of data exchange with the solid mechanics module, while more traditional flat-surface contacts driven by loads generate a complex iterative procedure. More specifically, the proposed contact model is based on the previously developed method of memory diagrams that allows one to automatically obtain memory-dependent solutions to frictional contact problems in the particular case of partial slip. Here we extend the solution onto cases of total sliding and contact loss which is possible while using the displacement-driven formulation. The method requires the knowledge of the normal contact response obtained in our case as a result of statistical consideration of roughness of contact faces.

Two dimensional modeling of elastic wave propagation in solids containing cracks with rough surfaces and friction - Part II: Numerical implementation.

Our study aims at the creation of a numerical toolbox that describes wave propagation in samples containing internal contacts (e.g. cracks, delaminations, debondings, imperfect intergranular joints) of known geometry with postulated contact interaction laws including friction. The code consists of two entities: the contact model and the solid mechanics module. Part I of the paper concerns an in-depth description of a constitutive model for realistic contacts or cracks that takes into account the roughness of the contact faces and the associated effects of friction and hysteresis. In the crack model, three different contact states can be recognized: contact loss, total sliding and partial slip. Normal (clapping) interactions between the crack faces are implemented using a quadratic stress-displacement relation, whereas tangential (friction) interactions were introduced using the Coulomb friction law for the total sliding case, and the Method of Memory Diagrams (MMD) in case of partial slip. In the present part of the paper, we integrate the developed crack model into finite element software in order to simulate elastic wave propagation in a solid material containing internal contacts or cracks. We therefore implemented the comprehensive crack model in MATLAB® and introduced it in the Structural Mechanics Module of COMSOL Multiphysics®. The potential of the approach for ultrasound based inspection of solids with cracks showing acoustic nonlinearity is demonstrated by means of an example of shear wave propagation in an aluminum sample containing a single crack with rough surfaces and friction.

Simulation Study of the Localization of a Near-Surface Crack Using an Air-Coupled Ultrasonic Sensor Array.

The importance of Non-Destructive Testing (NDT) to check the integrity of materials in different fields of industry has increased significantly in recent years. Actually, industry demands NDT methods that allow fast (preferably non-contact) detection and localization of early-stage defects with easy-to-interpret results, so that even a non-expert field worker can carry out the testing. The main challenge is to combine as many of these requirements into one single technique. The concept of acoustic cameras, developed for low frequency NDT, meets most of the above-mentioned requirements. These cameras make use of an array of microphones to visualize noise sources by estimating the Direction Of Arrival (DOA) of the impinging sound waves. Until now, however, because of limitations in the frequency range and the lack of integrated nonlinear post-processing, acoustic camera systems have never been used for the localization of incipient damage. The goal of the current paper is to numerically investigate the capabilities of locating incipient damage by measuring the nonlinear airborne emission of the defect using a non-contact ultrasonic sensor array. We will consider a simple case of a sample with a single near-surface crack and prove that after efficient excitation of the defect sample, the nonlinear defect responses can be detected by a uniform linear sensor array. These responses are then used to determine the location of the defect by means of three different DOA algorithms. The results obtained in this study can be considered as a first step towards the development of a nonlinear ultrasonic camera system, comprising the ultrasonic sensor array as the hardware and nonlinear post-processing and source localization software.

Strain wave evolution equation for nonlinear propagation in materials with mesoscopic mechanical elements.

Nonlinear wave propagation in materials, where distribution function of mesoscopic mechanical elements has very different scales of variation along and normally to diagonal of Preisach-Mayergoyz space, is analyzed. An evolution equation for strain wave, which takes into account localization of element distribution near the diagonal and its slow variation along the diagonal, is proposed. The evolution equation provides opportunity to model propagation of elastic waves with strain amplitudes comparable to and even higher than characteristic scale of element localization near Preisach-Mayergoyz space diagonal. Analytical solutions of evolution equation predict nonmonotonous dependence of wave absorption on its amplitude in a particular regime. The regime of self-induced absorption for small-amplitude nonlinear waves is followed by the regime of self-induced transparency for high-amplitude waves. The developed theory might be useful in seismology, in high-pressure nonlinear acoustics, and in nonlinear acoustic diagnostics of damaged and fatigued materials.