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Introduction and objectives
Context
Generally, this PhD thesis work is related to nondestructive testing based on contact acoustical nonlinearity. The principle underlying this research is the fact that the presence of internal contacts (defects) in solids considerably modifies acoustic propagation and results in contact acoustical nonlinearity which, in turn, generates a number of detectable nonlinear signatures. These signatures can be accurately measured by using appropriate techniques and then used for interpreting the material properties and characterizing the defects.
The study described here was performed in the framework of a European Project entitled « A Life-cycle Autonomous Modular System for Aircraft Material State Evaluation and Restoring System » (ALAMSA). The four-years project (2012-2016) funded by the Framework 7 Programme of the European Union brought together the efforts of ten European academic, research and industrial partners. Its main objective was the creation of an innovative self-restoring system for aircraft materials. Physically, the self-healing principle is based on the integration into composite materials of breakable fibers filled with chemical reagents. Any event that results in breaking the fibers liberates the reagents whose chemical reaction creates a rigid agent that solidifies the damaged material.
For many years it has been known that nonlinear acoustic non-destructive testing (NDT) is capable of robust and precise detection of damage in various materials and structures and therefore suggests an opportunity to test the final efficiency of a self-healing process. The nonlinear acoustic NDT now uses a whole range of techniques, each developed for specific applications in order to meet some particular requirements. In our case, these requirements include at least two essential aspects: the method should be sufficiently robust and sensitive in order to detect weak nonlinearities and, at the same time, it should be suitable for using in real field but not laboratory conditions. In fact, these requirements are related to each other; indeed, the necessity to remotely test a complex structure with a number of geometric features often makes the measurable signatures weak even when the actual damage is strong. Generally, an attempt to apply the developed techniques in real field greatly increases the requirements to robustness and sensitivity. Ideally, the goal should not only be to develop a damage detection technique but an imaging method capable not only of detecting damage located somewhere but of its localization as well.
On the other hand, purely experimental investigations in NDT are frequently not sufficient. The matter is that a nonlinear signature by itself does not characterize the materials and the damage in there directly. In any case, some interpretation that links the measurable properties and the actual damage parameters is of interest. Certainly, such an interpretation should be applicable for structures of complex geometries and, in addition, should be based on physics of internal contacts otherwise its efficiency is not guaranteed.
Objectives
Summarizing these desired requirements we formulate the following objectives of the present study:
Experimental: develop a nonlinear acoustical NDT technique
• sufficiently sensitive for robust detection of weak or hidden damage
• having the potential for imaging
• explore the possibility for remote detection and real field applications
Theoretical: create a numerical model or, eventually, numerical tool for modeling wave propagation in materials containing defects
• taking into account real complex geometries of samples
• based on physically plausible contact models Practical:
• contribute to the creation of novel self-repairing aeronautical materials
Dissertation structure
This document is organized as follows. It contains five chapters, including the introductory one (Chapter I) in which the concept and models of contact acoustical nonlinearity are discussed as well as the most recent existing nonlinear NDT methods. The content of the Chapters II-V is original. The first two of them concern two experimental techniques: nonlinear coda wave interferometry and nonlinear air coupled ultrasonic method. In these chapters, the methodology (background, principle, strengths), experimental setup, measurements results are explained in detail. Chapters IV and V are related to a theoretical development. In particular, in Chapter IV a contact model based on roughness and friction is introduced. Chapter V contains the description of the implementation procedure and demonstrates how the contact model was integrated into a standard commercial finite element software (COMSOL). The last part of the manuscript contains summary, conclusions, and perspectives.
Each chapter contains sections numbered 1, 2, 3. etc. Some sections include subsections 1.1, 1.2, 1.3, etc. Equations and figures are numbered in consecutive order as Eq. (5), Fig. 7, etc, within each chapter. In cases when it is necessary to refer to a figure or equation from another chapter, they are referred to as Eq. (I.12), Fig. IV.3, etc. Literature references in the document are cited as [Ada-95] for a paper published by Adams et al. in 1995. The complete list of cited references can be found at the end of the manuscript.
Contact nonlinearity
Contact nonlinearity is the third class of mechanical nonlinearities considered here. The former two classes are related to uniform materials containing no defects in their structure. At the same time, pure, uniform and regular materials are exceptional in common life. 99% of the time mankind produces, treats and uses materials which have impurities, irregularities, inclusions, defects etc., which are inherent properties of their microstructure. Internal defects can be roughly categorized in 3 types: 1D dislocations, 2D internal contacts and 3D pores, voids, etc. Amongst these, the second type is the most essential in terms of material performance, since the presence of internal contacts manifests itself in the most drastic way. Indeed, influence of dislocations is negligible if we speak about seismology or building constructions, whereas pores and voids usually contribute to the most interesting material properties much less than cracks and contacts do (e.g., failure loads, acoustic and static nonlinearities, sound attenuation, etc). This makes solids with internal contacts to be an extremely important class of materials, and justifies the fact that an accurate description of their mechanical properties is critical.
Most typical examples of materials with internal contacts are unconsolidated granular materials in which the only physical link between the constituents (grains) is through internal contacts, and consolidated materials in which there exist a solid matrix whose properties are modified by the presence of contacts. In the latter class, two groups can be distinguished. In some materials, internal contacts are present as an inherent part of their structure (consolidated grainy materials such as geomaterials or building construction materials). Generally speaking, all solids that are not single crystals can be regarded as materials with inherent random structure at a mesoscopic scale, i.e., a scale which significantly exceeds the atomic size but is still small compared to macroscopic dimensions. Finally, there are solids in which internal contacts appear as defects (cracks, delaminations, etc.). Studies for materials of this class form a basis for theories underlying nonlinear NDT techniques.
Contact nonlinearities appear even when the material itself is perfectly linear. An obvious reason for that is the fact that the contact can be open or closed. In the former case the faces do not interact while in the latter one there is an interaction. This effect alone results in bimodality i.e. dependence of elastic moduli in a material on the states of contacts. Another nonlinear mechanics is related to the contact geometry. In most cases, contacting faces have some profiles, including regular shapes or random topographies such as roughness. The simplest example is Hertzian spheres. Even for perfectly elastic materials and for spheres always staying at contact (no bimodality effect), the force-displacement relationship in such a system is nonlinear. The issue is that higher displacements involve deformations of deeper layers of the material, whereas in the linear case the ’amount’ of strained material stays the same.
In the next sections we consider existing models for contact nonlinearity in more detail.
Existing models for contact nonlinearity
For modeling the nonlinear elastic behavior of materials, there exist a vast set of models. Here we concentrate only on theories capable of producing nonlinear stress-strain relationships, which is of primary importance for building up numerical models imitating nonlinear wave propagation, for the final purpose of creating a numerical tool for nonlinear NDT applications. Besides, there are many models that predict other characteristics, such as wave dispersion and attenuation, slow dependence of parameters on time, modification of linear elastic properties in the presence of damage, etc. In addition to the classical Landau theory, there exist two classes of so-called « nonclassical » models: phenomenological, in which some desired behavior is directly postulated as a simple or complex stress-strain relation, and physical, when it is attempted to take into account the physical comportment of real internal contacts. Most of the models target a 1D case only and are primarily suitable for simple wave propagation geometries.
Phenomenological models
Clapping or bimodal model
The simplest phenomenological model addresses a single contact (crack) perpendicular to the direction of plane longitudinal wave propagation. If the incident wave has a stress amplitude that exceeds the static stress of the originally closed interface, it opens the crack which results in a change of stiffness of the whole material.
Sliding friction model
Whilst the previous model addresses the case of normal wave incidence, the sliding friction model is related to the tangential wave-to-interface interaction. Consider the non-bounded interface between two friction-coupled surfaces subjected to an oscillating tangential traction (shear wave scattering) strong enough to cause their sliding. Then suppose that gross sliding of the interfaces occurs when the shear wave stress ε exceeds certain a value ε1. Then, the tangential stiffness, which has a value of C in the stick phase, drops to zero in the sliding phase
Table of contents :
Chapter I. Contact acoustical nonlinearity and non-destructive testing
1. Geometric, material and contact nonlinearities
1.1. Geometric nonlinearity
1.2. Material nonlinearity
1.3. Contact nonlinearity
2. Existing models for contact nonlinearity
2.1. Phenomenological models
2.2. Physical models
3 Recently developed nonlinear acoustic NDT methods
3.1. Guided wave tomography using RAPID algorithm
3.2. Resonant scanning laser vibrometry
3.3. Resonant thermosonics
3.4. Resonant shearosonics
Chapter II. Nonlinear coda wave interferometry technique
1. Introduction
2. Coda wave interferometry
2.1. Doublet technique and Snieder’s model
2.2. Stretching technique
2.3. Choice of the time window used in the CWI technique
3. One-channel time reversal focusing
3.1. Time reversal
3.2. Principle of one-channel time reversal
3.3. Chaotic cavity transducer
3.4. LabVIEW data analysis tools for one-channel time reversal focusing
4. Principle of nonlinear coda wave interferometry
5. Experimental setup
5.1. Experimental setup description
5.2. Choice of the signal processing method used in chaotic cavity transducers
5.3. Choice of the frequency range of the sweep used in chaotic cavity transducers
5.4. Comparison with other source types
6. Measurements and results
6.1. Measurements on a thermally shocked glass plate
6.2. Measurements on a rectangular glass plate with impact damage
7. Conclusions
Chapter III. Nonlinear air-coupled ultrasonic method with the scale subtraction post-processing
1. Principle of the technique
1.1. Scale subtraction method
1.2. Local defect resonance excitation
2. Experimental setup
3. Measurements and results
3.1. Measurements on a CFRP laminate with a 35×35 mm2 delamination at half thickness
3.2. Measurements on a CFRP laminate with a 20×20 mm2 delamination at 1/4th thickness
3.3. Measurements on a GRFP sample
4. Conclusions
Chapter IV. Contact models for shift with friction
1. Brief history
2. Geometric extensions
3. Method of memory diagrams
3.1. Simplest memory diagram for an initial curve
3.2. Evolution of memory diagrams
3.3. « Reading » memory diagrams
3.4. Numerical implementation and examples
3.5. Summary: assumptions of the MMD
Chapter V. Modeling for elastic wave propagation in materials with cracks
1. Force-driven and displacement-driven crack models
2. Normal loading curves for contact of rough surfaces
3. Tangential contact interactions: full sliding and partial slip
4. Numerical implementation of wave-crack interactions
5. Illustrative example
5.1. Model specifications
5.2. Simulated normal and tangential reaction curves
5.3. Clapping- and friction- induced nonlinear features
5. Conclusions and perspectives
General summary and conclusions
References
