Nonlinear Elastic Wave Spectroscopy (NEWS) Techniques to Discern Material Damage,Part II: Single-Mode Nonlinear Resonance Acoustic Spectroscopy

Abstract

The presence of mesoscopic features and damage in quasi-brittle materials causes significant second-order and nonlinear effects on the acoustic wave propagation characteristics. In order to quantify the influence of such micro-inhomogeneities, a new and promising tool for nondestructive material testing has been developed and applied in the field of damage detection. The technique focuses on the acoustic nonlinear (i.e., amplitude-dependent) response of one of the material's resonance modes when driven at relatively small wave amplitudes. The method is termed single-mode nonlinear resonance acoustic spectroscopy (SIMONRAS). The behavior of damaged materials is manifested by amplitude dependent resonance frequency shifts, harmonic generation, and nonlinear attenuation. We illustrate the method by experiments on artificial slate tiles used in roofing construction. The sensitivity of this method to discern material damage is far greater than that of linear acoustic methods.     

Nonlinear Elastic Wave Spectroscopy (NEWS) Techniques to Discern Material Damage,Part I: Nonlinear Wave Modulation Spectroscopy (NWMS)

Abstract

The level of nonlinearity in the elastic response of materials containing structural damage is far greater than in materials with no structural damage. This is the basis for nonlinear wave diagnostics of damage, methods which are remarkably sensitive to the detection and progression of damage in materials. Nonlinear wave modulation spectroscopy (NWMS) is one exemplary method in this class of dynamic nondestructive evaluation techniques. The method focuses on the application of harmonics and sum and difference frequency to discern damage in materials. It consists of exciting a sample with continuous waves of two separate frequencies simultaneously, and inspecting the harmonics of the two waves, and their sum and difference frequencies (sidebands). Undamaged materials are essentially linear in their response to the two waves, while the same material, when damaged, becomes highly nonlinear, manifested by harmonics and sideband generation. We illustrate the method by experiments on uncracked and cracked Plexiglas and sandstone samples, and by applying it to intact and damaged engine components.     

Nonlinear Elastic Wave Spectroscopy (NEWS) Techniques to Discern Material Damage, Part I: Nonlinear Wave Modulation Spectroscopy (NWMS)

The level of nonlinearity in the elastic response of materials containing structural damage is far greater than in materials with no structural damage. This is the basis for nonlinear wave diagnostics of damage, methods which are remarkably sensitive to the detection and progression of damage in materials. Nonlinear wave modulation spectroscopy (NWMS) is one exemplary method in this class of dynamic nondestructive evaluation techniques. The method focuses on the application of harmonics and sum and difference frequency to discern damage in materials. It consists of exciting a sample with continuous waves of two separate frequencies simultaneously, and inspecting the harmonics of the two waves, and their sum and difference frequencies (sidebands). Undamaged materials are essentially linear in their response to the two waves, while the same material, when damaged, becomes highly nonlinear, manifested by harmonics and sideband generation. We illustrate the method by experiments on uncracked and cracked Plexiglas and sandstone samples, and by applying it to intact and damaged engine components.     

Detecting Damage in Composite Material Using Nonlinear Elastic Wave Spectroscopy Methods

Modern aerospace structures make increasing use of fibre reinforced plastic composites, due to their high specific mechanical properties. However, due to their brittleness, low velocity impact can cause delaminations beneath the surface, while the surface may appear to be undamaged upon visual inspection. Such damage is called barely visible impact damage (BVID). Such internal damages lead to significant reduction in local strengths and ultimately could lead to catastrophic failures. It is therefore important to detect and monitor damages in high loaded composite components to receive an early warning for a well timed maintenance of the aircraft. Non-linear ultrasonic spectroscopy methods are promising damage detection and material characterization tools. In this paper, two different non-linear elastic wave spectroscopy (NEWS) methods are presented: single mode nonlinear resonance ultrasound (NRUS) and nonlinear wave modulation technique (NWMS). The NEWS methods were applied to detect delamination damage due to low velocity impact (<12 J) on various composite plates. The results showed that the proposed methodology appear to be highly sensitive to the presence of damage with very promising future NDT and structural health monitoring applications.     

Local Acoustic Resonance Spectroscopy (LARS) for Glass Fiber-Reinforced Polymer Applications

Polymer composite materials combine high strength with low weight. This makes composites an interesting material for different industrial applications. In the aerospace industry, the use of composites is already common practice, while in the automotive industry carbon fiber-reinforced polymers have begun to replace metal in some parts. However, the nature of damage within composites is different from that within metal parts, so common techniques available for damage detection in metal may not work for composites thus new techniques for damage detection need to be developed. A technique that is often used but requires experienced technicians is the so-called coin tapping test where changes in sound waves generated by the impact of a hard object are detected. LARS is a (new) technique that avoids the errors due to variations in operator technique by using a instrumented impact device to generate controlled sound signals. If a hammer is used as an impact device it could be equipped with a dynamic force sensor to measure and record the excitation force of the sound signal. The force and the excited sound signal are related to the contact stiffness between the hammer and the test part. Flaws such as voids and delaminations affect the contact stiffness and can be detected under certain conditions. To the knowledge of the authors, no such technique has appeared in the literature. In regard to the frequencies, LARS is operated at much shorter wavelengths than in vibration analysis techniques (making it “local”) and at much larger wavelengths than in ultrasound. The material is excited to frequencies that are recorded by a microphone. To demonstrate the method, it is applied to the inspection of wind turbine rotor blades.     

Effects of Shear‐Transverse Coupling and Plasticity in the Formulation of an Elementary Ply Composites Damage Model,Part II: Material Characterisation

Abstract: In this two‐part study, we examine the effects of neglecting plasticity and shear‐transverse coupling in a continuum damage mechanics model for composites. In part I, two models were formulated: one in which plasticity was neglected, and one in which both plasticity and shear‐transverse damage coupling were neglected, and the predictive capabilities for both models were examined. In this second part of the paper, the procedure and results of the experimental test series carried out to determine input parameters for the above two models are presented. Two materials were tested: one a carbon fibre‐reinforced plastic, the other an S2‐glass fibre‐reinforced plastic. Both material systems are currently used in the aerospace industry so the experimental results should be of interest to that community. Both materials exhibited non‐linear intralaminar shear behaviour, whereas the S2‐glass fibre‐reinforced plastic also exhibited a significantly non‐linear transverse response. Tests on ±45º and 10º off‐axis coupons indicated that a reasonable estimate of shear strength could be obtained from the ±45º test specimens. Some further insight is provided into the model predictions that were presented in part I.     

一类非线性(3+1)维波动方程的周期解

通过行波约化一类(3+1)维非线性波动方程和建立与立方非线性Klein-Gordon方程间变换的联系,由此得到其孤立波解和周期解.     

一类非线性(3+1)维波动方程的周期解

通过行波约化一类(3+1)维非线性波动方程和建立与立方非线性Klejn-Gordon方程间变换的联系,由此得到其孤立波解和周期解。     

Polybutylacrylate/poly (methyl methacrylate) Core-Shell Elastic Particles as Epoxy Resin Toughener: Part II Toughness on DGEBA/DDM system

Mechanical properties of epoxy resin were investigated by adding core-shell elastic particles (CSEP). The results indicated that optimized core-shell ratio was 60/40 and the loading volume of CSEP was 10 phr (per hundred parts of epoxy resin by weight). The impact strength of modified systems increased apparently with the decrease of core sizes. However, the shearing strength changed gently with the particle sizes. CSEP with lightly crosslinked rubbery core showed more effectiveness on toughness than others. With solution blending, CSEP could be dispersed in epoxy matrix well, and the morphologies of dispersed rubber domains were controlled perfectly by CSEP whose structure was predesigned. A cavitation-shearing band toughness mechanism was observed from the SEM micrographs of fracture surface. It also was found that the deforming temperature (DT) of modified epoxy did not decline apparently.     

German women in chemistry, 1925-1945 (Part II)

The paper traces the role of German women into the chemistry profession from 1925 to 1945, examining their relative numbers and experience in higher education, in academic and industrial careers as well as in professional organizations such as the Verein Deutscher Chemikerinnen. The paper examines the effect of the 1930s Depression, National Socialism, and World War II on women chemists, considering both general trends as well as the experiences and achievements of several individual women in a variety of situations. Finally, it considers the longterm consequences of these developments, such as the Nazi expulsion of Jewish women, destruction of women's organizations and devaluing of women's achievements, in limiting the recognition and participation of German women chemists after 1945.     

Finite Element Analysis of 2.5D Woven Composites,Part II: Damage Behavior Simulation and Strength Prediction

In the first part of the work, a new 2.5D woven composites finite element model (2.5D WCFEM) which took into consideration the impact of face structures and can accurately predict the main elastic performances has been established. In this part, the stress–strain behavior and the damage characteristic of this material under uniaxial tension are simulated using nonlinear progressive damage analysis based on damage mechanics. Meanwhile, experimental investigation and fracture analysis are conducted to evaluate the validity of the proposed method. Finally, the influence of woven parameters on the mechanical behavior is discussed. Compared with the test results, a good agreement between the computational and experimental results has been obtained. The progressive damage characteristic and main failure modes are also revealed.     

Comparing rutting of airfield pavements to simulations using Pavement Analysis Using Nonlinear Damage Approach (PANDA)

This study presents the rutting performance results of full-scale pavement test sections subjected to F-15E and C-17 aircraft wheels at two different temperatures. Pavement structures for the tests were constructed under shelter in the U.S. Army Engineer Research and Development Center's (ERDC) pavement test facility. The full-scale test results are used to validate viscoelastic, viscoplastic and hardening-relaxation constitutive relationships implemented in the Pavement Analysis Using Nonlinear Damage Approach (PANDA) model. PANDA is a mechanistic-based model which incorporates nonlinear viscoelastic, viscoplastic, hardening-relaxation, viscodamage, moisture-induced damage and ageing constitutive relationships. Results of dynamic modulus and different repeated creep-recovery laboratory tests are analysed to extract the parameters associated with viscoelastic, viscoplastic and hardening-relaxation constitutive relationships implemented in PANDA. Once calibrated, PANDA is used to predict the rutting performance observed in full-scale pavement test sections. The simulation results illustrate that PANDA is capable of predicting the rutting of airfield pavements subjected to heavy aircraft wheel loads at intermediate and high temperatures. It is shown that PANDA successfully predicts the effect of shear flow and upheaval at the edges of the wheel. The data from simulation suggested that PANDA, once calibrated, can provide insight into the critical locations of tensile and compressive stresses within the pavement structure. PANDA simulations not only provide a tool for evaluating existing structures, but also can be used in designing more sustainable pavement structures and materials.     

Conversion of polycarbosilane (PCS) to SiC-based ceramic Part II Pyrolysis and characterisation

The conversion to ceramic of a commercial polycarbosilane (PCS) under various pyrolysis conditions has been investigated. The products of pyrolysis have been characterised by solid state ²⁹Si and ¹³C NMR spectroscopy and X-ray diffraction (XRD). Some of the phases identified in the present study were found to differ from those reported previously, particularly in the earlier literature. Oxidation-cured PCS, when pyrolyzed up to 1400 °C in argon, generally produced silicon oxycarbide (SiO _x C _y ) as the second major phase with -SiC as the major phase, and smaller amounts of free carbon. With increasing temperature above 1200 °C, the silicon oxycarbide phase decomposed to give -SiC. Silica (SiO₂) was also found to evolve from this silicon oxycarbide phase. Loss of some of the silica, probably by reaction with carbon, was found at 1400 °C, possibly yielding SiO, CO and SiC. At 1500 °C, crystalline -cristobalite was found as a minor phase with -SiC as the major phase and a lower amount of free carbon. Pyrolysis in vacuum leads to production and crystallization of -SiC at a lower temperature than required if pyrolyzed in argon flow. After pyrolysis at 1600 ° in vacuum, the cured PCS converted to almost stoichiometric -SiC.     

Nonlinear Response of Imperfect Eccentrically Stiffened Ceramic-Metal-Ceramic Sigmoid Functionally Graded Material (S-FGM) Thin Circular Cylindrical Shells Surrounded on Elastic Foundations Under Uniform Radial Load

This article researches nonlinear response of imperfect eccentrically stiffened symmetric FGM thin circular cylindrical shells with ceramic-metal-ceramic layers, which are symmetric through the middle surface by Sigmoid-law distribution (S-FGM) and have stiffeners surrounded on elastic foundations under uniform radial load. The Donnell classical shell theory, stress function, and Galerkin method are used for investigation of the nonlinear stability of the S-FGM shell. The obtained results show the effects of the stiffeners, elastic foundations, mechanical load, and material parameters on the nonlinear buckling response of symmetric S-FGM circular cylindrical shells.     

Polybutylacrylate/poly(methyl methacrylate) Core-Shell Elastic Particles as Epoxy Resin Toughener: Part I Design and Preparation

Polybutylacrylate (PBA)/poly(methyl methacrylate) (PMMA) core-shell elastic particles (CSEP), whose rubbery core diameter ranged from 0.08 μm to 1.38μm, were synthesized by using conventional emulsion polymerization, multi-step emulsion polymerization, and soapless polymerization. Allyl methacylate (ALMA) and ethylene glycol dimethacrylate (EGDMA) were selected as crosslinking reagents for core polymerization. Methacrylic acid (MAA) was used as functional co-monomer with methyl methacrylate as shell component. The content of vinyl groups in PBA rubbery core increased with the amount of crosslinking reagents. The core-shell ratio affected great on the morphology of the complex particles. Furthermore, the amounts of carboxyl on the surface of core-shell particles, copolymerized with acrylic acid, were determined by potentiometric titration. Results showed that methylacrylic acid was distributed mostly on the surface of particles.     

On the resistance to penetration of stiffened plates,Part II: Numerical analysis

A series of indentation tests have been carried out quasi-statically on various configurations of stiffened panels. These represent hull plates in ships subjected to grounding or collision actions. The results of the scaled down tests are reported in the first part of this two-part companion paper. This part (II) presents results from numerical analyses with focus on fracture prediction.     

Optimal spatiotemporal reduced order modeling, Part II: application to a nonlinear beam

A geometrically nonlinear, simply supported beam under the influence of time-dependent external forcing serves as a testbed to demonstrate application of the optimal spatiotemporal reduced order modeling (OPSTROM) framework proposed in Part I of this work. Fully resolved simulations, which are relatively expensive to perform, are used to accurately predict the beam response for a few forcing parameters. More affordable simulations are achieved with a conventional finite-difference scheme by coarsening the computational grid in space and time. Discretization errors are reduced with OPSTROM as subgrid-scale models are designed to account for the underlying space-time statistical structure using principles of mean-square error minimization, conditional expectations and stochastic estimation. When included in the under-resolved simulations, these optimal subgrid-scale models are shown to significantly improve the accuracy of predictions for both periodic and chaotic response types. This improved accuracy is further demonstrated through a set of numerical experiments designed to capture the complex bifurcation behavior of the beam response.