Relative Nonlinear Coefficient Research Articles

A quantitative monitoring method for the pretightening state of bolts based on nonlinear Lamb waves and incremental learning

ABSTRACTThe degradation of the pretightening state of bolts is a multistage process. Utilising a single model to monitor the pretightening state in the full degradation stage and continuously updating the monitoring model is important. Therefore, a quantitative monitoring method for the pretightening state of bolts based on nonlinear Lamb waves and incremental learning is proposed. In the proposed method, phase reversal technology is first adopted to enhance the sensitivity for bolt loosening, and then a relative nonlinear coefficient based on phase reversal (RCP) is constructed. The disadvantage that linear indicators are insensitive to early loosening is overcome and the critical points of the multidegradation process are identified by this indicator, the tight contact stage (TCS) and the significant loosening stage. After the TCS is determined, a quantitative monitoring model, which fuses seven nonlinear damage indexes, is established based on incremental canonical correlation forests (ICCF). This algorithm achieves incremental learning by continuously increasing the number of decision trees. To verify the effectiveness of the method, an experimental study is carried out on four bolts. The monitoring effects of different indicators show that the method has higher accuracy and retains the ability to dynamically update data.

Fatigue damage quantitative evaluation of carbon fiber composites at different stress ratios based on nonlinear ultrasonic

In order to investigate the fatigue behavior of carbon fiber composites and the influence of different stress levels on their fatigue damage characteristics, the fatigue experiments of carbon fiber composites under different stress ratios are carried out. The nonlinear ultrasonic technique is used to online detect the fatigue damage process of carbon fiber composites, the relative nonlinear coefficient β under different stress ratios and different measuring positions is analyzed with the fatigue loading period. The experimental results indicate the relative nonlinear coefficient increases significantly and the rising trend accelerates when the fatigue life of specimen reaches 50%, it is the most sensitive to the change of material microstructure by comparing other parameters and can be used as the characteristic parameter to evaluate the fatigue damage of materials. In addition, the fatigue damage factor D is proposed by analyzing the relationship between the relative nonlinear coefficient and the damage degree of materials, the nonlinear ultrasonic quantitative analysis is carried out and the fatigue damage prediction model based on the relative nonlinear coefficient is established to characterize the severity of fatigue damage of materials. Therefore, the nonlinear ultrasonic quantitative evaluation method for carbon fiber composites is established, it provides a new method and data support for quantitative evaluation of fatigue damage degree of materials by nonlinear ultrasonic method.

Near surface residual stress detection of metallic materials using the high order ultrasonic nonlinear coefficient

Because residual stress seriously affects the mechanical properties of metallic components, in the study the nonlinear property of LCR wave is studied and the near surface residual stress within a certain depth beneath the component surface is nondestructively detected for the safe service of metal components. The stress detection system based on LCR wave is constructed using the oblique incident method with one-in-one-out mode. The high order relative nonlinear coefficients, β′ and δ′, during 45 steel tensile process are measured to investigate the correlation between nonlinear property of ultrasonic and stress. Two pairs of relative nonlinear coefficients monotonically increase and the stress sensitivity of δ′ is better than β′. In order to eliminate the sensitivity difference, the comprehensive nonlinear parameter is proposed. Three stress detection models based on experimental data are established and the error of residual stress evaluation are all below 4%, this indicates the nonlinear characteristics of LCR wave can be used to detect the stress level within a certain depth beneath the component surface. So the high-order ultrasonic nonlinear coefficients of LCR wave provides an effective method of rapid non-destructive detection the near surface residual stress of metallic material.

Nonlinear lamb wave imaging method for testing Barely Visible Impact Damage of CFRP laminates

The traditional linear ultrasonic technique may not provide a clear indication of the underlying damage in some cases of invisible or barely-visible impact damage. Considering nonlinear ultrasonic methods have been used for the detection of defects such as closed crack or delamination, a new nonlinear Lamb wave imaging method for detecting the Barely Visible Impact Damage (BVID) of Carbon Fiber Reinforced Polymer (CFRP) laminates was proposed in this work. First, the testing platform of nonlinear Lamb wave was built, and the test specimen with different impact damages was prepared. Second, the Lamb wave modes that meet the requirements of nonlinear testing were excited, and then, the correlation between the relative non-linear coefficient and status of low-energy impact damage were investigated. Lastly, the scanning imaging methods were developed, and the Damage Index (DI) for imaging impact damage was defined. The research results indicated that the DI based on the relative non-linear coefficient has higher detection sensitivity for low-energy impact damage, and the BVID and the extension of macro damage can be displayed intuitively by use of the new nonlinear Lamb wave imaging method.

Simulation and experimental research on nonlinear ultrasonic testing of composite material porosity

Porosity is related to the composite material performance and affects the product quality. It is very necessary to detect the porosity. Due to the lack of precision of the linear ultrasonic testing for small pores, the nonlinear ultrasonic testing of composite porosity is simulated and tested in this paper. The random pore model is introduced to perform nonlinear ultrasonic simulation in order to consider the randomness of pore size, morphology, and distribution characteristics. Different pore length, pore width and porosity models were created to investigate the relations of the ultrasonic propagation characteristic with pore parameters. And the real porous graphite composite materials are performed nonlinear ultrasonic simulation and experimental study. The results show that the relative nonlinear coefficient increases with the increasing pore length and decreases with the increasing pore width. The simulation and experimental results show that relative nonlinear coefficient increase with the increase of porosity. This paper provides a reference for nonlinear ultrasonic technology to detect the porosity of composite materials.

Research on high cycle fatigue damage characterization of FV520B steel based on the nonlinear Lamb wave

In this study, high-strength steel FV520B sheets were subjected to high-cycle tensile-tension fatigue experiments at room temperature in order to obtain fatigue-damaged specimens. Then Lamb waves were used to perform nonlinear ultrasonic testing on them to obtain the normalized relative nonlinear coefficients, β′/ β0. The corresponding relationship between β′/ β0 and the percentage of fatigue life was obtained. Finally, the microstructural changes of the damaged samples were observed by a scanning electron microscope in order to explore the correlation mechanism between β′/ β0 and the degree of micro-defects and fatigue damage. The experimental results showed that as the number of fatigue cycles increased, β′/ β0 first slowly rose, then quickly rose to reach a peak, and finally declined, which was consistent with the generation and propagation of dislocations and cracks during fatigue damage. As the length and number of microcracks increased, β′/ β0 also increased, especially in the initial stage of fatigue crack initiation. β′/ β0 was very sensitive to the size of fatigue cracks, so the change of β′/ β0 can be used to detect the degree of early fatigue damage of the material.

Theoretical Considerations of Photonic Crystal Fiber with All Uniform-Sized Air Holes for Liquid Sensing

A novel liquid-infiltrated photonic crystal fiber model applicable in liquid sensing for different test liquids—water, ethanol and benzene—has been proposed. One core hole and three air hole rings have been designed and a full vector finite element method has been used for numerical investigation to give the best results in terms of relative sensitivity, confinement loss, power fraction, dispersion, effective area, nonlinear coefficient, numerical aperture and V-Parameter. Specially, the assessed relative sensitivities of the proposed fiber with water, ethanol and benzene are 94.26%, 95.82% and 99.58%, respectively, and low confinement losses of 1.52 × 10−11 dB/m with water, 1.21 × 10−12 dB/m with ethanol and 6.01 × 10−16 dB/m with benzene, at 1.0 μm operating wavelength. This novel PCF design is considered simple and can be easily fabricated for practical use, and the assessed waveguide properties has determined the potential applicability in real liquid sensing applications.

Evaluation of Damage Process of a Coating by Using Nonlinear Ultrasonic Method

During the service or external loading of the surface coating, the damage accumulation may develop in the coating or at the interface between the substrate and the coating, but it is difficult to measure directly in the early stage, so the acoustic nonlinear parameters are used as the early damage index of the coating. In this paper, the nonlinear wave motion equation is solved by the perturbation method and the new relationship between the relative ratio of second-order parameter and third-order parameter was derived. The nonlinear ultrasonic testing system is used to detect received signals during tensile testing of for the specimen with Al2O3 coatings. It is found that when the stress is less than 260 MPa, the appearance of the coating has no obvious change, but the nonlinear coefficients measured by the experiment increase with the increase of the tensile stress. By comparing the curves of nonlinear coefficients and stress respectively, the fluctuation of curves the second-order nonlinear coefficient A2 and the relative nonlinear coefficient β′ to stress is relatively small, and close to the linear relationship with the tensile stress, which indicates that the two parameters of the specimen with Al2O3 coatings are more sensitive to the bonding conditions, and can be used as an evaluation method to track the coating damage.

Mechanical structural health prognosis with nonlinear mixed frequency ultrasonic signal analysis

In order to detect the early fatigue crack of mechanical components simply, this paper puts forward the ultrasonic testing technology of different side collinear mixing. Firstly, based on the nonlinear ultrasonic theory, the method of calculating the difference frequency and sum frequency nonlinear coefficients of mixing ultrasonic is deduced. Then, the ram-5000 SINAP ultrasonic system is used to detect the aluminum alloy specimens with five different depth fatigue cracks, and the corresponding spectrum diagram is drawn. From the experimental results, we get that the crack depth is positively correlated with the nonlinear coefficients of difference frequency and sum frequency within a certain crack depth. Finally, by analyzing and fitting the experimental data, the prediction models of the difference frequency and sum frequency nonlinear coefficients on the crack depth are established. Through the analysis and combination of the above two prediction models, the prediction model of the mixing relative nonlinear coefficient is established, and the average error of the three prediction models is compared. The results show that the mixing relative nonlinear model has better results. The research work in this paper makes a useful exploration for crack detection and crack depth prediction.

Fatigue Crack Detection in AISI 304 Austenitic Stainless Steel Using Nonlinear and Linear Ultrasonic Testing Methods

Fatigue cracks are often underestimated by traditional linear ultrasonic techniques due to the poor direction as well as narrow gaps within the cracks. The nonlinear ultrasonic testing technique is a promising method that may be used to solve this problem. In this study, the effects of traditional C scan imaging in measuring fatigue cracks are analyzed by comparing their results with that of metallography. Then, the finite amplitude method of nonlinear ultrasonic testing is used to detect micro-damages, and the influences of excitation voltage on the nonlinear coefficient are investigated. The results indicated that the accuracy in C scan imaging becomes worse when the crack’s surface is not perpendicular to the incident wave or if the crack’s gap is very small. In contrast, relative nonlinear coefficients under an optimum voltage increase according to the degree of micro-damage, which was found to not be affected by the status of macro-cracks but was particularly sensitive to the accumulation of micro-damage. This study suggests that nonlinear ultrasonic techniques be implemented to achieve beneficial effects in testing fatigue damage.

Non-linear property analysis of deformed metallic components using a longitudinal critically refracted wave

In order to apply the ultrasonic non-linear coefficient for non-destructive detection in actual engineering applications, the non-linear property of deformed metallic components is studied using a longitudinal critically refracted (LCR) wave. Firstly, dog-bone components are loaded in two different modes, which ensures that components with different stress states and the corresponding macroscopic deformation of components are measured. Then, online and offline non-linear ultrasonic experiments are conducted on pre-stress components and the relative non-linear coefficient is calculated. Experimental results indicate that the relative non-linear coefficient and the deformation state monotonically increase with stress levels and they have similar variation trends in both online and offline measurements. Furthermore, Pearson correlation coefficients between the relative non-linear coefficient and the macroscopic deformation are 0.988 and 0.9876 for two types of experiment, which indicates that they have a strong correlation relationship. The power-exponent function is applied to establish this dependence relationship. The index coefficients are 1.276 and 0.7305, respectively, and the difference may be due to the microstructure disparity caused by the different loading modes. Therefore, the interrelationship between the relative non-linear coefficient and the macroscopic deformation of metallic components can be applied to predict the variation of the relative non-linear coefficient from the macroscopic point, which is very convenient for damage detection in actual engineering applications.

Effect of sintering temperature and Ho2O3 on the properties of TiO2-based varistors

In this study, a series of TiO2-based ceramics doped with different contents of Ho2O3 in the range of 0–0.6 mol% are prepared by means of a conventional solid-state reaction method. Phase composition, microstructure and element distribution are studied by use of X-ray diffraction (XRD), scanning electron microscopy (SEM) and energy dispersive X-ray spectroscopy (EDS) separately. The influence of sintering temperature and Ho2O3 on the properties of samples is explored. The results show that the breakdown voltage decreases continuously while both the nonlinear coefficient and the relative dielectric constant ascend firstly and then descend with the sintering temperature increasing. Meanwhile, the relative dielectric constant and nonlinear coefficient of samples firstly ascend and then descend with the increasing of Ho2O3. Although the minimum breakdown voltage (3.3 V/mm) is obtained when sample is sintered at 1450 °C, the sample doped with 0.45 mol% Ho2O3 sintered at 1400 °C exhibits high comprehensive electrical properties, with breakdown voltage of 6 V/mm, the nonlinear coefficient of 5.5 and the relative dielectric constant of 1.88 × 105.

The fatigue damage evaluation of gear in sugarcane presser using higher order ultrasonic nonlinear coefficients

Abstract The fatigue damage of gear in sugarcane presser is one of the most common damages, which is very difficult to detect in sugar factory. The nonlinear ultrasonic technique is used to evaluate the fatigue damage of gear in this paper. The perturbation method is applied to solve the nonlinear wave equation, the relationship between relative nonlinear coefficient and higher harmonics is analyzed which the second and third order relative nonlinear coefficients are applied to evaluate the fatigue damage. The gear in sugarcane presser after three years service is the research objective, which thirty-two points at tooth root and sixteen points at tooth centre are conducted the nonlinear ultrasonic experiment. Experimental results indicate different detection points have different damage degree, and the fatigue damage degree of tooth No. 14 and 15 are more serious than other teeth. While for the same tooth, the damage degree of tooth root is much severer than the tooth centre. Therefore, the measured relative nonlinear coefficients could be applied to evaluate the fatigue damage of gear, which provides the practical method for internal damage evaluation of gear in sugar factory.

Stress evaluation of metallic material under steady state based on nonlinear critically refracted longitudinal wave

Abstract This paper presents the study of applying the nonlinear ultrasonic wave to evaluate the stress state of metallic materials under steady state. The pre-stress loading method is applied to guarantee components with steady stress. Three kinds of nonlinear ultrasonic experiments based on critically refracted longitudinal wave are conducted on components which the critically refracted longitudinal wave propagates along x, x1 and x2 direction. Experimental results indicate the second and third order relative nonlinear coefficients monotonically increase with stress, and the normalized relationship is consistent with simplified dislocation models, which indicates the experimental result is logical. The combined ultrasonic nonlinear parameter is proposed, and three stress evaluation models at x direction are established based on three ultrasonic nonlinear parameters, which the estimation error is below 5%. Then two stress detection models at x1 and x2 direction are built based on combined ultrasonic nonlinear parameter, the stress synthesis method is applied to calculate the magnitude and direction of principal stress. The results show the prediction error is within 5% and the angle deviation is within 1.5°. Therefore the nonlinear ultrasonic technique based on LCR wave could be applied to nondestructively evaluate the stress of metallic materials under steady state which the magnitude and direction are included.

Feasibility of Residual Stress Nondestructive Estimation Using the Nonlinear Property of Critical Refraction Longitudinal Wave

Residual stress has significant influence on the performance of mechanical components, and the nondestructive estimation of residual stress is always a difficult problem. This study applies the relative nonlinear coefficient of critical refraction longitudinal (LCR) wave to nondestructively characterize the stress state of materials; the feasibility of residual stress estimation using the nonlinear property of LCR wave is verified. The nonlinear ultrasonic measurements based on LCR wave are conducted on components with known stress state to calculate the relative nonlinear coefficient. Experimental results indicate that the relative nonlinear coefficient monotonically increases with prestress and the increment of relative nonlinear coefficient is about 80%, while the wave velocity only decreases about 0.2%. The sensitivity of the relative nonlinear coefficient for stress is much higher than wave velocity. Furthermore, the dependence between the relative nonlinear coefficient and deformation state of components is found. The stress detection resolution based on the nonlinear property of LCR wave is 10 MPa, which has higher resolution than wave velocity. These results demonstrate that the nonlinear property of LCR wave is more suitable for stress characterization than wave velocity, and this quantitative information could be used for residual stress estimation.

Nonlinear Ultrasonic Properties of Stress in 2024 Aluminum

Perturbation method is used to resolve one-dimensional wave equation under the assumption of small strain conditions. The relationship of the second order relative nonlinear coefficients (SORNC) β', the third order relative nonlinear coefficient (TORNC) δ' as the functions of fundamental and harmonic amplitudes is determined. The specimens are loaded from-200 MPa to 320 MPa at increments of 40 MPa by the electron universal testing machines. The SORNC β' and TORNC δ' are detected by the nonlinear ultrasonic testing system when ultrasonic waves propagate in the specimens. Results show that the relative nonlinear coefficients increase with the stress. The SORNT β' is approximately linear with the stress when stress is lower than 84.6% of the yield strength. The TORNC δ' is approximately linear with the stress when stress is lower than 76.9% of the yield strength.

Research on the Nonlinear Ultrasonic Testing of CFRP Based on Abaqus

In order to overcome the limitations of conventional ultrasonic testing method to detect small defects of carbon fiber composite material, ultrasonic nonlinear detection method was proposed based on finite amplitude. Firstly the detection mechanism of finite amplitude method was studied, then the detection model was created, and ultrasonic nonlinear characteristics of carbon fiber composites was analyzed by finite element simulation, finally relative non-linear coefficients follow the change of defect length and width show that the finite amplitude method has a high sensitivity to detect small defects.

Effects of Doped Cu, Mn on Electrical Properties of SrTiO<sub>3</sub>-Based Varistor Ceramics

CuO and MnCO3 doped SrTiO3-based multifunction ceramics were prepared respectively with solid state reaction method under vacuum condition. The electrical properties’ change with the oxidation temperature and microstructure were investigated. The results show that acceptor dopants behaves differently with the same sintering conditions. CuO-doped ceramic possess relative higher dielectric loss, dielectric constant and relative lower nonlinear coefficient, varistor voltage in contrast with MnCO3 doped ceramic with the same contents under the same sintering conditions. The grain size of CuO-doped sample is significantly larger than the sample doped with MnCO3. The grain distributions of CuO-doped sample is more homogeneous. The electrical properties of the ceramics are different due to the different behaviors of CuO and MnCO3 accepter dopants during the sintering process.

Influence of Doped Mn, Cu, Ni and Fe on Electrical Properties of SrTiO<sub>3</sub> Ceramics

MnCO3, CuO, NiO and Fe2O3 doped SrTiO3 multifunction ceramics were fabricated firstly. The microstructure and electrical properties were investigated. The results show that MnCO3 doped ceramic and CuO doped ceramic possess relative higher resistivity (ρ),nonlinear coefficient (α), varistor voltage (V1mA) and relative lower dielectric constant (ε),dielectric loss (tgδ) in contrast with NiO doped ceramic and Fe2O3 doped ceramic with the same contents under the same sintering conditions. The electrical properties among the ceramics doped are different due to the different behaviors of Mn,Cu,Ni and Fe acceptor dopants during the sintering course.

Linear and nonlinear optical properties of a novel material: Urea-(DL)tartaric acid single crystal (UDLT)

A urea-(DL)tartaric acid single crystal has been prepared for the first time as a SHG material. It is in a monoclinic system with space group P2 1. The linear properties and relative effective nonlinear coefficient are presented in this paper.