飞机多层金属板隐藏缺陷远场涡流探头设计及试验研究

由于飞机多层金属板结构厚度大、复杂等特性,现有检测方法无法发现原位内部缺陷,对于多层板金属缺陷的检测一直都是航空无损检测的难题。远场涡流检测技术因打破趋肤效应的限制,涡流能量可穿透较厚的被测试件,对金属板结构中隐藏缺陷的检测具有潜在优势。该文针对飞机多层金属板隐藏裂纹的原位检测,建立多层金属板构件隐藏裂纹平面远场涡流检测有限元仿真模型,研究不同角度、不同深度裂纹检测幅值、相位的变化规律。为验证该仿真模型的正确性,开展远场涡流检测多层金属板的试验。试验结果表明:设计开发的远场涡流探头可检测埋深13 mm的裂纹缺陷,当裂纹倾斜角度为0°时,检测灵敏度最高,当裂纹倾斜角度为90°时,检测灵敏度最低,与仿真结果保持一致,且能够对缺陷进行精准定位,可为飞机多层金属板构件隐藏裂纹的定量检测提供依据。     

An alternative numerical approach for computing eddy currents: Case of the double-layered plate

A numerical approach is presented for cases where induced eddy current densities are to be computed in axisymmetric situations. Conductors are represented as stacks of inductively coupled, concentric, metal rings in which current is excited by an external coil. Matrix techniques are used to solve the resulting set of circuit equations. Sinusoidally induced currents in a sandwich plate consisting of two layers of different metals are discussed as an application. Comparison is made with a finite element calculation and with results obtained via an analytical approach. Nonsinusoidal excitation is also briefly discussed.     

Numerical simulations of an electromagnetic acoustictransducer-receiver system for NDT applications

The development of a multistage numerical model of an electromagnetic acoustic transducer (EMAT), with particular emphasis on an EMAT receiver, is presented. The model includes five separate modeling states: static magnetic field simulation of an electromagnet; pulsed eddy current distribution of a generic meander-line coil suspended over a conducting specimen; Lorentz force distribution due to the interaction of the static magnetic field with the eddy current distributions; acoustic wave generation and propagation based on the dynamic Lorentz forces; and acoustic wave detection by an EMAT receiver. In particular, it is shown how the transient particle displacement fields are converted into an induced voltage response as part of the EMAT receiver system. Numerical simulations show that the voltage response is dependent on the wire spacing of the receiver coil     

高冲击载荷作用下平面式电涡流阻尼器特性数值模拟研究

为探究平面式电涡流阻尼器在冲击环境中的应用特点,开展了高冲击载荷作用下平面式电涡流阻尼器响应特性数值模拟研究.基于ANSYS Maxwell电磁学有限元软件建立平面式电涡流阻尼器二维数值仿真模型,分析了永磁体和磁靴结构尺寸、导电层和导磁层厚度以及气隙间距对电磁阻尼力的影响.研究结果表明:平面式电涡流阻尼器能够满足安全制...     

混凝土裂纹扩展过程模拟的扩展有限元法研究

扩展有限元法(theextendedFiniteElementMethod,XFEM)为数值模拟结构裂纹扩展过程提供了一条有效途径。该文介绍了用扩展有限元法对混凝土结构裂纹扩展过程进行数值模拟的实现方法。采用虚拟裂缝模型模拟混凝土非线性断裂行为,针对二维四边形单元推导了详细的有限元列式。采用3种方案对非线性方程系统进行求解,分析了其求解思路并概括了其求解步骤。通过对带初始边缘裂纹的单向拉伸混凝土板的数值模拟,对3种求解方案的计算结果进行了分析和讨论。     

Fatigue crack growth and life prediction of a single interference fitted holed plate

To understand the different aspects of fatigue behaviour of complex structural joints it will be much helpful if the effects of different parameters are studied separately. In this article, to study the isolated effect of interference fit on fatigue life a pined hole specimen is investigated. This specimen is a single‐holed plate with an oversized pin which force fitted to the hole. The investigation was carried out both experimentally and numerically. In the experimental part, interference fitted specimens along with open hole specimens were fatigue tested to study the experimental effect of the interference fit. In the numerical part, three‐dimensional finite element (FE) simulations have been performed in order to obtain the created stresses due to interference fit and subsequent applied longitudinal load at the holed plate. The stress distribution obtained from FE simulation around the hole was used to predict crack initiation life using Smith–Watson–Topper method and fatigue crack growth life using the NASGRO equation with applying the AFGROW computer code. The predicted fatigue life obtained from the numerical methods show a good agreement with the experimental fatigue life.     

Eddy-current interaction of a long coil with a slot in a conductive plate

We describe a truncated-domain method for calculating eddy currents in a plate with a long flaw. The plate is modeled as a conductive half-space and the flaw is a long slot with a rectangular cross section. A long two-dimensional (2-D) coil carrying an alternating current is aligned parallel to the slot. The coil impedance variation with frequency is determined for an arbitrary coil location. The electromagnetic field due to a long coil above a conductive half-space can be expressed as integrals of trigonometric functions. For a half-space with a long slot, however, additional boundary conditions must be satisfied at the slot walls. The truncated-domain method makes this possible by recasting the problem in a finite domain; as a result, the Fourier integral is replaced by a series. The domain can be made arbitrarily large, thereby yielding results that are numerically as close to the infinite domain solution as desired. We have used the truncated domain approach to study both eddy-current flaw interactions and edge effects in the limiting case of a very wide and deep slot. We confirmed the theoretical predictions by comparing them with results of a 2-D finite element calculation and of experiments.     

基于涡流成像的碳纤维增强树脂基复合材料细观结构可视化

对碳纤维增强树脂基复合材料（CFRP）的细观结构成像方法进行了研究,利用涡流成像技术实现了CFRP层合板中纤维方向及纤维缺失、褶皱和空隙过大等缺陷的可视化。首先通过有限元仿真和电路理论分析了CFRP板中涡流的生成机制和分布特性,阐述了基于涡流法的CFRP细观结构成像机制。然后介绍了用于扫描成像的高频涡流检测（HF-ECT）实验系统并确定了涡流探头的形式及其参数。最后利用涡流成像技术分别对单层板、正交层合板和四方向斜交层合板进行了检测,绘制了涡流检测（ECT）信号的三维伪彩图并得到了清晰的纤维纹路分布。通过引入滤波去噪技术和二维快速傅里叶变换（2D-FFT）对图像进行进一步处理,提高了图像分辨率并完成了不同方向上纤维纹路的分离,从而实现对层合板每单向层中缺陷的精确定位。     

Physical and geometric singularities modelling techniques for electrostatics and electromagnetism problems

Singularities appear in many problems in electrical engineering. They may be geometric (for example peaks, corners or ridges in Electrostatics) or physical (for example, changes in electromagnetic properties on thin depths). Classical numerical methods like finite elements technique are badly adapted to the simulation of these singularities. The authors present the techniques that they have developed to take these singularities into account. It consists of crack elements in eddy current non destructive testing, and of bilinear elements to control insulating materials. The particularity of these techniques is the association of a numerical resolution using finite elements technique, with an analytical resolution using singular elements. The authors recall, moreover, the techniques introduced in their Boundary Integral Equations package, in order to take into account geometrical singularities in electrostatic problems.     

A Model of Quasibrittle Fracture Caused by Pulsed Loading

We study the stress-strain state formed in a plate containing a stationary crack of finite length subjected to pulsed loading, develop a model of quasibrittle fracture caused by loads of this type, and deduce analytic expressions for the stress-strain state near the tip of the stationary crack in the plate. The proposed model admits rigorous physical justification and enables one to describe the development of brittle and quasibrittle fracture processes in materials with cracklike defects under dynamic and static loads within the framework of the same approach. The results of numerical simulation are in good qualitative agreement with the experimentally established regularities of the behavior of the critical parameters of fracture processes.     

Finite element modelling of closed cracks in eddy current testing

The eddy current inspection of small fatigue cracks in Ti–6AL–4V is evaluated in both a finite element model and experiments. The crack was created in a fatigue process and an eddy current measurement was carried out as the resulting crack was subjected to different levels of static load. The signal showed a strong dependency of the time between the creation of the fatigue crack and the eddy current measurement. This dependency is proposed to be related to oxides forming on the crack faces. The oxide is favourable for the detection of fatigue cracks. The narrow width of the fatigue crack is important to consider in eddy current inspection and as static loads are applied across the crack faces, electrical connections arise within the crack, which has a strong influence on the eddy current signal. Four different models of the contact behaviour were implemented within the finite element model. It is shown that the electrical connections that arise within small fatigue cracks, as well as the influence from the narrow opening as tensile loads are applied, can be predicted by a finite element model of the eddy current method.     

Numerical simulations of cracked plate using XIGA under different loads and boundary conditions

This article deals with the numerical simulation of cracked plate using extended isogeometric analysis (XIGA) under different loads and boundary conditions. The plate formulation is done using first-order shear deformation theory. The crack faces are modeled by the Heaviside function, whereas the singularity in stress field at the crack tip is modeled by crack tip enrichment functions. The stress intensity factors for the cracked plate are numerically computed using a domain-based interaction integral. The results obtained by XIGA for the center and edge crack plate are compared with extended finite element method and/or literature results for different types of loads and boundary conditions.     

一种新型电涡流阻尼器及阻尼性能研究

基于电涡流原理提出一种新型的可用于航天器振动被动抑制的电涡流阻尼器。首先,依托数值仿真建立阻尼器的磁场和力学有限元分析模型,对阻尼器的性能进行分析计算。其次,在振动测试实验台上进行阻尼特性测试,获得了小位移0.1 mm、大位移1 mm下的1 Hz～50 Hz频率范围内正弦激励作用工况下的阻尼系数。然后根据Bouc-Wen滞回模型建立了阻尼器的力学模型,研究了负载、阻尼器结构、交变洛仑兹力之间的关系。研究结果表明这种新型的电涡流阻尼器在外载激励作用下能够输出与仿真结果较为接近的阻尼力,且阻尼系数随激励频率变化具有明显的规律性,根据仿真和实验结果建立的阻尼力力学模型可以很好地用于电涡流阻尼器的力学特性仿真分析。     

基于特征线分离算法的大涡模拟

将基于特征线的分离算法与大涡模拟相结合,推导了不可压流大涡模拟有限元离散方程组,并将该方法应用于三维流场的层流及湍流非定常计算。将不同雷诺数下的三维顶盖驱动空腔流动计算结果与实验数据以及直接数据模拟结果进行对比,吻合较好,验证了方法的可靠性和准确性。     

Inverse method for identifying the underlying crack distribution in plates with random strengths

Summary In the current investigation we seek to identify the underlying crack number and crack length distributions in brittle plates with a known strength distribution. The inverse problem in probabilistic fracture mechanics is defined, and the numerical procedure to solve the inverse problem is constructed. The simulation process of generating simulated plates containing simulated random cracks is elaborated. The maximum strain energy release rate criterion (G _max) is applied to each simulated random crack to find the crack strength. The strength of the simulated plate is equated to the strength of the weakest simulated crack in the plate based on the weakest link notion. The underlying crack number and crack length distributions are obtained by minimizing the difference between the simulated plate strengths and the known plate strengths. The gamma, lognormal and two-parameter Weibull distributions are employed for the underlying crack length distribution, and are compared in order to identify the best choice. Numerical examples demonstrate that the three PDFs are all acceptable for reasons to be explained. In the appendix, the direct problem in probabilistic fracture mechanics is presented as part of the demonstration of a method for using the crack distribution identified in the inverse problem to predict the strength and the probability of fracture in a practical application.     

Determination of dynamic fracture toughness for PMMA

A dynamic FEM (finite element method) and a strain gage method are applied to analyze the dynamic fracture toughness and SIF (stress intensity factor) for PMMA (polymethyl methacrylate). The analyses are carried out for plates with an edge crack subjected to one-point bending in a plane of the plate. A simple procedure that the present author has proposed is applied to the problem of using a triangular element of assumed constant strain on finite element analysis. The numerical simulation by FEM provides values for the applied forces as measured with the strain gages. Also, a crack initiation time is measured with the strain gage mounted around the crack tip. The dynamic fracture toughness is determined by adapting the crack initiation time to the simulation curve of the dynamic SIF calculated by the FEM. In this study, the usefulness of the method to determine the dynamic fracture toughness is investigated by comparing predictions with the experimental results for dynamic stresses and SIFs.     

Prediction of stable crack growth in surface cracked plate of Aluminum 7050 alloy

To simulate stable crack growth, three-dimensional finite element analysis using the constant Crack Tip Opening Angle (CTOA) fracture criterion was performed for a thin plate made of Aluminum 7050 alloy. The critical CTOA value was experimentally obtained by the Rubber Impression Method, which directly measures the three-dimensional crack profiles by inserting the gel-state silicon rubber into the crack, and taking out the solid-state rubber later. From the microscopic observation from the broken specimen, it was found that, as the crack extends, the amount of crack growth near the free surface is more than that in the depth/thickness direction, which creates the special tunneling, e.g., canoe-shaped crack extension. For the numerical simulation, the surface-cracked plate was analyzed by quasi-static elastic-plastic finite strain analysis with the node release and the reloading technique. Consistent with experimental observations, numerical simulation with constant CTOA fracture criteria produced tunneling of a surface crack, but the shape of the crack front deviated from the experimental crack front as the free surface was approached. To address the local crack tip constraint effect on the stable crack growth, various fracture parameters - crack tip triaxiality, equivalent plastic strain, and void growth ratio as the crack extends – were also investigated.     

Cracks emanating from a square hole in rectangular plate in tension

A numerical analysis of cracks emanating from a square hole in a rectangular plate in tension is performed using a hybrid displacement discontinuity method (a boundary element method). Detailed solutions of the stress intensity factors (SIFs) of the plane elastic crack problem are given, which can reveal the effect of geometric parameters of the cracked body on the SIFs. By comparing the calculated SIFs of the plane elastic crack problem with those of the centre crack in a rectangular plate in tension, in addition, an amplifying effect of the square hole on the SIFs is found. The numerical results reported here also prove that the boundary element method is simple, yet accurate, for calculating the SIFs of complex crack problems in finite plate.     

Analysis of the crack growth propagation process under mixed-mode loading

In the present paper, a computational model for crack growth analysis under Mode I/II conditions is formulated. The focus is on two issues – crack path simulation and fatigue life estimation. The finite element method is used together with the maximum principal stress criterion and the crack growth rate equation based on the equivalent stress intensity factor. To determine the mixed-mode stress intensity factors, quarter-point (Q-P) singular finite elements are employed. For verification purposes, a plate with crack emanating from the edge of a hole is examined. The crack path of the plate made of 2024 T3 Al Alloy is investigated experimentally and simulated by using the finite element method with the maximum tangential stress criterion. Then, the validation of the procedure is illustrated by applying the numerical evaluation of the curvilinear crack propagation in the polymethyl methacrylate (PMMA) beam and the Arcan specimen made of Al Alloy for which experimental results are available in the literature. In order to estimate fatigue life up to failure of the plate with crack emanating from the edge of a hole, the polynomial expression is evaluated for the equivalent stress intensity factor using values of stress intensity factors obtained from the finite element analysis. Additionally, the fatigue life up to failure of the Arcan specimen is analyzed for different loading angles and compared with experimental data. Excellent correlations between the computed and experimental results are obtained.     

Indirect measuring of crack growth by means of a key-curve-method in pre-cracked Charpy specimens made of nodular cast iron

The determination of dynamic crack resistance curves from single specimen fracture tests requires information about the crack advance during the experiment. Here, attention is focused on crack resistance curves for nodular cast iron based on experimental data from instrumented Charpy tests. In order to estimate the actual crack length a key curve method (KCM) is employed. On the other hand, the Charpy impact tests were realized numerically using finite element calculations in conjunction with a continuum damage model (CDM) to simulate ductile crack growth. The parameters of the CDM model were determined from the experimental data of single specimen fracture tests. Equivalence between the experimental and the numerical realization of a fracture test was ensured by validating the predictions of the numerical simulations by means of low blow fracture tests. Comparison between the crack advance predicted by the numerical simulations and the results obtained using the proposed KCM shows a sufficiently well agreement with the actual crack length. Furthermore, crack resistance curves obtained from single specimen tests using either standard estimation schemes in conjunction with the KCM or numerical simulations are compared with the predictions based on low blow fracture tests.