Analytical and finite element prediction of Lamb wave scattering at delaminations in quasi-isotropic composite laminates

This paper presents a theoretical and finite element (FE) investigation of the scattering characteristics of the fundamental anti-symmetric (A₀) Lamb wave at delaminations in a quasi-isotropic (QI) composite laminate. Analytical models based on the Mindlin plate theory and Born approximation are presented to predict the A₀ Lamb wave scattering at a delamination, which is modelled as an inhomogeneity, in an equivalent isotropic model of the QI composite laminate. The results are compared with FE predictions, in which the delamination is modelled as a volume split. The equivalent isotropic model and QI composite laminate are used to investigate the feasibility of the common theoretical approach of modelling the delamination as the inhomogeneity. A good correlation is observed between the theoretical solutions and FE results in the forward scattering amplitudes, but there exists a larger discrepancy in the backward scattering amplitudes. The FE results also show that the fibre direction of the outer laminae has a pronounced influence on the forward and backward scattering amplitudes, which is not predicted by the analytical models.     

Schlieren ultrasonic visualization of delaminations in composite materials

The application of Schlieren ultrasonic techniques to the visualization of delaminations in composite materials is described and discussed. It is shown that this technique can provide an efficient, practical, non-destructive testing method.     

NDT capability of digital shearography for different materials

In this paper, the capabilities of shearography for detecting hole and crack type defects in polymeric and metallic materials using thermal loading were investigated. In order to improve the ability of the identifying defect, the fringe multiplication technique was applied to some suspectable shearography fringe patterns. Based on the test results empirical rules for inspection plates of different material with specific thicknesses were established. For aluminium plates with thicknesses of 3 mm, minimum diameter of a surface breaking hole which is detectable is approximately equal to 2.5–3.0 times the depth of the defect, and for polymer plates with a thickness of 10 mm, the minimum detectable diameter is 0.8–1.3 times of the depth. For polymeric materials results from the increasing temperature period are approximately the same as those from the decreasing temperature period. When the orientation of the image shearing is not perpendicular to the longitudinal direction of the crack type defects, the sensitivity for defect detection is relatively higher than with perpendicular image shearing.     

Surface exchange reactions and diffusion in composite materials: A finite element approach

A two-dimensional square grain model has been applied to model oxygen exchange processes between a gas phase and a ceramic composite consisting of two randomly distributed phases of equal grain size (side length of squares). Both average diffusion profiles for thin films and the time dependence of the total amount of exchanged oxygen (relaxation curves) have been calculated numerically by means of the finite element method. The boundary conditions refer to an instantaneous change of the oxygen partial pressure in the surrounding gas phase, which gives rise to surface exchange reactions as well as to diffusion in the composite. Both local equilibrium at the interface between different phases (host phase and inclusions) and blocking heterophase boundaries have been taken into account. The numerical results are compared with the analytical solution for diffusion in a homogeneous medium introducing effective diffusion and surface exchange coefficients. When the relaxation time for effective medium diffusion is considerably shorter than that for the transport process from the host phase into the inclusions, relaxation curves with two separate time constants are predicted. Based on analytical approximations, relaxation times for various limiting cases are given.     

激光激发黏弹表面波有限元数值模拟

研究黏弹性材料中激光激发的Rayleigh波的传播特征. 考虑到黏弹性材料的黏性特征,在频域内建立黏弹性材料中激光激发Rayleigh波的有限元数值模型. 在验证有限元频域数值模型正确性的基础上,模拟脉冲激光作用在黏弹性材料上激发出Rayleigh波,进而讨论激光激发的黏弹Rayleigh波的传播特征,并比较黏弹性材料与弹性材料中激光激发的Rayleigh波差异,同时分析了材料的黏性劲度参量变化对Rayleigh波特征的影响. 关键词： 表面波 激光超声 有限元方法 黏弹性     

基于有限元模拟的超声应力系数标定及分析*

应力系数的标定作为超声应力检测最为关键的环节,直接决定应力检测结果的准确性。传统的应力系数试验标定对于被测物的表面粗糙度、耦合剂厚度、声匹配块与被测物接触力等因素十分敏感,但缺少基本参照值。基于COMSOL建立多物理场耦合的超声应力检测模型,施加不同的拉伸载荷,计算临界折射纵波到达时间与不同应力值之间的关系,模拟标定45#钢的超声应力系数为13.7MPa/ns。单轴水平拉伸试验标定的45#钢应力系数为16.5MPa/ns。结果表明,通过两种方法标定的应力系数较为接近,试验标定的应力系数偏大,这是由于有限元方法能够消除试验过程中各种不确定因素对声时精确测量所造成的影响,能够更加纯粹的反映材料的声弹性效应,因此具有作为基础数据的参考价值。有限元方法作为传统试验方法的补充,可以减小试验标定数据的离散性,提高超声应力检测结果的可信度。     

Calculation of leaky Lamb waves with a semi-analytical finite element method

A semi-analytical finite element method (SAFE) has been widely used for calculating dispersion curves and mode shapes of guided waves as well as transient waves in a bar like structures. Although guided wave inspection is often conducted for water-loaded plates and pipes, most of the SAFE techniques have not been extended to a plate with leaky media. This study describes leaky Lamb wave calculation with the SAFE. We formulated a new solution using a feature that a single Lamb wave mode generates a harmonic plane wave in leaky media. Dispersion curves obtained with the SAFE agreed well with the previous theoretical studies, which represents that the SAFE calculation was conducted with sufficient accuracy. Moreover, we discussed dispersion curves, attenuation curves, and displacement distributions for total transmission modes and leaky plate modes in a single side and both two side water-loaded plate.     

Three-dimensional modeling of thermo-mechanical finite element analysis in edge-pumped composite Yb:YAG/YAG thin-disk laser

A study of the thermo-mechanical analysis in edge-pumped composite Yb:YAG disk laser is presented. A three-dimensional model of disk and cooling system was created in ANSYS software. Heat load density applied on active medium was 14.6% of power absorption density. Temperature, stress and strain analysis showed a uniform distribution in the upper surface and maximum in the center. Finally, optimum heat exchanger coefficient and temperature of cooling system were obtained by comparing with different analyses and results.     

Effective permittivity of periodic composite materials: Numerical modeling by the finite element method

The effective properties of composite materials are closely related to the composition and arrangement of its constituents. Many studies and articles are actively studying the dielectric properties of heterogeneous structures with random and periodic arrangement. In the quasistatic limit, we use the finite element method as a numerical tool to evaluate the effective permittivity of two and three component composites. Two heterostructures are investigated; the first is formed by crossed dielectric cylinders in permanent contact and arranged in three layers. The cylinders are immersed in a dielectric host medium. The second structure is similar to the first except that the tubes are covered by an interphase layer. The numerical tool used to extract the exact value of the effective permittivity takes into account all internal multipolar interactions which contribute to the polarization of the material medium. The impacts of the relative permittivity and volume fraction of cylinders, the thickness of interphase and its dielectric constant are reported. The Maxwell–Garnett theory fails to predict the effective permittivity of the studied structures for high volume fraction and permittivity contrast. To overcome this problem, an amendment was made to the McLachlan equation McQ also termed the Two Exponent Single Percolation Equation TESPE. The first exponent t is held equal to 1 and the other exponent s is depending on the volume fraction. s is calculated so that the whole values of the effective permittivity obtained by the McQ rule are exactly the same values obtained by the simulations. Finally, we obtained a chart and a model to find the values of s, a fast way that is very useful for practitioners and design engineers of composite materials.     

Three-dimensional magnetic properties of soft magnetic composite materials

A three-dimensional (3-D) magnetic property measurement system, which can control the three components of the magnetic flux density B vector and measure the magnetic field strength H vector in a cubic sample of soft magnetic material, has been developed and calibrated. This paper studies the relationship between the B and H loci in 3-D space, and the power losses features of a soft magnetic composite when the B loci are controlled to be circles with increasing magnitudes and ellipses evolving from a straight line to circle in three orthogonal planes. It is found that the B and H loci lie in the same magnetization plane, but the H loci and power losses strongly depend on the orientation, position, and process of magnetization. On the other hand, the H vector evolves into a unique locus, and the power loss approaches a unique value, respectively, when the B vector evolves into the round locus with the same magnitude from either a series of circles or ellipses.     

基于空耦超声的复合材料黏弹性评价方法*

复合材料的黏弹性是表征其内在阻尼机制的重要力学特性,而内在阻尼机制是材料安全性能的一个重要评价指标。该文提出了空气耦合超声波的材料黏弹性评价方法。首先讨论了黏弹性进行评价的相关理论,利用接触式超声波底面回波法与空气耦合超声波透射法对比验证,其结果基本一致,证明了空气耦合超声对材料黏弹性检测的有效性。并且对一批不同铺层方向的碳纤维复合材料进行了评价,其结果与期望值完全相符,验证了该方法的可行性和准确性,为复合材料的动态力学特性评价和安全评价提供了新的思路。     

Application of nano-indentation, nano-scratch and single fibre tests in investigation of interphases in composite materials

Three novel experimental techniques were employed in this work in order to investigate the influence of the interphase region in polymer–glass composites on the bulk material properties: (i) the microdroplet test is a single fibre test designed to characterize the fibre–matrix bond (interface region) and to determine the interfacial shear stress in composite material; (ii) the nano-indentation test, a novel nano-hardness technique with ability to produce an indent as low as a few nanometres was employed in order to measure nano-hardness of the fibre–matrix interphase region; and (iii) the nano-scratch test, used in conjunction with the nano-indentation test for measurement of the interphase region width. The microdroplet test (MDT) has been used to characterize the interfacial bond in fibrous composite materials. The specimen consists of a fibre with a drop of cured resin pulled while the drop is being supported by a platinum disc with a hole. A properly tested specimen fails at the droplet’s tip–fibre interface, revealing the ultimate interfacial shear strength. In this study, finite element analysis (FEA) of the MDT has been focused toward simulation of the fibre–matrix interphase region. The influence of several functional variations of the material properties across the interphase layer on the stress distribution at the droplet’s tip was analysed. The results showed that the variation of the interphase properties significantly affects the stress distribution at the fibre–droplet interface, and, therefore, the stress redistribution to composite material. These results led to further experimental investigation of the interphase region, in order to obtain the material properties essential for the interfacial stress analysis. The interphase region in dry and water aged polymer–glass composite materials was investigated by means of the nano-indentation and the nano-scratch techniques. The nano-indentation test involved indentation as small as 30 nm in depth, produced along a 14 μm path between the fibre and the matrix. The distinct properties of the interphase region were revealed by 2–3 indents in dry materials and up to 15 indents in water aged, degraded materials. These results indicated interdiffusion in water aged interphase regions. The nano-scratch test involves moving a sample while being in contact with a diamond tip. The nano-scratch test, used in conjunction with the nano-indentation test, accurately measured the width of the interphase region. The results showed that the harder interphase region dissolved into the softer interphase region (both regions being harder/stronger than the matrix) expanding its width after aging in water.     

Correlations among micro- and macromechanical properties of composite materials based on the interphase concept

In this paper an attempt was made to define microstructural properties of carbon fiber/PP composites, with respect to fiber surface chemistry and morphology. In order to define the effects of the fiber surface sizings and morphology on the polymer microstructure, the interphase and mechanical properties of the composites, carbon fibers with similar, but not identical surface chemistry (CH and CT) were used. Characterization was performed by several techniques: SEM, POM, reflection microscopy, DSC, FTIR, XPS, contact angle measurements. For microstructural analysis, the geometrical method, method of intercept and DIF method were used. It was found that both carbon fibers have a strong influence on the nucleation mechanism and crystallization as well as on the microstructural parameters in the model and macro composites. Nucleation efficiency of the fibers has been confirmed by the nucleation parameter Q, measured by Muchova–Lednicky method and by the interfacial energy parameters. Microstructural analysis based on the photographs obtained by POM, SEM and reflection microscopy has shown that in the CH/PP model and macrocomposites the sieve-grain network was formed, which indicates better mechanical properties. The results obtained for the macromechanical properties of PP composites reinforced with CH and CT have confirmed the prediction based on micostructural analysis.     

乳腺超声断层成像系统的有限元仿真分析

本文利用有限元仿真软件COMSOL进行乳腺超声断层成像仿真,仿真模型置于水中,重建区域包含乳腺软组织和一个圆形铁块障碍物。256个换能器等角度环形分布于乳腺外部,采用一个换能器发射、其余所有换能器接收的方式进行,依次进行256次仿真来实现环形扫描。仿真得到随时间变化的二维声压分布云图,提取接收电压获得信号矩阵。利用等角扇束滤波反投影重建算法进行图像重建,仿真实验结果证明了换能器呈360?进行环形扫描的方式可行。     

纤维增强复合材料激光烧蚀效应的数值模拟

考虑材料的热解、氧化、相变及辐射和内外对流换热等物理过程,给出了激光烧蚀纤维增强复合材料的物理模型及数学模型。以碳纤维/环氧树脂复合材料为例,编程计算了材料的激光烧蚀过程,计算结果与实验结果符合得较好。计算结果表明：考虑复合材料的内对流时得到的结果更准确;较强功率密度激光辐照时,氧化对烧蚀的贡献可以忽略;功率密度一定时,烧蚀质量随时间近似为线性变化,功率密度越高,烧蚀效率越高。以辐照结束时背表面温度及烧蚀质量为目标物理量,对烧蚀过程做了参数敏感性分析,结果表明：热容及热导率对背表面温度的影响较大;树脂含量对烧蚀质量的影响较大,但其相对敏感度随激光功率密度增加而下降;激光功率密度超过1 kW/cm2时,辐射系数对烧蚀质量影响较大,但其相对敏感度随激光功率密度增加而下降。     

Discrete element simulation of localized deformation in stochastic distributed granular materials

The deformation in granular material under loading conditions is a problem of great interest currently. In this paper, the micro-mechanism of the localized deformations in stochastically distributed granular materials is investigated based on the modified distinct element method under the plane strain conditions, and the influences of the confining pressure, the initial void ratio and the friction coefficient on the localized deformation and the stability of granular materials are also studied. It is concluded, based on the numerical simulation testing, that two crossed shear sliding planes may occur inside the granular assembly, and deformation patterns vary with the increasing of transverse strain. These conclusions are in good agreement with the present experimental results. By tangential velocity profiles along the direction normal to the two shear sliding planes, it can be found that there are two different shear deformation patterns: one is the fluid-like shear mode and the other is the solid-like shear mode. At last, the influences of various material parameters or factors on localized deformation features and patterns of granular materials are discussed in detail. Supported by the Key Project of the National Natural Science Foundation of China (Grant No. 10532040)     

3D finite element simulation of explosive welding of three-layer plates

A 3D finite element model of the explosive welding process of three-layer plates with materials of steel-copper-copper is established. Based on the presented model, the bonding mechanism is simulated and analyzed, different detonation modes are also comparatively studied to indicate the driving force spread in few microseconds. The results show that the three layer plates bond together after many times of impact between the flyers and the base driven by detonation wave, which is damping rapidly at each impa...     

Numerical simulation of premixed combustion using an enriched finite element method

In this paper we present a novel discretization technique for the simulation of premixed combustion based on a locally enriched finite element method (FEM). Use is made of the G-function approach to premixed combustion in which the domain is divided into two parts, one part containing the burned and another containing the unburned gases. A level-set or G-function is used to define the flame interface separating burned from unburned gases. The eXtended finite element method (X-FEM) is employed, which allows for velocity and pressure fields that are discontinuous across the flame interface. Lagrange multipliers are used to enforce the correct essential interface conditions in the form of jump conditions across the embedded flame interface. A persisting problem with the use of Lagrange multipliers in X-FEM has been the discretization of the Lagrange multipliers. In this paper the distributed Lagrange multiplier technique is adopted. We will provide results from a spatial convergence analysis showing good convergence. However, a small modification of the interface is required to ensure a unique solution. Finally, results are presented from the application of the method to the problems of moving flame fronts, the Darrieus–Landau instability and a piloted Bunsen burner flame.     

反射声波成像测井的有限元模拟

应用有限元法对新兴的反射声波成像测井进行了数值模拟研究，计算了井旁附近存在不同倾角声阻抗不连续界面对声波的反射，使用的井内激励源为幅度加权相控线阵声波辐射器。从计算出的声全波波形上可以清楚地看到沿井壁传播的折射波和来自井旁界面的反射纵波。应用偏移叠加等数据处理技术对数值模拟波形进行了处理，从偏移剖面上反演出的反射界面的尺寸、位置和倾角等几何特性与数值模拟输入参数基本一致。     

A spectral finite element for analysis of wave propagation in uniform composite tubes

A spectral finite element model (SFEM) for analysis of coupled broadband wave propagation in composite tubular structure is presented. Wave motions in terms of three translational and three rotational degrees of freedom at tube cross-section are considered based on first order shear flexible cylindrical bending, torsion and secondary warping. Solutions are obtained in wavenumber space by solving the coupled wave equation in 3-D. An efficient and fully automated computational strategy is developed to obtain the wavenumbers of coupled wave modes, spectral element shape function, strain-displacement matrix and the exact dynamic stiffness matrix. The formulation emphasizes on a compact matrix methodology to handle large-scale computational model of built-up network of such cylindrical waveguides. Thickness and frequency limits for application of the element is discussed. Performance of the element is compared with analytical solution based on membrane shell kinematics. A map of the distribution of vibrational modes in wavelength and time scales is presented. Effect of fiber angle on natural frequencies, phase and group dispersions are also discussed. Numerical simulations show the ease with which dynamic responses can be obtained efficiently. Parametric studies on a clamped-free graphite-epoxy composite tube under short-impulse load are carried out to obtain the effect of various composite configurations and tube geometries on the response.