Propagation of guided waves in bonded composite structures with tapered adhesive layer

Adhesively bonded composites are becoming increasingly important in engineering applications due to its advantages for structural repair and integrated manufacturing of advanced composite structures. Characteristics of guided waves propagation in bonded composite structures with tapered adhesive layer are investigated in this paper. Hamilton’s principle and a semi-analytical finite element method are combined to study the wave propagation problem numerically that account for different properties of adhesive layer. Several adhesive bonded composite models are analyzed, including dimensions of adhered joints, local separation of adhesive and material degradation. Dispersion curves of different bonded states are studied numerically by accounts for effects of varying adhesive thickness. Results provided some suggestions in selecting more suitable mode for interrogating of adhesive bonded composite with different states.     

Analysis of extension propagation process of interface crack between belts of a radial tire using a finite element method

A radial tire is a very complex structure made from rubber elastomers and fiber–rubber composite materials. During its use, extension propagation of interface crack between belts can occur, which obviously affects its durability and life. In the present paper, a new mathematical model of extension propagation of interface crack in complex composite structures is presented. The model can reveal the extension propagation dependence of interface crack on the relative size of energy release rates at the left and right crack tips and on the interfacial material properties. The extension propagation model of interface crack, Irwin’s virtual crack close technique and the finite element analysis method are used together in simulating numerically the extension propagation process of a interface crack between belts of a radial tire. The present study numerical results show that the extension propagation model of interface crack proposed in this paper can more realistically characterize the complexity of the extension propagation process of interface crack in complex composite structures.     

Investigation of the local behavior of different cohesive zone models

Cohesive interface elements are well suited for three-dimensional crack propagation analyses as long as the crack path is known. This is the case e.g. in delamination analyses of laminated composite structures or failure analyses of adhesively bonded joints. Actually, they are widely used in such applications for both brittle and ductile systems. As long as the strength and fracture toughness of the material are accurately captured it is generally accepted that the shape of the cohesive law has little to no influence on the mechanical behavior of the investigated structures. However, when having a look on the local behavior of different cohesive zone models, such as stress distribution in the fracture process zone, the results exhibit certain differences. These will be studied in the present contribution. Especially the local stress distribution will be investigated and the effect on the computational efficiency will be pointed out. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Three-Dimensional Variational Analysis of Composite Structures Using Bernstein Polynomial Approximations. Report 1

The paper overviews the previous 3D variational analysis approaches and the numerical results obtained with the use of piecewise polynomial splines. A recently developed 3D displacement-assumed variational analysis approach is also described, where the Bernstein approximation polynomials of arbitrary degree are used as the shape functions for a 3D hexahedral discrete element of a composite body.     

Numerical simulation of the non‐linear crack problem with non‐penetration

Here the numerical simulation of some plane Lamé problem with a rectilinear crack under non‐penetration condition is presented. The corresponding solids are assumed to be isotropic and homogeneous as well as bonded. The non‐linear crack problem is formulated as a variational inequality. We use penalty iteration and the finite‐element method to calculate numerically its approximate solution. Applying analytic formulas obtained from shape sensitivity analysis, we calculate then energetic and stress characteristics of the solution, and describe the quasistatic propagation of the crack under linear loading. The results are presented in comparison with the classical, linear crack problem, when interpenetration between the crack faces may occur. Copyright © 2004 John Wiley & Sons, Ltd.     

Out-of-plane displacement measurement near the crack tip during a crack propagation: Validation of a 3D formulation for a specimen in PMMA loaded in mode I.

The fundamental aim of this study is the determination zone of the 3D effects and the transient one at the vicinity of the crack tip during a crack propagation in brittle materials ( PMMA ) using an optical method (Michelson interferometer). With the obtained interferograms, we can extract the phase (thus the relief) by using a new numerical approach based on the principle of images correlation between real fringes and virtual fringes. Different dynamic tests are realized by a plate loaded in mode I under a constant loading. We compare the obtained data with the two-dimensional theory of Westergaard (plane stress hypothesis) [1]. With the divergence is established, we propose a new 3D formulation, based on a formulation employed for static crack, which takes into account 3D and transient effects. For the static cracks, the 3D effects relate to a presence of the state of three-dimensional stresses. However in dynamics, the transient effects appear and are related to the crack propagation velocity. The 3D effects and transient effects lead to results equivalent to experimental ones in terms of displacement but are completely different to results given by the two-dimensional theory near the crack tip. It is possible to quantify the zone when the plane stress hypothesis is not valid according to the crack propagation speed V. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Effect of Coulomb friction on the fiber/matrix debonding and matrix cracking in unidirectional fiber-reinforced brittle-matrix composites

A model for a macroscopic crack transverse to bridging fibers is developed based upon the Coulomb friction law, instead of the hypothesis of a constant frictional shear stress usually assumed in fiber/matrix debonding and matrix cracking analyses. The Lamé formulation, together with the Coulomb friction law, is adopted to determine the elastic states of fiber/matrix stress transfer through a frictionally constrained interface in the debonded region, and a modified shear lag model is used to evaluate the elastic responses in the bonded region. By treating the debonding process as a particular problem of crack propagation along the interface, the fracture mechanics approach is adopted to formulate a debonding criterion allowing one to determine the debonding length. By using the energy balance approach, the critical stress for propagating a semi-infinite fiber-bridged crack in a unidirectional fiber-reinforced composite is formulated in terms of friction coefficient and debonding toughness. The critical stress for matrix cracking and the corresponding stress distributions calculated by the present Coulomb friction model is compared with those predicted by the models of constant frictional shear stress. The effect of Poisson contraction caused by the stress re distribution between the fiber and matrix on the matrix cracking mechanics is shown and discussed in the present analysis. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 43, No. 2, pp. 171–190, March–April, 2007.     

Analysis of crack formation in bonded lap joints using finite fracture mechanics on the basis of linear elasticity solutions.

In this work, crack formation and the corresponding failure load of bonded lap joints is analyzed. The analysis is based on linear elasticity solutions for bonded lap joints and makes use of the finite fracture mechanics. A hybrid criterion is applied that states the spontaneous formation of a crack of finite size if a stress and an energy criterion are fulfilled simultaneously. The stress distribution of a linear elasticity solution is used for the stress criterion and for the calculation of the incremental energy release rate which is necessary for definition of the energy criterion. The resulting fracture criterion is compared to literature results and shows a good agreement. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Detonation-driven fracture in thin shell structures: Numerical studies

Detonation-driven fracture of thin structures is studied numerically by a 3D discrete crack meshfree method. These types of failure mechanisms play an important role in pipes and vessels. I therefore proposed a three-dimensional meshfree method and an efficient discrete crack model to describe crack propagation. The method is based on separation of particles similar to the visibility method but its implementation is more efficient. I assume here through-thickness cracks though the method can be extended to crack growth in arbitrary directions. The load is applied as travelling pressure wave obtained from pure fluid simulation in accordance with experimental measurements. Numerical results to experimental data show good agreement.     

Prediction and Measurement of Residual Strains for a Composite Bonded Joint

A quasi-isotropic composite laminate/adherend of IM6/3501-6 and a composite bonded specimen were manufactured and tested. The bonded specimen was fabricated by postbonding composite adherends together using a 177°C adhesive resin. Predictions for the residual curing strains in the composite adherends and the adhesively bonded composite specimen were performed using a thermomechanical linearly elastic analysis. The analysis was performed using a computer program based on a polynomial spline displacement approximation method [1]. The residual strains of the specimens were measured using the moiré interferometry technique. Diffraction gratings were replicated at room temperature onto the edges of polished laminated adherends and on the edge of a fully cured adhesively bonded specimen. The specimens were cut through their entire thickness in the middle of the diffraction grating area, resulting in a redistribution of the residual curing stresses, with corresponding changes in the strain field at the edges of the cut. A full-field deformation pattern was obtained in the grating area by analyzing the recorded fringe patterns. The deformation field induced by the cut in the laminated adherends and the adhesive bondline were estimated by the linear thermomechanical analysis. A good agreement between the analysis and the experimental results was obtained.     

求解层间界面反平面剪切破坏的剪切梁模型(Ⅰ)——基本特性

在反平面剪切载荷及侧压力共同作用下引起的裂纹及裂纹扩展导致的层间界面失效,是岩土工程层间界面及砌体结构中界面层上典型的失效方式.运用弹性力学和断裂力学的理论原理,提出了能够反映上述层间界面断裂失效问题力学特性的剪切梁模型.文中采用具有应力软化特性的“粘性裂纹”(内聚力裂纹)模型来表述层间裂纹前方损伤过程区的本构行为.对通过粘性层结合在一起的两个弹性板,在反平面剪切载荷及侧压力共同作用下的力学行为作了解析分析计算,研究了层间界面裂纹扩展规律.     

自由来流湍流与三维壁面局部粗糙诱导平板边界层不稳定T-S波的数值研究

采用直接数值模拟（DNS）方法,研究了在自由来流湍流与三维壁面局部粗糙作用下平板边界层内诱导产生不稳定T-S波的物理问题.数值结果可知,在平板边界层内发现了二维和三维T-S波组成的波包空间序列以及求得了波包向前传播的群速度大小,从而证明了自由来流湍流与三维壁面局部粗糙作用是激励平板边界层内诱导产生不稳定T-S波的一种机制.随后,建立了平板边界层内被激发的二维和三维T S波的初始幅值与自由来流湍流度,三维壁面局部粗糙的流向长度、展向宽度及法向高度之间的关系.这一问题的深入研究,进一步完善了流动稳定性与湍流理论.     

一种基于校正无线电传播时间的室内三维定位模型

对室内终端进行基于无线通信基站的三维定位时,由于无线电在传播过程中,存在建筑物或树木遮挡、反射、折射等物理现象,导致基站到终端传播时间的测量值与精确值之间存在误差.为了减少上述误差对定位精度的影响,运用无线定位原理建立了一种基于校正无线电传播时间的改进的室内三维定位模型.通过对2016年全国研究生数学建模问题C题所提供的不同场景的数据分析,发现基站与终端无线电传播时间的测量值与其精确值之间存在线性关系,而且同一场景下近似有相同的线性关系,场景不同线性关系一般不同.基于这一现象,对基本的定位模型进行了合理的修正形成了改进的定位模型,数值实验表明改进的定位模型有很好的定位精度和鲁棒性.     

K型管状接头随机疲劳强度和裂纹扩展规律的研究

分析了K型焊接管状接头受轴向和面外弯曲载荷作用下的随机疲劳问题。通过将焊趾处的表面裂纹的初始尺寸和材料常数作为随机变量处理,并计及焊缝的影响,共产生500个随机样本,最终得到裂纹扩展寿命和裂纹形状变化影响的统计计算结果,并与有关实验数据比较,给予了回归分析。同时,也考察了裂纹扩展规律。     

Analysis solution method for 3D planar crack problems of two-dimensional hexagonal quasicrystals with thermal effects

An analysis solution method (ASM) is proposed for analyzing arbitrarily shaped planar cracks in two-dimensional (2D) hexagonal quasicrystal (QC) media. The extended displacement discontinuity (EDD) boundary integral equations governing three-dimensional (3D) crack problems are transferred to simplified integral-differential forms by introducing some complex quantities. The proposed ASM is based on the analogy between these EDD boundary equations for 3D planar cracks problems of 2D hexagonal QCs and those in isotropic thermoelastic materials. Mixed model crack problems under combined normal, tangential and thermal loadings are considered in 2D hexagonal QC media. By virtue of ASM, the solutions to 3D planar crack problems under various types of loadings for 2D hexagonal QCs are formulated through comparison to the corresponding solutions of isotropic thermoelastic materials which have been studied intensively and extensively. As an application, analytical solutions of a penny-shaped crack subjected uniform distributed combined loadings are obtained. Especially, the analytical solutions to a penny-shaped crack subjected to the anti-symmetric uniform thermal loading are first derived for 2D hexagonal QCs. Numerical solutions obtained by EDD boundary element method provide a way to verify the validity of the presented formulation. The influences of phonon-phason coupling effect on fracture parameters of 2D hexagonal QCs are assessed.     

夹层压电材料中垂直于界面的共线双裂纹动力学问题分析

采用Schmidt方法分析了在简谐反平面剪切波作用下,两个半空间夹层压电材料中的共线裂纹的动力学行为．压电材料层内裂纹垂直于界面,电边界条件假设为可导通．通过Fourier变换,使问题的求解转换为两对三重积分对偶方程．通过数值计算,给出了裂纹的几何尺寸、压电材料常数、入射波频率等对于应力强度因子的影响．结果表明,在不同的入射波频率范围,动力场将阻碍或促使压电材料内裂纹的扩展．与不可导通电边界条件相比,导通裂纹表面的电位移强度因子比不可导通裂纹的电位移强度因子要小许多．     

Analysis of Elastomeric Composites Based on Fiber Systems. 4. 3D Composites

The elastic properties of 3D elastomeric composite materials under large deformations are considered. The investigation is based on the structural macroscopic theory of stiff and soft composites. The results of micro- and macromechanical analyses of composite materials with compressible and poorly compressible matrices are presented. The character of interaction between the fibers of various reinforcing systems in these matrices is revealed. The deformation characteristics of the composites in tension and shear are presented as functions of their orientation and loading parameters. The evolution of the configuration of a composite material with a compressible matrix during loading is traced.     

Comparison of electromigration simulation in test structure and actual circuit

With the rapid increase in circuit complexity, accurate reliability simulator is necessary as reliability testing for fabricated circuit is progressively more time and resource consuming. Simple 2D electromigration (EM) simulator has many limitations and most of the 3D EM simulations in the literature are using simple line-via structure which is only part of the real circuit structure. In this paper, a thorough comparison between simple 3D line-via structure model and 3D circuit model under different test conditions is performed using class-AB amplifier as an example, and the results showed that simple line-via structure simulation may not always correctly represent the real circuit failure site.     

Long-term failure of a layered viscoelastic composite material with a crack under a time-dependent load

The long-term failure of a layered viscoelastic composite caused by precritical propagation of a coin-shaped crack is studied. It is assumed that the crack is located inside a viscoelastic layer (the layer of binder) parallel to the layer orientation. The crack development due to stretching of the composite massive by uniformly distributed external forces increasing with time is described. It is assumed that these forces act perpendicularly to the plane of crack propagation. The investigation is carried out within the framework of Boltzmann-Volterra linear theory for resolving integral operators with difference kernels describing the deformation of a material with time-dependent rheological properties. An irrational function of the viscoelastic integral operator is presented in the form of a proper continued fraction and transformed using the method of operator continued fractions. Numerical solutions are obtained for resolving integral operators with the kernel in the form of Rabotnov exponential-fractional function. The kinetics of crack growth with a prefailure zone commensurable with the crack length is described. A comparison with the results obtained in terms of the concept of thin structure of the crak tip is given.Timoshenko Institute of Mechanics, Ukrainian National Academy of Sciences, Kiev, Ukraine. Translated from Mekhanika Kompozitnykh Materialov, Vol. 36, No. 4, pp. 545–558, July–August, 2000.     

双材料界面运动Griffith裂纹

本文分析了位于两个拼接的半无限各向同性弹性体界面上的运动Ｇｒｉｆｆｉｔｈ裂纹的应力强因子。