Comparative study on orthotropic solid waves by time-domain BEM and dynamic photoelasticity

Experimental research and numerical analysis are two basic tools in the study of wave propagation problems in orthotropic media. In this paper, an experimental method, namely dynamic orthotropic photoelasticity, which studies the dynamic behavior of orthotropic materials on a macroscopic scale by employing orthotropic birefringent materials, is established. Meanwhile, a numerical method, namely time domain boundary element method (BEM) for wave propagation in orthotropic media, is also presented. The two methods are used together in the analysis of semi-infinite orthotropic plates with and without a circular hole modeled by a unidirectional fiber-reinforced composite under impact loading. The propagation, reflection and diffraction of stress waves in the orthotropic media are recorded experimentally and investigated. Time histories of birefringent fringe orders or stresses for specific points of the plates are obtained, respectively, from the two methods and compared with each other. The comparative study demonstrates the applicability and accuracy of the two methods for wave propagation problems in orthotropic media.     

A 2.5D-Fourier-BEM model for vibrations in a tunnel running through layered anisotropic soil

A boundary element model of a tunnel running through horizontally layered soil with anisotropic material properties is presented. Since there is no analytical fundamental solution for wave propagation inside a layered orthotropic medium in 3D, the fundamental displacements and stresses have to be calculated numerically. In our model this is done in the Fourier domain with respect to space and time. The assumption of a straight tunnel with infinite extension in the x direction makes it possible to decouple the system for every wave number k_x, leading to a 2.5D-problem, which is suited for parallel computation. The special form of the fundamental solution, resulting from our Fourier ansatz, and the fact, that the calculation of the boundary integral equation is performed in the Fourier domain, enhances the stability and efficiency of the numerical calculations.     

Stress and strength analysis of composite joints using direct boundary element method

In this paper, the stress distribution and the strength of bolted joints of orthotropic composite plates under uniform loading are investigated. A direct boundary element method with quadratic isoparametric elements in conjunction with a fundamental solution derived by Rizzo and Shippy¹ is used. Plates with rigid bolts are treated as two-dimensional plane stress problems, and the bolt size is considered to be identical to the hole dimension. The prediction of the laminate strength is based on the Yamada-Sun² failure criterion. Some numerical results for various edge distances and material properties are presented for illustrative purposes.     

Wave propagation analysis in inhomogeneous piezo‐composite layer by the thin‐layer method

The thin‐layer method (TLM) is used to study the propagation of waves in inhomogeneous piezo‐composite layered media caused by mechanical loading and electrical excitation. The element is formulated in the time‐wavenumber domain, which drastically reduces the cost of computation compared to the finite element (FE) method. Fourier series are used for the spatial representation of the unknown variables. The material properties are allowed to vary in the depthwise direction only. Both linear and exponential variations of elastic and electrical properties are considered. Several numerical examples are presented, which bring out the characteristics of wave propagation in anisotropic and inhomogeneous layered media. The element is useful for modelling ultrasonic transducers (UT) and one such example is given to show the effect of electric actuation in a composite material and the difference in the responses elicited for various ply‐angles. Further, an ultrasonic transducer composed of functionally graded piezoelectric materials (FGPM) is modelled and the effect of gradation on mechanical response is demonstrated. The effect of anisotropy and inhomogeneity is shown in the normal modes for both displacement and electric potential. The element is further utilized to estimate the piezoelectric properties from the measured response using non‐linear optimization, a strategy that is referred to as the pulse propagation technique (PPT). Copyright © 2005 John Wiley & Sons, Ltd.     

Detection and Modelling of Nonlinear Elastic Response in Damaged Composite Structures

In this paper the nonlinear material response of damaged composite structures under periodic excitation is experimentally and numerically investigated. In particular, the nonlinear wave propagation problem was numerically analysed through a finite element model able to predict the nonlinear interaction of acoustic/ultrasonic waves with damage precursors and micro-cracks. Such a constitutive model is based on the Landau’s semi-analytical approach to account for anharmonic effects of the medium, and is able to provide an understanding of nonlinear elastic phenomena such as the second harmonic generation. Moreover, Kelvin tensorial formulation was used to extend the wave propagation problem in orthotropic materials to the 3D Cartesian space. In this manner, the interaction of the stress waves with the 3D crack could be analysed. This numerical model was then experimentally validated on a composite plate undergone to impact loading. Good agreement between the experimental and numerical second harmonic response was found, showing that this material model can be used as a simple and useful tool for future structural diagnostic applications.     

孔口缝合补强对含孔层板应变集中影响的实验研究

对复合材料开口缝合补强结构进行了实验研究。测试了不同缝合参数(针距、行距、边距、单重和双重缝合) 补强的含孔复合材料层板的拉伸强度, 研究了孔边应力集中、应变集中对强度、刚度等力学性能参数的影响, 分析讨论了孔边及邻近区域应变集中及应变分布的规律, 得到不同缝合参数、孔边不同位置以及不同载荷条件下的应变集中系数。结合实验结果和分析讨论, 给出了含孔复合材料层板缝合补强的缝合设计参数。      

Design of composite structures reinforced curvilinear fibres using FEM

This paper describes a method of modelling a curvilinear reinforcement structure, for a composite plate with a hole that allows trajectories of fibres to be adapted to geometric discontinuities (holes, notches, bolts, etc.). For this method, it is assumed that the trajectories of fibres are curvilinear and continuous, as well as located along the trajectories of maximum principal stress. On the basis of these trajectories, the functionally graded material is simulated by means of the finite element method (FEM). Each element of this structure has its own mechanical properties, depending on the fibre direction and a change in the distance between the fibres. It is demonstrated that the maximum value of the stress concentration factor in the fibre direction for the plate with the curvilinear reinforcement structure reduces by 3.2 times in comparison with the same plate with a rectilinear reinforcement structure (orthotropic material).     

爆炸荷载下缺陷介质裂纹扩展规律数值分析研究

利用爆炸加载数字激光动态焦散线试验系统,同时借助ABAQUS有限元分析中内聚力模型数值计算方法,研究了爆炸应力波作用下缺陷介质裂纹扩展规律,并将试验结果与数值计算结果进行了对比。研究表明:在爆炸应力波作用下预制缺陷两端产生了两条翼裂纹A、B,扩展长度基本相同,方向垂直于预制缺陷。两条翼裂纹的扩展基本是对称的,只是在尾端发生轻微翘曲;翼裂纹扩展速度先增大至峰值又振荡减小,之后又增大至第二个较小的峰值,然后又减小,这种变化趋势和裂纹尖端应力强度因子KⅠ保持一致;扩展角β为85°时,计算结果较为接近试验,内聚力模型为动态裂纹扩展的研究提供了一种有效的方法。     

Photoelastic studies for composite dynamics

The orthotropic birefringent composites suitable for the study of dynamic photoelasticity are investigated and the determination of residual birefringence in the materials is briefly described. A stress-optic law for dynamic photoelastic analysis of orthotropic birefringent composites is postulated based on the static stress-optic law of Hyer and Liu. Subsequently, practical methods of calibrating dynamic mechanical constants and dynamic stress-fringe values are proposed. With dynamic strain measurements and time domain BEM for anisotropic media, three calibration specimens (0°, 90° and 45°) are used to verify the proposed stress-optic law in uniaxial-stress fields and a plate of unidirectional fiber-reinforced birefringent composite under impact loading, with the loading direction parallel, perpendicular and at 45° to the fiber direction, is analyzed to verify the proposed stress-optic law in biaxial-stress fields. Results show that the dynamic stress-optic law for orthotropic birefringent composites is valid in the two cases.     

Numerical and analytical calculation of the orthotropic heat transfer properties of fibre reinforced materials

This paper is on the investigation of the orthotropic heat transfer properties of unidirectional fibre reinforced materials. The orthotropic effective thermal conductivity of such composite materials is investigated based on two different approaches: the finite element method as a representative for numerical approximation methods and an analytical method for homogenised models based on the solution of the respective boundary value problem. It is found that fibre reinforced composites possess strong orthotropic heat transfer properties, which are getting more distinctive with increasing deviation of the thermal conductivities of matrix and reinforcements. Furthermore, the effect of small perturbations of the periodic configuration of fibres in the matrix on the thermal conductivity is investigated.     

A modified analysis for stress transfer in fibre-reinforced composites with bonded fibre ends

The elastic stress transfer from the matrix to the embedded fibre in fibre-reinforced composites has been analysed previously when the loading direction is parallel to the fibre axis and the fibre is bonded to the matrix. Stress transfer occurs both at the interface along the fibre length and at the ends of the fibre. However, the boundary condition at the bonded ends is ambiguous, and various assumptions have been made to obtain solutions for this stress transfer problem. To satisfy more rigorously the boundary condition for the bonded ends, a new technique of assuming imaginary fibres in the composite is proposed in the present study. Compared to the previous analytical solution, the present analytical solution bears more physical meaning and is in better agreement with numerical and experimental results     

Finite element method and experimental investigation on the residual stress fields and fatigue performance of cold expansion hole

Cold expansion is an efficient way to improve the fatigue life of an open hole. The residual stress fields of cold expansion holes are vital for key components designing, manufacturing and fatigue properties assessment. In this paper, three finite element models have been established to study the residual stress fields of cold expansion hole, experiments were carried out to measure the residual stress of cold expansion hole and verify simulation results. Three groups of specimens with different cold expansion levels are examined by fatigue test. The fracture surfaces of specimens are observed by scanning electron microscope. The finite element method (FEM) results show, with interference values develop, the maximum values of circumferential residual compressive/tensile stresses increase in “infinite” and “finite” domain, and a higher positive stress values are obtained at the boundary of “finite” domain. The effects of the friction between the mandrel and the hole’s surface and two cold expansion techniques on the distribution of residual stress is local, which only affects the radial residual stress around the maximum value and the circumferential residual stress near the hole’s edge. Crack always initiates near entrance face and the crack propagation speed along transverse direction is faster than that along axial direction.     

Analyse the role of the non‐singular stress in brittle fracture by BEM coupled with eigen‐analysis

A coupled model resulting from the boundary element method and eigen‐analysis is proposed in this paper to analyse the stress field at crack tip. This new combine method can yield several terms of the non‐singular stress in the Williams asymptotic expansion. Then the maximum circumferential stress (MCS) criterion taken the non‐singular stress into account is introduced to predict the brittle fracture of cracked structures. Two earlier experiments are re‐examined by the present numerical method and the role of the non‐singular stress in the brittle fracture is investigated. Results show that if more terms of non‐singular stress are taken into account, the predicted crack propagation direction and the critical loading by MCS criterion are much closer to the existing experimental results, especially for dominating mode II loading conditions. Moreover, numerical results manifest that Williams series expansion can describe the stress field further from the crack tip if more non‐singular stress terms are adopted.     

分层对复合材料机械连接结构承载能力的影响

针对含孔边分层复合材料沉头螺栓连接结构,通过挤压试验及有限元仿真,研究了孔边分层对复合材料连接结构力学性能的影响。通过连接孔的挤压试验,得到了不同类型试验件的承载能力与破坏模式。有限元仿真中,基于ABAQUS有限元分析软件建立了复合材料机械连接的三维有限元模型,进行复合材料渐进失效损伤模拟,并采用内聚力单元来模拟预制分层。有限元计算得到载荷-位移曲线和变形模式与试验吻合较好,从而验证了有限元模型的有效性。在此基础上,分析了含孔边分层的复合材料机械连接结构的破坏机制,并研究了分层位置、分层面积大小和分层形状对该结构承载能力的影响。研究表明：复合材料的破坏始于沉头孔中的直孔区域,且当预制分层位于直孔区域时,结构的承载能力最低;分层形状为圆形和正方形时,会严重影响结构的承载能力,分层形状为椭圆形时,对承载能力影响较低。无论分层形状如何变化,分层总是从受挤压的一侧开始,以半圆弧的形状向受挤压方向进行扩展。     

Concise formula for tensile strength of knitted fabric reinforced composite

Abstract

A simple one-dimensional formula, as concise as Krenchel's model for stiffness calculation, is presented in this paper to calculate the ultimate tensile strength of a knitted fabric reinforced composite in the loading direction. Its deteriorated form can be used to determine the off axial strength of a unidirectional composite. The formula has been developed based on the understanding of internal stresses generated in the constituent fibre and matrix materials. These stresses are explicitly expressed as functions of the overall applied load, and only the stress components in the loading direction are retained. The ultimate strength of the composite is defined as the overall applied stress under which one of the constituent materials fails. The proposed formula has been applied to calculate the off axial strength of a unidirectional composite and the tensile strengths of two plain weft knitted glass fibre fabric reinforced epoxy matrix composites subjected to wale and course direction loads. All the calculated strengths are in reasonable agreement with experimental data.     

Random fatigue life prediction of carbon fibre-reinforced composite laminate based on hybrid time-frequency domain method

To evaluate fatigue life of composite laminate with hole under random loading, a random fatigue life prediction model is established by hybrid time-frequency domain method in this paper. Firstly, dynamic response of composite laminate is obtained from FE model in frequency domain. Secondly, root mean square of stress of six stress components of critical damage point in frequency domain are transferred to stresses in time domain. At last, 3D Tsai–Hill static failure criterion is adopted to convert the multiaxial stress into the uniaxial equivalent stress. Fatigue life is predicted by equivalent stress fatigue life code. The method is validated with the random vibration fatigue test of carbon fibre-reinforced composite laminate. Numerical results are compared with random fatigue experiments which show good agreement with numerical results.     

Finite element micromechanical modelling of a unidirectional composite subjected to axial shear loading

A micromechanical model is presented which predicts the behaviour of a unidirectional composite subjected to axial shear load using standard finite elements. Only a three-dimensional model can handle the necessary shear loading boundary conditions when using such elements. These boundary conditions give shear stress components but no direct stress components within the composite. A parametric study is carried out on unidirectional carbon fibre/epoxy within the linear elastic regime of both constituents. The study reveals that the most critical parameters controlling the axial shear modulus of the composite are matrix modulus and fibre volume fraction whilst the stress state in the composite is mainly controlled by geometrical features of the composite, i.e., fibre volume fraction and fibre spacing. Comparison between the predicted axial shear modulus based on the concentric cylinder model and the current finite element model shows good agreement for low and intermediate fibre volume fractions. Both predictions lie within the Hashin bounds and the finite element prediction tends to be closer to the upper Hashin bound for fibre volume fractions greater than 60%. The initial tangent shear modulus predicted with the finite element model and that measured differ by less than 2.5%. The non-linear shear stress/strain response of the composite material is also predicted and agreement with the experimental results is good.     

不同聚能爆破模式应力波传播及裂纹扩展规律研究

为研究双向聚能拉伸爆破应力波传播及裂纹演化规律,采用理论分析、数值模拟等方法,研究单孔爆破、连孔爆破、间隔爆破爆炸应力波的传播形式和裂纹扩展规律。结果表明,连孔聚能爆破和间隔聚能爆破的裂纹扩展长度都在水平径向上达到了900 mm,而单孔聚能爆破仅600 mm,说明连孔聚能爆破时应力波的叠加使切向拉应力增大,聚能方向形成了与孔心连线相平行的裂纹,裂纹开裂延伸,直至贯通。间隔爆破时随着应力波的传播,裂纹尖端张拉应力区也不断向前推移,促使裂纹继续发展,直至贯通。该项研究在岩石成型爆破中提供了有效真实的参考依据,具有广阔的应用前景。     

Free edge delamination in carbon-epoxy laminates: a novel numerical/experimental approach

A geometrically and physically nonlinear finite element approach is presented for the analysis of mode-I and mixed-mode free edge delamination in composite laminates which properly accounts for the effects of initial thermal and hygroscopic stresses. A constitutive model based on nonlinear fracture mechanics is used to describe delamination. An orthotropic softening plasticity model is used to determine the initiation and propagation of delamination. Although the orthotropic yield surface is based on stresses, it is proved, that, in combination with a softening type of post-failure response controlled by the fracture toughness, the approach results in a unique and physically realistic solution upon mesh refinement. The results from the nonlinear finite element computations, including predictive analysis, are compared with mode-I and mixed-mode free edge delamination experiments. This comparison shows that the numerical results are within 10% of the experimental data.