含裂纹复合材料板的应力计算

针对含裂纹的复合材料板，根据非均质各向异性弹性理论和复变函数理论，通过保角映射方法建立精确的边界条件，解决了裂纹的边界条件问题。建立了基于准确边界条件的边界积分方程，对裂纹周围应力在不同的外载荷及不同位置的情况下进行了仿真计算，得到了含裂纹复合材料板裂纹周围应力场的精确解析解。     

Stress singularities in dissimilar orthotropic composites containing an interlaminar crack

The problem of an interlaminar crack in dissimilar orthotropic composite materials under in-plane and anti-plane loading conditions is investigated. In the analytical model, orthotropic half-spaces are assumed to be bound together by a matrix interlayer which represents the matrix-rich interlaminar region in the fiber-reinforced composite laminate. The crack is embedded within the interlayer. With the utilization of the stiffness matrix approach, a system of singular integral equations of the first kind is derived for the current mixed boundary value problem. Numerical results are obtained for the interlaminar crack in a [0°/90°] fibrous composite laminate subjected to three basic loadings in fracture mechanics. Under each applied loading, variations of major and coupling stress intensity factors with respect to relative crack size, crack location, and fiber volume fraction are illustrated.     

Effect of fiber orientation on interfacial fracture toughness for adhesively bonded composite plates

In this study, interfacial fracture toughness was investigated experimentally and numerically in laminated composite plates with different fiber reinforcement angles bonded with adhesive. The composite plates are four-layered and the layer sequence is [0º/θ]_s. DCB test was applied to composite plates reinforced with epoxy resin matrix and unidirectional carbon fiber. The experimental sample model for the DCB test was made using the ANSYS finite element package program. In the numerical study, four layered composites were prepared in three dimensions. Under critical displacement value; mode I fracture toughness at the crack tip was calculated using VCC (virtual crack closure) technique. Numerical values consistent with experimental results have presented in graphical forms. At 60o and 75° the greatest fracture toughness was obtained. In addition, numerical results have shown that fiber orientation prevents the uniform distribution of stress on the interface crack tip and causes stress accumulation, especially at the edge of the plate.

     

The effect of bridging on fatigue crack growth behavior in Aramid Patched Aluminum Alloy(APAL)

A new hybrid composite (APAL: Aramid Patched Aluminum Alloy), consisting of a 2024-T3 aluminum alloy plate sandwiched between two aramid/epoxy laminate (HK 285/RS 1222), was developed. Fatigue crack growth behavior was examined at stress ratios of R=0.2, 0.5 using the aluminum alloy and two kinds of the APAL with different fiber orientation (0°/90° and 45° for crack direction). The APAL showed superior fatigue crack growth resistance, which may be attributed to the crack bridging effect imposed by the intact fibers in the crack wake. The magnitude of crack bridging was estimated quantitatively and determined by a new technique on basis of compliances of the 2024-T3 aluminum alloy and the APAL specimens. The crack growth rates of the APAL specimens were reduced significantly as comparison to the monolithic aluminum alloy and were not adequately correlated with the conventional stress intensity factor range(ΔK). It was found that the crack growth rate was successfully correlated with the effective stress intensity factor range (ΔK _eff =K _br -K _ct ) allowing for the crack closure and the crack bridging. The relation between da/dN and theΔK _eff was plotted within a narrow scatter band regardless of kind of stress ratio (R=0.2, 0.5) and material (2024-T3 aluminum alloy, APAL 0°/90° and APAL±45°). The result equation was as follow:da/dN=6.45×10⁻⁷(ΔK _eff )^2.4.     

Dynamic mixed mode crack propagation behavior of structural bonded joints

The stress field around the dynamically propagating interface crack tip under a remote mixed mode loading condition has been studied with the aid of dynamic photoelastic method. The variation of stress field around the dynamic interface crack tip is photographed by using the Cranz-Shardin type camera having 10⁶ fps rate. The dynamically propagating crack velocities and the shapes of isochromatic fringe loops are characterized for varying mixed load conditions in double cantilever beam (DCB) specimens. The dynamic interface crack tip complex stress intensity factors,K ₁ andK ₂, determined by a hybrid-experimental method are found to increase as the load mixture ratio of y/x (vertical/horizontal) values. Furthermore, it is found that the dynamically propagating interface crack velocities are highly dependent upon the varying mixed mode loading conditions and that the velocities are significantly small compared to those under the mode I impact loading conditions obtained by Shukla (Singh & Shukla, 1996a, b) and Rosakis (Rosakis et al., 1998) in the USA.     

Improved modeling of the effects of thermal residual stresses on single fiber pull-out problem

The single fiber pull-out technique has been commonly used to characterize the mechanical behavior of fiber/matrix interface in fiber reinforced composite materials. In this study, an improved analysis considering the effect of thermal residual stresses in both radial and axial directions is developed for the single fiber pull-out test. It is found to have the pronounced effects on the stress transfer properties across the interface and the interfacial debonding behavior.     

Analytical study on elastic transition in short-fiber composites for plane strain case

An analytical approach for short-fiber-reinforced composites is developed for three-dimensional (3D) elastic stress field distribution subjected to an applied axial load. Two sets of exact displacement solutions for matrix and fiber, which are respectively called far-field and transient solutions, are derived based on the theory of elasticity. The superposition state of these solutions are then used to obtain the analytical expressions for the 3D stress field components over the entire composite system, including the fiber end region, through the adding imaginary fiber technique. The fiber/matrix 3D stress field components fully satisfy the equilibrium and compatibility conditions in the theory of elasticity. The stress field components also satisfy the overall boundary, interface continuity, and axial force equilibrium conditions. The analytical results obtained are then validated by finite element method modeling.     

小范围屈服条件下复合材料裂纹尖端塑性区分析

基于复合材料力学,推导Tsai-Hill强度准则在平面应力和平面应变条件下的一般表达式,得到了小范围屈服条件下,含中心裂纹无限大板Ⅰ型裂纹、Ⅱ型裂纹和Ⅰ/Ⅱ复合型裂纹尖端塑性区的解析解。针对不同裂纹倾角及泊松比 和,对裂尖塑性区进行了计算和分析。结果表明平面应变条件下塑性区范围小于平面应力条件下塑性区范围,参数、和 对复合材料裂尖塑性区范围和形状有明显的影响,不同的参数值得到的塑性区结果差别很大。另外,该解既适用于各向异性复合材料,也适用于各向同性材料。     

积分方程法对含复杂孔形复合材料板孔边应力分布的研究

根据非均质各向异性弹性理论对含复杂孔形复合材料板进行孔边应力分析,解决复杂孔形的边界条件问题.建立基于准确的边界条件的边界积分方程,最终得到开口结构的应力分布,给出含六边形、矩形和机翼检修孔复合材料板的精确解析解,并用有限元方法进行对比计算.平面应力场借助保角映射的方法通过复变应力函数得到.     

Dynamic crack growth in TDCB specimens

Dynamic crack propagation in tapered double cantilever beam (TDCB) specimens is analysed via beam theory and the finite element method. Steady state and transient solutions of the energy release rate G are given for various load conditions. Finite element analysis is performed to obtain the dynamic G at given crack speed or the crack history for a given fracture toughness. The stress wave effects on the dynamic G are discussed. The beam solutions are compared with the finite element results and some experimental phenomena are explained.     

基于HyperWorks 的不同铺层方式复合材料剪切强度有限元分析

剪切强度和剪切韧性是反映复合材料构件在复合受力状态下承载能力及耗能能力的重要指标,不同铺层方式的单向玻璃纤维与短切玻璃纤维混杂增强复合材料层合板的层间剪切性能有明显差异。文中基于HyperWorks 商用有限元软件建立了精确的复合材料层合板模型,通过数值模拟分析不同铺层方式复合材料层合板的层间剪切性能。研究结果表明,铺层材料对复合材料层合板的层间剪切性能影响较大,而铺层顺序对复合材料层合板的层间剪切性能影响较小。     

Numerical investigation of the stress field near a crack normal to ceramic-metal interface

Ceramic-metal interfaces are often present in composite materials. The presence of cracks has a major impact on the reliability of advanced materials, such as fiber or particle reinforced ceramic composites, ceramic interfaces and laminated ceramics. The understanding of the failure mechanisms is very important, as is as the estimation of fracture parameters at the tip of the crack approaching an interface and crack propagation path. A cracked sandwich plate loaded with axial uniform normal stress was numerically investigated using plane strain Finite Element Analysis. The numerical results for the singularity orders were compared with the analytical solution. The influences of the material combination and crack length on the radial and circumferential stresses and displacement distributions were investigated. The Stress Intensity Factors were determined based on numerical results using a displacement extrapolation method. The results for the non-dimensional stress intensity factors show that at lower crack lengths the influence of material mismatch is lower, but this influence increases with increasing crack length.     

Numerical study on crack propagation in functionally graded CNT-reinforced composite plates

This paper presents a numerical method for simulating the crack propagation in functionally graded carbon nanotube-reinforced composite (FG-CNTRC) plates. The numerical method is based on 2-D natural element method (NEM) which can overcome the inherent demerits of FEM and conventional meshfree methods. The 3-D displacement field of cracked orthotropic plate is formulated using the (1, 1, 0)* hierarchical model and approximated by 2-D NEM. The thickness-wise mixed-mode stress intensity factors (SIFs) are computed using the modified interaction integral I^(1,2) and the 2-D complex-valued crack-tip singular fields. The crack propagation angle is determined by the modified maximum circumferential stress (MCS) criterion, and the crack trajectories are predicted by an incremental crack propagation simulation scheme. The present numerical method is verified from the comparison of predicted crack trajectories with the published reference solutions. Moreover, using the developed numerical method, the crack trajectory characteristics of FG-CNTRC plates are parametrically investigated with respect to the major parameters. From the parametric investigation, it is found that the crack trajectories of FG-CNTRC are significantly influenced by the material orientation angle and the stiffness ratio. But, the effects of the initial crack angle and the volume fraction and volume fraction pattern of CNTs are not remarkable.

     

不同铺层转角T700/E44 复合材料拉伸强度有限元分析

碳纤维复合材料的失效行为与复合材料内部的应力状态有关,不同铺层转角的单向碳纤维复合材料层合板的性能具有明显差异。文中利用HyperWorks 商用有限元软件建立了T700/E44 复合材料层合板拉伸模型,基于Chang-Chang 复合材料失效模型对不同铺层转角复合材料层合板的 X 向及 Y 向拉伸性能进行了数值模拟分析。研究结果表明,复合材料层合板以45° 铺层转角对称结构层合时,复合材料有着最佳的综合拉伸性能。这对高性能雷达中复合材料部件的铺层结构设计具有重要的指导意义。     

Mechanical behavior and numerical estimation of fracture resistance of a SCS6 fiber reinforced reaction bonded S13N4 continuous fiber ceramic composite

Continuous fiber ceramic composites (CFCCs) have advantages over monolithic ceramics: Silicon Nitride composites are not well used for application because of their low fracture toughness and fracture strength, but CFCCs exhibit increased toughness for damage tolerance, and relatively high stiffness in spite of low specific weight. Thus it is important to characterize the fracture resistance and properties of new CFCCs materials. Tensile and flexural tests were carried out for mechanical properties and the fracture resistance behavior of a SCS6 fiber reinforced Si₃N₄ matrix CFCC was evaluated. The results indicated that CFCC composite exhibit a rising R curve behavior in flexural test. The fracture toughness was about 4.8 MPa m^1/2 , which resulted in a higher value of the fracture toughness because of fiber bridging. Mechanical properties as like the elastic modulus, proportional limit and the ultimate strength in a flexural test are greater than those in a tensile test. Also a numerical modeling of failure process was accomplished for a flexural test. This numerical results provided a good simulation of the cumulative fracture process of the fiber and matrix in CFCCs.     

Micromechanics analysis of progressive failure in cross-ply carbon fiber/epoxy composite under uniaxial loading

Three-dimensional micromechanics models were created for cross-ply carbon fiber/epoxy composite with a layer stacking-sequence arranged in [0/90]_s. Elasto-plastic finite element (FE) analysis was performed to study the effects of thermal residual stress and the stress redistribution as individual fiber fractures. The modified Rice and Tracey (RT) void growth model was used to predict the location of transverse matrix crack. The stress amplification factors (SAF) in intact fibers adjacent to a fractured fiber were calculated and compared with the planar array composite. The FE results show that small defects have already formed in curing process, and ply-delamination is likely to occur near the comer of free-edges. The transverse matrix crack was predicted to occur near the fiber fracture location in the models having little inter-fiber spacing.     

Enriched finite element method for three-dimensional viscoelastic interface crack problems

The enriched finite element method is developed for three-dimensional problems of an interface crack between elastic and viscoelastic (including dissimilar viscoelastic) materials. According to the displacement fields of elastic interface crack, the displacement fields of viscoelastic interface crack are derived through the correspondence principle. By incorporating the displacement expressions into the displacement model of regular element, the incremental formulations of enriched element are derived. The stress intensity factors and strain energy release rates can be solved based on the enriched degree of freedoms. A 3-D through interface crack at the center of jointed dissimilar viscoelastic plate subjected to remote tension and a quarter-circular viscoelastic interface corner crack subjected to uniform thermal loading was investigated using the enriched finite element method. It is shown that the present solutions are consistent with the analytical solutions, which indicates the present method is correct and efficient.

     

Fatigue crack propagation behavior at a notch for needled C/SiC composite under tension-tension loading

Fatigue test of a needled C/SiC composite with a notch under tension-tension cyclic loading was completed, and the main fatigue crack propagation curve of the needled composite was obtained by the in situ observation of the fatigue process. By analyzing the influence of the failure number and distribution on the tensile loading subjected by 0° fiber bundles, the relationship between the main fatigue crack propagation and the distribution of 0° fiber bundles in the needled composite was established. By observing the fracture microstructure (especially the distribution of 0° fiber bundles) of the needled composite through scanning electron microscopy, the reasons for the varying fatigue resistance of different notched specimens were also explained. In addition, acoustic emission (AE) was also used to analyze the AE energy characteristics during the fatigue crack propagation process of the needled composite.

     

On strain energy release rates for interfacial cracks

The bimaterial constant ε is necessarily used in the interfacial crack problems. Some authors tried to neglect the effects of the bimaterial constant ε. To investigate the effects of the bimaterial constant ε, the individual strain energy release rates,G _I ^* andG _II ^*, which are obtained by neglecting the bimaterial constant ε, are examined. Three examples were investigated to see the importance of the effects of the bimaterial constant ε. Firstly, the analytical results of a center interfacial crack between two dissimilar materials in an infinite plate are illustrated for various loading conditions. The phase angles of a center interfacial crack are also examined to check the importance of the bimaterial constant ε. Secondly, the individual energy release rates of a center crack paralleling an interface are examined. Thirdly, the finite element results of a four-point bending beam with two symmetrical cracks paralleling an interface are illustrated. Considering the analytical and numerical results, we can see that the bimaterial constant ε is an important factor in the interfacial crack problem, which can not be neglected.