A multilayer hybrid-stress finite element analysis of a through-thickness edge crack in A ± 45° laminate

A solution is given for the three-dimensional stress field near a through-thickness edge crack in a thin ± 45° laminate having elastic ply moduli typical of graphite/epoxy. The stress distribution was obtained by a three-dimensional multilayer finite element analysis based on the hybrid stress model, formulated through the minimum complementary energy principle. The results indicate that the in-plane stresses of each individual ply follow the classical $\text{1}\text{√r}$ stress singularity, but that the shape of isostress contours in the crack tip region is strongly distorted from predictions based on two-dimensional anisotropic fracture mechanics theory. The interlaminar shear stresses increase rapidly as the crack tip is approached, but are restricted to a local region around the crack tip and flanks. The interlaminar normal stress is assumed to be negligible in the formulation of the analysis.     

Thermally-induced interlaminar crack-tip singularities in laminated anisotropic composites

Thermally-induced stress singularities of an interlaminar crack in a fiber-reinforced composite laminate under a state of generalized plane deformation are examined within the framework of steady-state anisotropic thermoelasticity. The crack is assumed to be embedded within a matrix-rich interlaminar region of the composite. The Fourier integral transform technique and the flexibility/stiffness matrix method are introduced to formulate the current mixed boundary value problem. As a result, two sets of simultaneous Cauchy-type singular integral equations of the first kind are derived for the heat conduction and thermoelasticity. Within the context of linear elastic fracture mechanics, the mixed-mode thermal stress intensity factors are defined in terms of the solutions of the corresponding integral equations. Numerical results are presented, addressing the effects of laminate stacking sequence, crack location, and crack surface partial insulation on the values of thermal stress intensity factors.     

单向连续碳纤维-玻璃纤维层间混杂增强环氧树脂基复合材料的力学性能

为了研究连续单向纤维的层间混杂方式对复合材料力学性能及破坏方式的影响,采用碳纤维-玻璃纤维体积比为1∶1,以拉-挤成型法制备了具有不同层间混杂结构的连续单向纤维增强环氧树脂基复合材料,并研究了不同层间混杂结构的连续单向碳纤维-玻璃纤维增强环氧树脂基复合材料的力学性能及破坏形式。结果表明：具有层间混杂结构的复合材料抗拉强度处于纯碳纤维/环氧树脂复合材料和纯玻璃纤维/环氧树脂复合材料之间,复合材料的拉伸断裂方式为劈裂;具有层间混杂结构的复合材料的层间剪切强度均优于纯碳纤维/环氧树脂复合材料和纯玻璃纤维/环氧树脂复合材料,复合材料的剪切断裂方式为层间断裂。     

莫来石纤维增强SiO_2气凝胶复合材料的力学性能试验

为了探究莫来石纤维增强SiO_2气凝胶复合材料的拉伸和层间剪切性能,开展了相关试验。首先,进行了复合材料在室温下的面内拉伸试验,获得了复合材料的室温面内拉伸模量;然后,采用引伸计方法和数字图像相关法分别对拉伸变形进行测量,并对2种方法进行了对比分析;最后,开展了不同温度下的层间剪切试验,研究了复合材料在不同温度下的层间剪切性能,并对其微观结构进行了分析。结果表明:复合材料的拉伸模量约为285.17 MPa;由引伸计方法测得的拉伸变形计算出的拉伸模量比数字图像相关法获得的拉伸模量高2.4%;在室温和高温下,试样呈现明显的层间剪切破坏;对复合材料的微观分析发现,SiO_2气凝胶基体主要分布在层间区域,增强纤维主要分布在铺层内。所得结论表明莫来石纤维增强SiO_2气凝胶复合材料拉伸和层间性能较差,当承受层间载荷时,SiO_2气凝胶基体起主要作用,且温度对复合材料的性能影响较大。     

Synchronous effects of multiscale reinforced and toughened CFRP composites by MWNTs-EP/PSF hybrid nanofibers with preferred orientation

MWNTs-EP/PSF (polysulfone) hybrid nanofibers with preferred orientation were directly electrospun onto carbon fiber/epoxy prepregs and interlaminar synchronously reinforced and toughened CFRP composites were successfully fabricated. With MWNTs-EP loading increasing, the oriented nanofibers were obtained accompanying with enhanced alignment of inner MWNTs-EP. Flexural properties and interlaminar shear strength of composites were improved with increasing MWNTs-EP loadings, whereas fracture toughness attained maximum at 10 wt% MWNTs-EP loading and then decreased. Based on these results, multiscale schematic modeling and mechanism schematic of hybrid nanofibers reinforced and toughened composites were suggested. Due to the preferred orientation of nanofibers, MWNTs-EP was inclined to align vertically to carbon fiber direction along the in-plane of interface layer. The proposed network structures, containing four correlative phases of MWNTs-EP/PSF sphere/carbon fiber/epoxy matrix, contributed to simultaneous improvement of strength and toughness of composites, which was realized by crack pinning, crack deflection, crack bridging and effective load transfer.     

Crack Healing under Antiplane Deformation of Anisotropic Bodies

Strength of Materials - A mathematical model of longitudinal shear crack healing in an anisotropic body was constructed. The problem was reduced to the solution of the singular integro-differential...     

Interlaminar stresses in laminated composite plates, cylindrical/spherical shell panels damaged by low-velocity impact

Prediction of damage caused by low-velocity impact in laminated composite plate cylindrical/spherical shell panels is an important problem faced by designers using composites. Not only the in-plane stresses but also the interlaminar normal and shear stresses play a role in estimating the damage caused. The work reported here is an effort in getting better predictions of damage in composite plate cylindrical/spherical shell panels subjected to low-velocity impact.

The low-velocity impact problem is treated as a quasi-static problem. First, the in-plane stresses are calculated by 2-D nonlinear finite element analysis using a 48 degrees of freedom laminated composite shell element. The damage analysis is then carried out using a Tsai-Wu quadratic failure criterion and a maximum stress criteria. Interlaminar normal and shear stresses are predicted after taking into account the in-plane damage caused by low-velocity impact. The interlaminar stresses are obtained by integrating the 3-D equations of equilibrium through the thickness. The deformed geometry is taken into account in the third equation of equilibrium (in the thickness direction). After evaluating the formulation and the computer program developed for correctness, the interlaminar stresses are predicted for composite plates/shell panels which are damaged by low-velocity impact.     

Quantitative evaluation of the fatigue limit of a metal with an arbitrary crack under a stress controlled condition – Stress Ratio R=−1

The static crack problem of a functionally graded coating-substrate structure with an internal or edge crack perpendicular to the interface is investigated under an in-plane load. The structure is made up of a functionally graded coating with an internal or edge crack and a homogeneous substrate of finite thickness. The material properties are assumed to vary continuously from the coating to the substrate. By use of Fourier transform method, the mixed boundary value problem is reduced to a singular integral equation which can be solved numerically. During the analysis, a higher-order term is obtained in the asymptotic analysis of the singular kernel to improve the convergence efficiency of numerical integrals. The influences of material constants and the geometry parameters on the stress intensity factors (SIFs) are studied. In Part II of this paper, the transient response of the structure subjected to an in-plane impact is investigated.     

Hybrid multi-scale epoxy composite made of conventional carbon fiber fabrics with interlaminar regions containing electrospun carbon nanofiber mats

Herein we report the development and evaluation of hybrid multi-scale epoxy composite made of conventional carbon fiber fabrics with interlaminar regions containing mats of electrospun carbon nanofibers (ECNs). The results indicated that (1) the interlaminar shear strength and flexural properties of hybrid multi-scale composite were substantially higher than those of control/comparison composite without ECNs; in particular, the interlaminar shear strength was higher by ∼86%; and (2) the electrical conductivities in both in-plane and out-of-plane directions were enhanced through incorporation of ECNs, while the enhancement of out-of-plane conductivity (∼150%) was much larger than that of in-plane conductivity (∼20%). To validate the data reduction procedure, a new shear stress formula was formulated for composite laminates, which took into account the effect of layup and inter-layers. The study suggested that ECNs could be utilized for the development of high-performance composites, particularly with the improved out-of-plan properties (e.g., interlaminar shear strength).     

复合材料层合板缺口强度的CDM三维数值模型

针对复合材料层合结构缺口强度问题,基于连续损伤力学（CDM）提出了一种三维损伤数值模型。模型区分了层内损伤（纤维失效、纤维间失效）和层间分层损伤的不同失效模式。采用三维Puck准则与Aymerich准则对上述2类损伤进行判定,材料失效后基于CDM中线性软化模型对材料损伤进行演化。模型考虑了复合材料层合板子层的就位效应和剪切非线性行为。对Carlsson的AS4/3501-6缺口拉伸强度试验进行数值模拟。结果表明:分析结果与试验结果吻合良好,证明了该模型能够准确地预测含缺口复合材料层合板面内拉伸强度。      

Transient anti-plane crack problem of a functionally graded piezoelectric strip bonded to elastic layers

Summary. This paper examined the dynamic electromechanical behavior of a crack in a functionally graded piezoelectric layer bonded between two elastic layers under the combined anti-plane mechanical shear and in-plane electric impacts. Fourier cosine transforms are used to reduce the problem to the solution of a set of singular integral equations. It is found that the impermeable crack condition is more reasonable than the permeable crack condition to analyze the influence of electric loading, and the energy density factor is more acceptable than the energy release rate to be used as the fracture criterion. In addition, numerical results are also presented to show the influences of the crack position, electromechanical combination factor and material gradient parameter on the fracture behavior.     

Dynamic steady-state crack propagation in a transversely isotropic viscoelastic body

The problem considered herein is the dynamic, subsonic, steady-state propagation of a semi-infinite, generalized plane strain crack in an infinite, transversely isotropic, linear viscoelastic body. The corresponding boundary value problem is considered initially for a general anisotropic, linear viscoelastic body and reduced via transform methods to a matrix Riemann–Hilbert problem. The general problem does not readily yield explicit closed form solutions, so attention is addressed to the special case of a transversely isotropic viscoelastic body whose principal axis of material symmetry is parallel to the crack edge. For this special case, the out-of-plane shear (Mode III), in-plane shear (Mode II) and in-plane opening (Mode I) modes uncouple. Explicit expressions are then constructed for all three Stress Intensity Factors (SIF). The analysis is valid for quite general forms for the relevant viscoelastic relaxation functions subject only to the thermodynamic restriction that work done in closed cycles be non-negative. As a special case, an analytical solution of the Mode I problem for a general isotropic linear viscoelastic material is obtained without the usual assumption of a constant Poissons ratio or exponential decay of the bulk and shear relaxation functions. The Mode I SIF is then calculated for a generalized standard linear solid with unequal mean relaxation times in bulk and shear leading to a non-constant Poissons ratio. Numerical simulations are performed for both point loading on the crack faces and for a uniform traction applied to a compact portion of the crack faces. In both cases, it is observed that the SIF can vanish for crack speeds well below the glassy Rayleigh wave speed. This phenomenon is not seen for Mode I cracks in elastic material or for Mode III cracks in viscoelastic material.     

On higher order parameters in cracked composite plates under far‐field pure shear

This paper presents the analytical solution of the crack tip fields as well as the crack parameters in an infinitely large composite plate with a central crack subjected to pure shear loading. To this end, the complex variable method is employed to formulate an asymptotic solution for the crack tip fields in an anisotropic plane. Using a stress‐based definition of the crack tip modes of loading, only the mode II crack parameters are found to be non‐zero under pure shear load. Special focus is given to the determination of the higher order parameters of the crack tip asymptotic field, particularly the first non‐singular term, ie, the T‐stress. Unlike the isotropic materials, in which the T‐stress is zero under pure shear, it is found that the T‐stress is non‐zero for the case of anisotropic materials, being the only material‐dependent crack tip stress parameter. The veracity of our exact crack tip fields is assessed and verified through a comparison made with respect to the finite element (FE) solution. Finally, we demonstrate the significance of the T‐stress on stresses near the crack tip in composite plates under pure shear loads.     

湿热环境下碳纤维增强乙烯基树脂复合材料长期力学性能

碳纤维增强聚合物基复合材料(CFRP)因其耐腐蚀、轻质高强等特点被广泛应用于海洋环境,进而长期遭受湿热环境的考验。为了解湿热环境和极端温度对碳纤维增强乙烯基树脂复合材料的影响,测试了湿热老化前后和不同温度下CFRP的压缩性能、面内剪切性能和层间剪切强度变化。FTIR和SEM结果表明：纯树脂试样在湿热环境中发生了水解,使试样表面的微裂纹和孔隙不断扩展并向试样内部渗透;碳纤维的埋入抑制了水的扩散和水解,因而CFRP的吸湿曲线与Fickian模型高度吻合;纯树脂由于水解反应影响了吸湿通道使吸湿曲线偏离Fickian模型。力学性能表明：湿热老化90天后压缩强度和层间剪切强度分别降低7.6%、12.3%;试样在高温(70℃)下的压缩强度、面内剪切强度、层间剪切强度分别急剧降低36.2%、26.9%、37.4%,且高温对试样力学性能的影响具有部分可逆性。     

Delamination in composite plates: influence of shear deformability on interfacial debonding

An elastic interface model is introduced to investigate the effects of in-plane and out-plane shear stresses on interfacial debonding in laminated composite plates by means of the energy release rate concept. This is done by utilising an improved laminated plate model in which the Reissner–Mindlin kinematics type for each layers is coupled with an adhesion mechanism modelled by means of a linear interface model, acting in the opening and sliding failure mode directions. The problem is faced through an analytical solution procedure. Increasing the stiffnesses of the interface leads to restoring displacement continuity at the interface between layers and to recovering energy release rate components through the work performed by the singular stress field at the crack tip. In view of the great importance of shear deformation in laminated composite plates the effect of shear stresses on the mechanism of delamination are investigated pointing out new features which emerge from the interaction of normal and shear stresses acting on the transverse section near the crack tip. Several examples of mixed mode delamination schemes used in experimental applications are examined, showing the influence of transverse shear stresses in coupling with normal stresses on energy release rates determination.     

Stress intensity factor for a Griffith crack interacting with a coated inclusion

Stress investigation for the interaction problem between a coated circular inclusion and a near-by line crack has been carried out. The crack and the coated inclusion (a coated fiber) are embedded in an infinitely extended isotropic matrix, with the crack being along the radial direction of the inclusion. Two loading conditions, namely, the tensile and shear loading ones are considered. During the solution procedure, the crack is treated as a continuous distribution of edge dislocations. By using the solution of an edge dislocation near a coated fiber as the Green's function, the problem is formulated into a set of singular integral equations which are solved by Erdogan and Gupta (1972) method. The expressions for the stress intensity factors of the crack are then obtained in terms of the asymptotic values of the dislocation density functions evaluated from the integral equations. Several numerical examples are given for various material and geometric parameters. The solutions obtained from the integral equations have been checked and confirmed by the finite element analysis results.     

Surface crack problem for functionally graded magnetoelectroelastic coating-homogeneous elastic substrate system under anti-plane mechanical and in-plane electric and magnetic loading

A functionally graded magnetoelectroelastic material layer bonded to a homogeneous elastic substrate is investigated. The functionally graded magnetoelectroelastic layer contains a surface crack that is perpendicular to the surface of the medium. The structure is subjected to anti-plane mechanical and in-plane electric and magnetic loads, the crack problem involves the anti-plane elastic field coupled with the in-plane electric and magnetic field. The elastic layer can be an ideal insulator or an ideal conductor. Integral transform and dislocation density functions are employed to reduce the problem to the solution of a system of singular integral equations. Numerical results show the influences of the material gradient parameter and crack configuration on field intensity factors and energy release rates of the functionally graded magnetoelectroelastic coating-homogeneous elastic substrate structure.     

Effect of on-axis tensile loading on shear properties of an orthogonal 3D woven SiC/SiC composite

The present study examines in-plane and out-of-plane shear properties of an orthogonal 3D woven SiC fiber/SiC matrix composite. A composite beam with rectangular cross-section was subjected to a small torsional moment, and the torsional rigidities were measured using an optical lever. Based on the Lekhnitskii’s equation (Saint–Venant torsion theory) for a orthotropic material, the in-plane and out-of-plane shear moduli were simultaneously calculated. The estimated in-plane shear modulus agreed with the modulus measured from ±45° off-axis tensile testing. The effect of on-axis (0°/90°) tensile stress on the shear stiffness properties was also investigated by the repeated torsional tests after step-wise tensile loading. Both in-plane and out-of-plane shear moduli decreased by about 50% with increasing the on-axis tensile stress, and it is mainly due to the transverse crack propagation in 90° fiber bundles and matrix cracking in 0° fiber bundles. It was demonstrated that the torsional test is an effective method to estimate out-of-plane shear modulus of ceramic matrix composites, because a thick specimen is not required.     

Anti-plane problem of periodic interface cracks in a functionally graded coating-substrate structure

In this paper, the interface cracking between a functionally graded material (FGM) and an elastic substrate is analyzed under antiplane shear loads. Two crack configurations are considered, namely a FGM bonded to an elastic substrate containing a single crack and a periodic array of interface cracks, respectively. Standard integral-transform techniques are employed to reduce the single crack problem to the solution of an integral equation with a Cauchy-type singular kernel. However, for the periodic cracks problem, application of finite Fourier transform techniques reduces the solution of the mixed-boundary value problem for a typical strip to triple series equations, then to a singular integral equation with a Hilbert-type singular kernel. The resulting singular integral equation is solved numerically. The results for the cases of single crack and periodic cracks are presented and compared. Effects of crack spacing, material properties and FGM nonhomogeneity on stress intensity factors are investigated in detail.     

Moving Dugdale crack along the interface of two dissimilar magnetoelectroelastic materials

In this paper, the concept of Dugdale crack model and Yoffe model is extended to propose a moving Dugdale interfacial crack model, and the interfacial crack between dissimilar magnetoelectroelastic materials under anti-plane shear and in-plane electric and magnetic loadings is investigated considering the magneto-electro-mechanical nonlinearity. It is assumed that the constant moving crack is magneto-electrically permeable and the length of the crack keeps constant. Fourier transform is applied to reduce the mixed boundary value problem of the crack to dual integral equations, which are solved exactly. The explicit expression of the size of the yield zone is derived, and the crack sliding displacement (CSD) is explicitly expressed. The result shows that the stress, electric and magnetic fields in the cracked magnetoelectroelastic material are no longer singular and the CSD is dependent on the loading, material properties and crack moving velocity. The current model can be reduced to the static interfacial crack case when the crack moving velocity is zero.