Failure surface of epoxy-modified fiber-reinforced composites under transverse tension and out-of-plane shear

The mechanical behavior of uniaxially fiber-reinforced composites with a ductile rubber-toughened epoxy matrix was studied through the finite element analysis of a RVE of the composite microstructure. The fibers were represented by elastic and isotropic solids, while the rubber-modified epoxy matrix behaved as a elasto-viscoplastic solid. The matrix flow stress followed the model developed by Jeong [Jeong, H.-Y., 2002. A new yield function and a hydrostatic stress-controlled void nucleation model for porous solids with pressure-sensitive matrices. International Journal of Solids and Structures 39, 1385–1403.], which included the inherent pressure-sensitivity of the yield stress in the epoxy matrix, the damage due to the cavitation of the rubber particles and subsequent void growth, and the particular features of elastic–viscoplastic behavior in glassy polymers, particularly the intrinsic softening upon yield followed by hardening. Composites with either perfect or weak fiber/matrix interfaces (the latter introduced through cohesive elements) were studied to assess the influence of interface strength on the composite behavior. Simulations under transverse tension and out-of-plane shear were carried out to establish the effect of loading conditions on the dominant deformation and failure micromechanisms. In addition, the corresponding failure locus was obtained and compared with the predictions of current phenomenological failure criteria for composites. The range of validity of these criteria and the areas for further improvement were established by comparison with the numerical results.     

A periodic unit-cell simulation of fiber arrangement dependence on the transverse tensile failure in unidirectional carbon fiber reinforced composites

The effect of fiber arrangement on transverse tensile failure in unidirectional carbon fiber reinforced composites with a strong fiber-matrix interface was studied using a unit-cell model that includes a continuum damage mechanics model. The simulated results indicated that tensile strength is lower when neighboring fibers are arrayed parallel to the loading direction than with other fiber arrangements. A shear band occurs between neighboring fibers, and the damage in the matrix propagates around the shear band when the interfacial normal stress (INS) is sufficiently high. Moreover, based on the observation of Hobbiebrunken et al., we reproduced the damage process in actual composites with a nonuniform fiber arrangement. The simulated results clarified that the region where neighboring fibers are arrayed parallel to the loading direction becomes the origin of the transverse failure in the composites. The cracking sites observed in the simulation are consistent with experimental results. Therefore, the matrix damage in the region where the fiber is arrayed parallel to the loading direction is a key factor in understanding transverse failure in unidirectional carbon fiber reinforced composites with a strong fiber/matrix interface.     

Inelastic behavior of an AS4/PEEK composite under combined transverse compression and shear. Part I: experiments

The nonlinear behavior in shear and transverse compression of unidirectional AS4/PEEK and their interaction are investigated experimentally. The composite is rate dependent even at room temperature and its rate exponent is similar to that of neat PEEK. The material is tested under pure shear, pure compression and under biaxial loading histories. The biaxial tests are performed in a custom facility on thin strips of the material. The facility allows freedom to choose the loading path in the biaxial stress and strain spaces of interest. Tests are performed for three biaxial loading paths. In the first, the specimen is sheared then compressed while the shear stress is held constant; in the second, the specimen is compressed then sheared while the compressive stress is held constant; and in the third, the specimen is loaded simultaneously by proportional amounts of compression and shear. It was found that the induced deformation is influenced significantly by the loading history followed. Also, initial loading in shear or compression has only a modest effect on subsequent loading of the other type. An unorthodox yielding behavior for the composite results from this lack of interaction. Finally, the stresses at failure are found to trace an elliptical path in the shear–transverse compression plane, but the failure stress state is not significantly affected by the loading path followed.     

Determination of the first ply failure load for a cross ply laminate subjected to uniaxial tension through computational micromechanics

A method for determining the in situ strength of fiber-reinforced laminas for three types of transverse loading including compression, tension and shear is presented. In the framework of this method, an analysis of local stresses that are responsible for the coalescence of matrix cracks is carried out by using a multi-fiber unit cell model and finite element method. The random distribution of fibers, fiber–matrix decohesion and matrix plastic deformations are taken into account in the micromechanical simulations. The present study also shows that the nonlinear hardening behavior of matrix reflects more realistically the influence of plastic deformations on the in situ transverse strength of lamina than the perfectly plastic behavior of matrix. The prediction of the in situ transverse strength is verified against the experimental data for a cross ply laminate subjected to uniaxial tension.     

Buckling of nano-fibre reinforced composites: a re-examination of elastic buckling

Elastic buckling of layered/fibre reinforced composites is investigated. Assuming the existence of both shear and transverse modes of failure, the fibre is analysed as a layer embedded in a matrix. Interacting stresses, acting at the interfaces are determined from an exact derived stress field in the matrix. It is shown that buckling can occur only in the shear buckling mode and that the transverse buckling mode is spurious. As opposed to the well known Rosen shear buckling mode solution (predicated on an infinite buckling wavelength), shear buckling is shown to exist under two régimes: buckling of dilute composites with finite wavelengths and buckling of non-dilute composites with infinite wavelengths. Based on the analysis, a model is constructed which defines the fibre concentration at which the transition between the two régimes occurs. The buckling strains are shown to be (approximately) constant for dilute composites and, in the case of very stiff fibres, to have realistic values compatible with elastic behaviour. For the case of non-dilute composites, the strains are found to be in agreement with those given by the Rosen shear buckling solution. Numerical results for the buckling strains and stresses are presented and compared with the Rosen solution. These reveal that the Rosen solution is valid only for the case of non-dilute composites. The investigation demonstrates that elastic buckling may be a dominant failure mechanism of composites consisting of very stiff fibres fabricated in the framework of nano-technology.     

Mechanisms of stress transfer and interface integrity in carbon/epoxy composites under compression loading: Part I: Experimental investigation

Raman spectroscopy is used to get an insight into the microstructural aspects of the compressional behavior of carbon fiber composites. This is done by a comparative assessment of the stress transfer efficiency in tension and compression in single-fiber discontinuous model geometries. It was found that axial stress is transferred in the fiber through the generation of shear stresses at the interface for both tension and compression loading. Experimental evidence is presented to verify that the values of the maximum interfacial shear stress that the system sustains is a function of the applied strain and independent of the type of loading. However, compressive failure is quite different as fiber fragments remain in contact, thus can still bear load.     

弱粘结的斜交铺设层合圆柱壳的柱形弯曲

导出了两端简文的具有弱粘结界面的任意斜交铺设层合圆柱壳柱形弯曲问题的一个精确弹性理论解。分析中采用线性弹簧模型来表征界面的弱粘结特性。引进新的物理量改写了基本方程,导出了对应的状态空间列式,并利用变量替换技术将该状态方程转换成常系数状态方程,从而方便求解。最后给出了数值算例,并讨论了弱界面的影响。     

A micromechanical study of residual stress and its effect on transverse failure in polymer–matrix composites

Cure residual stress and its effect on damage in unidirectional fibre-reinforced polymer–matrix composites under transverse loading were studied using a micromechanical unit cell model and the finite element method. The overall residual stress introduced from curing was determined by considering two contributions: volume shrinkage of matrix resin from the crosslink polymerization during isothermal curing and thermal contraction of both resin and fibre as a result of cooling from the curing temperature to room temperature. To examine the effect of residual stress on failure, a model based on the Maximum Principal Stress criterion and stiffness degradation technique was used for damage analysis of the unit cell subjected to mechanical loading after curing. Predicted damage initiation and evolution are clearly influenced by the inclusion of residual stress. Residual stress is always detrimental for transverse compressive loading and pure shear loading. For transverse tensile loading, residual stress is detrimental for relatively low resin strength and beneficial for relatively high resin strength. Failure envelopes were obtained for both biaxial normal loading and combined shear and normal loading and the results show that residual stress results in a shifting and contraction of the failure envelopes.     

Inelastic behavior of an AS4/PEEK composite under combined transverse compressionand shear.Part II: modeling

A micromechanical model is presented for simulating the nonlinearities exhibited by AS4/PEEK composites in shear and transverse compression, their interaction, and their rate dependence at room temperature. The fibers are assumed to be transversely isotropic and to be distributed in a hexagonal pattern in the matrix. The PEEK matrix is modeled as an elastic–powerlaw viscoplastic, isotropic solid through two related models. Model I is the simple J₂–type viscoplasticity; Model II is a rate dependent version of the non-associative Drucker-Prager model. Both models are calibrated so that they reproduce the shear response of the composite. Model II is also calibrated to its transverse compression response. Both models capture the rate dependence of the composite well. Model I is significantly less stiff in transverse compression than the experimental data. However, it does a reasonable job of predicting other aspects of the biaxial experiments and captures the important trends of behavior observed. Model II does better in transverse compression, but shearing in the presence of transverse compression is found to be stiffer than the measured responses. The unit cell model allows us to examine the stresses in the composite, providing an explanation for the lack of interaction between the constant stress and the increasing stress observed experimentally for certain loading paths.     

Shear Evolution of Fiberglass Composites Under Compression

Woven composites can offer mechanical improvements over more traditional engineering materials, yet understanding the complex interplay between the fiber-matrix architecture during loading remains a challenge. This paper investigates the evolution of shear failure behavior during the compression of high performance fiberglass composites with varying resin binders at both quasi-static and dynamic strain rates. All samples are comprised of commercially available woven glass cloth with approximately 56 % fiber volume fraction. Laminates with thermosetting resin binders of silicone, melamine, and epoxy were examined. High-speed imaging reveals that failure occurs within a localized shear band region through multiple fiber-weave matrix interface failure with a characteristic macroscopic angle. The shear evolution was spatially mapped using grayscale histograms of the light intensity in the shear regions, and the resulting characteristic angles were measured and analyzed in the context of a Mohr-Coulomb failure criterion. Optical microscopy and high-speed imaging of the shear formation shows initiation appears due to local instabilities from kinking and microbuckling, influenced by the stacking and interlacing regions of tows.     

Modeling long-term creep rupture by debonding in unidirectional fibre-reinforced composites

Delayed fracture due to debonding can be observed in many unidirectional fibre-reinforced composites when the fibre/matrix interface experiences creep. The aim of this work is to describe such a phenomenon within the recently proposed modeling framework of transverse isotropy that allows for a neat decomposition of the mechanical behavior into fibre-directional, transverse, and pure shear parts. Specifically, debonding is here chosen to be governed by the tension transverse to the fibres. One can then speak of a mode-I debonding if use is made of the terminology adopted in fracture mechanics. On another hand, the time-dependent response is attributed to the matrix constituent. As the role of this latter is to deform and support stresses primarily in shear, a viscoelastic behavior is introduced that affects solely the pure shear part of the behavior. We show that both characteristics can be easily embedded into the aforementioned formulation. Among others, the occurrence of tertiary creep is made possible to predict. It is otherwise found that the predicted debonding path always propagates along the direction of the fibres in agreement with many experimental observations found in the literature. On the numerical side, the algorithmic treatment of debonding is independent of the one for viscoelasticity. This renders the implementation within the context of the finite element method very easy.     

Prediction of progressive failure in multidirectional composite laminated panels

A mechanism-based progressive failure analyses (PFA) approach is developed for fiber reinforced composite laminates. Each ply of the laminate is modeled as a nonlinear elastic degrading lamina in a state of plane stress according to Schapery theory (ST). In this theory, each lamina degrades as characterized through laboratory scale experiments. In the fiber direction, elastic behavior prevails, however, in the present work, the phenomenon of fiber microbuckling, which is responsible for the sudden degradation of the axial lamina properties under compression, is explicitly accounted for by allowing the fiber rotation at a material point to be a variable in the problem. The latter is motivated by experimental and numerical simulations that show that local fiber rotations in conjunction with a continuously degrading matrix are responsible for the onset of fiber microbuckling leading to kink banding. These features are built into a user defined material subroutine that is implemented through the commercial finite element (FE) software ABAQUS in conjunction with classical lamination theory (CLT) that considers a laminate as a collection of perfectly bonded lamina (Herakovich, C.T., 1998. Mechanics of Fibrous Composites. Wiley, New York). The present model, thus, disbands the notion of a fixed compressive strength, and instead uses the mechanics of the failure process to provide the in situ compression strength of a material point in a lamina, the latter being dictated strongly by the current local stress state, the current state of the lamina transverse material properties and the local fiber rotation. The inputs to the present work are laboratory scale, coupon level test data that provide information on the lamina transverse property degradation (i.e. appropriate, measured, strain–stress relations of the lamina transverse properties), the elastic lamina orthotropic properties, the ultimate tensile strength of the lamina in the fiber direction, the stacking sequence of the laminate and the geometry of the structural panel. The validity of the approach advocated is demonstrated through numerical simulations of the response of two composite structural panels that are loaded to complete failure. A flat, 24-ply unstiffened panel with a cutout subjected to in-plane shear loading, and a double notched 70-ply unstiffened stitched panel subjected to axial compression are selected for study. The predictions of the simulations are compared against experimental data. Good agreement between the present PFA and the experimental data are reported.     

分块法研究圆柱绕流升阻力

 使用新的分块耦合方法，分别对单圆柱和串列双圆柱绕流进行了数值 模拟. 对于单圆柱绕流，低$Re$下计算所得到的定常涡尺寸与实验非常接近. 对于 串列双圆柱绕流，研究分析了改变双圆柱中心间距对上下游圆柱的升阻力系数和脉动频率所 产生的影响，计算结果与实验非常吻合，为进一步研究涡致振动提供了依据.     

Vibration and buckling of laminated sandwich plates having interfacial imperfections

The vibration and buckling characteristics of sandwich plates having laminated stiff layers are studied for different degrees of imperfections at the layer interfaces using a refined plate theory. With this plate theory, the through thickness variation of transverse shear stresses is represented by piece-wise parabolic functions where the continuity of these stresses is satisfied at the layer interfaces by taking jumps in the transverse shear strains at the interfaces. The transverse shear stresses free condition at the plate top and bottom surfaces is also satisfied. The inter-laminar imperfections are represented by in-plane displacement jumps at the layer interfaces and characterized by a linear spring layer model. It is quite interesting to note that this plate model having all these refined features requires unknowns only at the reference plane. To have generality in the analysis, finite element technique is adopted and it is carried out with a new triangular element developed for this purpose, as any existing element cannot model this plate model. As there is no published result on imperfect sandwich plates, the problems of perfect sandwich plates and imperfect ordinary laminates are used for validation.     

Experimental simulation of matrix cracking and debonding in a model brittle matrix composite

A model composite material system was designed to simulate typical damage mechanisms in unidirectional fiber reinforced brittle matrix composites. Experiments were performed at low to high quasistatic, macroscopic loading rates . At all loading rates reversal of the transverse strain was observed and was correlated to matrix cracking and debonding. The optical method of coherent gradient sensing (CGS) was used to obtain qualitative information regarding the stress fields and to observe the progression of damage. It was found that the sequence of damage formation (damage path) depended on the macroscopic loading rate. At lower loading rates periodic matrix cracks developed; minimal debonding of the reinforcement-matrix interface occurred only much later in the experiment. At higher loading rates extensive debonding followed propagation of the initial matrix crack, and periodic cracking was not observed. Several features of the material response of the model material system were also observed in a previously studied unidirectional ceramic matrix composite.     

<Emphasis Type="Italic">In-situ</Emphasis> Full Field Measurements During Inter-Facial Debonding in Single Fiber Composite Under Transverse Load

The fibre/matrix interfacial damage mechanisms of fiber-reinforced composites (FRCs) are investigated for single-fiber composites under transverse load. A stereo microscope setup is used for 3D digital image correlation during in-situ quasi-static tests of single-fiber standard dog-bone specimens. Macro-fibers (0.9 mm diameter) with radically different interfacial bonding with the epoxy matrix are used. Damage appears to initiate with fiber debonding at the free surface along the tensile direction. The crack then propagates around the interface while slightly growing along the fiber until a lateral crack initiates on the debonded free surface, provoking specimen failure. The final failure mechanisms appears to be different for strong and weak fiber/matrix bonding. 3D DIC is used to provide precise measurements of displacements, strains, and out-of-plane displacement during the whole test. Quantitative differences in the displacement fields are measured in the cases of strong and weak bonding between the fiber and matrix. 3D DIC with macro-fibers is shown to be a promising technique to provide a better understanding of the damage mechanisms in a single-fiber composite and to determine interfacial toughness of a specific fibre/matrix couple in order to perform accurate modeling of damage in FRCs. Displacement, strain, and confidence field results for each pixel from each experiment and at each time step are also provided for detailed comparison with simulation results.     

Mesoscale modeling of nonlinear elasticity and fracture in ceramic polycrystals under dynamic shear and compression

Dynamic deformation and failure mechanisms in polycrystalline ceramics are investigated through constitutive modeling and numerical simulation. Two ceramics are studied: silicon carbide (SiC, hexagonal crystal structure) and aluminum oxynitride (AlON, cubic crystal structure). Three dimensional finite element simulations incorporate nonlinear anisotropic elasticity for behavior of single crystals within polycrystalline aggregates, cohesive zone models for intergranular fracture, and contact interactions among fractured interfaces. Boundary conditions considered include uniaxial strain compression, uniaxial stress compression, and shear with varying confinement, all at high loading rates. Results for both materials demonstrate shear-induced dilatation and increasing shear strength with increasing confining pressure. Failure statistics for unconfined loading exhibit a smaller Weibull modulus (corresponding to greater scatter in peak failure strength) in AlON than in SiC, likely a result of lower prescribed cohesive fracture strength and greater elastic anisotropy in the former. In both materials, the predicted Weibull modulus tends to decrease with an increasing number of grains contained in the simulated microstructure.     

Analysis of plastic deformation in nanoscale metallic multilayers with coherent and incoherent interfaces

Nanoscale metallic multilayered (NMM) composites possess ultra high strength (order of GPa) and high ductility, and exhibit high fatigue resistance. Their mechanical behavior is governed mainly by interface properties (coherent and/or incoherent interfaces), dislocation mechanisms in small volume, and dislocation-interface interaction. In this work, we investigate these effects within a dislocation dynamics (DD) framework and analyze the mechanical behavior of two systems: (1) a bi-material system (CuNi) with coherent interface and (2) a newly developed tri-material system (CuNiNb) composed of both coherent and incoherent interfaces. For the bi-material case we analyze the influence of networks of interfacial dislocations whose nature and distribution are commensurate with the level of relaxation and loading of the structure. Misfit and pre-deposited interfacial dislocation arrays, as well as combinations of both, are studied and the dependence of strength on layer thickness is reported, along with observed dislocation mechanisms. It is shown that interfacial defect configurations significantly alter the strength and mechanical behavior of the material. Furthermore, it is shown that the implementation of penetrable interfaces in DD captures the strength dependence at layer thicknesses on the order of 3-7 nm. For the tri-material case we analyze the effects of coherent and incoherent interfaces in large-scale simulations. The results show that these materials have strong strength-size dependence but are limited by the strength of the incoherent (CuNb) interface which is weak in shear. The weak interface acts as a dislocation sink. This in turn induces an internal shear stress field that activates cross-slip in the adjacent CuNi interlace and thus causing softening. Moreover, it is shown that the yield stress of the CuNiNb system is controlled by the volume fraction of the Nb. Because Nb is the most compliant of the three materials, an increase in volume fraction of Nb decreases the overall yield strength of the material.     

一种预测层合板层间剪应力的新后处理方法

层合板是航空航天领域典型的承力构件,过大的层间应力是导致其分层失效的主要原因.准确的层间应力预测往往依赖于三维平衡方程后处理方法(TPM).然而,该方法需要计算面内应力的一阶导,使得基于C0型板理论构造的线性单元无法使用TPM计算横向剪应力.本文在三维平衡方程后处理方法的基础上,提出了一种新后处理方法(NPM).新后处理方法通过虚功等效法消除了三维平衡方程后处理方法中产生的位移参数的高阶导.基于提出的新后处理方法和C0型板理论,仅需使用线性单元就可以预测层合板的横向剪应力.为了验证所提方法的有效性,本文基于修正锯齿理论(RZT)和所提方法构造了一种C0连续的三节点三角形线性板单元.数值算例表明,所提方法和三维平衡方程后处理方法具有相同的计算精度,提出的板单元能够准确高效地预测层合板的横向剪应力.此外,所提方法便于结合现有的有限元商用软件使用,基于商用软件中板壳单元获得的节点位移,使用新后处理方法极易获得准确的层间剪应力.     

The microbuckling failure of Dyneema~? composites under compression

Two grades of Dyneema~?composite laminates with the commercial designations of HB26 and HB50 were cut into blocks with or without an edge crack and compressed in the longitudinal fiber direction. The cracked and uncracked specimens show similar compressive responses including failure pattern and failure load. The two grades of Dyneema~? composites exhibits different failure modes: a diffuse, sinusoidal buckling pattern for Dyneema~? HB50 due to its weak matrix constituent and a kink band for Dyneema~? HB26 due to its relatively stronger matrix constituent. An effective finite element model is used to simulate the collapse of Dyneema~? composites, and the sensitivity of laminate compressive responses to the overall effective shear modulus, interlaminar shear strength, thickness and imperfection angle are investigated. The change of failure mode from kink band to sinusoidal buckling pattern by decreasing the interlaminar shear strength is validated by the finite element analyses.