Initial Fiber Misalignment Research Articles

Micromechanical modeling of longitudinal compression behavior and failure mechanism of unidirectional carbon fiber reinforced aluminum composites involving initial fiber misalignment

AbstractA micromechanical model with realistic initial fiber misalignment (IFM) was developed to simulate the longitudinal compression behavior of unidirectional carbon fiber/aluminum composites. The matrix and fiber were modeled using ductile damage law and brittle fracture model, respectively. The interfacial properties were firstly determined by the single‐fiber push‐out and transverse tensile tests, and the cohesive zone model was adopted to capture the interfacial behavior. The calculated compressive response curve is in alignment with the experimental data. Compression failure can be attributed to fiber kinking, possibly triggered by the matrix shear damage. The increase of IFM angle makes the failure mode being transformed from fiber crushing to fiber kinking, along with a significant decrease in compressive strength. With the fiber content increasing, the compressive strength increases first and then decreases, while the compressive modulus increases monotonically. Increasing interfacial strength significantly improves the compressive strength, but this is limited by the matrix properties.

Reduced order multiscale model for compression kink-band failure in composites

A multiscale model for compression kink band failure in fibrous composites is presented. The computational model predicts the progression of damage associated with the formation of kink bands, which experiments demonstrate to involve excessive shear straining of the matrix material and fiber fracture. The uniqueness of the study is establishing the concurrent treatment of nonlinear deformation and failure of the composite constituents at the scale of the material microstructure, and the formation of kink bands at the mesoscopic scale. The model incorporates computational homogenization of the material response, a nonlocal gradient regularization scheme, and a curvature-based criterion for macroscopic fiber break to predict kink band formation. The multiscale approach resolves mesoscale mechanisms associated with kink banding while offering computational benefits compared to direct mesomechanical approaches. An accessible implementation within finite element analysis software is presented and the model is verified with analysis of a mesoscale domain incorporating initial fiber waviness. In quasi-static simulations, the kink band initiates due to matrix softening that results in the onset of buckling and is completely formed when fibers break as a result of localized curvature. Results from parametric studies confirm that compression strength is not directly related to measures of the kink band morphology, but it is strongly correlated with the shear strength and initial fiber misalignment angle. The predicted effects of material properties representing various carbon fiber reinforced polymers and a range of fiber misalignment angles on kink band width and failure strength corroborate analytical and experimental results presented in the literature.

Effects of fiber and matrix properties on the compression strength of carbon fiber reinforced polymer composites

The axial compressive strength of carbon fiber reinforced polymer composites (CFRP) is significantly lower than the tensile strength, which hinders its wide applications. The failure mechanism of CFRP under unidirectional compression parallel to the fiber alignment direction is complex, but research on this issue is limited. In order to understand this mechanism more deeply and intuitively, a two-dimensional microscopic numerical model is proposed. The influences of various properties of the fiber and matrix on the compressive strength of CFRP are investigated, including the axial elastic modulus of the fiber (Ef1), the transverse elastic modulus of the fiber (Ef2), the shear modulus of the fiber (Gf12), the elastic modulus of the matrix (Em), the proportional strength limit of the matrix (σp), the yield strength of the matrix (σs) and the degree of initial fiber misalignment. Results show that the model is capable of explaining the failure mechanism of CFRP under a unidirectional compressive load. Shear stress plays an important role in the compressive failure process. The localization of shear stress caused by initial fiber misalignment leads to plastic yield of the matrix and finally a kink band. Changes in these propertiesdirectly affect the concentration of shear stress in the defect areas, thereby affecting the compressive strength of the CFRP. When the values of Ef1, Ef2, Gf12, Em, σp, σs are separately increased by 10% or the degree of initial fiber misalignment is decreased by 10%, the compressive strength of CFRP is increased by 2.33%, 0%, 0.39%, 3.38%, 1.17%, 2.30% and 2.52% respectively. Em has the greatest influence on the compressive strength of CFRP, followed by the initial fibermisalignment. The effects of the plastic properties of the matrix on the compressive strength of CFRP are obvious.

Simulation on kink-band formation during axial compression of a unidirectional carbon fiber-reinforced plastic constructed by X-ray computed tomography images

X-ray computed tomography was used to obtain cross-sectional images of a unidirectional carbon fiber-reinforced plastic, where fiber locations in each cross-sectional image were identified. The three-dimensional model with fiber waviness was developed by connecting the fiber locations along the fiber direction. Numerical simulation for the initiation and formation of a kink-band during axial compression was performed using the three-dimensional finite element model. The load was increased almost linearly until it reached the compressive strength, after which both load and displacement were decreased, showing snap-back behavior. The matrix yielded locally with the increased axial compression, and fibers started to fall due to insufficient support by the yielded matrix. A kink-band was formed with an increase in the yielded area, and thus, the initiation of a kink-band was defined as the local yielding of the matrix. It was also shown that the kink-band was formed at the longitudinal location at which the average of initial local fiber misalignment angles in the cross-section was relatively large.

A micromechanical model for longitudinal compressive failure in unidirectional fiber reinforced composite

Abstract A micromechanics-based 2D numerical model is proposed to comprehensively trace the longitudinal compressive failure of unidirectional carbon fiber reinforced polymers (UD-CFRP), in which microscopic damage mechanisms (namely the fiber fracture, matrix plastic yield and fiber-matrix interface crack) are considered. With this model, the predicted compressive modulus, strength and failure pattern are in good agreements with the experimental results, which validate the effectiveness of the proposed model. It concludes that the longitudinal compressive failure is governed by the matrix damage rather than the fiber fracture and the interface crack triggers the matrix damage. In addition, the influence of some microscopic parameters, including the fiber volume fraction, initial fiber misalignment, initial fiber-matrix interface stiffness, interface strength and fracture energies, on the longitudinal compressive failure is disclosed. The compressive modulus increases with the fiber volume fraction while it is almost unaffected by the rest four parameters. The compressive strength increases with the increment of the initial interface stiffness or the decrement of the initial fiber misalignment while it is immune to the interface fracture energies. Moreover, a limited increment of the fiber volume fraction or the interface strength is beneficial for enhancing the compressive strength.

Micro-Mechanical Analysis About Kink Band in Carbon Fiber/Epoxy Composites Under Longitudinal Compression

Kink band is a typical phenomenon for composites under longitudinal compression. In this paper, theoretical analysis and finite element simulation were conducted to analyze kink angle as well as compressive strength of composites. Kink angle was considered to be an important character throughout longitudinal compression process. Three factors including plastic matrix, initial fiber misalignment and rotation due to loading were considered for theoretical analysis. Besides, the relationship between kink angle and fiber volume fraction was improved and optimized by theoretical derivation. In addition, finite element models considering fiber stochastic strength and Drucker-Prager constitutive model for matrix were conducted in ABAQUS to analyze kink band formation process, which corresponded with the experimental results. Through simulation, the loading and failure procedure can be evidently divided into three stages: elastic stage, softening stage, and fiber break stage. It also shows that kink band is a result of fiber misalignment and plastic matrix. Different values of initial fiber misalignment angle, wavelength and fiber volume fraction were considered to explore the effects on compressive strength and kink angle. Results show that compressive strength increases with the decreasing of initial fiber misalignment angle, the decreasing of initial fiber misalignment wavelength and the increasing of fiber volume fraction, while kink angle decreases in these situations. Orthogonal array in statistics was also built to distinguish the effect degree of these factors. It indicates that initial fiber misalignment angle has the largest impact on compressive strength and kink angle.

Comparison of a composite model and an individually fiber and matrix discretized model for kink band formation

Failure by kink band instability in a unidirectional fiber composite is analyzed. A micromechanical discretized finite element model is used and compared to an existing composite constitutive model. The comparison is made in a fiber angle vs. applied compressive stress space. An investigation on the relation between the kink band angle and the fiber angle is conducted in the postbuckling regime. The critical kink band angle is examined for different initial fiber misalignment angles.

Mechanics of kinking in fiber-reinforced composites under compressive loading

A novel approach to analyze kink banding failure in fiber reinforced composites is presented in this paper. By considering a single fiber–matrix unit cell and utilizing a fiber deformation representation that can simultaneously account for instability due to increasing fiber amplitude and fiber rotation, a sequence of events that lead to the formation of a kink band is elucidated. It is shown that peak compressive strength does not necessarily correspond to the onset of yielding (non-linearity) in the matrix and is dictated by the interaction between matrix non-linearity and initial fiber misalignment. Predictions of compressive strength and kink band formation, utilizing the new model, are found to be in good agreement with reported experimental data and associated higher-order finite element analysis.

Analytical studies on the imperfection sensitivity and on the kink band inclination angle of unidirectional fiber composites

Imperfections stemming from the manufacturing process influence the compressive strength and fiber kinking of unidirectional composites significantly. Therefore, the effect of initial fiber misalignment is addressed herein by re-visiting a previous analytical model for unidirectional composites. The precursor model is improved by taking into account such imperfections and the formulations are subsequently validated against experimental data. Significant improvements are achieved for the accuracy of the initial compressive strength. The model is furthermore capable to determine the post-buckling response precisely which is of importance since composites can exhibit substantial post-buckling strength. The kink band geometry, especially its inclination angle β with respect to the fiber direction, is inherently related to the analytical formulations. However, to date no recognized expression for β exists, thus the band inclination in analytical modeling is commonly assumed based on experiments. Herein, a newly developed approach to determine β is derived yielding excellent comparison with experimental data.

樹脂埋めしたＣＦ単繊維の圧縮強度

Micro-buckling characteristic of a carbon mono-fiber in matrix was studied. A fiber was modeled in matrix as a column on elastic foundation. Buckling stress of the fiber was calculated incorporating the initial fiber misalignment and non-linearity of the matrix. The effect of bending on compressive stress was also taken into considered to estimate failure initiation at fiber surface. Two processes of ultimate fiber failure were considered. First one is a compressive fracture at fiber surface due to compression and bending. Second one is a matrix-yielding initiated unstable fiber deformation. Compression test of a carbon fiber in matrix was performed by means of a four point bending test. Electrical resistance of the carbon fiber was measured during the compression test to recognize initiation of the compressive fracture. Fiber breaks at two adjacent locations were observed, which was caused by micro-buckling of the fiber. Apparent compressive strength of the fiber was measured in the experiment. Actual compressive strength of the fiber was predicted from the apparent compressive strength. Correlation between compressive strengths based on the elastic foundation model and the kink band model was discussed.

Effects of fiber misalignment and transverse shear modulus on localization and shear crippling instability in thick imperfect cross-ply rings under external pressure

Abstract The effect of transverse shear modulus on the compressive response of a thick plane strain cross-ply ring (very long cylindrical shell) weakened by the presence of a modal imperfection is investigated. The present study is primarily motivated to obtain the hitherto unavailable results pertaining to the effect of reduced transverse shear modulus, G LT ∗ , of a lamina weakened by the presence of randomly distributed fiber misalignments. A simple expression for the reduced transverse shear modulus, G LT ∗ , of a layer material is derived in terms of the average fiber misalignment angle. A fully nonlinear finite element analysis, that employs a cylindrically curved 16-node layer-element and is based on the assumption of layer-wise linear displacement distribution through thickness (LLDT), is utilized in the analysis of the afore-mentioned cross-ply ring. The interaction of a micro-structural defect in the form of initial fiber misalignments with its macro-structural counterpart represented by a modal imperfection is a key to understanding this meso-structural level phenomenon. Hitherto unavailable numerical results pertaining to the influence of this effect on the localization of buckling patterns and the ensuing shear crippling instability are also presented.

Effects of fiber nonlinear properties on the compressive strength prediction of unidirectional carbon–fiber composites

Compressive strength of unidirectional carbon–fiber composites is analyzed with emphasis on the nonlinear elasticity of carbon fiber. The deformation and stress state in a kink band is solved numerically using an incremental form of the governing equations, and compressive strength is determined for a given kink band angle and initial fiber misalignment. Constitutive equations are based on one-parameter plasticity model and nonlinear elasticity, which is attributed to matrix plasticity and fiber nonlinearity, respectively. Effects of fiber nonlinear properties on the predicted compressive strength are investigated under various conditions of initial fiber misalignments, kink band angles, and fiber properties. Nonlinear fiber properties turn out to reduce the predicted compressive strength of unidirectional composites in the cases of small fiber misalignments.

Mechanics of micromechanical clips for optical fibers

The use of single-mode optical fibers in telecommunications is widespread. However, current laser pig-tailing methods employing either glue or weld to secure the fibers in place are costly and there are inherent problems such as initial fiber mis-alignment, movement during bonding and instability during the service life. An innovative mechanical solution using silicon or silicon nitride clips has recently been proposed to address the issue (Strandman and Bäcklund 1995 Proc. SPIE 2639 18, Strandman and Bäcklund 1997 J. Microelectromech. Syst. 6 35, Strandman and Bäcklund 1998 J. Micromech. Microeng. 8 39, Bostock et al 1998 J. Micromech. Microeng. 8 343, Liu and Lu 2001 J. Micromech. Microeng. 11 195). This paper analyses the mechanical properties of such clips, with special focus placed on crack initiation and propagation due to excessive loading. The singular stress fields near the corner of the clip and substrate are calculated by the method of finite elements, and theoretical models are developed to predict the initiation of failure for clip/substrate systems having various geometrical dimensions and material combinations. The orientations of the initial crack as well as crack growth processes are discussed. The predicted failure modes are compared with those observed in silicon nitride/silicon systems.

Modeling of compressive failure in fiber reinforced composites

The classical results of compressive strength in fiber reinforced composites are briefly reviewed. The microbuckling analysis by Rosen (1965) and the Argon-Budiansky analysis for kink band formation ( Argon, 1972; Budiansky 1983) are discussed and their results are rederived by using a new generalized Timoshenko beam model which is developed for a two-dimensional periodic matrix–fiber–matrix laminate. Introducing a ‘shear hinge’ to simulate a kink band and using the method of split rigidities it is shown that not only an initial fiber misalignment but also any misalignment in the loading system can affect the critical stress for kinking. A new mechanism based on shear instability of matrix is proposed for kink band formation and a simple formula is then derived to predict the kink band angle. Finally, a criterion for matrix yielding combining axial compressive stress and transverse shear perturbation is applied to modify the Argon–Budiansky kinking formula.

Failure mechanisms in thick composites under compressive loading

Failure mechanisms were studied in a unidirectional carbon/epoxy composite under uniform and linearly varying longitudinal compression. The first failure mechanism is shear yielding or shear failure in the matrix precipitated by initial fiber misalignment. It was shown how an initial fiber misalignment of 1.5° can produce the measured compressive strength of 1725 MPa (250 ksi). Matrix failure is followed by fiber buckling and fracture, resulting in the formation of a kink band. The kink band orientation is constant in the range of β = 20–30°, whereas the kink angle a varies from a small initial value to a maximum value of 2β. Kink band widths varied between 4 and 20 fiber diameters. Kink bands can occur on different planes which can rotate along the band. Kink band multiplication or broadening with increasing stress was observed at points where the maximum kink angle α was reached.

On the buckling/kinking compressive failure of fibrous composites

In this paper, it is demonstrated that the compressive response of unidirectionally reinforced composites may initiate in a micro-buckling mode and subsequently switch to a micro-kinked configuration. The foregoing possibility derives from a mechanics model that considers initial fiber misalignments, a non-linear shear response of the matrix, shear deformable fibers, and stochastic fiber spacings. The last-mentioned non-uniformity in fiber spacings plays a major role in the generation of fiber kinks.Various features of the compressive deformation and failure process are exhibited by computational examples.

Model for the Micro-Buckling/Micro-Kinking Compressive Response of Fiber-Reinforced Composites

This article focuses on the effects that non-uniform fiber spacings have on the compressive response of composites. The above type of imperfection is included in a model which incorporates initial fiber misalignments and accounts for non-linear shear response of the matrix and shear-deformable fibers. It is shown that the disparate response of fibers embedded within matrix layers of different thicknesses results in reduced levels of compressive strengths and leads to failure modes which contain discontinuities in the fiber shear strains.

Compressive Kinking of Fiber Composites: A Topical Review

This is a review of the results of several selected theoretical studies concerned with the localized kinking, or microbuckling, of aligned fiber composite materials subjected to compression in the fiber direction. Compressive kinking is of primary concern in polymer matrix composites, for which kinking failure can limit the compressive strength to a value that is usually much lower than the tensile strength. A similar situation can occur in carbon matrix fiber composites. Compressive kinking failure may be understood on the basis of an elementary theoretical approach that ignores the influence of bending resistance of the reinforcing fibers, but takes into account the nonlinearity of composite constitutive relations as well as the effects of initial imperfections in fiber alignment. Kink bands bounded by fiber breaks are produced by deformations that occur after the attainment of peak compressive loads. The theoretical calculation of the widths of such kink bands does require consideration of fiber bending resistance; on the other hand, the results for kink width are not sensitive to the sizes of initial fiber misalignments. Progress in the study of the following additional kinking topics is summarized briefly: correlation of static kinking strength and random fiber misalignment; effects of shear and transverse loads on static kinking; viscoelastic and creep kinking; kinking fatigue; and a phenomenological theory of kinking “toughness”.

Compressive strength of unidirectional fiber composites with matrix non-linearity

A study has been made of the effect of fiber misalignment and non-linear behavior of the matrix on fiber microbuckling and the compressive strength of a unidirectional fiber composite. The initial fiber misalignment constituted the combined axial and shear stress state in the matrix, and the state of stress just prior to the buckling was considered to be the initial state of stress in bifurcation analysis. The expression for the critical microbuckling stress was found to be the same as that for the elastic shear-mode microbuckling stress except that the matrix elastic shear modulus was replaced by the matrix elastic-plastic shear modulus. Incremental theory of plasticity and deformation theory of plasticity were used to model the matrix non-linearity. The analysis results showed reasonable correlation with available experimental data for AS4/3501-6 and AS4/PEEK graphite composites with 2° to 4° range of initial fiber misalignment.

Compressive Strength and Failure Time Based on Local Buckling in Viscoelastic Composites

The axial compressive strength and failure time of unidirectional, viscoelastic composites are investigated. Effects of nonlinear shear behavior and fiber misalignment are emphasized because they are important strength-limiting factors in those strongly anisotropic composites which fail by local buckling in the shear mode of deformation. We first describe the basic buckling model and then, neglecting hereditary effects, predict the compressive strengths of an untoughened and a rubber-toughened carbon/epoxy composite. Next, using a nonlinear viscoelastic constitutive equation for shear behavior, failure time for constant load and compressive strength for increasing load history are predicted by a numerical method. Additionally, approximate analytical formulas are developed which enable one to easily estimate buckling response as a function of initial fiber misalignment angle as well as loading and material parameters.