Fiber Kinking Research Articles

Constitutive model for imperfectly bonded fibre-reinforced composites

A constitutive model for fibre-reinforced composites has been developed that takes imperfect fibre/matrix interfacial bonding into account. The model can predict the nonlinear material response of a composite in the large strain regime. Independent constitutive laws can be used for the constituents behaving elastic or elastic-plastic. A constitutive equation is derived for the composite moduli relating stresses to strains. The model is used to predict the development of the compressive failure; fibre kinking that is either formed by bifurcation or due to an initial fibre imperfection. A three-dimensional finite element model for kink band formation is used to validate the results obtained using the constitutive model with varying levels of interfacial bonding.

Fatigue loading of tendon results in collagen kinking and denaturation but does not change local tissue mechanics

Fatigue loading is a primary cause of tendon degeneration, which is characterized by the disruption of collagen fibers and the appearance of abnormal (e.g., cartilaginous, fatty, calcified) tissue deposits. The formation of such abnormal deposits, which further weakens the tissue, suggests that resident tendon cells acquire an aberrant phenotype in response to fatigue damage and the resulting altered mechanical microenvironment. While fatigue loading produces clear changes in collagen organization and molecular denaturation, no data exist regarding the effect of fatigue on the local tissue mechanical properties. Therefore, the objective of this study was to identify changes in the local tissue stiffness of tendons after fatigue loading. We hypothesized that fatigue damage would reduce local tissue stiffness, particularly in areas with significant structural damage (e.g., collagen denaturation). We tested this hypothesis by identifying regions of local fatigue damage (i.e., collagen fiber kinking and molecular denaturation) via histologic imaging and by measuring the local tissue modulus within these regions via atomic force microscopy (AFM). Counter to our initial hypothesis, we found no change in the local tissue modulus as a consequence of fatigue loading, despite widespread fiber kinking and collagen denaturation. These data suggest that immediate changes in topography and tissue structure – but not local tissue mechanics – initiate the early changes in tendon cell phenotype as a consequence of fatigue loading that ultimately culminate in tendon degeneration.

Progressive failure analysis of Z-pinned composite laminates under tension loading

Based on micromechanical characters of Z-pinned composite laminate, a finite element model is established to predict progressive failure properties of Z-pinned composite laminate under tension loading. For Z-pinned composite laminates, four failure modes: matrix cracking, matrix compressive failure, fibre breakage and fibre kinking are included in the present model. The calculated failure strength is compared with those obtained from experiments and other model. Failure mode pictures and stress-strain curves under tension load are obtained. The results indicate fibre breakage due to the matrix cracking is the main failure mode in Z-pinned carbon/epoxy composites under tension.

A failure mechanism based model for numerical modeling the compression-after-impact of foam-core sandwich panels

A failure mechanism-based progressive damage growth model is developed, applied and validated for modeling woven polymer-based foam-core sandwich panels under compression-after-impact. A Schapery theory based constitutive model, which takes account of intra-ply shear inelasticity and fiber kinking and resulting fracture is developed for the impacted plain weave fabric laminated face-sheets under compression loading. Each ply of the face-sheets is modeled as an orthotropic nonlinear elastic lamina degrading as characterized through laboratory experiments. The behavior of woven plies in the warp and fill directions is elastic until the attainment of local instability in compression. The phenomenon of fiber micro-buckling leading to kink banding, which was observed to be the mechanism controlling failure of the impacted face-sheets and hence the sandwich panels, is explicitly accounted for by allowing the fiber rotation at a material point. In the shear direction, plasticity is also considered to represent the elastic-plastic in-plane shear behavior of woven fabric plies. The constitutive model is numerically implemented using the commercially available finite element package ABAQUS through a user defined material subroutine (UMAT). The previous 3D damaged FE model which was proven to accurately capture the low–velocity impact damages is imported and subjected to a compression loading modeling. The numerical results in terms of deformation, failure mode and residual strength show a remarkable agreement with experimentally measured ones, allowing the model to be validated.

Computational micromechanics of fiber kinking in unidirectional FRP under different environmental conditions

The determination of ply properties of Fiber Reinforced Polymers (FRP) for particular operational environmental conditions in aeronautical applications is mandatory in order to fulfill current industry stringent certification requirements. However, the traditional experimental approach requires massive investments of resources and time. From the behaviour obtained experimentally, constitutive equations including failure criteria are then devised to be used in the design of FRP structures. The ply longitudinal behaviour under compression is generally the most difficult to measure and characterize. In this work, an alternative coupled experimental-computational micromechanics approach is proposed to determine the longitudinal compression properties of unidirectional FRP plies under different environmental conditions. This methodology includes experimental characterization of matrix and fiber/matrix interface, combined with numerical simulations of realistic microstructures. The interface decohesion is simulated using cohesive-frictional interactions. A pressure dependent, elasto-plastic model that includes tensile damage is employed to capture the matrix nonlinear behaviour. The numerical predictions match the experimentally-obtained ply properties available in the literature in a remarkable way and suggest that virtual ply property characterization is a mature and reliable approach to conduct screening of materials.

Mesh objective implementation of a fibre kinking model for damage growth with friction

A newly developed physically based model for the longitudinal response of laminated fibre-reinforced composites during compressive damage growth is implemented in a Finite Element (FE) software. It is a mesoscale model able to capture the physics of kink-band formation by shear instability, the influence of the matrix in supporting the fibres and the rotation of the fibres during compression, resulting in more abrupt failure for smaller misalignments. The fibre kinking response is obtained by solving simultaneously for stress equilibrium and strain compatibility in an FE framework.Strain softening creates pathological sensitivity when the mesh is refined. To make the model mesh objective, a methodology based on scaling the strain with the kink-band width is developed. The FE implementation of the current model is detailed with focus on mesh objectivity, and generalized to irregular meshes. The results show that the current model can be used to predict the whole kinking response in a 3D framework and thus account for the correct energy dissipation.

Microscale based prediction of matrix crack initiation in UD composite plies subjected to multiaxial fatigue for all stress ratios and load levels

A criterion is developed which predicts matrix fatigue crack initiation for Uni-Directional (UD) composite plies subjected to multiaxial fatigue load at all stress-ratio's: Tension-Tension, Compression-Compression and Tension-Compression. This research is based on physical observations of matrix damage types and their respective driving forces. Existing fatigue prediction formulations, that partly succeed in predicting fatigue life to initiation, are investigated for their key attributes which are subsequently combined in a coherent way. The framework requires 7 material parameters: 4 for Tension-Tension load, 2 for Compression-Compression load and 1 to take into account the accelerated occurrence of damage under Tension-Compression load. The material parameters can be calibrated from only 7 crack initiation S-N curves. 5 experimental datasets, a variety of the two most common reinforcing fibres and matrix (Carbon and Glass fibres combined with an epoxy or PEEK resin), are selected for a thorough verification and validation of the criterion. The agreement of the prediction with experiment is, remarkably, excellent for Glass/Epoxy, good for Carbon/Epoxy and reasonable for Carbon/PEEK. This new framework establishes a solid base for further developments to predict matrix crack initiation and the inclusion of other failure types such as fibre kinking.

Tensile Behavior of Pultruded Fiber-Reinforced Polymer Laminates with Bonded and Bolted Splice Joints

This paper presents an experimental investigation on double-lap joints of grit-blasted surface finish fiber-reinforced polymer (FRP) splice plates bonded and bolted to FRP laminates. Eighteen coupon joint specimens were tested under tensile loading with varying types of FRP splice plates and FRP laminates. Four types of bolts were evaluated: FRP bolts, high corrosion-resistant steel (HCRS) bolts, stainless steel (SS) bolts, and SS bolts wrapped with glass FRP (GFRP) (referred to as “SF” bolts). The test results indicated that double-lap splice joints, which incorporated HCRS bolts, epoxy adhesive, and grit-blasted surface finish FRP splice plates, provided strong bonds with FRP laminates. The grit-blasted surface finish of the FRP splice plates and the epoxy adhesive contributed to improving joint stiffness and strength. The specimens with FRP bolts showed brittle behavior and failed at relatively low ultimate load. The failures of those specimens were debonding of epoxy layers followed by shearing of the FRP bolts. The specimens with steel bolts (i.e., HCRS, SS, and SF bolts), however, exhibited ductile behavior and failed at a much higher ultimate load than did the FRP bolt specimens. Typical failure modes of the steel bolt specimens were fracturing of the FRP laminate (resulting from fiber rupture or kink, shear-out, and delamination failure of the GFRP plies and bearing failure of FRP materials near the edge of bolt holes in the load direction), bearing failure of the FRP splice plates, epoxy debonding, and yielding of bolts. Although FRP wraps may enhance the durability of the SS bolts, the use of SF bolts may significantly affect the failure mode of the splice joints.

Revealing complex aspects of compressive failure of polymer composites – Part II: Failure interactions in multidirectional laminates and validation

The compressive failure of multidirectional laminates can be considered as an interaction of four failure mechanisms: fiber kinking, fiber splitting, matrix cracking and delamination. The interaction of these four failure mechanisms is responsible for the macroscopically observed nonlinear behavior and ultimate failure of the structure.In this paper, a numerically efficient 3D Finite Element modeling approach is presented combining the benefits of homogenizing material models and micromechanical modeling strategies. The micro model is used to resolve the regions which are prone to fiber kinking. In all other regions, a single UD ply is considered as a continuum (i.e. in a homogenized way) and the material properties are represented using a transversely-isotropic constitutive model. At both scales, fully 3D elastic–plastic material models regarding nonlinearities and failure under multiaxial loading conditions are used.With this approach, the progressive failure of multidirectional laminates under compressive loading can be simulated in detail considering the complete kinking process and the progression of kink bands. The sequence and interaction of the different failure mechanisms is studied and discussed. In order to validate the numerical results, the nonlinear stress–strain response and ultimate failure stress of selected carbon epoxy laminate layups is predicted and compared with experimental results.

Revealing complex aspects of compressive failure of polymer composites – Part I: Fiber kinking at microscale

The fact that complex simulation can be carried out at present days allows to go further to answer new questions in the compressive failure of polymer composites. A thorough understanding of fiber kinking is essential for the prediction of stiffness and strength of fiber reinforced composites. The goal of this paper is to give a deep understanding of some topics which are still unclear in the micro modeling of fiber kinking. Such are the kinking mechanism and the difference in the kinking mechanics between global and local imperfections, the determination of kink band angle and consideration of statistical distributions of fiber waviness.3D micro models are presented in Part-I in order to simulate the compressive failure in continuous fiber reinforced composites under pure compression considering the effect of fiber kinking. It is shown that the kinking mechanism is changed by changing the type of fiber waviness, the angle of the kink band is depend on the tensile strength of the fibers and the kink bands in a model with statistical distributions of fiber waviness are located at the edges of the specimen.

Modeling the fiber length-scale response of Kevlar KM2 yarn during transverse impact

In this study, transverse impact of a cylindrical projectile onto a 600 denier Kevlar KM2 yarn (400 individual fibers) is studied using a fiber length-scale three-dimensional finite element model to better understand projectile–fiber and fiber–fiber contact interactions on wave propagation and fiber failure within the yarn. A short time scale response indicates significant transverse compressive deformation in the fiber that increases with impact velocity. Fiber-level modeling predicts a flexural wave that induces curvatures in the fibers significant enough to induce compressive fiber kinking and fibrillation. A spreading wave normal to the direction of projectile impact develops and spreads the fibers at high velocity. The models predict bounce velocities of the individual fibers within the yarn that varies based on spatial location. These mechanisms result in non-uniform loading and progressive failure of fibers within the yarn. In addition, the models show a gradient in the axial tensile stress in the fiber cross-section at the location of failure. Current state-of-the-art experimental capabilities in yarn/fabric impact testing do not have the spatial resolution to track individual single-fiber micron length-scale deformations in real time. These fiber-level mechanisms may explain the experimentally observed lower breaking speed for yarns better the classic Smith solution, which assumes yarns are homogenous (i.e. individual fibers and their interactions are not considered) and loaded uniformly in tension (multi-axial loading and stress gradients are neglected).

A physically based model for kink-band growth and longitudinal crushing of composites under 3D stress states accounting for friction

A material model to predict kink-band formation and growth under a 3D stress state is proposed. 3D kinking theory is used in combination with a physically based constitutive law of the material in the kink-band, accounting for friction on the microcracks of the damaged material. In contrast to existing models, the same constitutive formulation is used for fibre kinking and for the longitudinal shear and transverse responses, thereby simplifying the material identification process. The full collapse response as well as a crush stress can be predicted. The model is compared with an analytical model, a micromechanical finite element analysis and crushing tests. In all cases the present model predicts well the different stages of kink-band formation and crushing.

On the role of kinking in the bearing failure of composite laminates

Fibre kinking is one of the main failure modes of composite laminates under compression loading. In this paper, the role of kinking in the failure of quasi-isotropic composites subjected to a bearing load is investigated. High-resolution CT scans show that kinking is largely involved in the events leading to laminate collapse, notably by triggering other damage modes such as delamination. Kink bands develop extremely progressively, leading to the formation of a wide localization zone (or FPZ, failure process zone). Such behaviour calls for a non-local modelling approach. Local damage models would lead to overly conservative sizing. A simple model, based on Hashin failure criteria and non-local effective stresses is confronted to experiments, and its limits are highlighted. It will be shown that proper modelling of the bearing failure requires the characteristic behaviour of kink bands to be taken into account.

Investigation of the Thermomechanical Behavior of a 2 × 2 TWILL Weave Fabric Advanced Textile Composite

The thermomechanical performance of a 2 × 2 twill weave fabric advanced textile composite was evaluated. The tensile, compressive, and flexural properties of flat beam specimens of the composite were tested at room temperature, in water (24.9 to 96.7°C), and in liquid nitrogen (−96.9 to 99.4°C) by using a high-precision instrument called the dynamic mechanical analyzer (DMA). The storage modulus and tanδ of the carbonfiber-reinforced plastic (CFRP) specimens at various temperatures were evaluated. The scanning electron micrograph (SEMs) of deformed composite specimens revealed their failure mode (fiber pull-out, debonding, crack propagation, delamination, matrix cracking, and kinking of fibers).

Quasi-static bearing failure of CFRP composite in biaxially loaded bolted joints

Hybrid composite-aluminium bolted joints develop internal loads at elevated temperatures, due to the difference in thermal expansion properties of their constituent materials. In aircraft joints, the thermally induced bolt loads are commonly directed perpendicular to the mechanical loads, inducing a biaxial bearing load state. In this work, carbon–epoxy laminate specimens were tested in uniaxial and biaxial quasi-static bearing failure experiments in a specially designed test rig, at elevated temperature. A microscopy study of a failed specimen revealed that the failure process was mainly driven by fibre kinking, although extensive matrix cracking and delaminations were also found. The experiments were simulated by three-dimensional, explicit, finite element analyses, which included intralaminar damage and delamination. The experimental and simulated bearing failure loads differed by 1.7% in the uniaxial case and 2.1% in the biaxial case. It was suggested that the load–displacement response is influenced by the interaction of all damage mechanisms. Delamination modelling was, however, not essential for the prediction of the maximal bearing strength. The same effective bearing strengths were obtained for the biaxially loaded specimens as for the uniaxially loaded ones, but the damage accumulation process and the resulting damage distributions were different.

OS1101-114 破壊モードを考慮した複合材の損傷進展解析 : その1:静的圧縮を受ける有孔平板について

OS1101-114 破壊モードを考慮した複合材の損傷進展解析 : その1:静的圧縮を受ける有孔平板について

OS1102-115 破壊モードを考慮した複合材の損傷進展解析 : その2:衝撃後に静的圧縮を受ける平板について

Compression after impact (CAI) strength is a key design criteria for composite structure. In this study, impact damage and CAI strength were simulated by progressive damage analysis. The LaRC03 failure criteria which consider fiber kink failure mode was employed for each lamina, and cohesive zone modelling was applied for interlaminar resin layer. In these analyses, impact load and static compression load were applied successively. The simulated impact damage area and CAI strength were compared to tests results. Consequently, simulation well predicted test results for both of impact damage and CAI strength. In addition, it was suggested that CAI failure is caused by fiber kink in each lamina, not by propagation of delamination.

An Investigation of the Mechanical Behaviors of [45/-45/0/90]ns Satin Weave Composite at Different Loading Rates

The objective of this article is to investigate the compressive behaviors of [45/-45/0/90]ns satin weave E-7781 glass/Eepoxy composite laminate under different loading strain rates along the in-plane direction. The low strain rate tests were conducted with an INSTRON testing machine, and the high strain rate tests were conducted using a pulse shaper modified compression Split Hopkinson Pressure Bar (SHPB) apparatus. Failure strength and strain at peak stress were evaluated experimentally at different strain rates. The results showed that failure strength and strain at peak stress were rate sensitive. A few strain rate dependent constitutive models were referred to describe the dynamic mechanical behaviors of woven composites with various stacking sequence, and the constants in the equations could be confirmed from experiment data. Optical and microscopic graphs on the specimens were carefully examined to determine operative failure modes. Within the studied strain rate regimes, the failure mode was observed to change from splitting followed by fiber kink banding to predominantly delamination and shear fracture as the strain rate increases from quasi-static to high strain rates.

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.

Dynamic Compressive Behaviors of Multi Directional Woven Composite Laminates at Different Strain Rates

This paper discusses the experimental study on the response of multi directional satin weave E-glass/epoxy composite laminates subjected to quasi-static and high strain rate compression loading along in-plane direction. Composite laminates were fabricated from satin weave glass fabric reinforced epoxy matrix pre-impregnated tapes which were manually laid up into laminates with stacking sequence of [45/-45/0/90] The low strain rate tests were conducted with an INSTRON™ testing machine, and the high strain rate tests done using a pulse shaper modified compression Split Hopkinson Pressure Bar (SHPB) apparatus. Compressive strength, modulus and strain at peak stress are evaluated experimentally at different strain rates. The results show that compressive strength, modulus and strain at peak stress are rate sensitive and enhanced at high strain rate compared with those at quasi-static loading. Under high strain rate loading, compressive strength and modulus increase as the strain rate increases. Optical and microscopic graphs on the specimens are carefully examined to determine operative failure modes. With the studied strain rate regimes, the failure modes are observed to change from splitting followed by fiber kink buckling to predominantly delamination and shear fracture as the strain rate increases from quasi-static to high strain rate.