Micromechanical modelling and simulation of chopped random fiber reinforced polymer composites with progressive debonding damage

The aim of the present paper is to provide a quantitative prediction of the elastic-damage behaviour of randomly oriented fiber polymer composites. A constitutive model based on micromechanical considerations is presented. The nucleation and growth of voids induced by progressive fiber debonding is combined with the constitutive relationship. Failure resulting of excessive damage accumulation is captured by a critical void volume criterion and a vanishing element technique. Experimentally, damage accumulation in random glass fiber–polyester composites was monitored by a videoextensometry technique able to control the local strain rate. Good agreement of model predictions with experimental data is pointed out. The model was implemented into a finite element program and numerical applications on composite structures (a tensile specimen and a plate containing a central hole) are presented to illustrate the capability of the approach. Digital image correlation method was also used to measure the full-field strain in a notched specimen under tensile loading. The simulated results compared favourably with those obtained from experiments.     

Damage evolution and debonding in hybrid laminates with a cohesive interfacial law

The hybridisation of fibres reinforced laminates, i.e., the combined use of two or more families of fibres, is an effective technique to achieve a pseudo-ductile response and overcome the inherent brittleness which limits the wider use of composite materials. In this paper, a one-dimensional analytical model for unidirectional hybrid laminates is derived. The model considers two elastic–brittle layers bonded together by a cohesive elasto–plastic–brittle interface. This formulation is applied to the study of the debonding and fracture of laminates under uniaxial loading and the results compared to experiments available from the open literature. This study shows that the proposed model provides a close fit to the experimental data and it is able to match accurately the crack patterns seen in the experiments. The model predicts four different failure mechanisms and is able to discriminate among them according to the geometrical and mechanical properties of the layers.

     

An exact theory of interfacial debonding in layered elastic composites

An exact theory of interfacial debonding is developed for a layered composite system consisting of distinct linear elastic slabs separated by nonlinear, nonuniform decohesive interfaces. Loading of the top and bottom external surfaces is defined pointwise while loading of the side surfaces is prescribed in the form of resultants. The work is motivated by the desire to develop a general tool to analyze the detailed features of debonding along uniform and nonuniform straight interfaces in slab systems subject to general loading. The methodology allows for the investigation of both solitary defect as well as multiple defect interaction problems. Interfacial integral equations, governing the normal and tangential displacement jump components at an interface of a slab system are developed from the Fourier series solution for the single slab subject to arbitrary loading on its surfaces. Interfaces are characterized by distinct interface force–displacement jump relations with crack-like defects modeled by an interface strength which varies with interface coordinate. Infinitesimal strain equilibrium solutions, which account for rigid body translation and rotation, are sought by eigenfunction expansion of the solution of the governing interfacial integral equations. Applications of the theory to the bilayer problem with a solitary defect or a defect pair, in both peeling and mixed load configurations are presented.     

Nonlinear progressive waves in elastic materials

Summary Progressive harmonic waves in nonlinear elastic materials are generally considered as small disturbances superposed on a finite deformation. In this first approximation they are governed by essentially the same laws as in linear elasticity. In the present paper a second-order theory is developed which allows for nonlinear effects on progressive waves in a finitely deformed elastic material. The problem is investigated by means of a perturbation procedure using intrinsically two time scales. After providing the kinematical prerequisites a transport equation is derived which governs the distortion of the wave profile. A closedform solution is obtained for the case of a plane wave in a homogeneous medium. The influence of nonlinearity is closely related to the evolution of acceleration waves.

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Zusammenfassung Fortschreitende harmonische Wellen in nichtlinearen elastischen Stoffen werden meist als kleine Störungen betrachtet, die einer endlichen Verformung überlagert sind. In dieser ersten Näherung genügen sie im wesentlichen den gleichen Gesetzen wie in der linearen Elastizitätstheorie. In der vorliegenden Arbeit wird eine Theorie zweiter Ordnung entwickelt, die auch nichtlineare Effekte bei fortschreitenden Wellen in einem endlich verformten elastischen Material berücksichtigt. Das Problem wird mit Hilfe einer Störungsmethode behandelt, welche implizit zwei verschiedene Zeitmaßstäbe zuläßt. Nach Bereitstellung der kinematischen Hilfsmittel wird eine Transportgleichung hergeleitet, welche die Verzerrung des Wellenprofils beschreibt. Für ebene Wellen in einem homogenen Medium wird eine geschlossene Lösung angegeben. Der Einfluß der Nichtlinearität zeigt eine enge Verwandtschaft zur zeitlichen Entwicklung von Beschleunigungswellen.

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A continuum model for fiber reinforced materials with debonding

A continuum theory for a fiber-reinforced material with debonding between the constituents is presented. The debonding phenomenon is simulated by imposing the continuity of the normal displacements at the fiber-matrix interfaces while allowing free tangential slip there. The derived theory is of the lowest order and is obtained by using a first order expansion in the displacements in the fiber and matrix phases. The theory is applied to investigate the effect of debonding on the propagation of waves in a boron/epoxy fiber reinforced material. It is shown that an additional mode of propagation is obtained as compared with the usual case of perfect bonding     

Spherical indentation of composite laminates with controlled gradients in elastic anisotropy

Three-dimensional elastic analyses and experiments of indentation of thick laminated plates of carbon fiber reinforced epoxy are presented. Pointwise, the material is characterized as a linear elastic orthotropic material. The in-plane orientation of the carbon fibers is systematically varied as a function of depth. The influence of fiber orientation as a function of depth on the indentation response is considered along with the relationship between the indenter force vs depth. The fiber orientation profiles considered are those of a continuous linear variation between 90° at the outer surfaces and 0° at the center plane of the laminate, and a cross ply laminate involving alternating 90° and 0° layers through thickness. Experimentally, it is found that for the case of a cross-ply laminate, the indentation produces delaminations localized at the interfaces that separate planes of dissimilar orientation. For this case, stress concentrations at interfaces between plies of dissimilar orientation coincide with the observed sites of delamination. For the graded case, evidence of enhanced nonlinear deformation is found, without the nucleation of cracks. Computations show that for the graded material, tensile stresses perpendicular to fibers are suppressed significantly, possibly explaining the absence of matrix cracks in this material. Measured and computed indenter force-depth variations were found to be in good agreement. Experiments and computations also reveal that the orientation-graded material is more compliant when subjected to indentation than the conventional cross-ply laminate.     

Wave propagation in elastic laminates using a second order microstructure theory

A generalization of the simpler microstructure theory developed earlier for elastic laminates by Sun, Achenbach and Herrmann is used to analyze steady state plane wave propagation. This new version incorporates higher-order thickness variations in the displacement functions and includes restrictions on both displacement and stress at the laminate interfaces.To assess the potential of a second-order microstructure theory for accurate modeling of mechanical processes in laminates, dispersion results and especially mode shape data for both displacements and stresses are obtained and compared to corresponding solutions obtained by the theory of elasticity. The comparisons indicate that while dispersion results may be nearly identical, extremely significant differences may be observed in the mode shapes.     

Three-dimensional modelling of elastic bonding in composite laminates using layerwise differential quadrature

In an effort to overcome the limitations of existing rigid bonding analysis of composite laminates, the current three-dimensional elastostatic model is proposed. In this model, the three-dimensional interlaminar elastic stress field is determined using the technique of layerwise differential quadrature. The new formulations allowed us to determine the influence of a natural bonding layer upon the field variables in the laminated structure. The interfacial characteristics of continuity and discontinuity satisfy the kinematic continuity conditions through the elastic-bonding layer. A number of case studies are examined, comparisons with rigid bonding and finite element analyses are provided, and the influence of the pertinent parameters on the interlaminar stress field is evaluated and discussed.     

Bounds and estimates for elastic constants of random polycrystals of laminates

In order to obtain formulas providing estimates for elastic constants of random polycrystals of laminates, some known rigorous bounds of Peselnick, Meister, and Watt are first simplified. Then, some new self-consistent estimates are formulated based on the resulting analytical structure of these bounds. A numerical study is made, assuming first that the internal structure (i.e., the laminated grain structure) is not known, and then that it is known. The purpose of this aspect of the study is to attempt to quantify the differences in the predictions of properties of the same system being modelled when such internal structure of the composite medium and spatial correlation information is and is not available.     

Dynamic fiber debonding and frictional push-out in mode composite systems: Experimental observations

In the present work a modified Split Hopkinson Pressure Bar (SHPB) system is adopted to perform dynamic fiber push-out experiments on model single fiber composite systems. A tapered punch and a support connect a monofilament composite with the incident and transmitted bars of the SHPB. The tapered punch is used to apply compressive loading to a single fiber (either steel or aluminum) embedded in a surrounding matrix material (EPON 862). The SHPB allows real time measurement of relative fiber/matrix displacement and push-out force, as the debonding and push-out event progresses. Using this technique we have studied the effect of loading rate, material mismatch, fiber length, and surface roughness on the push-out event. It was seen that maximum push-out force increases with increasing loading rate. In addition dynamic interfacial strength and toughness is highly dependent on fiber surface roughness. Results from a finite element analysis incorporating a cohesive failure model were used to extract interface strength and toughness values. It was found that the particular aluminum/EPON interface used is characterized by a dynamic shear failure strength of 48±8 MPa, a mode II fracture toughness of 160±40 N/m, and a friction coefficient of 0.2 at a sliding rate of 6 m/s. For the rates tested here these quantities were found to be approximately constant.     

Nonlinear progressive damage model for composite laminates used for low-velocity impact

In order to effectively describe the progressively intralaminar and interlam- inar damage for composite laminates, a three dimensional progressive damage model for composite laminates to be used for low-velocity impact is presented. Being applied to three-dimensional （3D） solid elements and cohesive elements, the nonlinear damage model can be used to analyze the dynamic performance of composite structure and its failure be- havior. For the intralaminar damage, as a function of the energy release rate, the damage model in an exponential function can describe progressive development of the damage. For the interlaminar damage, the damage evolution is described by the framework of the continuum mechanics through cohesive elements. Coding the user subroutine VUMAT of the finite element software ABAQUS/Explicit, the model is applied to an example, i.e., carbon fiber reinforced epoxy composite laminates under low-velocity impact. It is shown that the prediction of damage and deformation agrees well with the experimental results.     

DAMAGE PROGRESSIVE MODEL OF COMPRESSION OF COMPOSITE LAMINATES AFTER LOW VELOCITY IMPACT

IntroductionCompressivepropertiesofcompositelaminatesafterlowvelocityimpactareoneofthemostseriouscircumstanceswhichmustbetakenintoaccountindamagetolerancedesignofcompositestructures[1].Impactdamagegenerallymanifestsintheformsofdelaminations,matrixcracksandfibrefracture[2 ,3].Sofaralotofresearcheshavebeentakeninlowvelocityimpactbehaviorofcompositelaminatesandtheirpost_impactcompressiveproperties.Compressivefailuremechanismsofcompositelaminatesafterlowvelocityimpacthavenotbeenknownclearly .Ther…     

Crack growth in planar elastic fiber materials

Particularly attention is here given to crack growth in opening mode in fiber networks. Low- and high-density cellulose fiber materials are used in synchrotron X-ray microtomography tensile experiments to illustrate phenomena arising during crack growth. To capture the observed fundamental mechanisms, significantly different from classical continua, a mechanical model based on a strong nonlocal theory is applied in which an intrinsic length reflects a characteristic length of the microstructure. Nonlocal stress and strain tensor fields are estimated by analytical solutions on closed form to a modified inhomogeneous Helmholtz equation using LEFM crack-tip fields as source terms. Justified by experimental observations, physical requirements of finite stresses and strains at infinity and at the tip are applied to remove singularities. The near-tip nonlocal hoop stress field is used to estimate crack growth directions and sizes of fracture process zones. Experimental observations are shown to be qualitatively well in accordance with numerical predictions, which justifies the adopted approach.     

Transmission and band gaps of elastic SH waves in functionally graded periodic laminates

Time-harmonic plane elastic SH-waves propagating in periodically laminated composites with functionally graded (FG) interlayers are investigated in this paper. A finite stack of periodic layers between two identical elastic half-planes is considered. Two different power laws are used to describe the property variation of the FG interlayers within the unit-cell. Two different models are developed to deal with the FG interlayers, namely, the explicit FG model and the multilayer model. In conjunction with the transfer matrix method, the wave reflection and transmission coefficients, and band gaps of the FG periodic laminates are computed. Numerical results are presented and discussed to reveal the influences of the FG and homogeneous interlayers, the incidence angle of time-harmonic plane SH wave on the location and width of band gaps. The explicit FG model developed in this study is accurate and capable to simulate the full wave pattern within the periodic laminates, and it can be easily extended to periodic laminates with defects. The corresponding results presented in this paper may have important applications in optimizing and developing novel acoustic devices such as wave filters and noise insulators.     

Meso cell model of fiber reinforced composite: Interface stress statistics and debonding paths

The primary goal of this work is to develop an efficient analytical tool for the computer simulation of progressive damage in the fiber reinforced composite (FRC) materials and thus to provide the micro mechanics-based theoretical framework for a deeper insight into fatigue phenomena in them. An accurate solution has been obtained for the micro stress field in a meso cell model of fibrous composite. The developed method combines the superposition principle, Kolosov–Muskhelishvili’s technique of complex potentials and Fourier series expansion. By using the properly chosen periodic potentials, the primary boundary-value problem stated on the multiple-connected domain has been reduced to an ordinary, well-posed set of linear algebraic equations. The meso cell can include up to several hundred inclusions which is sufficient to account for the micro structure statistics of composite. The presented numerical examples demonstrate an accuracy and high numerical efficiency of the method which makes it to be a promising tool for studying progressive damage in FRCs. By averaging over a number of random structure realizations, the statistically meaningful results have been obtained for both the local stress and effective elastic moduli of disordered fibrous composite. A special attention has been paid to the interface stress statistics and the fiber debonding paths development, which appear to correlate well with the experimental observations.     

含孔复合材料层合板静拉伸三维逐渐损伤分析

针对面内静拉伸纤维增强复合材料含中孔层合板，发展了参数化三维逐渐损伤模型. 该模型 可以模拟含中孔层合板损伤起始、发展及最终结构破坏整个过程，并能较好地预测含中孔层 合板的破坏模式和破坏强度. 采用所发展的模型和有限元三维逐渐损伤分析技术即应力分 析、失效判定准则及损伤过程中材料性能退化等，对其他文献所提供的9种不同类型含中孔层合板进行了损伤扩展分析及强度预测，同时对层合板的损伤基本机理、类型及其相互关联作用进行了探讨，计算结果与文献实验结果非常吻合.     

Elastic and elastic–plastic singular fields around a crack-tip in particulate-reinforced composites with progressive debonding damage

This paper deals with elastic and elastic–plastic singular fields around a crack-tip in particulate-reinforced composites with debonding damage of particle-matrix interface. Numerical analyses are carried out on a crack-tip field in elastic-matrix and elastic–plastic-matrix composites reinforced with elastic particles, using a finite element method developed based on an incremental damage theory of particulate-reinforced composites. A particle volume fraction and interfacial strength between particles and matrix of the composites are parametrically changed. In the elastic-matrix composites, a unique elastic singular field is created on the complete damage zone in the vicinity of a crack-tip in addition to the conventional elastic singular field on the no damage zone. The macroscopic stress level around a crack-tip is reduced by the debonding damage while the microscopic stress level of the matrix remains unchanged. In the elastic–plastic-matrix composites, the damage zone develops in addition to the plastic zone due to matrix plasticity, and both the macroscopic and microscopic stress revels around a crack-tip are reduced by the debonding damage. It is concluded from the numerical results that the toughening due to damage could be expected in the elastic–plastic-matrix composites, while it is questionable in the elastic-matrix composites.     

On the modeling of fiber dispersion in fiber-reinforced elastic materials

When an isotropic material is subject to a uniaxial tension, the principal strain transverse to the direction of applied load is always negative. However, in fiber reinforced materials the transverse principal strain can change its sign as the load increases, passing through the zero-points, known as perversions. We investigate how the number of perversions in a material reinforced by two symmetrically aligned families of distributed fibers depends both on the degree of fiber dispersion and the model used for fiber dispersion. Angular integration and three variants of the generalized structure tensor approach are considered and discussed. The study of perversions clearly demonstrates the qualitative difference between these approaches in the case of high dispersion of fibers. The results suggest that this difference is primarily due to the way compressive fibers are modeled.     

Prediction of the thermal conductivity of the constituents of fiber reinforced composite laminates

Three empirical formulas are developed to predict the thermal conductivities of fiber-reinforced composite laminates (FRCL) and its constituents. The inherent two or three-dimensional problem that is common in composites is simplified to a one-dimensional problem. The validity of the models is verified through finite element analysis. This method utilizes the parallel and series thermal models of composite walls. The models are tested at different fiber-to-resin volume ratios (30:70–75:25) and various fiber-to-resin thermal conductivity ratios (0.2–5). The predicted thermal conductivity of the fiber can be accurately predicted throughout the spectrum via two models. The first model is a first-order formula (R ² = 0.94) while the second model is a second-order formula (R ² = 0.976). These two models can be used to predict the fiber thermal conductivity based on the easily measured resin and laminate values. A third model to predict the overall laminate thermal conductivity is introduced. The thermal conductivity of the composite panel is predicted with very high accuracy (R ² = 0.995). The thermal conductivity predicted via the use of these models has an excellent agreement with the experimental measurements. Another use of these models is to determine the fiber-to-resin volume ratio (if all thermal conductivities of fiber, resin and laminate are known).