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Continuous Parallel Fiber Composites: Deformation and Strength

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Abstract

This article provides a summary of some analytical methods that may be used to estimate the effective thermo-elastic constants of unidirectionally fiber reinforced composites. Both multi-phase and two-phase composites are considered. Matrix yielding effects and failure processes during uniaxial loading are also considered. Fiber failure and matrix cracking modes of damage are considered, and in addition compression strength, transverse compression strength, and in-plane longitudinal shear strength.

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... Finally the initiating fibres buckle and fracture, passing the loading on to adjacent fibres. When fibres run transversely to the applied force the composite will fail through fibre/matrix debonding and matrix shear cracking[119]. Typically laminar composites are relatively thin; this can result in Euler buckling of the coupon itself. ...
Article
The tensile failure of unidirectional alumina fibre reinforced aluminium is studied in uniaxial loading along the fibre axis. The tensile strength is measured as a function of matrix yield strength, which is varied by varying the testing temperature, from RT to 600°C. Over the range of matrix yield strength (i.e., of temperature) examined, the fracture mode remains brittle. Batdorf’s (J Reinforced Plastics Compos 1982;1:153–164) simple ideal local load-sharing model describes well the observed behaviour, under the condition that it be adapted to account for the actual number of nearest neighbours characteristic of the fibre distribution in the composite. This is shown to be close to three, i.e., at variance with the usually assumed idealized hexagonal or square fibre arrangement patterns.
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Full-text available
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The initiation and growth of damage in composite materials are phenomena that precede the failure event where a material sample or component separates into two pieces. In fatigue, the damage grows slowly and leads to a gradual deterioration of mechanical properties. For the prediction of the fatigue behavior of unidirectional and laminated titanium composites, it is necessary to be able to take account of the effects on the thermoelastic constants of matrix cracking that is induced by fatigue stress cycling. The values of the thermoelastic constants for microcracked composites are determined by the way in which stress is transferred between fiber and matrix in unidirectional composites, and between neighboring plies in laminates, as a result of microcrack formation in the matrix. A summary is given of the recent progress that has been made at the National Physical Laboratory (NPL) on the development of analytical stress transfer models for unidirectional and laminated composites. The models are each based upon just a single assumption concerning the stress field that leads to stress and displacement solutions for which the Reissner energy function, used in a variational calculation, has stationary values. The use of the Reissner function allows both applied traction and displacement conditions to be imposed on the fiber/matrix interface and external boundary. In contrast to other applications of variational techniques, the models provide both the stress and displacement distributions at every point in the composite. Thus, complete solutions can be derived that satisfy exactly the equilibrium equations, the interface conditions, the stress-strain relationships apart from one, and the boundary conditions involving tractions. The remaining stress-strain relationship and boundary conditions involving displacements are satisfied in an average sense. For unidirectional composites, both perfectly bonded and frictionally slipping interfaces (such that the interfacial shear stress is a constant) are considered; while for laminates, consideration is restricted to interfaces that remain perfectly bonded in the presence of transverse cracks. The analytical stress transfer models are of high quality to the extent that they represent the best models that can be derived subject to the single assumption on which they are based. The models do, therefore, offer life prediction methodologies the opportunity of confidently making use of analytical methods that obey the important principles of mechanics. The estimation of effective stress intensity factors for bridged matrix cracks that occur in titanium composites subject to fatigue loading at modest load levels is an important element in the prediction of composite performance. Assuming that fibers remain intact, the paper makes use of the stress transfer models to predict the dependence of stress intensity factors (for long cracks) on the applied stress and crack separation, for bridged cracks in both unidirectional and laminated composites. The effects of crack interaction are determined, and the new model predictions are compared to those of shear-lag theory modified to take account of residual stresses arising from thermal expansion mismatch effects. It is also shown how predictions can be made for the dependence of the thermoelastic constants of unidirectional and laminated titanium matrix composites on the nonuniform spacings of matrix cracks that can be encountered in practice.
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Article
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Article
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Article
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Article
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Article
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Article
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Article
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Article
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Article
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Article
This paper reviews the formulation of the problem of a bridged crack in an elastic medium as an integral equation, noting explicit forms for specimens of various common shapes. Numerical methods are provided for the convenient and efficient self-consistent solution of the integral equation when the bridging tractions, p, are a function of crack opening displacement, u, rather than an explicit function of position in the crack. Methods are presented for determining physically and computationally unstable crack configurations for various forms of p(u), including functions possessing a peak. Knowledge of both stable and unstable solutions is essential to demarking the transition from noncatastrophic (or ductile) failure to catastrophic (or brittle) failure.
Article
Matrix fracture in brittle-matrix fiber composites is analyzed for composites that exhibit multiple matrix cracking prior to fiber failure and have purely frictional bonding between the fibers and matrix. The stress for matrix cracking is evaluated using a stress intensity approach, in which the influence of the fibers that bridge the matrix crack is represented by closure tractions at the crack surfaces. Long and short cracks are distinguished. Long cracks approach a steady-state configuration, for which the stress intensity analysis and a previous energy balance analysis are shown to predict identical dependence of matrix cracking stress on material properties. A numerical solution and an approximate analytical solution are obtained for smaller cracks and used to estimate the range of crack sizes over which the steady-state solution applies.
Article
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Article
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Article
A model is developed for fatigue growth of matrix cracks in metals reinforced with aligned continuous elastic fibers. The mechanics of elastic cracks bridged by frictionally constrained fibers is used to develop the model, which provides estimates of the tip value of the stress intensity factor amplitude, ΔKTIP. It is found that when the applied load amplitude is held fixed during fatigue crack growth, ΔKTIP, and thus the rate of growth approach an asymptotic value independent of crack length. The residual strength after fatigue crack growth is also discussed. In some cases, the residual strength is unaffected by prior fatigue growth. But, in another regime, the matrix crack length allows fibers to begin breaking before the matrix crack grows. The strength is then inversely proportional to the square root of fatigue crack length.
Article
Embedded single-fiber tests are often used to characterize the fiber/matrix interface, but their interpretation is usually limited by reliance on the qualitative view of the stresses provided by shear-lag analyses. This paper describes a new, three-dimensional, axisymmetric solution for the stresses around breaks in embedded fibers. The new solution is obtained using variational mechanics. It obeys equilibrium and traction boundary conditions exactly, obeys compatibility approximately, includes all components of the stresses, accounts for interacting fiber breaks, and includes residual thermal stresses. We apply the stress analysis to the single-fiber fragmentation test. In some sample calculations, we plot all components of stress at the fiber/matrix interface and give predictions for an “ideal” single-fiber fragmentation test. The stress analysis technique is readily adaptable to new problems such as the single-fiber pull-out test, the microdrop debond test, the description of interfacial fracture or yielding, and the effect of interfacial friction.
Article
A new simple model for predicting the uniaxial stress–strain behavior of a unidirectional ceramic matrix composite, including stochastic matrix crack evolution, stochastic fiber damage and ultimate failure, is presented. The model demonstrates an important transition in composite behavior. “Brittle” (low failure strain) behavior occurs when the matrix cracking stresses are sufficiently high; the composite fails during the matrix cracking regime of deformation and at a strain that is controlled by the matrix flaw population and elastic properties. “Tough” (high failure strain) behavior occurs when the matrix cracking stresses are lower; matrix cracking is completed prior to failure and the failure strain of the composite is controlled by the fibers. In both cases, the failure strength is fiber-controlled. The model is applied to study SiC/SiC 500-fiber minicomposite deformation, using data recently obtained by Lissart and Lamon on two material types, “B” and “C”. Parameters for the matrix flaw population are used to fit the experimental stress–strain data but the failure is controlled by the measured fiber strength statistics. Excellent agreement is found for the “C” materials, which are in the transition regime between the brittle and tough limits and variations in fiber strength are postulated to be responsible for the wide range of behaviors found in the “B” materials. The fitted matrix flaw parameters are then used to predict the fiber/matrix interfacial sliding resistance and the values obtained are in excellent agreement with independent values determined from both unload/reload hysteresis loops and fiber pullout lengths. The new model provides a useful tool for understanding the interplay matrix and fiber flaw distributions and the overall dependence of stress–strain behavior on all the underlying constituent material properties.
Article
The objective of this work is to study the effect of a frictional interface on the extent of interfacial debonding and internal stress distribution within a unidirectional ceramic matrix composite under thermo-mechanical loading. The configuration considered is a concentric cylinder with an annular crack in the axial plane of the matrix while the fiber-matrix interface is made to obey the Coulomb friction law. The present approach of employing a variational model is shown to satisfy all boundary and inequality conditions in the slip and stick regions and at the slip-stick transition point. The results are also shown to be in very good agreement with a numerical elasticity solution for points away from the matrix crack tip while some of the peculiarities near the crack tip associated with the numerical solution are identified.
Article
A classical result due to Daniels is that the strength of a bundle of parallel fibres is asymptotically normally distributed. Extensions of this result are obtained and applied to a series-parallel model consisting of a long chain of bundles arranged in series. This model is of importance in studying the reliability of fibrous materials. Improved approximations are also obtained which reduce the error associated with Daniels' approximation both for the single bundle and for the series-parallel system.
Article
Fiber reinforced composites strength by limit analysis methods
Article
Composite mechanics disciplines are presented and described at their various levels of sophistication and attendant scales of application. Correlation with experimental data is used as the prime discriminator between alternative methods and level of sophistication. Major emphasis is placed on: (1) where composite mechanics has been; (2) what it has accomplished; (3) where it is headed, based on present research activities; and (4) at the risk of being presumptuous, where it should be headed. The discussion is developed using selected, but typical examples of each composite mechanics discipline identifying degree of success, with respect to correlation with experimental data, and problems remaining. The discussion is centered about fiber/resin composites drawn mainly from the author's research activities/experience spanning two decades at Lewis.