Planar Stability Problem of Composite Weakly Reinforced by Short Fibers

2008

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The instability of a composite material reinforced with a periodic row of parallel short fibers is studied considering the interaction of neighboring fibers. Emphasis is on the mutual influence of short fibers in the matrix during loss of stability, depending on the distance between them. A piecewise-homogeneous medium model and the three-dimensional linearized theory of stability of deformable bodies are used Keywords: composite materials, nanocomposites, short fibers, nanotubes, three-dimensional linearized theory of stability, inhomogeneous stress-strain state, finite-difference method, interaction of fibers, critical strain, instability modeIntroduction. As seen during recent development of the composite technology, composite materials can exhibit very interesting combinations of major properties such as high strength, high-temperature range, oxidation resistance, fatigue strength, etc. Fibrous materials such as carbon fibers, oxide fibers and whiskers, and carbides used as reinforcements reduce the weight of composites, preserving their strength. This is why the greatest success in the use of composites was achieved in aerospace technology, manufacture of gas-turbine engines, high-speed cars, extreme yachts and raceboats, etc. The major factors that limit the use of most composites are the high cost of reinforcement fibers and technology-related difficulties that do not allow gaining the greatest benefit from the strength of reinforcing fibers in structural elements made of composites.Composites owe their strength to the combination of two materials with different mechanical properties. For maximum strength, the harder component should play the role of reinforcement. Reinforcing elements should be long enough to provide strong bonding with the matrix. Therefore, the most favorable form of reinforcement is a thin fiber because, as is well known, the thinner the fiber, the stronger it is. However, continuous, very long fibers cannot always be used for technological reasons since the geometry of too many products is such that they cannot be made of continuous fibers. Moreover, very long fibers cannot be made of all available materials and fibers should be laid up so as not to reduce their strength. For example, Fig. 1 [2] shows an end of a TaC-(Co+Ni-Cr) unidirectional eutectic alloy pickled after crystallization on which monocrystal whiskers can be seen.The recent years saw the advent of nanocomposites, a new class of composites. Their reinforcing elements measure several nanometers. A nanocomposite is a material consisting of a matrix and nanoparticles (nanotubes) as a reinforcement (Fig. 2 [13]). This type of structure is in full compliance with the terminology of the micromechanics of composites with polymeric or metal matrix.Consider a simplified nanotube model. A perfect nanotube (CNT) is a seamless cylinder formed by rolling a flat hexagonal graphite sheet. Such a tube does not form seams upon rolling and has hemispherical caps at the ends, which include six regular pentagons, along with regular hexagons...

Section: Analysis Of the Calculated Resultsmentioning

confidence: 98%

“…Using the results of stability analysis of composites weakly reinforced with short fibers [7] and with pairs of parallel short fibers [6] and being guided by physical considerations, we assume that buckling of reinforcement occurs as shown in Fig. 6.…”

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confidence: 99%

Plane instability problem for a composite reinforced with a periodic row of short parallel fibers

2008

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“…Stability analysis of composites under-reinforced with short fibers [2,10] and with pairs of collinear short fibers [11] and physical considerations suggest that reinforcement of this kind may follow different microbuckling mechanisms shown in represents the case where the matrix between inclusions is weak enough to produce a kind of a plastic hinge under buckling and to cause inclusions to bend.…”

Section: Problem Formulationmentioning

confidence: 98%

Two-dimensional buckling problem for a composite reinforced with a periodic row of collinear short fibers

2006

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A solution is found to the two-dimensional buckling problem for a composite material reinforced with a periodic row of collinear short fibers and compressed along the fibers. The problem formulation is based on the piecewise-homogeneous model and the three-dimensional theory of stability of deformable bodies. The dependence of the critical strain and buckling mode on the fiber spacing is studied for various material and geometrical characteristics of the composite components Keywords: composite material, short fibers, three-dimensional theory of stability of deformable bodies, inhomogeneous stress-strain state, finite-difference method, critical strain, buckling modeIntroduction. Microbuckling is the basic mechanism of failure of fibrous and laminated composites under compression. It is obvious that this very complex phenomenon cannot be adequately described under two-dimensional applied theories of stability of thin-walled members (beams, plates, and shells)-it is expedient to apply the three-dimensional theory of stability of deformable bodies.It should be noted that the results to be discussed below have been obtained using the piecewise-homogeneous model and the three-dimensional linearized theory of stability of deformable bodies [1,6,7,9]. This formulation for composite micromechanics problems is currently the most rigorous and exact in solid mechanics. Solving such problems under the three-dimensional linearized theory of stability of deformable bodies is very difficult because of the inhomogeneity of the resulting (two-or three-dimensional) subcritical state and is only possible with up-to-date numerical methods.Of considerable interest is the question of whether the results presented here can be applied to study nanomaterials and nanocomposites. It should be noted that the term "nanocomposite" in nanomechanics seems to refer to two different types of nanomaterials. One type is nanocomposites consisting of a matrix and nanoparticles as reinforcement; such terminology is used in the micromechanics of polymer-or metal-matrix composites. Approaches and methods of composite micromechanics are applicable to composites for which the applicability conditions for continuum solid mechanics formulated in [13] are satisfied. The other type is nanocomposites in which each nanoparticle or nanoformation is a rather complex structure that may be considered a nanocomposite with its own microstructure. There is no material medium (analog of matrix in composite micromechanics) between particles (as in the case of nanotubes); and particles interact via interatomic forces. This interpretation of the term "nanocomposite" is ruled out in the micromechanics of polymer-or metal-matrix composites because it treats each element of the reinforcement as a solid body (solid mechanics is a division of continuum mechanics) and requires multilevel models to be developed under fracture mesomechanics, as shown in [8]. However, it seems to be preferred to describe a particle under continuum mechanics if it is an element of the microstructu...

“…Large classes of near-surface buckling problems for laminated and fibrous materials have recently been solved using the three-dimensional linearized theory of stability of deformable bodies [1][2][3]9] for unidirectional fibrous and laminated composites unbounded along the line of action of compressive stresses. Internal instability of fibrous unidirectional composites reinforced with short fibers (fibers finite in the longitudinal direction) was studied in [6,7,12,13]. Moreover, these and present study are of special interest in nanocomposite mechanics for which the basic theory and some recent results are outlined in [5,8,10,11].…”

mentioning

confidence: 96%

“…It is obvious that if the distance from an inclusion to the boundary surface is rather large, then instability of the composite is internal and we deal with the buckling of a fiber in an infinite matrix [6]. The closer the fiber to the boundary surface, the more probable the near-surface instability of the composite.…”

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confidence: 99%

Near-surface instability of composites weakly reinforced with short fibers

2008

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The paper is concerned with loss of stability near the free flat surface of a weakly short-fiber-reinforced composite material under compression along the fibers. Emphasis is on the effect of the mechanical and geometrical parameters of the composite and the distance between fibers and to the free surface on the critical strains. The piecewise-homogeneous medium model and the rigorous three-dimensional linearized theory of stability of deformable bodies are used Keywords: composite material, short fibers, three-dimensional linearized theory of stability, inhomogeneous stress-strain state, finite-difference method, near-surface instability, critical strainIntroduction. The theory of stability of composites distinguishes internal instability of a material (critical loads are only dependent on the relationship between the mechanical and geometric characteristics of the reinforcement and matrix) and instability of the composite as a structural member. In the latter case, the critical values of the key parameters depend not only on all the above-mentioned properties of the composite, but also on its size and shape. Along with internal instability, surface instability is possible in composites with one or several boundary surfaces. This type of instability is observed near the surface of the composite medium and decays with distance from it. As a rule, near-surface instability precedes internal instability. Therefore, by studying it, we can establish the minimum critical loads under which there can be loss of stability near the surface. In analyzing this problem, it is customary to model composites by a semibounded body of regular or irregular structure and to satisfy the conditions of decay at infinity. Large classes of near-surface buckling problems for laminated and fibrous materials have recently been solved using the three-dimensional linearized theory of stability of deformable bodies [1-3, 9] for unidirectional fibrous and laminated composites unbounded along the line of action of compressive stresses. Internal instability of fibrous unidirectional composites reinforced with short fibers (fibers finite in the longitudinal direction) was studied in [6,7,12,13]. Moreover, these and present study are of special interest in nanocomposite mechanics for which the basic theory and some recent results are outlined in [5,8,10,11]. Using the three-dimensional linearized theory of stability of deformable bodies complicates the solution of such problems considerably because the precritical (two-or three-dimensional) state is inhomogeneous in this case. It is therefore obvious that specific results can only be obtained here with modern numerical methods.The present paper reports on the results from a study into the near-surface instability of a composite material weakly reinforced with short fibers. Emphasis is placed here on the effect of the mechanical and geometrical parameters of the composite components and the distance between fibers and the free surface on the critical strains.It is obvious that if the distance from a...