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

Декрет, В. А.

doi:10.1007/s10778-006-0136-6

Cited by 12 publications

(8 citation statements)

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“…It is obvious that the compressive strain at infinity in the matrix calculated using the short-fiber model would be much higher than in the fiber because the fiber is much stiffer than the matrix. In [2][3][4], where the short-fiber model was used to analyze the instability of composites, the following critical compressive strain at infinity in the matrix was used:…”

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confidence: 99%

Stability of composite materials with two parallel short fibers

Декрет

2009

Int Appl Mech

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The stability of composite materials reinforced with two parallel short fibers is analyzed. The critical strains in the matrix and reinforcement are calculated. The dependence of the critical strains on the mechanical and geometrical parameters is analyzed Keywords: fibrous composite material, three-dimensional theory of stability, infinite-fiber model, short-fiber modelIntroduction. The most strict and physically correct results on the theory of stability of laminated and fibrous composites under compression were obtained using the three-dimensional linearized theory of stability of deformable bodies [6] and the piecewise-homogeneous material model. Such an approach was first proposed in [5]. A contemporary analysis of the three-dimensional linearized theory of stability of deformable bodies (or, in a broader sense, the three-dimensional linearized solid mechanics) can be found in [7][8][9]. In [9], emphasis was on the derivation of linearized constitutive equations for elastic and elastoplastic bodies. The approach of [7-9] was used to solve a number of problems of linearized solid mechanics. An example is the contemporary analysis [12] of the exact solutions to plane mixed problems of linearized solid mechanics presented in [14-16, etc.].Currently, research on the three-dimensional linearized theory of stability of laminated and fibrous materials that follows the approach of [5, 6] employs the infinite-fiber or short-fiber models. A comparative contemporary analysis of the results obtained with these models can be found in [11]. It should be noted that the overwhelming majority of results on the three-dimensional theory of stability of laminated and fibrous materials were obtained using the approach of [5,6] in combination with the infinite-fiber model (see [1, 10, 13, etc.] for a relevant contemporary analysis). The approach of [5,6] was only recently combined with the short-fiber model [2-4, etc.]. For this reason, the relevant results partially cited in [10] may be regarded as the beginning of research in this field.Note that the comparative analysis of the infinite-fiber and short-fiber models is strongly dependent on the quantities

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Stability of composite materials with two parallel short fibers

Декрет

2009

Int Appl Mech

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“…This study may be considered a continuation of the studies [11] for unidirectional fibrous composites reinforced with a periodic row of collinear short fibers. Emphasis will be on the interaction of short fibers in the matrix during loss of stability, depending on the distance between these fibers.…”

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

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2008

Int Appl Mech

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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...

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“…Analytical and numerical treatments of such systems were published already 30 years ago, see, e.g., [15]. With the upcoming of composites reinforced by collinear short fibres or whiskers the solution of the stability problem of those reinforcements has obtained a revival within the last decade, see, e.g., the papers by Dekret [3], [5], [4], and Guz and Dekret [9] as well as the literature cited in these papers. It is interesting to note that the problem of magnetic buckling as it occurs due to phase transformations in micromagnetic dots, see [17], can be seen as a special case of the more general situations considered here.…”

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confidence: 99%