Deformation and Microdamage of a Discrete-Fibrous Composite with Transversely Isotropic Components

Khoroshun, L. P.; Nazarenko, L. V.

doi:10.1023/a:1025797909306

Cited by 14 publications

(10 citation statements)

References 8 publications

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“…Both approaches are well developed for periodic granular composites with isotropic phases; for a review on the subject see [2,4,5]. The statistical theory of deformation and damage of composites with anisotropic phases is developed in [6][7][8]. All well-known applications of the regularization method are restricted to fibrous materials alone [1,4].…”

Section: Introductionmentioning

confidence: 99%

“…Introduction. The best known approaches to predicting the macroscopic properties of structurally inhomogeneous materials are, probably, the stochastic approach based on methods of statistical mechanics [5][6][7][8] and the regularization method [1,2,4,9,12]. The latter consists in modeling a real composite by a periodic structure and solving boundary-value problems, followed by averaging of local fields.…”

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confidence: 99%

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Effective elastic moduli of periodic granular composite with transversely isotropic phases

Кущ

2004

Int Appl Mech

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We find a rigorous solution describing the macroscopically uniform stress state of a periodic granular composite with transversely isotropic phases. The structure of the composite is modeled by a cube containing a finite number of arbitrarily arranged and oriented, transversely isotropic spherical inclusions. This provides the model with a flexible means of describing the microstructure. Applying periodic vector solutions and local expansion formulas reduces the initial boundary-value problem to a system of linear algebraic equations. By averaging the solution over the unit cell, we derived exact finite expressions for the components of the effective stiffness tensor. The numerical data presented help to evaluate the efficiency of the method and the limits of applicability of available approximate theories.Keywords: periodic granular composite, transversely isotropic elastic phases, periodic structural model, spherical inclusion, effective stiffness tensor 1. Introduction. The best known approaches to predicting the macroscopic properties of structurally inhomogeneous materials are, probably, the stochastic approach based on methods of statistical mechanics [5][6][7][8] and the regularization method [1,2,4,9,12]. The latter consists in modeling a real composite by a periodic structure and solving boundary-value problems, followed by averaging of local fields. Both approaches are well developed for periodic granular composites with isotropic phases; for a review on the subject see [2,4,5]. The statistical theory of deformation and damage of composites with anisotropic phases is developed in [6-8]. All well-known applications of the regularization method are restricted to fibrous materials alone [1,4].In the present paper, we will find a rigorous, asymptotically exact solution describing the elastic equilibrium of a periodic composite with spherical inclusions, assuming transverse isotropy of the phases. The unit cell is a cube containing a finite number of arbitrarily arranged and oriented, transversely isotropic spherical inclusions. This provides the model with a general and flexible means of describing the microstructure [2]. To derive the solution, we will employ the earlier results for a transversely isotropic body with one [10, 11] and several [3] inclusions and a fast-summation method for triple series [12].2. Composite Model. The generalized periodic structural model of a granular composite [2] is an infinite matrix containing periodically arranged spherical inclusions. This model has a unit cell in the form of a cube with side length a containing N spherical inclusions of radius R q centered at points Q q N q , , ,... , = 12 . This cell, when repeated in three mutually perpendicular directions, produces the entire structure of the composite. Both the matrix and inclusions are assumed elastic and

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Section: Introductionmentioning

confidence: 99%

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confidence: 99%

Effective elastic moduli of periodic granular composite with transversely isotropic phases

Кущ

2004

Int Appl Mech

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“…The calculated and experimental creep strains are in good agreement both at the initial stage of deformation and after long-term loading Introduction. To determine the deformation and strength characteristics of composite materials from the properties of their components, it is necessary to determine these properties experimentally and define them analytically [10,13]. In the case of viscoelastic composites, the deformation properties of their components are determined from creep curves [4,7].…”

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Calculating the Linear Creep Strains of Viscoelastic Fibers under Tension

2005

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The linearity domain for the viscoelastic properties of high-molecular organic fibers is determined. The linearity criteria are coincidence of experimental compliance curves and linearity of isochronic creep curves. Statistical criteria are used to establish linearity. The influence function in the constitutive equation of linear viscoelasticity is an Abel-type power kernel. The calculated and experimental creep strains are in good agreement both at the initial stage of deformation and after long-term loading Introduction. To determine the deformation and strength characteristics of composite materials from the properties of their components, it is necessary to determine these properties experimentally and define them analytically [10,13]. In the case of viscoelastic composites, the deformation properties of their components are determined from creep curves [4,7].A great variety of constitutive equations have been proposed to describe the creep of viscoelastic materials. The theory of hereditary viscoelasticity has been used most widely. The concept of linear viscoelasticity is well developed and widely applied. However, the parameters of constitutive equations are determined by approximating experimental creep curves plotted for several levels of stresses and averaging the resulting values. This necessitates extensive long-term creep tests and lead to significant errors in creep strains calculated using average coefficients. The issues remaining to be resolved are determining the linearity domain of viscoelastic properties and selecting a heredity kernel.A generalized rheological model based on the hypothesis of a unified isochronic deformation curve has been developed in [1]. The model allows us to predict the nature of creep (whether linear or nonlinear) and includes an easily implementable procedure of identifying the material constants. In the present paper, we use the model from [1] to calculate the linear creep strains of organic fibers used as reinforcement in organofibrous and hybrid composites. We will determine the domain of linear viscoelastic deformation of organic fibers and justify the structure of the heredity kernel that describes the features of creep of the fibers over the whole time interval.1. Problem Formulation. Subject of Research. The deformation properties of a linear viscoelastic medium under uniaxial tension may be described within the framework of small-deformation theory by the following constitutive equations of the Boltzmann-Volterra hereditary theory of viscoelasticity [9]:

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“…The papers [7,11] report on the results of studying the deformation, microdamage, and fracture of structurally inhomogeneous materials in the context of solid mechanics.…”

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Laws of Influence of Structural Characteristics on the Strength and Crack Resistance of Aging Metallic Materials

Nizhnik

Usikova

2005

Int Appl Mech

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The structural characteristics (the volume fraction, size, and shape of and the distance among hardening-phase particles) of aging alloys and steels, which define the behavior of the critical stress intensity factor during thermal hardening, are determined using the structural-mechanical approach we have developed. It is experimentally demonstrated for maraging steels that our approach is capable of proving the correlations of strength, plasticity, and crack-resistance with the structural characteristics, which were varied by changing the chemical composition of steel and thermokinetic aging conditions Introduction. The authors of [3, 10] analyzed and systematized the approaches, based on deformation failure criteria, to the evaluation of the characteristic K IC of elastoplastic metallic materials from uniaxial tension data for samples without cracks and the structural characteristics of undeformed metal that determine the size of the crack tip region.Our structural-mechanical approach is based on the results of experimental validation of the Hahn-Rosenfield relation for aging metallic materials [3,9]

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Deformation and Microdamage of a Discrete-Fibrous Composite with Transversely Isotropic Components

Cited by 14 publications

References 8 publications

Effective elastic moduli of periodic granular composite with transversely isotropic phases

Effective elastic moduli of periodic granular composite with transversely isotropic phases

Calculating the Linear Creep Strains of Viscoelastic Fibers under Tension

Laws of Influence of Structural Characteristics on the Strength and Crack Resistance of Aging Metallic Materials

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