Tlastoplastic properties of multicomponent composites

Сараев, Л. А.

doi:10.1007/bf00852499

J Appl Mech Tech Phys

1989

DOI: 10.1007/bf00852499

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Tlastoplastic properties of multicomponent composites

Л. А. Сараев¹

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“…When the structure is stochastic, the ergodic property [7,8] allows us to use preliminary statistical averaging at one point instead of averaging of the final solution over a macrovolume, which considerably simplifies the formulation and solution of the problem. The singular [8] or single-point [7] approximation enables solution of the spatial nonlinear problem only for quasispherical structural elements [5]. The method of conditional moments [7] made it possible to predict the effective properties of physically nonlinear composites with arbitrary structural elements by solving a system of nonlinear algebraic equations.…”

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Nonlinear deformation of a particulate material in complex stress state

Khoroshun

Shikula

2006

Int Appl Mech

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An algorithm is proposed to determine the effective deformation properties and stress-strain state of particulate composite materials with physically nonlinear components and complex stress state. The laws that govern the deformation of particulate composites are studied. A particulate composite is considered a two-component material of random structure. Its effective properties are determined by conditional averaging. The nonlinear equations that incorporate the physical nonlinearity of the components are solved by the method of successive approximations. The relationship between macrostresses and macrostrains is established. The effective deformation properties of a particulate composite as a function of the volume fractions of the components and stress state are studied Keywords: particulate composite, nonlinearity of deformation, complex stress state, effective deformation properties, stress-strain stateIntroduction. Under rather high loads, the macrostress-macrostrain relationship is nonlinear in many composite materials. This may be due to the physical nonlinearity of the components [3] or due to microdamages [6] appearing as microcracks or micropores during deformation [9][10][11][12][13][14][15]. The former type of nonlinearity is characteristic of composites based on plastic metal matrix or polymers at elevated temperatures. The latter type of nonlinearity is characteristic of brittle materials such as polymer composites at low temperatures, carbon-matrix composites, ceramic composites, etc.Extensive use is made of dispersion-reinforced composite materials, which are small solid quasispherical or quasispheroidal particles evenly distributed over a soft metal or polymer matrix. Such materials are usually subject to loading that induces a complex stress state. The dispersed particles are linearly elastic, and the matrix is nonlinear. The stress and strain interaction of the components results in the nonlinearity of the relationship between the macrostresses and macrostrains, which are determined by the volume fractions of the components and the shape and arrangement of particles. To predict the effective properties of such composites, it is necessary to solve a physically nonlinear elastic problem for a microinhomogeneous body. This problem is much more difficult to solve than the linear problem, especially for regular structures [1]. When the structure is stochastic, the ergodic property [7,8] allows us to use preliminary statistical averaging at one point instead of averaging of the final solution over a macrovolume, which considerably simplifies the formulation and solution of the problem. The singular [8] or single-point [7] approximation enables solution of the spatial nonlinear problem only for quasispherical structural elements [5]. The method of conditional moments [7] made it possible to predict the effective properties of physically nonlinear composites with arbitrary structural elements by solving a system of nonlinear algebraic equations.In the present paper, we outline a method and develop an ...

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confidence: 99%

Nonlinear deformation of a particulate material in complex stress state

Khoroshun

Shikula

2006

Int Appl Mech

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A variant of the method of correction of the elastoplastic properties of composites using estimates of the binding of constituents

Сараев¹,

Макарова²

1997

J Appl Mech Tech Phys

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Along with the nonlinearity of local constitutive equations, the limited statistical information on the structure of multicomponent composites is a handicap to the exact solution of the problem of determining the effective plastic properties of multicomponent composite materials. Therefore, in calculating the macroscopic characteristics of composites, one can ether determine their upper and lower bounds (the Khashin-Shtrikman fork) [1] or obtain approximate models. One method of allowing for data on the composite structure and increasing the accuracy of the calculation model is the expansion of moment functions in a series [2]. This. however, requires, a knowledge of the multipoint correlation moments, and this is very difficult to obtain in practice [3].Another method of designing a refined model for the macroscopic behavior of a composite involves adequate estimation of the binding of the constituents, which depends on the well-founded choice of parameters of a reference body [4].In this paper, we propose a variant of statisticM averaging of the equilibrium equations for an elastoplastic, isotropic, multicomponent composite to construct its macroscopic constitutive equations. To describe the geometrical features of the composite structure, a parameter that characterizes the degree of binding of the constituents is introduced into the original constitutive relations. This allows one to describe, using the proposed method, the nonlinear hardening of the composite beyond the elastic limit and to calculate its effective characteristics.The system of macroscopic constitutive equations for an elastoplastic isotropic composite formed by n different constituents is determined by statistical averaging of the equilibrium equation in displacements and has the form [4] (sij) = 2/~*(es)(eo ),where (

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Tlastoplastic properties of multicomponent composites

Cited by 2 publications

References 5 publications

Nonlinear deformation of a particulate material in complex stress state

Nonlinear deformation of a particulate material in complex stress state

A variant of the method of correction of the elastoplastic properties of composites using estimates of the binding of constituents

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