Effective elastic moduli of three-phase composites with randomly located and interacting spherical particles of distinct properties

Lin, P. J.; Ju, J. W.

doi:10.1007/s00707-008-0114-7

Cited by 32 publications

(18 citation statements)

References 38 publications

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“…interface tractions of one interface family do not influence the evolution of the dislocations of the other interface family, and vice versa. This renders the situation with uniform stress boundary conditions (10) as fundamentally different from the situation encountered with uniform strain boundary conditions (6), compare the concentration influence relations (12) and (13), with those of (8) and (9). Clarification of the reason for this interesting difference is one of the central aims of this paper.…”

Section: State Equations For Uniform Stress Boundary Conditionsmentioning

confidence: 99%

“…1, we consider a deformation state which is suddenly imposed at time t = 0 and kept constant thereafter (t > 0), see the uniform strain boundary conditions (6). Since time-dependent behavior of the composite is related to in-plane dislocations of the interfaces, see the viscous interface law (4), and given the structure of the state equation (11) together with the non-zero components according to (139-142), the time-dependent macroscopic strains obey the form of pure shear [note the analogy to Eq.…”

Section: Derivation Of Relaxation Functions For Interacting Interfacementioning

confidence: 99%

“…Matrix-inclusion composites are known to exhibit interaction among the inclusions [1][2][3][4][5][6][7]. When it comes to the special case of inclusions in form of flat interfaces, i.e., to that of matrix-interface composites, interaction among interfaces would be clearly expected as well; however, the two-dimensional nature of interfaces is responsible for particularly surprising interaction properties [8,9], reminiscent of the situation encountered with micro-cracked materials [10,11].…”

Section: Introductionmentioning

confidence: 99%

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How interface size, density, and viscosity affect creep and relaxation functions of matrix-interface composites: a micromechanical study

2015

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Matrix-inclusion composites are known to exhibit interaction among the inclusions. When it comes to the special case of inclusions in form of flat interfaces, interaction among interfaces would be clearly expected, but the two-dimensional nature of interfaces implies quite surprising interaction properties. This is the motivation to analyze how interaction among two different classes of microscopic interfaces manifests itself in macroscopic creep and relaxation functions of matrix-interface composites. To this end, we analyze composites made of a linear elastic solid matrix hosting parallel interfaces, and we consider that creep and relaxation of such composites result from micro-sliding within adsorbed fluid layers filling the interfaces. The latter idea was recently elaborated in the framework of continuum micromechanics, exploiting eigenstress homogenization schemes, see Shahidi et al. (Eur J Mech A Solids 45:41-58, 2014). After a rather simple mathematical exercise, it becomes obvious that creep functions do not reflect any interface interaction. Mathematical derivation of relaxation functions, however, turns out to be much more challenging because of pronounced interface interaction. Based on a careful selection of solution methods, including Laplace transforms and the method of non-dimensionalization, we analytically derive a closed-form expression of the relaxation functions, which provides the sought insight into interface interaction. The seeming paradox that no interface interaction can be identified from creep functions, while interface interaction manifests itself very clearly in the relaxation functions of matrix-interface materials, is finally resolved based on stress and strain average rules for interfaced composites. They clarify that uniform stress boundary conditions lead to a direct external control of average stress and strain states in the solid matrix, and this prevents interaction among interfaces. Under uniform strain boundary conditions, in turn, interfacial dislocations do influence the average stress and strain states in the solid matrix, and this results in pronounced interface interaction.

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Section: State Equations For Uniform Stress Boundary Conditionsmentioning

confidence: 99%

Section: Derivation Of Relaxation Functions For Interacting Interfacementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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How interface size, density, and viscosity affect creep and relaxation functions of matrix-interface composites: a micromechanical study

2015

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“…Further, Ju and Zhang [7,8] formulated the higher-order micromechanical formulation for continuous-fiber reinforced composites on the foundation of Ju and Chen's higher-order formulation. More recently, Lin and Ju [9] extended the Ju-Chen's pairwise interaction formulation to three-phase composites containing many randomly dispersed, isotropic spherical particles.…”

Section: Introductionmentioning

confidence: 99%

Micromechanics and effective elastic moduli of particle-reinforced composites with near-field particle interactions

Yanase

2010

Acta Mech

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A micromechanical framework is proposed to predict effective elastic moduli of particle-reinforced composites. First, the interacting eigenstrain is derived by making use of the exterior-point Eshelby tensor and the equivalence principle associated with the pairwise particle interactions. Then, the near-field particle interactions are accounted for in the effective elastic moduli of spherical-particle-reinforced composites. On the foundation of the proposed interacting solution, the consistent versus simplified micromechanical field equations are systematically presented and discussed. Specifically, the focus is upon the effective elastic moduli of two-phase composites containing randomly distributed isotropic spherical particles. To demonstrate the predictive capability of the proposed micromechanical framework, comparisons between the theoretical predictions and the available experimental data on effective elastic moduli are rendered. In contrast to higher-order formulations in the literature, the proposed micromechanical formulation can accommodate the anisotropy of reinforcing particles and can be readily extended to multi-phase composites.

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“…Additionally, Ju and Zhang [10,11] developed the higher-order micromechanical formulation for continuous fiber-reinforced composites. Recently, Lin and Ju [12] extended the Ju-Chen pair-wise interaction formulation to the three-phase composites containing many randomly dispersed isotropic spherical particles.…”

Section: Introductionmentioning

confidence: 99%

Micromechanical effective elastic moduli of continuous fiber-reinforced composites with near-field fiber interactions

Yanase

2010

Acta Mech

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A higher-order micromechanical framework is presented to predict the overall elastic deformation behavior of continuous fiber-reinforced composites with high-volume fractions and random-fiber distributions. By taking advantage of the probabilistic pair-wise near-field interaction solution, the interacting eigenstrain is analytically derived. Subsequently, by making use of the Eshelby equivalence principle, the perturbed strain within a continuous circular fiber is accounted for. Further, based on the general micromechanical field equations, effective elastic moduli of continuous fiber-reinforced composites are constructed. An advantage of the present framework is that the higher-order effective elastic moduli of composites can be analytically predicted with relative simplicity, requiring only material properties of the matrix and fibers, the fiber-volume fraction and the microstructural parameter γ . Moreover, no Monte Carlo simulation is needed for the proposed methodology. A series of comparisons between the analytical predictions and the available experimental data for isotropic and anisotropic fiber reinforced composites illustrate the predictive capability of the proposed framework.

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Effective elastic moduli of three-phase composites with randomly located and interacting spherical particles of distinct properties

Cited by 32 publications

References 38 publications

How interface size, density, and viscosity affect creep and relaxation functions of matrix-interface composites: a micromechanical study

How interface size, density, and viscosity affect creep and relaxation functions of matrix-interface composites: a micromechanical study

Micromechanics and effective elastic moduli of particle-reinforced composites with near-field particle interactions

Micromechanical effective elastic moduli of continuous fiber-reinforced composites with near-field fiber interactions

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