Effective elastic and failure properties of fiber aligned composites
01 Aug 2004-International Journal of Solids and Structures (Pergamon)-Vol. 41, Iss: 16, pp 4827-4844
TL;DR: In this article, a linear elastic composite medium is considered, which consists of a homogeneous matrix containing a statistically homogeneous set of ellipsoidal inclusions, and the multiparticle effective field method (MEFM) is applied for the estimations of second statistical moments of stresses in both the constituents and the interfaces between the matrix and fibers.
About: This article is published in International Journal of Solids and Structures.The article was published on 2004-08-01. It has received 4 citations till now. The article focuses on the topics: Fiber & Fiber-reinforced composite.
Citations
More filters
TL;DR: In this paper, the authors deal with statistical features of a distribution of carbon fibres in a transversal cross-sectional area in a unidirectional composite with epoxy matrix, based on various approaches used to quantify its microscopic randomness.
Abstract: Composite materials demonstrate a considerable extent of heterogeneity. A non-uniform spatial distribution of reinforcement results in variations of local properties of fibrous laminates. This non-uniformity not only affects effective properties of composite materials but is also a crucial factor in initiation and development of damage and fracture processes that are also spatially non-uniform. Such randomness in microstructure and in failure evolution is responsible for non-uniform distributions of stresses in composite specimens even under externally uniform loading, resulting, for instance, in a random distribution of matrix cracks in cross-ply laminates. The paper deals with statistical features of a distribution of carbon fibres in a transversal cross-sectional area in a unidirectional composite with epoxy matrix, based on various approaches used to quantify its microscopic randomness. A random character of the fibres’ distribution results in fluctuations of local elastic moduli in composites, the bounds of which depend on the characteristic length scale. A lattice model to study damage and fracture evolution in laminates, linking randomness of microstructure with macroscopic properties, is discussed. An example of simulations of matrix cracking in a carbon fibre/epoxy cross-ply laminate is given.
39 citations
TL;DR: In this article, a generalized version of the Multi-Particle Effective Field (MEFM) method is proposed to estimate the first statistical moments of stresses in the phases of a linearly thermoelastic composite media, which consists of a homogeneous matrix containing a statistically homogeneous random set of uncoated or coated inclusions.
Abstract: In this paper linearly thermoelastic composite media are treated, which consist of a homogeneous matrix containing a statistically homogeneous random set of ellipsoidal uncoated or coated inclusions. Effective properties (such as compliance, thermal expansion, stored energy) as well as the first statistical moments of stresses in the phases are estimated for the general case of nonhomogeneity of the thermoelastic inclusion properties. The micromechanical approach is based on the generalization of the ``multiparticle effective field'' method (MEFM, see [7] for references), previously proposed for the estimation of stress field averages in the phases. The refined version of the MEFM takes into account both the variation of the effective fields acting on each pair of fibers and inhomogeneity of statistical average of stresses inside the inclusions. One considers in detail the connection of the method proposed with numerous related methods. The explicit representations of the effective thermoelastic properties and stress concentration factor are expressed through some building blocks described by numerical solutions for both the one and two inclusions inside the infinite medium subjected to the homogeneous loading at infinity. Just with some additional assumptions (such as an effective field hypothesis) the involved tensors can be expressed through the Green's function, Eshelby tensor and external Eshelby tensor. The dependence of effective properties and stress concentrator factors on the radial distribution function of the inclusion locations is analyzed.
8 citations
Cites methods from "Effective elastic and failure prope..."
...The comparison of the available experimental data of effective moduli with the numerical results obtained by the method (103) and (210) (and also by other methods of micromechanics) was considered in detail in [29] and [ 36 ]....
[...]
TL;DR: Lower bounds on the second-order and higher-order moments of the phase stress and strain fields of a linearly elastic isotropic composite undergoing uniform macroscopic loading are provided in this paper.
2 citations
References
More filters
Book•
01 Jan 1976
TL;DR: In this article, the authors present a mathematical model for time-dependent correlation functions and response functions in liquid solvers, based on statistical mechanics and molecular distribution functions, and show that these functions are related to time correlation functions in Ionic and Ionic liquids.
Abstract: Introduction. Statistical Mechanics and Molecular Distribution Functions. Computer "Experiments" on Liquids. Diagrammatic Expansions. Distribution Function Theories. Perturbation Theories. Time-dependent Correlation Functions and Response Functions. Hydrodynamics And Transport Coefficients. Microscopic Theories of Time-Correlation Functions. Ionic Liquids. Simple Liquid Metals. Molecular Liquids. Appendices. References. Index.
9,144 citations
TL;DR: In this paper, a method of calculating the average internal stress in the matrix of a material containing inclusions with transformation strain is presented. But the authors do not consider the effects of the interaction among the inclusions and of the presence of the free boundary.
7,000 citations
Book•
01 Jan 1982TL;DR: In this paper, the authors present numerical simulation of intergranular and transgranular crack propagation in ferroelectric polycrystals using double kink mechanisms for discrete dislocations in BCCs.
Abstract: Preface Numerical simulation of intergranular and transgranular crack propagation in ferroelectric polycrystals Microstructure and stray electric fields at surface cracks in ferroelectrics Double kink mechanisms for discrete dislocations in BCC crystals The expanding spherical inhomogeneity with transformation strain A new model of damage: a moving thick layer approach On configurational forces at boundaries in fracture mechanics HotQC simulation of nanovoid growth under tension in copper Coupled phase transformations and plasticity as a field theory of deformation incompatibility Continuum strain-gradient elasticity from discrete valence force field theory for diamond-like crystals
4,951 citations
TL;DR: In this article, an operationally simple strength criterion for anisotropic materials is developed from a scalar function of two strength tensors, which satisfies the invariant requirements of coordinate transforma tion, takes into account the difference in strengths due to positive and negative stresses, and can be specialized to account for different material symmetries, multi-dimensional space, and multi-axial stresses.
Abstract: An operationally simple strength criterion for anisotropic materials is developed from a scalar function of two strength tensors. Differing from existing quadratic approximations of failure surfaces, the present theory satisfies the invariant requirements of coordinate transforma tion, treats interaction terms as independent components, takes into account the difference in strengths due to positive and negative stresses, and can be specialized to account for different material symmetries, multi-dimensional space, and multi-axial stresses. The measured off-axis uniaxial and pure shear data are shown to be in good agreement with the predicted values based on the present theory.
3,030 citations
Book•
19 Oct 2001TL;DR: In this article, a unified approach for the characterization of 2-dimensional (2-3D) moduli is presented. But the approach is not suitable for 3-dimensional moduli.
Abstract: Motivation and overview * PART I Microstructural characterization * Microstructural descriptors * Statistical mechanics of particle systems * Unified approach * Monodisperse spheres * Polydisperse spheres * Anisotropic media * Cell and random-field models * Percolation and clustering * Some continuum percolation results * Local volume fraction fluctuation * computer simulation and image analysis * PART II Microstructure property connections * Local and homogenized equations * Variational Principles * Phase-interchange relations * Exact results * Single-inclusion solutions * Effective medium approximations * Cluster expansions * Exact contrast expansions * Rigorous bounds * Evaluation of bounds * Cross-property relations * Appendix A Equilibrium Hard disk program * Appendix B Interrelations among 2-3D moduli* References * Index
3,021 citations