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Research Papers

A New Incremental Formulation of Elastic–Plastic Deformation of Two-Phase Particulate Composite Materials

[+] Author and Article Information
Hong Teng

Department of General Engineering,
University of Wisconsin-Platteville,
Platteville, WI 53818
e-mail: tengh@uwplatt.edu

Manuscript received October 19, 2013; final manuscript received January 17, 2014; accepted manuscript posted January 18, 2014; published online February 19, 2014. Assoc. Editor: John Lambros.

J. Appl. Mech 81(6), 061006 (Feb 19, 2014) (11 pages) Paper No: JAM-13-1436; doi: 10.1115/1.4026557 History: Received October 19, 2013; Revised January 17, 2014; Accepted January 18, 2014

In this study the double-inclusion model, originally developed to determine the effective linear elastic properties of composite materials, is reformulated in incremental form and extended to predict the effective nonlinear elastic–plastic response of two-phase particulate composites reinforced with spherical particles. The study is limited to composites consisting of purely elastic particles and elastic–plastic matrix of von Mises yield criterion with isotropic strain hardening. The resulting nonlinear problem of elastic–plastic deformation of a double inclusion embedded in an infinite reference medium (that has the elastic–plastic properties of the matrix) subjected to an incrementally applied far-field strain is linearized at each load increment through the use of the matrix tangent moduli. The proposed incremental double-inclusion model is evaluated by comparison of the model predictions to the exact results of the direct approach using representative volume elements containing many particles, and to the available experimental results. It is shown that the incremental double-inclusion formulation gives accurate prediction of the effective elastic–plastic response of two-phase particulate composites at moderate particle volume fractions. In particular, the incremental double-inclusion model is capable of capturing the Bauschinger effect often exhibited by heterogeneous materials. A unique feature of the proposed incremental formulation is that the composite matrix is treated as a two-phase material consisting of both an elastic and a plastic region.

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Figures

Grahic Jump Location
Fig. 1

The incremental double-inclusion model with the origin of the Cartesian coordinate system (x1, x2, x3) at the center of the particle

Grahic Jump Location
Fig. 2

Prediction of the incremental double-inclusion model and the exact result of Brassart et al. [17] for the unaxial stress–strain relation of a martensitic/ferritic two-phase steel with a particle volume fraction of 0.15

Grahic Jump Location
Fig. 6

Predictions of the incremental double-inclusion model and the exact results of Gonzalez et al. [4] for the shear stress–strain relations of ceramic-particle/metal-matrix composites with a particle volume fraction of 0.25

Grahic Jump Location
Fig. 9

Prediction of the incremental double-inclusion model and the experimental result [2] for the uniaxial stress–strain relation in the plastic region of a silica/epoxy particulate composite with a particle volume fraction of 0.15

Grahic Jump Location
Fig. 3

Prediction of the incremental double-inclusion model and the exact result of Brassart et al. [17] for the uniaxial stress–strain relation of a martensitic/ferritic two-phase steel with a particle volume fraction of 0.25

Grahic Jump Location
Fig. 4

Prediction of the incremental double-inclusion model and the exact result of Segurado et al. [20] for the uniaxial stress–strain relation of a ceramic-particle/metal-matrix composite with a particle volume fraction of 0.3

Grahic Jump Location
Fig. 5

Predictions of the incremental double-inclusion model and the exact results of Gonzalez et al. [4] for the uniaxial stress–strain relations of ceramic-particle/metal-matrix composites with a particle volume fraction of 0.25

Grahic Jump Location
Fig. 7

Prediction of the incremental double-inclusion model and the exact result of Brassart [18] for the uniaxial stress–strain relation of a SiC particle/aluminum matrix composite with a particle volume fraction of 0.25 and a matrix strain hardening exponent of 0.05

Grahic Jump Location
Fig. 8

Prediction of the incremental double-inclusion model and the exact result of Brassart [18] for the uniaxial stress–strain relation of a SiC particle/aluminum matrix composite with a particle volume fraction of 0.25 and a matrix strain hardening exponent of 0.4

Grahic Jump Location
Fig. 10

Prediction of the incremental double-inclusion model and the experimental result [2] for the uniaxial stress–strain relation in the plastic region of a silica/epoxy particulate composite with a particle volume fraction of 0.35

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