Keywords: fibre reinforced composites, metal-matrix, interphase, homogenization, finite elements.

A numerical model previously developed by Taliercio [2] is applied to the prediction of the macroscopic nonlinear behaviour of unidirectional metal-matrix composites (MMCs) reinforced by a regular array of long, parallel fibres, considering the presence of an interphase region between the fibres and the matrix. The interphase can be either originated by the manufacturing process, which often involves high temperatures and pressures, or purposely inserted between the fibres and the bulk matrix to improve their adhesion. As the interphase has properties different from the neighbouring materials, a three-phase composite is actually considered. The direct evaluation of the mechanical properties of the interphase is nearly unfeasible. Indirect testing techniques (fiber push-in, fiber push-out ) have been proposed, as well as ultrasonic methods or identification procedures in conjunction with micromechanical models.

The proposed numerical model is based on the finite element method in its displacement formulation. The overall response of the composite is predicted through the analysis of a single 2D unit cell, which is the cross-section of a prismatic representative volume element of unlimited length. Generalized plane strain conditions have to be assumed in the analysis of the unit cell, To this end, special finite elements are employed capable of describing 3D deformation modes invariant along the fibre axis [1]. To make the mechanical response of the unit cell representative of the macroscopic behaviour of a material element under arbitrary stresses, suitable periodicity conditions at the boundary of the cell have to be prescribed.

The three phases of the composite are supposed to be isotropic, elastic-perfectly plastic, and to conform with -plasticity. The compatibility matrix of the finite elements is modified, according to proposals of other authors, to avoid locking phenomena near the fully plastic range.

Some numerical applications are carried out to investigate the influence of a weakening interphase on the macroscopic mechanical behaviour of Ti/SCS, with particular attention to the macroscopic yield strength. To this end, the unit cell was subjected to particular macroscopic stresses of increasing intensity, namely, transverse tension, transverse shear and longitudinal shear. In the applications, the interphase was given decreasing strength values, , expressed as a fraction of the matrix strength, . The predicted macroscopic yield strength of the composite, normalized to the strength of the composite with matrix perfectly bonded to the fiber (i.e., with ), is reported in Table 1. The decrease in transverse tensile and shear strength with the interphase strength is nearly similar. The most detrimental effect of a weakening interphase is observed under longitudinal shear.

The theoretical results presented in the foregoing now await an experimental validation. The literature is quite sparse in terms of test data on MMCs embedding a weakening interphase. Another problem is that the interphase material exhibits a brittle behaviour under several stress conditions, such as tension and shear. This is why an extension of the present model has been started to accommodate damage phenomena at the interphase region: the ensuing results will be presented in a forthcoming paper.

1

A. Taliercio, V. Carvelli "2D finite elements for the analysis of fiber reinforced composites subjected to 3D stresses", Proc. ECCM-9 European Conference on 'Composite Materials - Science, Technology and Applications', München (D), August 30-September 3, 1999 (CD-Rom), 16 pp.

2

A. Taliercio, "Generalized plane strain finite element model for the analysis of elastoplastic composites", Int. J. Solids Structures, 42(8), 2361-2379, 2005. doi:10.1016/j.ijsolstr.2004.09.030

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