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Miscellany

Multi-Fiber Unit Cell for Prediction of Residual Stresses in Continuous Fiber Composites

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Pages 531-540 | Received 03 Jun 2006, Accepted 04 Sep 2006, Published online: 15 Oct 2007
 

Abstract

The mechanical properties of Continuous Fiber Metal Matrix Composite (CFMMC) materials are often affected by the residual stresses that arise during their fabrication process as a result of the mismatch between the Coefficients of Thermal Expansion (CTE) of the fibers and matrix. Three-dimensional finite element Unit Cell Models (UCM) are commonly used to predict such residual stress fields. However, the boundary conditions chosen in the past for these models neglect the effects of interactions between neighboring fibers, which results in poor correlations with experimental results. Previous research shows that the UCM approach usually overestimates the residual stress levels by about 30%. In this paper, two new three-dimensional finite element Multi Fiber Models (MFM) are developed in which the boundary conditions are shifted away from the fiber-matrix interface, in order to account for the effects of neighboring fibers on the stress distribution over such interfaces. One model assumes a hexagonal packing pattern of the neighboring fibers around the fiber-matrix interface where the residual stresses are calculated, whereas the other assumes that the neighboring fibers are packed in a square pattern. The proposed models are examined for two different scenarios regarding the contact surface between the fiber and the matrix, one where there is no bond over the interface and the other where the interface is perfectly bonded. The residual stress predictions of the new MFM models are compared to those of conventional UCM models by using an Alumina/Titanium (Al 2 O 3 /Ti-6Al-4Va) material system to represent, as a test case, a typical CFMMC material. The results indicate that the residual stresses predicted by the MFM models correlate much better with published experimental results than those provided by the UCM models. The effects of the fiber volume fraction and the fiber-matrix bond integrity on the magnitude and distribution of residual stresses are examined for both hexagonal and square packing patterns of neighboring fibers. The analysis demonstrates that all these factors can influence significantly the field of residual stresses that develops in the matrix when the material is cooled-down from its processing temperature. If the fiber-volume fraction is assumed to increase, from 10% to 30% for example, the MFM models predict, as expected, a reduction in the magnitude of such residual stresses, which for the scenario of perfectly bonded interfaces can be as high as 49% for the square fiber packing pattern or 41% for the hexagonal pattern. The numerical results show that the hexagonal fiber-packing pattern predicts, in general, higher residual stresses than the square packing system, so that it should be recommended for design as the more conservative approach.

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