Functionally graded metal matrix composite tubes

Abstract

Current advanced manufacturing techniques allow the continuous variation of fiber or inclusion volume fraction in metal matrix composites. With this technology, it is now possible to tailor a composite to the expected loads by using the constituent materials to redistribute the stress and strain states through the material. Lighter and more structurally efficient components will be obtained through this grading process. The focus of this paper is the evaluation of the effects of material property and fiber volume grading on the overall mechanical response of metal matrix composite tubes subjected to mechanical loadings. This is accomplished through the development of a fully elastic-plastic axisymmetric generalized plane strain tube model. This analytical model incorporates a micromechanics algorithm in order to determine the elastic-plastic response of a heterogeneous fiber-reinforced composite cylinder. An arbitrary number of heterogeneous concentric cylinders can be included in the model, each with independent material properties. The inelastic analysis is performed through the method of successive elastic solutions. The optimization algorithm used in conjunction with this solution procedure utilizes the method of feasible directions and accepts any combination of design variables, constraints, and objective functions. As an example of the effectiveness of this grading, it is possible to vary the fiber volume fraction in an SiC/Ti-24Al-11Nb tube in such a way that the effective stress at the critical inner surface of an internally pressurized tube is reduced. For a 50.8 mm (2in) thick tube with an internal radius of 25.4 mm (1 in) and an internal pressure of 206.8 MPa (30 ksi), a uniform 40% fiber volume fraction distribution results in a tube that begins to plastically yield at the inner radius. By grading the fiber volume fraction, the tube now behaves elastically under the same pressure loading, allowing the tube to have a wall thickness of 25.4 mm (1 in) before plastic yielding begins. This grading results in a 60% weight saving.