On the Mechanics of Microballoon-Reinforced Metal Matrix Composites

Abstract

The elastic/plastic response of ceramic microballoon reinforced metal matrix composites subject to uniaxial loading are examined using finite element analysis. The microballoons are assumed to be spherical and their morphology characterized by the ratio of wall thickness, t, to radius, R. The key parmeter investigated are the relative wall thickness, t/R, the modulus ratio (matrix/ceramic) and the yield and hardening characteristics of the matrix. The emphasis of the study is on the overall stress-strain response of the composite, the development of matrix plastidty and the development of stress within the microballoon. Typically, the volume fraction of microballoons is in the range of 50-60%. A micrograph of one such composite is shown in Fig. 1. The composites are being targeted for marine applications requiring high specific strength and stiffness and high damping capacity.The potential advantages of these systems over continuous fiber reinforced materials include superior mechanical isotropy, lower production costs and greater flexibility in component fabrication. Their main advantage over conventional particulate-reinforcedMMCs is their reduced density, a result of the void space within the reinforcements.The present paper examines the elastic/plastic response of microballoon reinforced MMCs subject to uniaxial loading (compressive or tensile). The majority of the results are based on a finite element analysis of axisymmetric unit cells. The key parameters investigated are: (i) the ratio of the matrix modulus, Em to that of the ceramic, Er, (ii) the microballoon morphology, characterized by the ratio of wall thickness, t, to microballoon radius, RX and (iii) the work hardening characteristics of the matrix. The focus of the work is on the overall stress-strain response of the composite, the development of matrix plasticity and the development of stresses within the microballoons. NUMERICAL MODELFinite element calculations were conducted on cylindrical unit cells containing a microballoon at the cell center. The height of the cylinder was taken to be equal to the diameter. The ratio of the microbaUoon wall thickness, t, to the microballoon radius, R, was varied from 0 to 1. In all cases, the total volume fraction of microbaloons was 50%.A typical finite element mesh for t/R -02. is shown in Fig. 2.The boundary conditions were prescribed to model a state of uniform tension or compression, applied parallel to the axis of the cylinder. The top face of the cylinder was required to remain planar, with an average normal traction, a, and zero shear traction. The lateral face was also required to remain planar but with zero average normal and shear tractions acting on it. The model was implemented using the finite element program ABAQUS, with 8-noded 2-dimensional axisymmetric biquadrilateral elements. A typical mesh contained 480 elements and 1565 nodes. The overall strain was increased by increments of Aseo = 0.1 for PAO < 5, •e•o = 0.2 for 5 < e/e1 < 10,and Ae/-o = 0.5 for PAO > 10. The effective (deviatoric) str...