The elastic-plastic behavior of composite materials

The elastic-plastic behavior of metal-matrix composites reinforced by continuous elastic fibers was investigated by using thin-walled tubular specimens. The unidirectional boron/6061-aluminum composite specimens were incrementally loaded by a computer controlled closed loop MTS servohydraulic system. The specimens were under a combined loading of axial force, torsion and internal pressure at room temperature. The experimental results show that the initial and subsequent yield surfaces have large flat segments associated with a matrix-dominated deformation. Apart from certain changes in size, which may be attributed to the distortions of the underlying matrix yield surfaces, the composite yield surfaces retain their shape during loading. The yield surface moves in a translation along the direction of the applied stress increment. Exceptions from this rule are found at the flat segments of the surface, and at certain vertices.1. Limit analysis of a thin-walled composite tube. A thin-walled composite tube, consisting of an elastic-perfectly plastic matrix reinforced by thin fibers with relatively high stiffness and strength, is subjected to torsion and internal pressure. The matrix is assumed to obey the Tresca's yield condition. The lower and upper bounds of the limit load were obtained by using the limit theory of plasticity. It is shown that the upper bound coincides with the lower bound only in a certain intermediate range of the fiber concentration. Some examples are given to find upper and lower bounds when the composite is more crowded with fibers. The influence of the fiber concentration on the limit load was discussed.2. Homogenization in elastic-plastic composite materials. The plastic normality and convexity of the yield surface are shown to survive the inhomogeneity based upon the homogenization technique.3. Axial shear loading of a cylindrical inclusion embedded in a matrix.In order to understand and interpret the results of the experimental program, some theoretical studies were undertaken as follows:4. On errors in homogenization.The program of homogenization introduces errors in estimating the fields of microstress and microstrain in an elastic body composed of a periodic arrangement of the copies of a heterogeneous cell. If the size of unit cell is much smaller than that of the composite body, these errors will be very small everywhere except in the vicinity of the boundary of the composite body and in places where the macrostresses obtained by homogenization have large gradients. This chapter is concerned with the estimation of errors in the above mentioned critical locations.