TABLE OF CONTENTS In the preceding chapter, the elastic behavior of the lamina was discussed primarily from a macroscopic point of view with only a brief review of the micromechanical relationships between lamina and constituent properties. In the case of failure phenomena and strength of a lamina, it is important to understand first the underlying failure mechanisms and processes within the constituents of the composite and their effect on the ultimate macroscopic behavior (see Sect. 2.6). For this reason, the micromechanics of failure is dealt with here in more detail and with more emphasis than was the micromechanics of elastic behavior in Chapter 3 and precedes the macromechanical discussion.
The failure mechanisms and processes on a micromechanical scale vary with type of loading and are intimately related to the properties of the constituents, i.e., fiber, matrix, and interface interphase. These processes and predictions of macroscopic strength are discussed below for various types of loading.
Under longitudinal tension, the phase with the lower ultimate strain will fail first. For perfectly bonded fibers, the average longitudinal stress in the composite, ? 1, is given by the rule of mixtures as
where
| ? f, ? m = | Average longitudinal stresses in the fiber and matrix, respectively |
| V f, V m = | fiber and matrix volume ratios, respectively |
Under the simple deterministic assumption of uniform strengths, two cases are distinguished depending on the relative magnitudes of the ultimate tensile strains of the constituents.
In...
