This paper deals with the tensile strength of composites. The fibers of the composites are considered to have a statistical distribution of flaws of the Weibull type. The tensile strength formulation developed explicitly contains the Weibull shape factor, m, stress concentration factors due to fiber fractures, Ci, and the ineffective length, δ. Here, m describes the uniformity of the fiber strength. The stress concentration factors, Ci, characterize the disturbance of stress in neighboring unbroken fibers when i numbers of fiber have broken together. They are related directly to the subsequent event of fracture propagation perpendicular to the fiber direction, which is an important failure mechanism in ceramic composites. The ineffective length, δ, hinges on the concept of “the weakest link” along the fiber direction and is the dominant factor in the bundle strength representation of the strength of polymer-based composites. There is a lack of systematic analysis addressing the competition of these two important failure mechanisms and their influence on the tensile strength of the composites. In this paper, we combine the theory of bundle strength with the mechanics of local stress concentration to develop a micromechanical model for tensile strength, and study the influence of micromechanical properties on the tensile strength of composites and optimal design for tensile-controlled loading applications.
Using the strength formulas developed in this paper, we study how tensile strength is influenced by the changes of the micromechanical properties, m, Ci, and δ, and also by the properties of the fiber and matrix, Ef and Gm. It is shown that the existence of stress concentrations due to fiber fractures increases the chance of local crack propagation and, therefore, decreases the strength values predicted by the bundle strength theory. Stress concentrations play a dominate role in determining the magnitudes of tensile strength, especially for large values of m. However, since the stress concentrations remain virtually constant, for composites with different Ef and Gm and regularly spaced fibers, the variation of the strength curve as a function Ef and Gm is still controlled by the changes of the ineffective length, δ. The predictions of strength from the present model are compared to experimental measurements to validate the accuracy of the formulation.
The strength consideration is more complicated when the existence of irregular fiber spacing and the lack of quantitative descriptions of the spacing are taken into account. We show that, even for polymeric composites, optimal strength (when material properties Ef and Gm are taken as design variables) can be achieved due to certain fiber spacing variations. Therefore, the fiber spacing of composites, although difficult to control in the manufacturing process and hard to determine for a specimen, must be considered carefully to eliminate, isolate, or correctly represent its effects on strength and other macromechanical properties of engineering importance.