Tensile Strength in the Fiber Direction

A unidirectional fiber-reinforced composite material deforms as the load increases in the following four stages, more or less, depending on the relative brittleness or ductility of the fibers and the matrix  

Because the fibers are more brittle than the matrix, they cannot elongate as much as the matrix. Thus, the fibers are the weak link, from the strain viewpoint, in the strength chain that the composite material comprises. 

Obviously, if fiber reinforcement is to lead to a greater strength than can be obtained with the matrix alone, then 

Equations (3.84) and (3.85) can be solved for the critical that must be exceeded to obtain fiber strengthening of the composite material  

For smaller values of Vj, the behavior of the composite material might not follow Equation (3.84) because there might not be enough fibers to control the matrix elongation. That is, the matrix dominates the composite material and carries the fibers along for the ride. Thus, the fibers would be subjected to high strains with only small loads and would fracture. If all fibers break at the same strain (an occurrence that is quite unlikely from a statistical standpoint), then the composite material will fracture unless the matrix (which occupies only of the representative volume element) can take the entire load imposed on the composite material, that is. 

---

The prediction of macromechanical strength properties of a unidirectional fiber-reinforced composite lamina using micromechanics models has met with less success than the elastic moduli predictions of the earlier sections. The structural designer will most likely rely primarily on results from mechanical tests that measure the macromechanical strength properties of the composite lamina directly. Nevertheless, it is instructive to look at the micromechanics model for tensile strength in the fiber direction of a lamina to gain a better understanding of how the composite functions. 

---