The formula to calculate the Longitudinal Strength of Discontinuous Fiber-Reinforced Composite (less than critical length) is:
\[ \sigma_{cd}' = \left(\frac{V_f \cdot l \cdot \tau_c}{d}\right) + \tau_m \cdot (1 - V_f) \]
The Longitudinal Strength of a Discontinuous Fiber-Reinforced Composite (less than critical length) is the strength of a composite material where the length of the fiber is smaller than the critical length in a discontinuous aligned fiber-reinforced composite. The Volume Fraction of Fiber is the fraction of the fiber in the composite. The Fiber Length is the statistical average length of fibers present in the composite. The Critical Shear Stress is either the fiber-matrix bond strength or the shear yield stress of the matrix, whichever is lower. The Fiber Diameter is the diameter of the fibers in the composite. The Stress in Matrix is the stress at the failure of the composite.
Let's assume the following values:
Using the formula:
\[ \sigma_{cd}' = \left(\frac{0.5 \cdot 0.001 \cdot 80,000,000}{1E-05}\right) + 70,000,000 \cdot (1 - 0.5) = 4,035,000,000 \]
The Longitudinal Strength of the Discontinuous Fiber-Reinforced Composite is 4,035,000,000 Pascal.
| Volume Fraction of Fiber | Fiber Length (meters) | Critical Shear Stress (Pascal) | Fiber Diameter (meters) | Stress in Matrix (Pascal) | Longitudinal Strength (Pascal) |
|---|---|---|---|---|---|
| 0.4 | 0.001 | 80000000 | 1.0E-5 | 70000000 | 3,241,999,999.999999523162842 |
| 0.45 | 0.001 | 80000000 | 1.0E-5 | 70000000 | 3,638,499,999.999999523162842 |
| 0.5 | 0.001 | 80000000 | 1.0E-5 | 70000000 | 4,034,999,999.999999523162842 |
| 0.55 | 0.001 | 80000000 | 1.0E-5 | 70000000 | 4,431,500,000.000000000000000 |