The formula to calculate the Longitudinal Strength of Discontinuous Fiber-Reinforced Composite is:
\[ \sigma_{cd} = \sigma_f \cdot V_f \cdot \left(1 - \frac{l_c}{2 \cdot l}\right) + \tau_m \cdot (1 - V_f) \]
The Longitudinal Strength of a Discontinuous Fiber-Reinforced Composite is the strength of a composite material that is discontinuous and aligned fiber matrix composite. The length of the fiber is greater than the critical length. The Tensile Strength of Fiber is the strength of the fiber in the composite. The Volume Fraction of Fiber is the fraction of the fiber in the composite. The Critical Fiber Length is the length necessary for effective strengthening and stiffening of the composite material. The Fiber Length is the statistical average length of fibers present 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:
\[ \sigma_{cd} = 170,000,000 \cdot 0.5 \cdot \left(1 - \frac{0.00025}{2 \cdot 0.001}\right) + 70,000,000 \cdot (1 - 0.5) = 109,375,000 \]
The Longitudinal Strength of the Discontinuous Fiber-Reinforced Composite is 109,375,000 Pascal.
| Tensile Strength of Fiber (Pascal) | Volume Fraction of Fiber | Critical Fiber Length (meters) | Fiber Length (meters) | Stress in Matrix (Pascal) | Longitudinal Strength (Pascal) |
|---|---|---|---|---|---|
| 160000000 | 0.5 | 0.00025 | 0.001 | 70000000 | 105,000,000.000000000000000 |
| 161000000 | 0.5 | 0.00025 | 0.001 | 70000000 | 105,437,500.000000000000000 |
| 162000000 | 0.5 | 0.00025 | 0.001 | 70000000 | 105,875,000.000000000000000 |
| 163000000 | 0.5 | 0.00025 | 0.001 | 70000000 | 106,312,500.000000000000000 |
| 164000000 | 0.5 | 0.00025 | 0.001 | 70000000 | 106,750,000.000000000000000 |
| 165000000 | 0.5 | 0.00025 | 0.001 | 70000000 | 107,187,500.000000000000000 |
| 166000000 | 0.5 | 0.00025 | 0.001 | 70000000 | 107,625,000.000000000000000 |
| 167000000 | 0.5 | 0.00025 | 0.001 | 70000000 | 108,062,500.000000000000000 |
| 168000000 | 0.5 | 0.00025 | 0.001 | 70000000 | 108,500,000.000000000000000 |
| 169000000 | 0.5 | 0.00025 | 0.001 | 70000000 | 108,937,500.000000000000000 |
| 170000000 | 0.5 | 0.00025 | 0.001 | 70000000 | 109,375,000.000000000000000 |
| 171000000 | 0.5 | 0.00025 | 0.001 | 70000000 | 109,812,500.000000000000000 |
| 172000000 | 0.5 | 0.00025 | 0.001 | 70000000 | 110,250,000.000000000000000 |
| 173000000 | 0.5 | 0.00025 | 0.001 | 70000000 | 110,687,500.000000000000000 |
| 174000000 | 0.5 | 0.00025 | 0.001 | 70000000 | 111,125,000.000000000000000 |
| 175000000 | 0.5 | 0.00025 | 0.001 | 70000000 | 111,562,500.000000000000000 |
| 176000000 | 0.5 | 0.00025 | 0.001 | 70000000 | 112,000,000.000000000000000 |
| 177000000 | 0.5 | 0.00025 | 0.001 | 70000000 | 112,437,500.000000000000000 |
| 178000000 | 0.5 | 0.00025 | 0.001 | 70000000 | 112,875,000.000000000000000 |
| 179000000 | 0.5 | 0.00025 | 0.001 | 70000000 | 113,312,500.000000000000000 |
| 180000000 | 0.5 | 0.00025 | 0.001 | 70000000 | 113,750,000.000000000000000 |