Calculator Inputs
Enter strengths in MPa and densities in g/cm³.
Example Data Table
This table uses the current values after submission, or default values before submission.
| Fiber Volume Fraction (%) | Fiber Weight Fraction (%) | Composite Strength (MPa) | Status |
|---|---|---|---|
| 0 | 0.00 | 35.00 | Example |
| 10 | 14.29 | 346.50 | Example |
| 20 | 27.27 | 658.00 | Example |
| 30 | 39.13 | 969.50 | Example |
| 40 | 50.00 | 1,281.00 | Example |
| 50 | 60.00 | 1,592.50 | Example |
| 60 | 69.23 | 1,904.00 | Example |
Formula Used
Composite longitudinal strength model
σc = ηfσfuVf + σm′(1 − Vf)
Critical fiber volume fraction
Vf,crit = (σmu − σm′) / (ηfσfu − σm′)
Fiber weight fraction conversion
Wf = (Vfρf) / (Vfρf + (1 − Vf)ρm)
The calculator solves the minimum fiber volume fraction where the composite longitudinal strength first matches the matrix strength reference. The fiber efficiency factor accounts for alignment, load transfer, or processing losses. Weight fraction conversion helps compare volume-based design targets with manufacturing data sheets.
How to Use This Calculator
- Enter the fiber ultimate strength in MPa.
- Enter the matrix ultimate strength in MPa.
- Enter the matrix stress at the fiber fracture strain.
- Set the fiber efficiency factor between 0 and 1.
- Enter fiber and matrix densities for weight conversion.
- Enter your planned fiber volume fraction for comparison.
- Press Calculate Now to display results and the graph.
- Use the download buttons to save CSV or PDF output.
Frequently Asked Questions
1) What does critical fiber volume fraction mean?
It is the minimum fiber volume fraction where the composite longitudinal strength matches the chosen matrix strength reference. Below that point, reinforcement may not deliver the expected strength crossover in this simplified model.
2) Why is matrix stress at fiber fracture different from matrix ultimate strength?
The matrix may carry a different stress when the fibers fail than it carries at its own ultimate failure point. Using σm′ improves the strength balance used in many composite strength derivations.
3) What does the fiber efficiency factor represent?
It reduces the ideal fiber contribution to reflect imperfect alignment, discontinuous fibers, processing effects, or less-than-ideal load transfer. A value of 1 means ideal effectiveness in this calculation.
4) Why can the result exceed 100%?
That means the selected material set cannot reach the required crossover within a physical fiber volume range. You may need stronger fibers, better efficiency, or a lower matrix stress term.
5) Does this calculator apply to all composite loading cases?
No. It is best for aligned fibers under longitudinal loading with rule-of-mixtures style assumptions. Transverse loading, woven architectures, nonlinear behavior, and damage evolution need more detailed models.
6) Why include density inputs?
Design targets are often specified in volume fraction, but manufacturing and procurement documents may use weight fraction. Density lets you convert the critical or planned volume fraction into an equivalent fiber weight fraction.
7) How should I choose the design fiber volume fraction?
Use your intended layup or processing target. Then compare it with the critical threshold. If the planned value is higher, the model predicts the composite can exceed the matrix strength reference.
8) Can I use this for short fibers?
Yes, cautiously, if the efficiency factor reflects short-fiber limitations. However, detailed short-fiber predictions often need extra terms for critical fiber length, orientation distribution, and interfacial bonding quality.