Calculate unidirectional composite compression strength parallel to the fiber direction using the Budiansky-Fleck model
Longitudinal compressive strength (σCL) is the maximum compressive stress that a unidirectional composite can sustain when loaded parallel to the fiber direction. Unlike tensile failure, which is largely fiber-dominated, compressive failure is controlled by fiber microbuckling, the shear response of the matrix, and the inevitable small misalignment of the fibers.
Because compression strength is typically only 60–70 % of the corresponding tensile strength for high-performance carbon-fiber composites, it is often the limiting design value for structures such as wing spars, wind-turbine blade spar caps and automotive crash structures.
The Budiansky-Fleck model is one of the most widely accepted analytical expressions for longitudinal compressive strength. It treats the fibers as imperfectly aligned and derives the critical stress at which the fibers undergo plastic microbuckling within a shear-yielding matrix:
Where:
The model captures the strong sensitivity of compressive strength to even small fiber misalignments (typically 1–3°) and to the shear properties of the matrix.
| Parameter | Typical Range | Notes |
|---|---|---|
| Matrix shear modulus Gm | 1000 – 1600 MPa | Epoxy matrices ≈ 1200–1400 MPa |
| Fiber volume fraction Vf | 0.50 – 0.65 | Aerospace prepreg typically 0.55–0.62 |
| Fiber misalignment φ | 1.0° – 3.0° | High-quality prepreg ≈ 1.5–2.5° |
| Matrix shear yield strain γy | 0.02 – 0.05 | Depends on matrix toughness and temperature |
Gm = 1250 MPa, Vf = 0.60, φ = 2.0°, γy = 0.03
This value is representative of high-quality unidirectional carbon/epoxy material used in aircraft primary structures and wind-turbine blade spar caps. Actual measured strengths are often 5–15 % lower because of additional defects (voids, fiber waviness, residual stresses).
In tension the fibers can develop their full strength. In compression the fibers become unstable and microbuckle; the supporting matrix shear stiffness and the initial fiber alignment therefore become the limiting factors.
Very sensitive. Increasing the misalignment angle from 1° to 3° can reduce predicted compressive strength by 30–40 % for typical aerospace matrices.
Yes, provided appropriate matrix shear properties and a realistic misalignment angle are used. Glass-fiber composites generally show lower compressive strengths than carbon-fiber systems of similar volume fraction.
After applying statistical allowables and environmental knockdowns, design compressive strengths are often in the range 900–1200 MPa, depending on the specific material and certification basis.
Once longitudinal compressive strength is known, engineers typically continue with: