Composite Material Failure Criteria Simulator

The Tsai-Wu criterion is a generalized quadratic failure model that accounts for stress interactions in anisotropic materials. It creates a single, smooth failure envelope in stress space.

Where $\sigma_1$ is stress along fibers, $\sigma_2$ is transverse stress, and $\tau_{12}$ is in-plane shear. The coefficients F are derived from basic strengths: $F_1 = 1/X_t - 1/X_c$, $F_{11}= 1/(X_t X_c)$, where $X_t, X_c$ are tensile and compressive strengths in the fiber direction. The interaction term $F_{12}$ is often determined experimentally.

Hashin's criterion separates failure into distinct, physically meaningful modes. This allows engineers to understand whether failure is driven by fiber breakage, matrix cracking, or shear.

Here, $Y_t, Y_c$ are transverse strengths, and $S$ is the shear strength. The simulator calculates each mode separately. The one that reaches 1 first dictates the failure mode, which is crucial for post-failure analysis.

Aerospace Wing & Fuselage Design: CFRP skins on aircraft wings experience complex biaxial tension and shear during flight. Engineers use these criteria to optimize ply angles (try changing the "Ply Angle" selector) to ensure the laminate doesn't fail under gust loads or during pressurization cycles, targeting a safe Strength Ratio.

Wind Turbine Blade Design: GFRP blades undergo massive bending and torsional loads. Hashin's criterion is vital here to distinguish between compressive fiber buckling on one side and matrix cracking on the other, informing where to add extra material or different ply sequences.

Automotive Chassis & Body Panels: In high-performance cars, carbon fiber tubs must absorb crash energy. Simulating failure under multi-axial impact loads (by adjusting the $\sigma_1$ and $\sigma_2$ sliders together) helps design a controlled, predictable crushing failure rather than sudden brittle fracture.

Sports Equipment (Bikes, Rackets): For a bicycle frame, the failure envelope under combined pedaling forces (axial) and cornering (bending/torsion) determines the layup. Using the simulator to find the "weakest" criterion for a given load case ensures the product is both lightweight and durable.

When you start using this simulator, there are several pitfalls that beginners in CAE often encounter. The first is the misconception that if the Failure Index (FI) exceeds 1, the entire part immediately shatters. In actual composite materials, especially laminates, "progressive failure" occurs where other plies take up the load even if one ply fails. An FI=1.2 is a sign that "failure begins in that ply," not the ultimate strength of the entire component. In practice, it's common to set a safety factor that keeps the FI around 0.5~0.8.

Next is input errors for material constants. For example, if you mistakenly swap the tensile strength (Xt) and compressive strength (Xc), the results become meaningless. For CFRP, the compressive strength in the fiber direction is often about 60-70% of the tensile strength. For instance, if Xt=1500MPa, then Xc=900~1000MPa is a good guideline. If this relationship is reversed, it's a sign you should review your inputs.

Finally, the tendency to search for the "strongest failure criterion". Tsai-Wu is convenient but doesn't tell you the failure mode. On the other hand, Hashin indicates the mode but may not fully account for fiber-matrix interactions. The key is "at which stage of design, and what do you want to know?" A practical approach is to use Tsai-Wu for a rough FI during conceptual design and then use Hashin to identify weak failure modes during detailed design.