How to Interpret Composite Failure Criteria

1. The Engineering Task

Apply a composite failure criterion to the ply-level stress state and interpret the failure index to determine whether the laminate is safe and which ply and failure mode govern.

2. When to Use This Method

Every composite strength assessment. Unlike metals, where von Mises stress is the universal criterion, composites require anisotropic failure criteria that distinguish between fibre and matrix failure.

3. What You Need Before Starting

• Ply-level stresses in the material coordinate system (σ₁, σ₂, τ₁₂) for each ply
• The ply allowables: longitudinal tension X₁t, longitudinal compression X₁c, transverse tension X₂t, transverse compression X₂c, shear S₁₂
• The selected failure criterion: Tsai-Wu, Puck, Hashin or maximum stress

4. Step-by-Step Method

1. Extract the ply stresses (σ₁, σ₂, τ₁₂) in the material coordinate system for each ply at each critical location
2. For Tsai-Wu: calculate the failure index FI using the quadratic interaction equation. FI > 1.0 indicates failure. The Tsai-Wu criterion does not distinguish between fibre and matrix failure
3. For Hashin: calculate separate failure indices for fibre tension, fibre compression, matrix tension and matrix compression. Hashin distinguishes failure modes
4. For Puck: calculate fibre failure (FF) and inter-fibre failure (IFF) indices. Puck provides the most physically detailed failure mode identification, including the fracture plane angle for matrix failure
5. For maximum stress: compare each stress component with its allowable independently. This is the simplest criterion but does not account for interaction between stress components
6. Identify the critical ply: the ply with the highest failure index. Note the failure mode (fibre or matrix) and the location
7. Calculate the reserve factor: RF = 1/FI (approximate for proportional loading). MS = RF − 1

5. What to Check

• Are the stresses in the ply material coordinate system? Element coordinate stresses are not valid for composite failure assessment
• Has the correct criterion been selected? Tsai-Wu is a general-purpose criterion; Puck and Hashin provide failure mode distinction
• Is the failure index calculated for every ply, not just the highest-stress ply? The critical ply may not be the one with the highest stress
• For Tsai-Wu: has the interaction coefficient F₁₂ been correctly specified? It is often approximated but should come from biaxial test data
• Has interlaminar failure (delamination) been checked separately? In-plane criteria do not predict delamination

6. How to Interpret the Result

A failure index below 1.0 means the ply has not failed. The critical ply is the one closest to FI = 1.0. The failure mode (fibre or matrix) determines the response: fibre failure is typically catastrophic, while matrix failure (first-ply failure) may be tolerated depending on the design allowables and the application. For damage tolerance, first-ply failure may be acceptable if the laminate can still carry the load after matrix cracking.

7. Common Mistakes

• Using element coordinate stresses instead of ply material coordinate stresses
• Reporting only the highest failure index without identifying the ply or failure mode
• Treating first-ply failure (matrix cracking) as ultimate failure — many laminates can carry load beyond first-ply failure
• Not checking interlaminar stresses — delamination may occur before in-plane failure
• Using the Tsai-Wu interaction coefficient F₁₂ = 0 — this can be unconservative; use the recommended value from test data

8. Further Reading

See the Composite Structures Knowledge category for composite failure theory and criteria comparison. See How to Model Composite Layups in FEA for the laminate definition that produces the stresses.