Composite Failure Criteria — Selection & Limitations

What Is It?

Multiple failure criteria exist for composite laminates, each with different theoretical bases, predictive capabilities and limitations. Selecting the appropriate criterion for a given analysis requires understanding what each criterion predicts, whether it identifies the failure mode, how it handles interaction between stress components, and what material data it requires. No single criterion is universally superior — the choice depends on the laminate, the load case and the available test data.

Why It Matters

The failure criterion determines what the analysis predicts. A criterion that does not distinguish failure modes cannot be used in a progressive damage analysis that needs mode-dependent degradation. A criterion with poor interaction modelling may over-predict or under-predict strength under combined loading. A criterion that requires material data which is not available is not usable. Selecting the wrong criterion can produce misleading results — or results that look correct but are based on the wrong physics.

No single failure criterion is universally superior. The choice depends on the laminate, the load case and the available test data. Understanding what each criterion predicts and its limitations is essential for credible composite analysis.

Maximum Stress Criterion

The maximum stress criterion compares each stress component independently against the corresponding strength. If any component exceeds its strength, failure is predicted. The criterion is simple and identifies which stress component caused failure — but it does not account for interaction between stress components. Under combined loading, it can be significantly non-conservative because the combined effect of multiple sub-critical stress components is not captured.

Maximum stress criterion:

Failure if ANY of:
  σ₁ ≥ X_T  or  σ₁ ≤ −X_C   (fibre direction)
  σ₂ ≥ Y_T  or  σ₂ ≤ −Y_C   (transverse)
  |τ₁₂| ≥ S                  (shear)

Identifies: which component caused failure
Interaction: NONE — each component checked independently
Limitation: non-conservative under combined loading

Maximum Strain Criterion

The maximum strain criterion is analogous to maximum stress but uses strains instead of stresses. Each strain component is compared against the corresponding ultimate strain. The criterion has the same limitations as maximum stress — no interaction — but may be preferred when strain-based design allowables are available, or when the analysis is strain-driven.

Tsai-Hill Criterion

Tsai-Hill adapts the von Mises yield criterion to anisotropic materials. It produces a single failure index that accounts for interaction between stress components. However, it does not distinguish between failure modes — it gives a single scalar failure index, not a fibre or matrix failure identification. It also does not distinguish between tension and compression strengths. Tsai-Hill is useful for overall strength screening but not for progressive damage analysis that requires mode identification.

• Accounts for interaction between stress components
• Does NOT distinguish failure modes — single scalar index
• Does NOT distinguish tension and compression strengths
• Useful for overall screening — not for mode-dependent progressive damage

Tsai-Wu Criterion

Tsai-Wu is a polynomial failure criterion that generalises the Tsai-Hill approach. It accounts for interaction between stress components and can distinguish between tension and compression strengths through the inclusion of additional terms. Like Tsai-Hill, it produces a single failure index and does not identify the failure mode. Tsai-Wu is widely used for overall strength screening but, like Tsai-Hill, is not suitable for progressive damage analysis that requires mode identification.

Tsai-Wu criterion (simplified):

FI = F₁σ₁ + F₂σ₂ + F₁₁σ₁² + F₂₂σ₂² + F₆₆τ₁₂² + 2F₁₂σ₁σ₂

where F terms combine tension and compression strengths.

FI = 1.0 → failure predicted

Distinguishes: tension vs compression (through F terms)
Does NOT distinguish: failure mode (fibre vs matrix)
Interaction: YES — through cross terms

Hashin Criterion

Hashin failure criteria distinguish between fibre and matrix failure modes, and between tension and compression. This mode identification makes Hashin suitable for progressive damage analysis where the degradation depends on the failure mode. Hashin uses separate equations for fibre tension, fibre compression, matrix tension and matrix compression, each with different interaction terms. The criteria are widely implemented in commercial FEA codes and are commonly used for composite damage analysis.

Puck Failure Theory

Puck failure theory is a physically-based criterion that identifies both fibre failure and inter-fibre failure (matrix failure) with explicit consideration of the fracture plane angle. For inter-fibre failure, Puck predicts the angle of the fracture plane, which provides additional physical insight. Puck requires more material data than Hashin — including transverse compressive strength under different stress states — but provides more physically detailed failure prediction. Puck is particularly useful for understanding the mechanics of matrix failure.

• Physically-based — identifies fibre and inter-fibre (matrix) failure
• Predicts the fracture plane angle for inter-fibre failure
• Requires more material data than Hashin
• Provides more physical insight into matrix failure mechanics
• Particularly useful for understanding failure mechanisms

LaRC-Type Criteria

LaRC (Langley Research Center) failure criteria are a family of advanced criteria that address specific failure mechanisms with detailed physics. They include fibre kinking under compression (with explicit consideration of fibre misalignment and matrix shear), matrix failure under combined loading, and in-plane shear effects. LaRC criteria are more physically detailed than Hashin and can predict mechanisms like fibre kinking that simpler criteria do not capture. They require material data that may not always be available.

• Advanced physically-based criteria from NASA Langley
• Address fibre kinking, matrix failure and shear with detailed mechanics
• Predict fibre kinking — not captured by simpler criteria
• Require additional material data (misalignment angle, etc.)
• Engineering-level overview — do not reproduce proprietary implementations

Comparison Summary

The table below summarises the key characteristics of each criterion family.

No Universal Superiority

No single criterion is universally superior. The best criterion for a given analysis depends on the laminate, the load case, the available material data, the analysis objective and the required level of physical detail. For screening, Tsai-Wu or maximum stress may suffice. For progressive damage, Hashin or Puck are appropriate. For detailed failure mechanism investigation, Puck or LaRC provide the most physical insight. The selection should be documented and justified.

Do NOT assume one criterion is universally superior. The choice depends on the laminate, load case, available data and analysis objective. For screening: Tsai-Wu or max stress. For progressive damage: Hashin or Puck. For mechanism investigation: Puck or LaRC. Document the selection.

Key Takeaways

• Multiple criteria exist — each with different capabilities and limitations
• Mode identification (fibre vs matrix) is essential for progressive damage — Tsai-Hill/Tsai-Wu do not provide it
• Hashin is the most common choice for progressive damage — mode identification with moderate data requirements
• Puck provides fracture plane prediction; LaRC provides detailed mechanism prediction — both need more data
• No criterion is universally superior — select based on laminate, load, data and objective