Composite Laminate Failure Criteria

Q: Which composite failure criterion is most accurate?

There is no single best criterion for all cases. The right choice depends on loading type and whether you need failure mode identification. See Which failure criterion should you use?

Q: What is a failure index in composite analysis?

A dimensionless ratio where FI below 1 means the ply has margin, FI = 1 is at failure load, and FI above 1 means failure has occurred. The safety factor follows from it per criterion: 1/FI for the linear criteria, 1/√FI for the quadratic ones. See Safety Factor and Failure Index.

Q: What is first ply failure (FPF)?

First ply failure (FPF) is the load at which the first ply in the laminate reaches its strength limit under any failure criterion. It is the conservative lower bound for laminate strength. After FPF the laminate can still carry load through progressive failure, but FPF is the standard design threshold for most engineering applications.

How composite failure criteria predict when a ply will fail under combined loading, and which criterion to use for your application.

What are failure criteria?

Failure criteria predict when a composite ply will fail under combined loading¹. Because composite plies are anisotropic, with different strengths in the fiber direction, transverse direction, and shear, simple yield checks used for metals do not apply. Instead, specialized criteria compare the stress state in each ply (in material coordinates) against the ply's measured allowable strengths.

Each ply has five strength allowables, measured from coupon tests:

S_1t: longitudinal tensile strength (fiber direction, tension)
S_1c: longitudinal compressive strength (fiber direction, compression)
S_2t: transverse tensile strength (perpendicular to fibers, tension)
S_2c: transverse compressive strength (perpendicular to fibers, compression)
S₁₂: in-plane shear strength

These define five possible failure modes: fiber tension, fiber compression, matrix tension, matrix compression, and shear. The applied ply stresses (σ₁, σ₂, τ₁₂) are compared against these allowables to determine whether failure occurs and which mode governs.

Maximum Stress

The Maximum Stress criterion compares each stress component independently to its allowable value:

Failure when any of:

|\sigma_1| \ge S_{1t} \;\text{(if } \sigma_1 > 0\text{)} \quad \text{or} \quad |\sigma_1| \ge S_{1c} \;\text{(if } \sigma_1 < 0\text{)}

|\sigma_2| \ge S_{2t} \;\text{(if } \sigma_2 > 0\text{)} \quad \text{or} \quad |\sigma_2| \ge S_{2c} \;\text{(if } \sigma_2 < 0\text{)}

|\tau_{12}| \ge S_{12}

Simple and intuitive: each stress component is checked independently.
Identifies the failure mode: tells you whether failure is fiber-dominated, matrix-dominated, or shear-driven.
Misses stress interactions: does not account for the combined effect of biaxial stress states, which can cause failure at lower individual stress levels.
Best suited for predominantly uniaxial loading or as a quick preliminary check. Note: Max Stress can be non-conservative under combined loading because it ignores stress interactions.

Maximum Strain

The Maximum Strain criterion follows the same philosophy as Maximum Stress but operates in strain space. Failure is predicted when any strain component exceeds its allowable limit:

Strains from compliance (including Poisson coupling):

\varepsilon_1 = \frac{\sigma_1}{E_1} - \frac{\nu_{12}}{E_1}\sigma_2 \qquad \varepsilon_2 = \frac{\sigma_2}{E_2} - \frac{\nu_{21}}{E_2}\sigma_1 \qquad \gamma_{12} = \frac{\tau_{12}}{G_{12}}

Failure when any of:

\frac{\varepsilon_1}{\varepsilon_{1T}} \ge 1 \;\text{or}\; \frac{-\varepsilon_1}{\varepsilon_{1C}} \ge 1 \qquad \frac{\varepsilon_2}{\varepsilon_{2T}} \ge 1 \;\text{or}\; \frac{-\varepsilon_2}{\varepsilon_{2C}} \ge 1 \qquad \frac{|\gamma_{12}|}{\gamma_{12u}} \ge 1

where allowable strains are derived from strengths: $\varepsilon_{1T} = S_{1t}/E_1$ , etc.

Includes Poisson coupling: unlike Maximum Stress, the strain in the fiber direction depends on the transverse stress (and vice versa), providing indirect stress interaction.
Identifies the failure mode: same five modes as Maximum Stress (fiber tension/compression, matrix tension/compression, shear).
Failure envelope: forms a parallelogram in stress space (vs. the rectangle of Maximum Stress), due to Poisson effects.
Elastic properties in the criterion itself: unlike Max Stress (which only needs E₁, E₂, G₁₂, v₁₂ for the upstream CLT step), Max Strain uses them directly in the failure check to convert stresses to strains via the compliance matrix.

Tsai-Hill

The Tsai-Hill criterion is a quadratic interaction criterion adapted from the Hill yield criterion for anisotropic metals:

\text{FI} = \left(\frac{\sigma_1}{S_1}\right)^2 - \frac{\sigma_1 \cdot \sigma_2}{S_1^2} + \left(\frac{\sigma_2}{S_2}\right)^2 + \left(\frac{\tau_{12}}{S_{12}}\right)^2

Failure when FI ≥ 1.0

Accounts for biaxial stress interaction: the cross-term (σ₁·σ₂) captures the combined effect of longitudinal and transverse stresses.
Strength selection: the implementation substitutes S₁t or S₁c (and S₂t or S₂c) based on the sign of each stress component. However, the quadratic form has no separate linear terms to account for different tension and compression allowables, unlike Tsai-Wu.
Limitation: can be non-conservative under certain biaxial stress states because there is no mechanism to capture asymmetric T/C behavior. Use Tsai-Wu when tension and compression strengths differ significantly.

Tsai-Wu

The Tsai-Wu criterion is a full tensor polynomial that properly distinguishes between tension and compression strengths²:

\text{FI} = F_1\sigma_1 + F_2\sigma_2 + F_{11}\sigma_1^2 + F_{22}\sigma_2^2 + F_{66}\tau_{12}^2 + 2F_{12}\sigma_1\sigma_2

where:

\begin{aligned} F_1 &= \frac{1}{S_{1t}} - \frac{1}{S_{1c}} & F_2 &= \frac{1}{S_{2t}} - \frac{1}{S_{2c}} \\ F_{11} &= \frac{1}{S_{1t} \cdot S_{1c}} & F_{22} &= \frac{1}{S_{2t} \cdot S_{2c}} \\ F_{66} &= \frac{1}{S_{12}^2} & F_{12} &= -\tfrac{1}{2}\sqrt{F_{11} \cdot F_{22}} \end{aligned}

Failure when FI ≥ 1.0

Most general criterion: the linear terms (F₁, F₂) allow different tension and compression strengths, unlike Tsai-Hill.
Biaxial interaction: the F₁₂ interaction term captures how longitudinal and transverse stresses combine. The value F₁₂ = −½√(F₁₁·F₂₂) is the most commonly used approximation (Tsai-Hahn).
Recommended for combined loading: most accurate for multiaxial stress states where tension/compression differences matter.
Limitation: the math produces a single failure index, not a specific failure mode. The ABD Composites dashboard approximates the dominant mode from stress ratios, but for definitive failure mode identification, compare with Maximum Stress results.

Hashin

The Hashin criterion⁴ (1980) separates failure into four distinct physical mechanisms, each evaluated independently. Unlike Tsai-Hill and Tsai-Wu, Hashin identifies the actual failure mode.

Four failure modes:

\text{Fiber tension } (\sigma_1 \ge 0): \quad \left(\frac{\sigma_1}{S_{1t}}\right)^2 + \left(\frac{\tau_{12}}{S_{12}}\right)^2 \ge 1

\text{Fiber compression } (\sigma_1 < 0): \quad \left(\frac{-\sigma_1}{S_{1c}}\right)^2 \ge 1

\text{Matrix tension } (\sigma_2 \ge 0): \quad \left(\frac{\sigma_2}{S_{2t}}\right)^2 + \left(\frac{\tau_{12}}{S_{12}}\right)^2 \ge 1

\text{Matrix compression } (\sigma_2 < 0): \quad \left(\frac{\sigma_2}{2S_T}\right)^2 + \left[\left(\frac{S_{2c}}{2S_T}\right)^2 - 1\right]\frac{\sigma_2}{S_{2c}} + \left(\frac{\tau_{12}}{S_{12}}\right)^2 \ge 1

where $S_T = S_{2c}/2$ (transverse shear strength approximation). Failure when any mode index reaches 1.0.

Identifies the failure mechanism: tells you exactly whether failure is fiber-dominated or matrix-dominated, and whether it is tensile or compressive.
Shear interaction in fiber tension: unlike Maximum Stress, shear stress contributes to the fiber tension failure index. A ply can fail in fiber tension at lower axial stress when shear is also present.
Widely used in FEA: Hashin is a built-in damage initiation criterion for fiber composites in mainstream commercial finite element codes, making it an industry standard for progressive failure analysis.
Limitation: fiber compression is simplified to a maximum stress check (no shear interaction). For more accurate compression prediction, consider Puck.

Puck

The Puck criterion⁵ (Puck & Schurmann, 2002) is a physically-based criterion that distinguishes fiber failure (FF) from inter-fiber failure (IFF). It is the only common criterion that predicts the fracture plane orientation, and is particularly accurate for matrix-dominated failures under compression.

Fiber failure (same as Max Stress in fiber direction):

\text{FF tension: } \frac{\sigma_1}{S_{1t}} \ge 1 \qquad \text{FF compression: } \frac{-\sigma_1}{S_{1c}} \ge 1

Inter-fiber failure (three modes based on transverse stress state):

\text{Mode A } (\sigma_2 \ge 0): \; \sqrt{\left(\frac{\tau_{12}}{S_{12}}\right)^2 + \left(1 - p_{\perp\parallel}^{(+)}\frac{S_{2t}}{S_{12}}\right)^2\left(\frac{\sigma_2}{S_{2t}}\right)^2} + p_{\perp\parallel}^{(+)}\frac{\sigma_2}{S_{12}} = 1

\text{Mode B } (\sigma_2 < 0, \text{shear-dominated}): \; \frac{1}{S_{12}}\left(\sqrt{\tau_{12}^2 + (p_{\perp\parallel}^{(-)}\sigma_2)^2} + p_{\perp\parallel}^{(-)}\sigma_2\right) = 1

\text{Mode C } (\sigma_2 < 0, \text{compression-dominated}): \; \left[\left(\frac{\tau_{12}}{2(1+p_{\perp\perp}^{(-)})S_{12}}\right)^2 + \left(\frac{\sigma_2}{S_{2c}}\right)^2\right]\frac{-S_{2c}}{\sigma_2} = 1

Inclination parameters $p_{\perp\parallel}^{(\pm)}$ and $p_{\perp\perp}^{(-)}$ default to 0.25 (recommended values when experimental data is not available).

Puck reports five distinct failure modes in the ABD Composites dashboard:

FF Tension / FF Compression: fiber failure under longitudinal tension or compression. Equivalent to the Max Stress check in the fiber direction.
IFF Mode A: inter-fiber (matrix) failure under transverse tension (σ₂ ≥ 0). The matrix cracks parallel to the fibers, with the fracture plane perpendicular to the ply.
IFF Mode B: inter-fiber failure under moderate transverse compression combined with significant shear. The fracture plane remains perpendicular to the ply (0 deg), similar to Mode A but on the compression side.
IFF Mode C: inter-fiber failure under dominant transverse compression (σ₂ < 0). The fracture plane tilts away from the loading direction, producing the characteristic wedge-shaped fracture that can cause delamination.

Physically motivated: based on Mohr-Coulomb fracture mechanics rather than curve-fitting. The three IFF modes correspond to different physical fracture mechanisms in the matrix.
Best for compression: Mode C accurately captures the wedge-shaped fracture under transverse compression, where simpler criteria tend to be less accurate.
Predicts fracture plane: the only common criterion that predicts the orientation of the fracture plane (0 deg for modes A/B, rotating for mode C).
German engineering standard: recommended by VDI 2014 Part 3⁷ for FRP component analysis and used in DNV GL wind turbine blade certification.
Limitation: requires inclination parameters that ideally come from biaxial testing. The default value of 0.25 is the conservative lower bound recommended by Puck & Schurmann⁵ (0.25-0.35 for CFRP, 0.25-0.30 for GFRP).

Which failure criterion should you use?

Criterion	Best for	Mode ID	Limitation
Max Stress	Uniaxial loading, quick preliminary check	Yes (5 modes)	Ignores stress interaction
Max Strain	Uniaxial loading with Poisson effects	Yes (5 modes)	Indirect interaction only (via Poisson)
Tsai-Hill	Biaxial loading, quick interaction check	No (estimated)	No tension/compression distinction
Tsai-Wu	Combined loading, general analysis	No (estimated)	No inherent mode identification
Hashin	Mode-dependent analysis, FEA validation	Yes (4 modes)	Simplified fiber compression
Puck	Matrix compression, fracture plane prediction	Yes (5 modes)	Requires inclination parameters

For general-purpose analysis, Tsai-Wu is recommended as it handles tension/compression asymmetry and biaxial interaction. For failure mode identification, use Max Stress (simplest), Hashin (industry standard), or Puck (most physically accurate). Tsai-Hill and Tsai-Wu produce a single failure index rather than identifying a specific mode. The ABD Composites dashboard approximates the dominant mode for these two criteria by comparing normalized stress ratios (the same logic used by Maximum Stress). For confident mode identification, compare Tsai-Wu results with Hashin or Puck. For a comprehensive treatment of composite failure analysis, see Daniel & Ishai⁶ and Tsai³.

Failure modes

Each criterion reports which stress component is driving the ply closest to failure. The five fundamental failure modes in a unidirectional ply are:

Fiber tension: the ply is pulled along the fiber direction beyond the longitudinal tensile strength (S_1t). Fibers break.
Fiber compression: the ply is compressed along the fiber direction beyond S_1c. Fibers buckle or kink.
Matrix tension: the ply is pulled perpendicular to the fibers beyond the transverse tensile strength (S_2t). The matrix cracks parallel to the fibers.
Matrix compression: the ply is compressed perpendicular to the fibers beyond S_2c. The matrix fails, often on an inclined fracture plane.
Shear: in-plane shear stress exceeds the shear strength (S₁₂). The matrix fails in shear along the fiber direction.

Not every criterion reports all five modes. Some criteria (Tsai-Hill, Tsai-Wu) produce a single failure index without inherent mode identification. On the First Ply Failure page the dashboard estimates a dominant mode for those criteria from stress ratios, and labels it as an estimate. Progressive Failure does not: there the mode decides which stiffnesses get degraded, so acting on an estimate would change the answer, and both criteria are treated as general material failure instead. The table below shows which modes each criterion identifies directly:

Criterion	Fiber tension	Matrix tension	Matrix compression	Shear
Max Stress
Max Strain
Tsai-Hill	Estimated from stress ratios (no inherent mode identification)
Tsai-Wu	Estimated from stress ratios (no inherent mode identification)
Hashin				Included in fiber/matrix modes
Puck		IFF-A	IFF-C	IFF-B

Puck uses different labels: fiber failure (FF) for the fiber modes, and inter-fiber failure (IFF) for the matrix modes. IFF Mode A corresponds to matrix tension, IFF Mode C to matrix compression, and IFF Mode B to shear-dominated failure under moderate transverse compression. See the Puck section above for details on each IFF mode.

The same laminate and load case under Puck. The mode comes back with its IFF label attached, here Matrix tension (IFF-A), so the plain mode name is still there, with the specific inter-fiber mode the criterion identified alongside it.

Safety Factor & Failure Index

The Failure Index (FI) is the output of the criterion evaluation for each ply. The Safety Factor (SF) is the load multiplier at which the most critical ply reaches failure:

\text{FI} < 1.0 \;\rightarrow\; \text{ply is safe} \qquad \text{FI} \ge 1.0 \;\rightarrow\; \text{ply has failed}

\text{SF} \ge 1.0 \;\rightarrow\; \text{laminate survives} \qquad \text{SF} < 1.0 \;\rightarrow\; \text{first ply has failed}

SF < 1.0 does not always mean the laminate is finished. This is a first ply failure check, so it reports the first ply to reach FI = 1.0 and stops there. If that ply failed in a matrix or shear mode, what happened is transverse cracking: its fibers are intact, the surviving plies redistribute the load, and the laminate carries on. A 0/±45 pressure vessel is the classic case, where the 0° plies craze transversely long before the ±45° plies give up.

Read the governing mode alongside the safety factor, and if it is matrix or shear, run Progressive Failure for the load the laminate actually carries. A fiber-mode SF below 1.0 is the one to treat as failure. One caveat in the other direction: for a pressure vessel, matrix cracking may still be your design limit even though it is not structural failure, because a crazed ply is a leak path.

The Safety Factor is the load multiplier at which the most critical ply reaches failure. How it is computed depends on the criterion:

Max Stress / Max Strain: SF = 1 / FI (FI is linear in stress/strain).
Tsai-Hill / Hashin: SF = 1 / √FI (FI is quadratic in stress).
Tsai-Wu: SF is found by solving the quadratic equation that results from scaling all applied stresses by a common factor R until FI = 1.
Puck: SF = 1 / f_E where f_E is the stress exposure factor (the failure index).

The ABD Composites dashboard uses color coding for quick visual assessment:

Green (SF ≥ 1.5): comfortable margin above failure.
Amber (1.0 ≤ SF < 1.5): safe but with limited margin. Review loading assumptions.
Red (SF < 1.0): laminate fails under the applied loads.

First ply failure for a 10-ply laminate under combined loading. The summary names the governing ply and its failure mode; the table below gives the failure index for every ply.

Failure Envelopes

A safety factor answers one question: how much more of this load can the laminate take? A failure envelope answers the wider one. Instead of scaling a single load direction, it scales every direction in a plane of the load space and records where failure occurs in each. Joining those points traces a closed curve, and that curve is the laminate's strength boundary: inside it the laminate survives, outside it a ply has failed.

The construction rests on the same load multiplier as the safety factor, usually written R in this context, the strength ratio. For each direction the whole load vector is scaled by R until the first ply reaches FI = 1, and the resulting load is one point on the envelope. Because CLT is linear in the applied load, ply stress is proportional to R, which is what makes each point an exact solution rather than something found by trial and error.

Reading an envelope

Your margin is a distance, and it has a direction. Plot the applied load as a point inside the envelope. How far it sits from the boundary along the direction the load would grow is the margin that matters. A load point comfortably far from the boundary in one direction can be very close to it in another, which a single safety factor number cannot show you.
The shape tells you which criterion you are looking at. Non-interactive criteria check each stress component separately, so their envelopes come out as polygons with corners. Interactive criteria combine all components into one polynomial, so theirs are smooth closed curves. Running several criteria over the same laminate makes the difference between them visible in a way a table of safety factors does not.
Asymmetry about the origin is real, not a glitch. Composites are much weaker in transverse tension than in transverse compression, so an envelope is normally offset rather than centred. A criterion whose envelope is symmetric, Tsai-Hill for instance, is telling you it does not distinguish tension from compression.
A dent or a corner is a change of governing mode. Where the boundary changes character, a different ply or a different failure mode has taken over as the critical one. Those transitions are worth noting, because a design sitting near one is sensitive to small changes in the load ratio.

What an envelope leaves out. The envelope drawn here is a first ply failure boundary, so it is conservative: many laminates carry considerably more load after the first ply cracks, which is what progressive failure analysis is for. It also spans two load components at a time, with the third held at zero, and it does not include applied moments or thermal and moisture loads. Those add a fixed stress that does not scale with R, which breaks the proportionality the construction depends on.

Author: Rick Schrijver

References

Jones, R.M., Mechanics of Composite Materials, 2nd Ed., Taylor & Francis, 1999.
Tsai, S.W. & Wu, E.M., "A General Theory of Strength for Anisotropic Materials", J. Composite Materials, Vol. 5, 1971. doi:10.1177/002199837100500106
Tsai, S.W., Theory of Composites Design, Think Composites, 1992.
Hashin, Z., "Failure Criteria for Unidirectional Fiber Composites", J. Applied Mechanics, Vol. 47, 1980, pp. 329-334. doi:10.1115/1.3153664
Puck, A. & Schurmann, H., "Failure Analysis of FRP Laminates by Means of Physically Based Phenomenological Models", Composites Science and Technology, Vol. 62, 2002, pp. 1633-1662. doi:10.1016/S0266-3538(01)00208-1
Daniel, I.M. & Ishai, O., Engineering Mechanics of Composite Materials, 2nd Ed., Oxford University Press, 2006.
VDI 2014 Part 3, "Development of Fibre-Reinforced Plastics Components - Analysis", Verein Deutscher Ingenieure, 2006.

Frequently Asked Questions

Which composite failure criterion is most accurate?

What is a failure index in composite analysis?

What is first ply failure (FPF)?

Apply these criteria to your laminate

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