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. That makes 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).

Cuntze

The Cuntze Failure-Mode-Concept (FMC)⁸ starts from the same position as Puck: one failure mode is one physical mechanism, governed by one basic strength. A unidirectional ply has five strengths, so it gets five independent failure conditions, and the interaction between them is added afterwards as a separate, explicit step. Alongside Puck, it is one of the two criteria recommended by the German engineering guideline VDI 2014 Part 3⁷.

Each mode produces a stressing effort Eff, the fraction of that mode's capacity in use (failure when Eff = 1):

\text{FF1 } (\sigma_1 \ge 0): \; \frac{\sigma_1}{S_{1t}} \qquad \text{FF2 } (\sigma_1 < 0): \; \frac{-\sigma_1}{S_{1c}} \qquad \text{IFF1 } (\sigma_2 \ge 0): \; \frac{\sigma_2}{S_{2t}} \qquad \text{IFF3 } (\sigma_2 < 0): \; \frac{-\sigma_2}{S_{2c}}

\text{IFF2 (shear)}: \; \frac{|\tau_{12}| + B_{\perp\parallel}\min(\sigma_2,\, 0)}{S_{12}}

The modes combine through a probabilistic series-failure model, and the reserve factor is the reciprocal of the combined effort:

\text{Eff}^{\dot m} = \sum_{\text{modes}} \left(\text{Eff}^{\text{mode}}\right)^{\dot m} \qquad \text{SF} = 1 / \text{Eff}

Friction parameter $B_{\perp\parallel} = 0.6$ and interaction exponent $\dot m = 2.5$ (representative literature values for UD plies).

Genuine mode decomposition: each effort is computed from its own strength before the interaction combines them, so the governing mode is an output of the method, not an estimate.
Mohr-Coulomb friction: transverse compression presses the potential fracture plane together, raising the apparent shear strength. The friction term captures this, and it is credited only under compression (the min(σ₂, 0) bracket), so transverse tension alone can never register as shear failure.
Linear formulation: Cuntze gives two ways to write the shear mode, a linear form in which friction reduces the acting stress and a nonlinear form in which it raises the shear allowable. ABD Composites implements the linear form, a common linearization in software implementations of this criterion, because it keeps the reserve factor an exact load multiplier: a ply at SF = 2 really does fail at twice the load. The two forms agree on each mode's failure surface; under combined transverse stress and in-plane shear the linear form reports higher reserve factors than the nonlinear one.
Limitation: the friction parameter and interaction exponent are material-specific curve fits. The defaults above are representative values from Cuntze's own publications, not measured properties of your ply.

Sun

The Sun criterion⁹ exists to fix one specific, well-documented shortcoming: moderate transverse compression increases the apparent in-plane shear strength of a ply, because squeezing the potential fracture plane together makes it harder to slide. Elliptical criteria such as Hashin's predict the opposite. Sun's criterion is Hashin-Rotem everywhere except matrix compression, where a friction term grows the shear allowable as compression deepens.

Four failure modes:

\text{Fiber tension } (\sigma_1 \ge 0): \; \frac{\sigma_1}{S_{1t}} \ge 1 \qquad \text{Fiber compression } (\sigma_1 < 0): \; \frac{-\sigma_1}{S_{1c}} \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}{S_{2c}}\right)^2 + \left(\frac{\tau_{12}}{S_{12} - \eta_L\,\sigma_2}\right)^2 \ge 1

The friction coefficient is derived from the fracture-plane angle measured in plain transverse compression tests (53° for both carbon and glass epoxies): $\eta_L = 0.7611\, S_{12} / S_{2c}$ .

The compression physics of Puck at a fraction of the machinery: the single friction denominator captures the shear strengthening that otherwise requires Puck's fracture-plane treatment.
No free parameters: the friction coefficient follows from the measured fracture angle and the ply's own S₁₂/S_2c ratio, so there is nothing to calibrate.
Numerical safety factor in one mode: in matrix compression, scaling the load also changes the shear allowable, so no closed form recovers the failure load and it is solved numerically. The governing mode is selected by lowest safety factor, which keeps the reported mode consistent with the reported margin.
Limitation: phenomenological rather than mechanism-based. For fracture-plane prediction or a physically derived compression treatment, use Puck.

Edge

The Edge criterion¹⁰ is the stress-based Grant-Sanders method, an industrial design approach developed at British Aerospace and contributed to the World-Wide Failure Exercise. Failure is checked with discrete per-mode conditions, and only two of them carry any stress interaction at all: shear-tension for matrix failure and shear-compression for fiber failure.

Five evaluated conditions:

\text{Fiber tension } (\sigma_1 \ge 0): \; \frac{\sigma_1}{S_{1t}} \ge 1 \qquad \text{Shear}: \; \frac{|\tau_{12}|}{S_{12}} \ge 1

\text{Fiber compression } (\sigma_1 < 0): \; \frac{-\sigma_1}{S_{1c}} + \frac{|\tau_{12}|}{S_{12}} \ge 1

\text{Matrix tension } (\sigma_2 \ge 0): \; \left(\frac{\sigma_2}{S_{2t}}\right)^2 + \left(\frac{\tau_{12}}{S_{12}}\right)^2 \ge 1 \qquad \text{Matrix compression } (\sigma_2 < 0): \; \frac{-\sigma_2}{S_{2c}} \ge 1

Sharp-cornered envelopes by design: because the checks are discrete, the failure envelope is a polygon rather than a smooth curve, and every corner is a change of governing mode. Each prediction names its mode, which was a design goal of the method.
Shear degrades compressive strength: the linear shear-compression interaction reflects that shear loading softens the matrix supporting the fibers, lowering the compressive failure level while the mechanism stays fiber-dominated.
Calibration note: Edge parameterises the shear-compression interaction with its own allowables and used 1.5 × S₁₂ for the shear term in his own work. ABD Composites uses S₁₂, which makes that interaction about 33% more severe in shear. This is the more conservative reading, chosen for agreement with independent cross-validation references.
Limitation: with only two interactions, combined stress states away from those two corners are treated as independent checks, and the WWFE follow-up found the shear-compression interaction overpredicts for glass/epoxy laminates.

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
Cuntze	Mode-separated analysis per VDI 2014	Yes (5 modes)	Friction and interaction parameters are curve fits
Sun	Matrix compression without Puck's machinery	Yes (4 modes)	Phenomenological, no explicit failure mechanism
Edge	Discrete per-mode checks, aerospace design practice	Yes (5 modes)	Only two stress interactions

For general-purpose analysis, use Tsai-Wu: it handles tension/compression asymmetry and biaxial interaction. For failure mode identification, use Max Stress (simplest), Hashin (industry standard), or Puck (most physically accurate). Cuntze offers the same friction-based, mode-separated treatment as Puck within the VDI 2014 framework, Sun is the lightweight choice when transverse compression governs, and Edge trades smooth interaction for the explicit per-mode checks of aerospace design practice. 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 these nine criteria identify 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
Cuntze
Sun				Included in matrix modes
Edge

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.

How the Safety Factor 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).
Cuntze: SF = 1 / Eff. Every mode effort is linear in stress, so the combined effort scales directly with the load.
Sun: closed form per mode except matrix compression, where scaling the load also changes the shear allowable, so the failure load is solved numerically.
Edge: each mode has its own linear or quadratic solution, and the governing mode is the one with the lowest SF.

The ABD Composites dashboard color-codes the safety factor:

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

Every criterion above returns a safety factor for the one load case you entered. Run that same calculation in every direction of a plane of the load space instead, and the failure points join into a closed curve: the laminate's strength boundary, with the loads it survives inside it. The multiplier that traces the curve is the strength ratio R, the same number the safety factor comes from.

Envelopes are also the clearest way to see what separates the criteria on this page. Two criteria that report similar safety factors for one load case can draw boundaries that diverge sharply somewhere else in the plane, and drawing them on the same axes shows you where and by how much. Read how to build and read a failure envelope, including which load planes are available and what the boundary leaves out.

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.
Cuntze, R.G., "Efficient 3D and 2D Failure Conditions for UD Laminae and their Application within the Verification of the Laminate Design", Composites Science and Technology, Vol. 66, 2006, pp. 1081-1096. doi:10.1016/j.compscitech.2004.12.046
Sun, C.T., Quinn, B.J. & Oplinger, D.W., Comparative Evaluation of Failure Analysis Methods for Composite Laminates, DOT/FAA/AR-95/109, 1996. Equations as given in Davila, C.G., Camanho, P.P. & Rose, C.A., "Failure Criteria for FRP Laminates", NASA/TM-2005-213530, 2005.
Edge, E.C., "Stress-Based Grant-Sanders Method for Predicting Failure of Composite Laminates", Composites Science and Technology, Vol. 58, 1998, pp. 1033-1041. doi:10.1016/S0266-3538(96)00139-X

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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