Puck failure analysis (2D)

Puck failure theory NOTE applies to unidirectional fibers. There are two different Puck failure criteria:

• Fiber failure criterion — In this criterion, two mutually exclusive fiber failure criteria equations are developed. One equation is used if fibers fail under tension and the other equation is used if fibers fail under compression.

• Matrix failure criterion — In this criterion, three mutually exclusive matrix failure criteria equations are developed. They are called:Inter-fiber failure mode AInter-fiber failure mode BInter-fiber failure mode CMatrix failure modes

The Puck failure theory needs the following empirical material properties that you specify in the Puck group of the Laminate Ply Material dialog box:

• Mean stress magnification factor, mσf. This factor is an empirical factor for the fibers in the direction perpendicular to the fibers. The magnification factor is due to the difference between the transverse modulus of the fiber and the modulus of the matrix.

• Shear strain coefficient, SC0. This coefficient is the constant term of the empirical shear correction term that is a function of shear strain.

• Inclination parameter (+) on the tension side, . This parameter sets the slope of the fracture envelope at zero normal transverse stress, on the tension side.

• Inclination parameter (–) on the compression side, . This parameter sets the slope of the fracture envelope at zero normal transverse stress, on the compression side.

These are empirical material properties and their value must be found experimentally. The following table summarizes the recommended values for these properties for two typical fiber reinforced polymers with 60% fiber volume fraction NOTE.

	mσf	SC0
Glass fiber / epoxy	1.3	10	0.3	0.25
Carbon fiber / epoxy	1.1	10	0.35	0.3

Fiber failure under tension

The fiber fails under tension when the following formula is true:

Failure Index

• The expression for the fiber failure index, Ff is:whereXTε is the tensile strain allowable in direction 1 of the unidirectional ply.νf12 is the Poisson’s ratio for the fiber.Ef1 is the Young’s modulus of the fiber in the fiber direction.

Margin of Safety

• The margin of safety for the fibers calculated as a percentage, MSf, is:

Strength Ratio

• The fiber strength ratio, SRf, is:

Fiber failure under compression

The fiber fails under compression when the following formula is true:

Failure Index

• The expression for the fiber failure index, Ff is:where XCε is the compressive strain allowable in direction 1 of the unidirectional ply.

To calculate the margin of safety and the strength ratio, the following equation is necessary:

Margin of Safety

• The margin of safety for the fibers calculated as a percentage, MSf, is:

Strength Ratio

• The fiber strength ratio, SRf, is:

Inter-fiber failure mode A

In this mode, the matrix fails in tension. Mathematically this is written as:

σ2 ≥ 0.

Failure Index

• The expression for the matrix failure index, Fm is:whereYT is the tensile stress allowable in direction 2 of the unidirectional ply.S is the shear strength of the unidirectional ply given by: S = YC.YC is the compressive stress allowable in direction 2 of the unidirectional ply.

Margin of Safety

• The margin of safety for the matrix calculated as a percentage, MSm, is:

Strength Ratio

• The matrix strength ratio, SRm, is:

Inter-fiber failure mode B

The matrix fails in this mode if the following two conditions are met:

• The matrix fails in compression. Mathematically this is written as:σ2 < 0.

• where

Failure Index

• The expression for the matrix failure index, Fm is:

Margin of Safety

• The margin of safety for the matrix calculated as a percentage, MSm, is:

Strength Ratio

• The matrix strength ratio, SRm, is:

Inter-fiber failure mode C

The matrix fails in this mode if the following two conditions are met:

• The matrix fails in compression. Mathematically this is written as: σ2 < 0.

Failure Index

• The expression for the matrix failure index, Fm is:

Margin of Safety

• The margin of safety for the matrix calculated as a percentage, MSm, is:

Strength Ratio

• The matrix strength ratio, SRm, is:

Look up more details

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Laminate failure analysis references

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Puck failure analysis (2D), Simcenter 3D 2021.1 Series

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Puck, A. and Schürmann, H., “Failure Analysis of FRP Laminates by Means of Physically Based Phenomenological Models”, Composites Science and Technology, Vol. 58, 1998, pp. 1045–1067.

Puck A., Kopp, J. and Knops, M., “Guidelines for determination of the parameters in Puck’s action plane strength criterion”, Composites Science and Technology, Vol. 62, 2002, pp. 371–378.

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