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COMPTEST’2006 – 10 to 12 of April of 2006 – University of Porto – PortugalExperimental and numerical studies of mode I,II, III and mixed-mode I-II energy release rate in laminates

EXPERIMENTAL AND NUMERICAL STUDIES OF MODE I, II, III AND MIXED-MODE I-II

ENERGY RELEASE RATE IN LAMINATES

Rosa Marat-Mendes, Manuel de Freitasrmendes@est.ips.pt

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SummaryIntroductionMaterial

PropertiesSamples

Experimental ProcedureMode IMixed Mode I-IIMode IIMode III

ResultsExperimentalAnalytical

Conclusions

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IntroductionLamination of composite structures is one of the most common manufacturing techniques used in the construction of composite components. One of the limiting factors of laminated structures is a failuremode known as delamination, which is the separation of individual layers of the laminated structure.There are three fundamental fracture modes for the crack propagation:

Mode I Mode II Mode III

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IntroductionIn reality delamination can occurs with a sobrepositionof the three modes. The Mixed Mode Bending (MMB) test combines the mode I (DCB) and the mode II (ENF) tests.In this work it is used the mode I, the mode II, the mode III separately and also a combined test of the two modes I and II to predict the delamination in mixed mode I-II.

+ =

Mode I(DCB)

Mode II(ENF)

Mixed Mode I-II(MMB)

L La

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The material used was a UE400 REM GLASS UD PREPREG from SEAL.- epoxy resin ET443- reinforced with unidirectional E glass fibers

The artificial pre-crack has been achieved inserting a single 13μm thick Teflon-foil Type A-FEP from Dupont in the mid plane of the specimens.

Material

580.25742600E Glass fiber420.44.51200Epoxy resin 913

V (%)υE (GPa)ρ (kg/m3)

∓

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Material – Fabric of the samples

1 - Lay-up 2 - Autoclave

3 - Final Sample

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Lamina properties

0.25

0.30

νLT

Mode III

Mode IMode II

Mixed Mode I-II

Tests

583.5816.7143.94[024]

[0/(±45)3/( 45)3/90]s 564.409.0043.42

Vf [%]GLT [GPa]ET [GPa]EL [GPa]

∓

Properties obtained through the tensile test and Incineration

Incineration Tensile test

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Samples for Mode I, Mode II e Mixed Mode I-II

[024]

[024]

[024]

[024]

[024]

[024]

[024]

[024]

Lay-up

161.70 – 23.43 – 6.40 – 32.30Mode I-IIUD_V_01_4

162.40 – 25.72 – 6.55 – 32.30Mode IIUD_V_01_3

161.95 – 25.23 – 6.55 – 31.70Mode IUD_V_01_2

162.25 – 23.58 – 6.93 – 31.50Mode IUD_V_01_1

161.85 – 24.18 – 6.30 – 32.60Mode I-IIUD_V_01_6

161.85 – 24.63 – 6.38 – 32.30Mode IIUD_V_01_5

162.05 – 23.88 – 6.40 – 33.30Mode I-IIUD_V_01_7

Mode I-II

Test

162.05 – 23.43 – 6.40 – 32.50UD_V_01_8

Dimensions [mm]w - b - 2h - a0

Sample

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Samples for Mode III

[0/(±45)3/( 45)3/90]s

[0/(±45)3/( 45)3/90]s

[0/(±45)3/( 45)3/90]s

[0/(±45)3/( 45)3/90]s

[0/(±45)3/( 45)3/90]s

[0/(±45)3/( 45)3/90]s

[0/(±45)3/( 45)3/90]s

[0/(±45)3/( 45)3/90]s

Lay-up

Mode III

Mode III

Mode III

Mode III

Mode III

Mode III

Mode III

Mode III

Tests

88.30 – 38.00 – 8.37 – 22.20 – 76.0 – 32.0UD_V_04_23C

88.70 – 37.97 – 8.03 – 21.40 – 76.0 – 32.0UD_V_04_23B

89.40 – 37.30 – 8.13 – 19.70 – 76.0 – 32.0UD_V_04_19C

88.70 – 37.50 – 8.37 – 19.20 – 76.0 – 32.0UD_V_04_19A

87.60 – 36.97 – 8.27 – 15.00 – 76.0 – 32.0UD_V_04_15C

81.60 – 38.10 – 8.30 – 16.10 – 76.0 – 32.0UD_V_04_15A

90.40 – 37.30 – 8.17 – 10.10 – 76.0 – 32.0UD_V_04_8C

81.80 – 37.80 – 7.97 – 10.70 – 76.0 – 32.0UD_V_04_8B

Dimensions [mm]L – b – 2h – a0 – l – wSamples

∓

P

0

∓

∓

∓

∓

∓

∓

∓

∓

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Mode I (DCB)DCB – Double Cantilever Beam

Standard D5528-01 ASTM

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Mode I-II (MMB)MMB – Mixed Mode Bending

Standard D6671-01 ASTMLoading Yoke

Lever

TabRoller

base

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Mode II (ENF)ENF – End notch flexure

No standardizationUse of standard D6671-01 ASTM (Mixed Mode I-II) with c=0

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Mode III (ECT)ECT – Edge crack torsion

No standardizationBased on Lee (1993)

Support Pins

Specimen

Loading Pin

Specimen

Guide Pins

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Experimental ProcedureAn Instron 5544 with a load cell of 2kN was used, with software Merlin.The samples were loaded continuously in displacement control with a rate of 0.5mm/min. The Load-displacement plot was recorded during the test.

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Experimental Results – Mode I and Mode IILoad-Displacement for Mode I (DCB) - UD_V_01_2

0

20

40

60

80

100

120

140

160

0 2 4 6 8 10 12

Dispalcement [mm]

Apl

ied

Load

[N]

Load-Displacement for Mode I (DCB) - UD_V_01_1

0

20

40

60

80

100

120

140

160

0 3 6 9 12 15

Displacement [mm]

Apl

ied

Load

[N]

Load-Displacement for Mode II (ENF) - UD_V_01_5

-1300

-1100

-900

-700

-500

-300

-100

-7-6-5-4-3-2-10

Displacement [mm]

Aplie

d Lo

ad [N

]

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Experimental Results – Mixed Mode I-II and Mode III

Load-Displacement for Mixed Mode I+II (MMB) UD_V_01_6

-280

-230

-180

-130

-80

-30

-11-9-7-5-3-1

Displacement [mm]

Aplie

d Lo

ad [N

]

Load-Displacement for Mixed Mode I+II (MMB) UD_V_01_7

-250

-200

-150

-100

-50

0-11-9-7-5-3-1

Displacement [mm]

Aplie

d Lo

ad [N

]

Load-Displacement for Mixed Mode I+II (MMB) UD_V_01_4

-450-400-350-300-250-200-150-100-50

0-10.0-8.0-6.0-4.0-2.00.0

Displacement [mm]

Aplie

d Lo

ad [N

]

Load-DIsplacement for Mode III (ECT) - UD_V_04

-2500

-2000

-1500

-1000

-500

0-11-9-7-5-3-1

Displacement [mm]

Aplie

d Lo

ad [N

]

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Results – Numerical SimulationFinite Element Analysis using ANSYS® with solid elements 46 Layered.

Mode I – DCB

Mode II – ENF

Mixed Mode I-II – MMB

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Results – Numerical Simulation

Mode III – ECT

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Results FEM – Strain energy release rate

DCB Test with VCCT (UD_V_01_1i)

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

0 0.2 0.4 0.6 0.8 1

x/L

G [J/mm2] GI

GII

GIII

ENF Test with VCCT (UD_V_01_5b)

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

0 0.2 0.4 0.6 0.8 1

x/L

G [J/mm2]GI

GII

GIII

MMB Test with VCCT (UD_V_01_8g)

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0 0.2 0.4 0.6 0.8 1

x/L

G [J/mm2]

GI

GII

GIII

ECT Test with VCCT (UD_V_04_19A)

0.0

1.0

2.0

3.0

4.0

5.0

6.0

0 0.2 0.4 0.6 0.8 1

x/L

G [J/mm2] GIGIIGIII

Load Point Support Point

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Strain energy release rate – Mode I

GI for UD_V_01

0

0.2

0.4

0.6

0.8

1

1.2

1.4

30 35 40 45 50 55 60 65 70 75 80

a [mm]

GI [J/mm2]

Experimental MBTExperimental CCExperimental MCCBeam Theory MBTBeam Theory CCBeam Theory MCCVCCT

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Strain energy release rate – Mode II

GII for UD_V_01_5

0.00.20.40.60.81.01.21.41.61.8

20 30 40 50 60 70

a [mm]

G [J/mm2]

Experimental

Beam Theory

VCCT

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Strain energy release rate – Mixed Mode I-II

Gc=GI+GII for UD_V_01_8

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

0 10 20 30 40 50 60 70 80

a [mm]

Gc [J/mm2]

Experimental

Beam Theory

VCCT

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Fracture Toughness vs Mode Mixture

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Mixed Mode ratio GII/Gc

Gc

[J/m

m

2 ]

ExperimentalBeam theoryVCCT

DCB, Pure Mode I MMB, Mode I and II ENF, pure Mode II

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Strain energy release rate – Mode III

GIII for UD_V_04

0.0

1.0

2.0

3.0

4.0

5.0

6.0

12.0 14.0 16.0 18.0 20.0 22.0 24.0

a [mm]

G [J/mm2]

GIIIc (NL) exp

GIIIc (5%) exp

GIIIc (5%) VCCT

GIII (NL) VCCT

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Mode I, Mode II, Mode III

0

0.5

1

1.5

2

2.5

3

3.5

4

G [J/mm2]

GI VCCTGII VCCTGIII VCCT

0

0.5

1

1.5

2

2.5

3

3.5

4

G [J/mm2]

GI ExpGII ExpGIII Exp

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ConclusionsAn analytical and experimental investigation was carried out on a glass/epoxy laminates to evaluate the Double cantilever beam (DCB), the End notch flexure (ENF), the Mixed mode bending (MMB) and the Edge crack torsion (ECT) interlaminar fracture toughness tests for laminated composites.

The mixed mode I-II procedure permits the simulation of delamination initiation in mode I and mode II simultaneous.

A three dimensional finite element analysis was used to compare the results calculated by the beam theory and by the VCCT technique with the experimental values.

The experimental results determined for mode I, mode II and mixed mode I-II are very close to the Finite Element using either Beam Theory and VCCT.

Using ECT test it can be obtained pure mode III at the middle ofthe specimen length away from both ends.

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THANK YOU

Rosa Marat-Mendes wishes to thank the support from the FCT (Fundaçãopara a Ciência e Tecnologia) for the PhD grant no. SFRH/BD/25561/2005.