1 08.06.2010 ECCM 2010 Outline Numerical expectations Effect of - PowerPoint PPT Presentation

DAMAGE IN TEXTILE LAMINATES OF VARIOUS INTER-PLY SHIFT Dmitry S. IVANOV, Yao DING, Larissa GORBATIKH, Stepan V. LOMOV, Ignaas VERPOEST Katholieke Universiteit Leuven, Belgium Department of Metallurgy and Materials Engineering Composite Materials Group 1 08.06.2010 ECCM 2010

Outline � Numerical expectations � Effect of stacking sequence: experiments Thermal crack – Acoustic emission: energy, events – Crack density – Macro properties – � Mechanisms of deformation: FE analysis Numerical expectations – New modelling concept for modelling arbitrary stacking – Results – 2

ε init Numerical expectations Strain at… , % Periodic Step Stairs Symmetric Intra-yarn crack, Puck 0.15 0.19 0.22 0.26 criterion, weft Intra-yarn crack, Puck 0.25 0.33 0.37 0.38 criterion, warp Inter-yarn delamination 0.34 0.48 0.70 0.86 onset, Mohr-Coulomb 1.13 1.13 0.95 0.95 0.89 0.89 0.87 0.87 Fibre Fibre failure, failure, Max- Max- Stress, warp Unbalanced twill carbon-epoxy composites, 6 plies 3

Mechanisms of deformation Uniaxial stress state within the Tensile + local shear in the 0- 0-yarns yarns = higher stress along fibres Strong shear in the intra-yarn space = higher probability for Zero shear in the intra-yarn inta-ply matrix failure space 4

Outline � Numerical expectations � Effect of stacking sequence: experiments Thermal crack – Acoustic emission: energy, events – Crack density – Macro properties – � Mechanisms of deformation: FE analysis Numerical expectations – New modelling concept for modelling arbitrary stacking – Results – 5

Stacking effects: manufacturing Glass plain weave, 850 g/m 2 , RTM, epoxy, 4 plies, t=3.1 mm 16 × 17 mm unit cell, Maximum inclination = 9.4 ° In-phase = periodical stacking 6 Out-of-phase = symmetrical stacking

Stacking effects: manufacturing Glass plain weave, 850 g/m 2 , RTM, epoxy, 4 plies, t=3.1 mm 16 × 17 mm unit cell, Maximum inclination = 9.4 ° In-phase = periodical stacking 7 Out-of-phase = symmetrical stacking

Stacking effects: Thermal cracks Thermal cracking Presence of the intra-yarn cracks: out-of phase only (at the outer plies – through the yarn width) out-of phase in-of phase 8

Stacking effects: Acoustic emission events In-phase: periodic stacking ε 2 1,0E+09 300 300 1,0E+08 ε 1 number of events in-phase 250 250 1,0E+07 out-of-phase 200 1,0E+06 200 Energy [eu] Stress [MPa] 1,0E+05 150 150 1,0E+04 100 1,0E+03 100 1,0E+02 Energy 50 50 Cumulative 1,0E+01 0 0 Stress Stress 1,0E+00 0 Total after ε 2 before ε 1 between number of ε 1 and ε 2 0,00E+00 5,00E-03 1,00E-02 1,50E-02 2,00E-02 2,50E-02 3,00E-02 events Strain Out-of-phase, symmetric stacking ε 2 1,0E+08 250 Big difference in the number 1,0E+07 ε 1 200 1,0E+06 of AE events: Energy [eu] 1,0E+05 Stress [MPa] 150 In-phase>>Out-of phase 1,0E+04 100 1,0E+03 1,0E+02 Energy 50 Cumulative 1,0E+01 Stress 1,0E+00 0 0,00E+00 5,00E-03 1,00E-02 1,50E-02 2,00E-02 2,50E-02 9 Strain

Stacking effects: Acoustic emission energy Cumulative Energy-Strain 1,0E+10 ε 2 1,0E+09 1,0E+08 ε 1 1,0E+07 nergy(eu) In1_2 1,0E+06 In1_3 1,0E+05 In1_4 In1_4 En 1,0E+04 In2_1 1,0E+03 In2_2 ε min 1,0E+02 out1_3 out1_4 1,0E+01 Out1_5 1,0E+00 0 0,002 0,004 0,006 0,008 0,01 0,012 0,014 0,016 Strain Big difference in the energy of AE events: In-phase>>Out-of phase 10

Stacking effects: Crack density Distance between the cracks: 1,8 1,6 1,4 k distance (mm) 1,2 1 0,8 crack 0,6 0,4 0,2 0 in-phase_CNTs in-phase out-of-phase Higher crack density (factor 2) in: In-phase >> Out-of phase 11

Stacking effects: Strength/ ultimate strain 3 300 250 2,6 200 Stress (MPa) 2,2 Strain (%) 150 1,8 100 1,4 In-phase-CNTs In-phase 50 Out-of-phase Out-of-phase 1 0 Strain Strength �������� ������������ ������������� ���������������� ����� ± �! � !"� ± ���# � $"� ± !�� ����� %�&����� �'� ± #(" �"� ± ��(! ��� ± �'( ����� )��*�������&�*� �("! ± �(� # �(�" ± �(��! �(�# ± �(�$� �+� ��*�������&��*� �(�!' ± �(��� �(�$ ± �(�� �(�## ± �(��� 12 Slightly lower strength for out-of phase

Comparison of 1-ply and 4-ply composites Approaching of 4-ply composite curve to the 1-ply composite curve: effect of delaminations σ , MPa 4-ply composite 1-ply composite ε , % 13 NB: a different glass-epoxy PW composite

Outline � Numerical expectations � Effect of stacking sequence: experiments Thermal crack – Acoustic emission: energy, events – Crack density – Macro properties – � Mechanisms of deformation: FE analysis Numerical expectations – New modelling concept for modelling arbitrary stacking – Results – 14

Superposition of periodic profiles To set the correct boundary conditions we have to predict the laminate deformed shape “Step” ~ ∞ u Periodic profile. Ply 1 z ~ ∞ u Periodic profile. Ply 2 z Superimposed profile � � � N 1 ∑ ~ ~ ( ) ( ) ∞ s = + u x u x s z z i N = i 1 Deformed profile of a textile laminate can be presented as a arithmetic average of periodic profiles for each of the plies 15

Actual and predicted profiles Superimposed/predicted ~ profile u z µ , m “Step”-wise shift x , mm 1 Profiles along the inter-layer boundaries Average profile in the laminate Predicted and average profiles are proportional ⇒ Energy-based scaling is also applicable here ⇒ ⇒ ⇒ 16 The scatter of the profiles is bigger than in the periodic stacking

New BC’s Outer and inner unit cells Energy of effective medium ( ) = σ ε + − σ ε E 2 N 2 11 11 11 11 E outer outer inner inner Energy of heterogeneous medium ( ) = σ ε + − σ ε E 2 N 2 H ij ij ij ij outer inner Deviation from the balance ( ) ∆ λ = − E E E H E Minimisation of the deviation Optimum scaling coefficients Number of the plies, N 2 3 4 5 6 Reference solutions 1.725 1.383 1.273 1.210 1.160 17 Numerical procedure 1.709 1.375 1.253 1.190 1.153

σ yz σ σ y x Results: FFE vs. ply solution Layer Outer Outer Outer Inner Inner Inner position Configur Step Stairs Periodic Step Stairs Periodic ation Transverse stress, warp, [MPa] FFE 60.3–157.6 84.1–161.5 47.1–132.3 74.0–145.8 103.2-169.4 59.5-123.1 UCA 65.3 – 153.9 100.2 – 167.1 46.8 – 130.2 78.1 – 144.4 111.3 – 170.1 54.8 – 121.2 Transverse stress, weft, [MPa] Transverse stress, weft, [MPa] FFE 3.7 – 15.1 3.2 – 12.7 3.2 – 15.1 4.7 – 12.3 4.3 – 10.7 3.9 – 15.7 UCA 2.6 – 13.2 3.2 – 11.4 3.4 – 14.7 3.1 – 13.9 5.3 – 12.4 3.5 – 15.6 Out-of plane shear stress, weft, [MPa] FFE -5.3 – 5.9 -3.5 – 3.6 -8.6–8.6 -6.0 – 6.0 -2.4 – 2.1 -9.5 – 9.5 UCA -6.4–6.4 -2.8 – 2.8 -8.9 – 8.9 -6.6 – 6.6 -2.2 – 2.2 -9.7 – 9.7 Good coincidence of the reference full scale solution with “the one-ply +BC” approach 18

The new scheme: � Distinguish between the outer and inner plies � Account for the number of plies in the composite � Account for the stacking of the composite � Give results with a good precision at low � Give results with a good precision at low computational cost � Potentially convenient instrument for modelling of the delaminations � Efficient to model woven laminates with (0, ±45) ° laminates 19