A numerical study on the failure strength of composite
tubes subjected to biaxial loading
Comptest 2015 - Madrid
Rui Marques, Hugo Faria
Madrid, 8th April 2015
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Presentation
Oporto
Oporto
Madrid
Rui Marques
Research Fellow
INEGI
Oporto, Portugal
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Index
1. Introduction
2. Theory
3. Methodology
4. Results
5. Conclusions
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Index
1. Introduction
2. Theory
3. Methodology
4. Results
5. Conclusions
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Introduction
Fibre reinforced plastic (FRP) tubes
• Advantages: High specific stiffness and strength , good corrosion
resistance and thermal insulation
• Applications: Gas and liquid transfer, farmland irrigation, chemical
plants, oil industry
• Manufacturing process: Filament winding
• Typical loading case: Pressure and axial efforts
• Failure types: Functional and structural failure
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Introduction – Work Objectives
•
Establish a validated modelling methodology to accurately represent
the tubes failure behaviour
• Study the influence of the winding angle and layup for a variety of load
conditions
• Get a better understanding on composite tubes failure
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Index
1. Introduction
2. Theory
3. Methodology
4. Results
5. Conclusions
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Theory – Biaxial loading
4 possible load combinations:
• σθ - Circunferencial stress
• σz - Axial stress
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•
•
•
•
Internal pressure + traction (P, F a)
Internal pressure + compression (P, - F a)
External pressure + traction (-P, F a)
External pressure + compression (-P, - F a)
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Theory – failure criteria groups
1. Not associated with failure modes:
•
•
Describe the failure surface as a function of the material strengths.
Only predict failure
Tsai-Wu, Tsai-Hill and Hoffman failure criteria
2. Associated with failure modes:
•
•
Uses the material strengths in each in-plane material direction
Can predict failure and failure modes
Maximum stress, Hashin, Christensen, Rotem, McCartney, Yamada-Sun,
Hinton, Chang-Chang, Puck and Huang failure criteria
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Theory – Adopted failure criteria
Maximum Stress
σ 1 ≥ X t or σ 1 ≥ X c
(1)
σ 2 ≥ Yt or σ 2 ≥ Yc
(2)
σ 12 ≥ S
(3)
Tsai-Hill
F11σ 12 + F22σ 22 + F66σ 62 + 2 F12σ 1σ 2 ≥ 1
(4)
F11σ 12 + F22σ 22 + F66σ 62 + F1σ 1 + F2σ 2 + 2 F12σ 1σ 2 ≥ 1
(5)
Tsai-Wu
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Theory – Failure envelopes
Note: R=σθ/σz
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Index
1. Introduction
2. Theory
3. Methodology
4. Results
5. Conclusions
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Methodology
•
E-glass fibre/Unsaturated polyester unid. lamina properties (fvf=60%)
Mechanical Property
E1 (GPa)
E22 (GPa)
ν12, ν13
ν23
G12, G13 (GPa)
G23 (GPa)
•
Composite
45.015
14.969
0.2815
0.5220
4.6227
4.9185
Strength Property
Xt [MPa]
Yt [MPa]
Xc [MPa]
Yc [MPa]
S [MPa]
Composite
1020
40
620
140
70
Studied layups (laminate total thickness = 2.4mm)
Variation
Laminate
Angle (group 1 Monolithic laminates)
[±15°]3 [±30°]3 [±45°]3 [±55°]3 [±65°]3 [±75°]3 [±90°]3
Layup (group 2 - Nonmonolithic laminates)
[±45°,±55°2] [±45°,±55°,±65°] [±45°,±90°,±65°]
[±55°2,±90°] [±55°,±90°,±55°] [±65°,±55°2]
[±90°,±55°,±90°] [±90°,±55°2]
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Methodology
• Abaqus
Relevant inputs:
R=70mm, L=400mm, e=2,4mm
Shell elements model
Pressure and axial force
1 fixed end, 1 free end
Outputs:
σ θ, σ z
σ1, σ2, σ12
MSTRS, TSAIH, TSAIW
• Matlab/excel – Result analysis
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Methodology
• Methods - Construction of failure envelopes
Simulation with arbitrary
loads (P and Fa)
Repeat for a variety of stress
ratios and winding angles
Failure measure
Results: σθ, σz or
Pcritical, Fa critical
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Index
1. Introduction
2. Theory
3. Methodology
4. Results
5. Conclusions
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Results – Load failure envelopes
[±15˚ ]3
[±30˚ ]3
[±45˚ ]3
[±55˚ ]3
[±65˚ ]3
[±75˚ ]3
[±90˚ ]3
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Monolithic laminates – group 1
Load failure envelopes
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Results – Load failure envelope
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Results – Stress failure envelopes
[±15˚ ]3
[±30˚ ]3
[±45˚ ]3
[±55˚ ]3
[±65˚ ]3
[±75˚ ]3
[±90˚ ]3
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Monolithic laminates – group 1
Stress failure envelopes
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Results – MSTRS comparison
R=0.1:1 [±15˚]3
R=0.5:1 [±30˚]3
R=2:1 [±55˚]3
R=1:0 [±90˚]3
R=-3:-1 [±65˚]3
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Results – Optimum laminate
[±15˚]3
[±55˚]3
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[±90˚]3
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Results (example: R=2:1 case) - MSTRS
Weak
direction
MSTRS
Lowest
σ2
[±55˚]3
Best
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Results – Monolithic vs. non-monolithic
Stress failure envelope
Monolithic [±45˚]3 [±55˚]3
[±45˚,±55˚2] Non-monolithic
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Results – Monolithic vs. non-monolithic
Load failure envelope
Monolithic [±45˚]3 [±55˚]3
[±45˚,±55˚2] Non-monolithic
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Results – Monolithic vs. non-monolithic
Monolithic [±45˚]3 [±55˚]3
[±45˚,±55˚2] Non-monolithic
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Results – Monolithic vs. non-monolithic
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Results – Monolithic vs. non-monolithic
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Results – All studied laminates
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Results – Optimum laminate
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Index
1. Introduction
2. Theory
3. Methodology
4. Results
5. Conclusions
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Conclusions
• Maximum stress, Tsai-Hill and Tsai-Wu had revealed similar behaviours;
• Higher winding angles for pressure applications and lower angles for
predominant axial force applications;
• Load and stress failure envelopes of monolithic laminates have shown the
same geometry;
• Laminate construction depends mainly on the load combination/stress ratio
applied;
• With Maximum stress failure criteria was possible to spot strong and weak
directions;
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Conclusions (cont.)
• Stress failure envelopes of non-monolithic laminates (for instance [±45,
±552]) always superpose some parts of the failure envelopes of their
constituent angles.
• For laminates with 3 different angles, the plies that fail were always the
maximum and minimum angle of that laminate.
• Monolithic laminates shown to have best performance than non-monolithic
laminates;
• The adopted methodology helped to construct optimum laminates
depending on the applied loads.
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Future work
• Specimens manufacturing – conducted (3 different specimens (45, 55 and
65° monolithic laminates, 3 samples for each 4 load combinations/stress
ratios);
• Validation of numerical models through experimental testing - to start;
• Analyse damage on experimental tests and relate them with cohesive
element models;
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Future work
• Determination of fibre-glass fracture toughness material properties (GIC
GIIC, matrix and fibre) to be implemented in numerical models;
• Modelling a 3D (solid) tube with cohesive elements to simulate fracture.
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Acknowledgments
• The author would like to acknowledge the project RES2IN – Research to
Innovation, from Programa Integrado IC&DT, co-funded by CCDRN –
Comissão de Coordenação e Desenvolvimento Regional do Norte.
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Bibliography
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Thank you!
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