frp tubes [2010]
DESCRIPTION
It is possible to determine the strength of complex bonded and bolted joints of GFRP, however, not using a stress-based approach. An actionable joint strength prediction method has been suggested, that foots on A statistical description of the material strength, A verified failure criterion of the involved materials. The suggested method has been applied and experimentally verified.TRANSCRIPT
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Architektur, Holz und BauEXPERIMENTAL AND NUMERICAL INVESTIGATIONS ON JOINTS COMPOSED OF PULTRUDED FRP TUBES AND FRP LAMELLA
Till Vallée, Rahul Meena, Thomas Tannert & Simon Hehl
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What it is about?
• Connections of pultruded elements• Bolted vs. bonded
• Practical application• Frequent requests from
industrial partners• e.g. joining struts
in a truss
• Question• Dimensioning?
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Outline
• Current investigation• Joining flat profiles to a tube
• Procedure• Experimental investigations• Numerical modelling• Probabilistic post-processing• Validation
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Composite Material
• Pultruded GFRP material• Fiberline A/S
• E≈ 32’500 MPa, fu ≈ 400 MPa
• GFRP tube• Ø=40mm, t=3mm
• GFRP flat profiles• b=100mm, t=10mm
• Connected through a aluminium clamp• To achieve an overlap of 100 mm
• M8-8.8 Bolts
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Experimental investigations
• Traction tests• Failure loads• Failure mode• Five of each
• Connections• SikaDur330
Linear-elastic and brittle• SikaForce7851
Elasto-plastic and ductile• Bolted
Herein 15M8-8.8
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Experimental ResultsBolted Joints
• Joint strengths• For the epoxy bonded
66.17±1.00 kN • For the PU bonded
82.30±1.87 kN
• Failure mode• In all cases failure triggered
inside the tube• Tearing-off the fleece,
depth tf ≈ 1.5 mm
≈ 1.5mm
≈ 1.5mm
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Experimental results
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Experimental ResultsBolted Joints
• Joint strength• For the bolted joints
44.7±3.9 kN
• Failure mode• In all cases failure
triggered inside the tube• Shear failure along
the fibres
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Strength determination strategies
1. Stress based• The most stressed part must fulfil the failure criterion
of the material• Previous investigations on SLJ & DLJ showed it
usually doesn’t work because of the stress peaks
2. Probabilistic methods & size effects• Based on the formulation of a probability of failure• Includes statistical size effects• “Smoothes away” the effects of stress peaks• Foots on Weibull theory
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Two different planes affected by failure
1-3
1-2
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Failure criterion along 1-3-plane
• Determination of the failure criterion of the GFRP
• X13, Y13 and S13 experimentally determined on over 200 individual test coupons using a ST-device
• Results summarised later
2 2 21 1 3 3 132 2 2
13 13 13 13 13
1X X Y Y S
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Failure criterion along 1-2-plane
• Determination of the failure criterion of the GFRP
• X12, Y12 and S12 experimentally determined on over 200 individual off-axis test coupons
• Results summarised later
2 2 21 1 2 2 122 2 2
12 12 12 12 12
1X X Y Y S
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Mechanical characterisation
Parameter X Y S sF,0 m
13-plane
434.23
9.36 22.56 1.03 17.37
12-plane 52.09 38.51 1.15 5.23
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Stress based verification
• Verification of the most stressed part• Stresses by FEA• Gathering of stress tensor at
each element• Implementation of the
corresponding failure criterion• For the elasto-plastic adhesive:
iteratively• For the bolted:
using contact elements
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Some comments on the FEA
• FEA indicates that stresses are maximum at the interface between the tube and the clamp• …where failure initiation has been experimentally
located
• FEA shows that the elasto-plastic properties of the polyurethane, compared to the linear-elastic epoxy, leads to a slight reduction of stress magnitudes
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Stress based verification
• The stress-based method delivers the following results• 27.72 kN for the Epoxy bonded and• 47.23 kN for the Polyurethane• 15.18 kN for the bolted
• Which underestimates the experimental values by around 50%• This is mainly due to the stress peaks
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Probabilistic strength prediction
• In a nutshell• No binary relation between stresses and failure• Stress magnitudes are associated to probabilities
of survival, respectively of failure
• Previous investigations have showed that…• Such procedures work best for brittle failure
modes• Weibull theory is a good basis to associate
stresses to probabilities of failure• Allows for a simple formulation of size effects
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A little bit of Weibull…
• Weibull-theory associates to each stress-state σ a probability of survival Ps
• Weibull-theory allows to derive a simple expression for size effects
s0
exp d
m
V
P V
1
1 1
2 2
mV
V
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A little bit of Weibull…
• m, and σ0, are obtained from the experimental data used to define material strength
Parameter X Y S sF,0 m
13-plane
434.23
9.36 22.56 1.03 17.37
12-plane 52.09 38.51 1.15 5.23
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The probabilistic procedure
• Based on FEA model, for each element• Determination of the stress components• …the corresponding magnitude of the failure criterion
• …the corresponding probability of failure Ps,i
• Back to the full joint• Global probability of failure is the “sum”, i.e. the
product, of the individual probabilities of failure of the individual elements; Ps = Π Ps,i
• “Predicted failure load” corresponds to Ps = 0.5
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The probabilistic procedure
1
1 1
2 2
mV
V
22 261 1 2 2
F 2 2 2X XY Y S
0
exp d
m
s
V
P V
F, F,
11 0 F,0 0 F,0
P exp exp
m mn n
i ii is
ii
V V
V V
Size effects
Weibull
Probabilistic
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Results of the probabilistic dimensioning
• Predicted joint strengths amount for • 76.1 kN for the Epoxy bonded• 88.8 kN for the Polyurethane• 42.7 kN for the bolted joint
• Strengths do only slightly diverge from the experimentally gathered values, i.e. by • 13% for the Epoxy,• 8% for the Polyurethane, and• 4% for the bolted joint
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Wrap-up and conclusion
1. It is possible to determine the strength of complex bonded and bolted joints of GFRP
• However, not using a stress-based approach
2. An actionable joint strength prediction method has been suggested, that foots on
i. A statistical description of the material strength
ii. A verified failure criterion of the involved materials
3. The suggested method has been applied and experimentally verified
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Thanks for your attention