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

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?

Outline

• Current investigation• Joining flat profiles to a tube

• Procedure• Experimental investigations• Numerical modelling• Probabilistic post-processing• Validation

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

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

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

Experimental results

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

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

Two different planes affected by failure

1-3

1-2

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

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

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

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

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

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

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

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

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

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

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

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

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

Thanks for your attention