1. TensiNet Symposium SOFIA 2010 – Tensile Architecture: Connecting Past and Future 16-18 September 2010, Sofia, Bulgaria Biaxial testing of architectural membranes and foils C. Galliot, R.H. Luchsinger Center for Synergetic Structures EMPA, Swiss Federal Laboratories for Materials Science and Technology Überlandstrasse 129, CH-8600 Dübendorf, Switzerland

2. Biaxial testing of architectural membranes and foils 2 Introduction 2. Coated fabrics shear behaviour New simple non-linear model - For use for finite element analysis - Comparison with linear orthotropic model 3. ETFE foils Experimental comparison : - Uniaxial tests - Biaxial extension of cruciform specimens - Bubble inflation 1. Coated fabrics yarn-parallel behaviour New test method: shear ramp - Experimental comparison with off-axis biaxial extension - Test validation

3. Biaxial testing of architectural membranes and foils 3 Biaxial test machine and optical system Introduction Needle extensometers (LVDT) ->Strain in warp, fill and 45° directions Load cells (10kN) -> Stress Aluminium grips Specimen size: about 1.5 x 1.5 m – central square is 500 mm wide 3D optical system

4. Biaxial testing of architectural membranes and foils 4 Strain/stress distribution in the specimens 1. Yarn-parallel behaviour of coated fabrics -> k=0.985 Stress correction factor Finite Element Analysis Digital Image Correlation

5. Biaxial testing of architectural membranes and foils 5 Test procedure 1. Yarn-parallel behaviour of coated fabrics 13 different load ratios are tested Load history Strain measurement

6. Biaxial testing of architectural membranes and foils 6 Experimental results 1. Yarn-parallel behaviour of coated fabrics Influence of the warp/fill interaction Stress-strain behaviour 1:1 2:1

7. Biaxial testing of architectural membranes and foils 7 Proposed non-linear model* 1. Yarn-parallel behaviour of coated fabrics *C. Galliot, R.H. Luchsinger. A simple model describing the non-linear biaxial tensile behaviour of PVC-coated polyester fabrics for use in finite element analysis. Composite Structures, Vol.90(4), October 2009, pp 438-447

8. Biaxial testing of architectural membranes and foils 8 Theory 2. Shear behaviour of coated fabrics Shear (biaxial 45°) Global coordinate system:  x = +   B  y =-  B Material coordinate system:  12 =(1/2)  x -(1/2)  y  12 =  B *C. Galliot, R.H. Luchsinger. The shear ramp: A new test method for the investigation of coated fabric shear behaviour – Part I: Theory. Composites: Part A (2010), doi:10.1016/j.compositesa.2010.08.008 x y Shear ramp (0°)* Linear stress variation  : stress varies from –  /2 to  /2 Non-linear shear stress distribution Estimated maximal shear stress (Airy stress functions):  xy max =(3/8)  R  R x y  y  x welded joint

9. Biaxial testing of architectural membranes and foils 9 Strain/stress distribution in the specimens 2. Shear behaviour of coated fabrics 45° 0° Digital Image Correlation  B  R Finite Element Analysis

10. Biaxial testing of architectural membranes and foils 10 Experimental data and correction 2. Shear behaviour of coated fabrics Stress correction factors MaterialShear 0°Shear 45° PVC-polyester0.741.14 PTFE-glass0.861.2 Corrected shear stress-strain curves 14 kN/m 13 kN/m15 kN/m 9 kN/m12 kN/m 15 kN/m 37 kN/m53 kN/m

11. Biaxial testing of architectural membranes and foils 11 Uniaxial test results 3. Mechanical behaviour of ETFE foils Stress-strain curves Strain rate 100%/min Influence of the strain rate yy E yy E

12. Biaxial testing of architectural membranes and foils 12 Biaxial test results (cruciform specimen) 3. Mechanical behaviour of ETFE foils Linear elastic isotropic material properties: E = 1180 MPa = 0.43 Elastic behaviour Failure test at 1:1 load ratio (4%/min) Failure at ≈7% of extension

13. Biaxial testing of architectural membranes and foils 13 Bursting test results 3. Mechanical behaviour of ETFE foils Stress at pole Failure at ≈75% of extension Strain distribution (DIC) After first yield After second yield

14. Biaxial testing of architectural membranes and foils 14 Experimental comparison 3. Mechanical behaviour of ETFE foils Equivalent stress vs equivalent strain (Von Mises) First yield Second yield Bilinear material model yy EeEe EpEp Isotropic material properties: Elastic: E e = 1040 MPa = 0.43 Plastic: E p = 95 MPa  y = 15.5 MPa Biaxial test 1:1 Bubble inflation

15. Biaxial testing of architectural membranes and foils 15 Conclusion and outlook 1. Coated fabric yarn-parallel behaviour: the non-linear behaviour can be well described with a simple model 5 parameters for the yarn-parallel behaviour Significant reduction of the error (factor 2 to 3 for most materials) Model efficiency: computation time increase by less than 3% 2. Coated fabric shear behaviour: the shear modulus can be estimated with the same sample and same machine that is already used for the investigation of the yarn- parallel behaviour Only one test procedure: time-saving The shear ramp results were compared to off-axis biaxial test and gave identical results Stress reduction factors are required 3. ETFE mechanical properties: they are no major advantages of investigating the mechanical behaviour of ETFE foils with biaxial tests (except for failure) The material behaviour could be derived from uniaxial tests for design analysis A bilinear elastic plastic model with 4 parameters describes well the material behaviour The strain-rate (and temperature) dependent behaviour must be taken into account Outlook: for coated fabrics: strain measurement on loaded structures (in situ behaviour) for ETFE foils: influence of initial plastic deformations (strain hardening)