Mechanical Measurement Lab, 2010.11.06 EDMS no. 1073153 Validation of strain measurements at cryogenic temperature A. Bouchardy, EN-MME Mechanical Measurement Lab, 2010.11.06 EDMS no. 1073153

Setup for the measurements Tests procedure Results Conclusion Outline Introduction Goal of the project Setup for the measurements Tests procedure Results Conclusion

Introduction : Mechanical measurements at CERN Equipment : Displacement Transducers Vibration Sensors Load / Tensile Sensors Strain Gauges Static and Dynamic Acquisition System Post-Processing and Analysis Parameters measured : Force , Stress, Strain, displacement, vibrations, temperature, etc... Environmental conditions : Magnetic field, cryogenic temperature, radiation

Introduction: Experimental stress analysis Why perform experimental stress analysis ? Validation of Finite Element Calculations (FEA) Failure analysis Measurement conditions at CERN : 1.9 K to 500 K High Magnetic field F. Regis TE/MSC

Introduction: Strain gauges The resistance of a wire (R) is a function of three parameters : F (N) with R (Ω), Length (m), Section (m²) and ρ (Ω /m) With an external force, the resistance value increases. A strain gauge is a long length of conductor arranged in a zigzag pattern on a membrane. When it is stretched, its resistance increases. with k : Gauge factor For 2000 m/m, R is equal to 11  Wheatstone bridge

Introduction: Wheatstone bridge Wheatstone bridge equation : V0 Vs R1 R4 R2 R3 +R1 +R4 +R2 +R3 Application with strain gauges : With k : Gauge factor Configuration : - ¼ bridge - Half bridge - Full bridge

Introduction: Mechanical properties Stress, Force relation (traction) σ = F / A With : σ : Mechanical stress (MPa) F : Force applied (N) A: Area (mm²) Rm Rp0.2 Rp Stress – Strain curve (Hook ‘s law) σ = E . ε= E. (∆L/L) With : σ : Mechanical stress (MPa) E : Young modulus (MPa) ε : Mechanical strain (m/m) Rp0.2 : Elastic limit = Yield point Rm : Breaking strength Microstrain με = 1x10-6 m/m = 1m/m

Introduction: Goal of the project Validation of the mechanical measurements performed with strain gauges for : Several temperatures : 293 K, 77 K, 4.2 K Several materials : Copper (HA), Aluminum (Antico), Stainless Steel 316LN Several electrical configurations : ¼, ½, or full Wheatstone bridge Several data acquisition cards : HBM - MGCPlus, HBM - CAN HEAD Three Steps : Identify and validate the setup for the measurements Measurements for several configurations of the test matrix Data analysis and accuracy calculations

Setup for the measurements Reference Force UTS100 Tensile Machine EN-MME/MM

Setup for the measurements Buckling calculations for the set up: Reference Force E: Young modulus (Pa) Fmax: Maximal Load (N) I : Quadratic moment L: Lengh (m) D: external diameter (m) D: internal diameter (m) with Calculation of the traction limits of the test specimen: Aluminium: Copper: Stainless steel: Wiring upgrade / Connection to the standard DAQ of the lab All the details are available in EDMS (EDMS1072489)

Setup for the measurements

Tests procedure Strain gauge LVDT’s Test specimen developped Young modulus determination by standard approach EN-MME/MM Young modulus determination using strain gauges in order to validation strain gauges measurements Standard Test specimen Test specimen developped for the tests Strain gauge LVDT’s Setup with LVDT’s and Load cell Setup with Strain gauges and Load cell

Correction of the strain gauge values Compensation of the full bridge configuration measured = 2real - 2 real = real x 2(1+||) K factor correction 10 % of variation between 300 K and 1.9 K Performance of Strain Gauges in Superfluid Helium,1997, K.Artoos

Example of results

Results: Comparison between three temperatures

Results: Comparison between several materials

Results: Comparison between several bridge configurations

Results: Accuracy of the strain measurements DAQ linearity by normal law DAQ precision by normal law Accuracy of the strain gauge measurements (Ref : An introduction to measurements using strain gauges,1989, K. Hoffmann) Tolerance on Gauge factor Wiring of gauges Thickness of the glue Strain gauges alignment Introduction to the stress Ustrain = 4% Force: DAQ linearity by normal law DAQ precision by normal law Resolution of load cell by uniform law Ustress = 0.4% Area: Resolution of the vernier caliper by uniform law

Results: Accuracy in strain measurement

Conclusion The strain measurements performed in several configurations show that the experimental stress analysis can be used at cryogenic temperatures for standard materials used at CERN. The strain measurements accuracy was evaluated at +/- 4% at 293K. The strain measurements accuracy was evaluated at +/- 5% at 4.2K, due to the k factor evolution at low temperature. Next steps: New measurements to evaluate the gauge factor with temperature should be perform in the future Repeatability measurements should be perform with a higher numbers of specimen in order to define the strain measurement precision.

Thanks to Thanks to Ofelia Capatina and Ramon Folch for this period at CERN… Special thanks to Michael… Thanks to my colleagues of the lab, Alexandre, and Raphael…

Thank you for your attention. Questions?

Results: Accuracy of the strain measurements DAQ linearity = 0.02%EM by normal law (0.02%*2/2)*1/3= 6.67*10-5 DAQ precision = +/-(0.05%Val meas+0.05%PE) by normal law +/- ((0.05%*2+0.05%*2)/3)= 6.67*10-4 Accuracy of the strain gauge measurements =+/-4% UStrain = 4% Force: DAQ linearity = 0.02%EM by normal law (0.02%*2/2)*1/3= 6.67*10-5 DAQ precision = +/-(0.05%Val meas+0.05%PE) by normal law +/- ((0.05%*2+0.05%*2)/3)= 6.67*10-4 Resolution of load cell = +/-0.005 by uniform law 0.005/√3=2.89*10-3 UForce = 0.3% Area: Length : Resolution of the vernier caliper =0.01 by uniform law 0.01/√3=3.33*10-3 Width: Resolution of the vernier caliper =0.01 UArea = 3% Stress: UStress = 0.4%

Results: Comparison between power supplies

Results