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

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

3. 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

4. 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

5. 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

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

7. 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

8. Introduction: Goal of the project
Validation of the mechanical measurements performed with strain gauges for :
Several temperatures : 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

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

10. 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 (EDMS )

11. Setup for the measurements

12. 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

13. 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

14. Example of results

15. Results: Comparison between three temperatures

16. Results: Comparison between several materials

17. Results: Comparison between several bridge configurations

18. 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

19. Results: Accuracy in strain measurement

20. 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.

21. 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…

22. Thank you for your attention.
Questions?

23. 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 /√3=2.89*10-3
UForce = 0.3%
Area:
Length : Resolution of the vernier caliper =0.01
by uniform law /√3=3.33*10-3
Width: Resolution of the vernier caliper =0.01
UArea = 3%
Stress:
UStress = 0.4%

24. Results: Comparison between power supplies

25. Results