Curve fitting of stress-strain curve and RRT of Ag/Bi-2212 round wires

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Curve fitting of stress-strain curve and RRT of
Ag/Bi-2212 round wires

• Presented by H.W. Weijers
• Measurements performed by Bob Walsh and Dustin
  McRea
• Presented at Andong National University
• Andong, July 15th 2009

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Outline

• Overview of recent testing
• Curve fitting
• RRT on Bi-2212
• Conclusions

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Recent testing

• Student ran measurements with support
• Hydraulic rig with calibrated load cell
• Used both Shepic (19 g, not balanced) and Nyilas
  type (4.2 g) extensometer
• 90 mm between grips
• Drill chucks for round wire
• Plate clamps for tape
• Grips128 g (zeroed out), pins 76.5g each (lower
  pin not zeroed out)

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Recent testinggrips and extensometers
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Load cell
Nyilas extensometer close up
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Bi-2223 3-ply Brassraw data
1,2 Shepic 3,3 Nyilas
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Bi-2223 3-ply stainless steelraw data
1,2 Shepic 3,3 Nyilas
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Bi2212 round wireraw data
1,2 Shepic 3,4 Nyilas
Return line slopes more useful than initial slope
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Curve fitting of initial slope

• Purposes
• Provide fit of data
• Section Annex 3
• Method to determine initial slope E0
• Section Annex 10
• Vary range to gain insight in quality of fit

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Linear and 2nd order poly fit comparison
to 20 MPa to 20 MPa to 20 MPa to 20 MPa to 40 MPa to 40 MPa to 40 MPa to 40 MPa to 60 MPa to 60 MPa to 60 MPa to 60 MPa to 80 MPa to 80 MPa to 80 MPa to 80 MPa to 100 MPa to 100 MPa to 100 MPa to 100 MPa
Material linear linear polynomial polynomial linear linear polynomial polynomial linear linear polynomial polynomial linear linear polynomial polynomial linear linear polynomial polynomial
  E GPa R2 E GPa R2 E GPa R2 E GPa R2 E GPa R2 E GPa R2 E GPa R E GPa R E GPa R E GPa R
                       
3U19-1 105 0.9915 93 0.9927 100 0.9983 111 0.9990 89 0.9949 114 0.9997 82 0.9939 106 0.9996      
3U19-2 103 0.9971 93 0.9978 100 0.9990 105 0.9992 98 0.9994 105 0.9998 96 0.9994 105 0.9999 93 0.9986 106 0.9999
3U19-3 95 0.9850 98 0.9850 96 0.9962 93 0.9963 96 0.9987 96 0.9987 94 0.9991 100 0.9994 93 0.9991 101 0.9997
3U19-4 104 0.9926 91 0.9940 101 0.9433 106 0.9984 98 0.9990 106 0.9994 95 0.9987 107 0.9998 92 0.9983 106 0.9999
                             
3B15-1 93 0.9964 91 0.9964 94 0.9995 93 0.9995 94 0.9998 96 0.9998 92 0.9996 98 0.9999 91 0.9996 97 0.9999
3B15-2 90 0.9976 94 0.9980 90 0.9993 89 0.9993 91 0.9997 88 0.9997 91 0.9998 89 0.9999 91 0.9999 91 0.9999
3B15-3 96 0.9927 87 0.9939 100 0.9983 93 0.9987 99 0.9992 101 0.9993 97 0.9994 103 0.9996 95 0.9992 104 0.9998
3B15-4 152 0.9711 140 0.9716 152 0.9974 106 0.9975 145 0.9982 110 0.9993 140 0.9985 107 0.9996 92 0.9986 104 0.9997
                             
Bi 2212-1 63 0.9943 84 0.9990 56 0.9939 69 0.9988 50 0.9917 65 0.9995 44 0.9870 62 0.9996      
Bi 2212-2 49 0.9990 45 0.9994 51 0.9990 47 0.9997 51 0.9996 50 0.9996 48 0.9967 56 0.9989      
Bi 2212-3 79 0.9978 88 0.9987 68 0.9937 83 0.9986 59 0.9876 80 0.9994 49 0.9788 74 0.9993      
Bi 2212-4 87 1.0000 87 1.0000 83 0.9998 82 0.9988 78 0.9974 91 0.9995            
Poly fit has almost always higher R2 value,
otherwise equal
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Fitting of initial curvewith increasing stress
range

• Linear fit No convergence of slope and R2
• 2nd order poly Convergence, same Eo as linear
  fits extrapolated to zero

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Curve fitting of initial slope

• 2nd order polynomial fit data better than 1st
  order (linear) fit
• Not surprising, but both fit with R2 gt 0.99
• Clearly higher R2 values linear fit trends down
  with increasing range for s,e, 2nd order fit
  doesnt.
• Comparable scatter in E0?
• Propose ?
• For reinforced conductor, linear and 2nd order
  poly fits could be used, but range and
  convergence criteria need to de defined

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Curve fitting over larger rangeR2 values fit to
0.3
Data for increasing strain only (return lines
removed)
power poly
3U19-1
3U19-2 0.9992 0.9999
3U19-3 0.9954 0.9999
3U19-4 0.9972 0.9999

3B15-1 0.9957 1
3B15-2 0.9936 0.9999
3B15-3 0.9964 1
3B15-4 0.9941 0.9999
range 0.9936-0.9992 0.9999-1

Bi 2212-1 0.9765 0.9989
Bi 2212-2 0.9131 0.9916
Bi 2212-3 0.9933 0.9974
Bi 2212-4 0.9711 0.9862
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Curve fitting of data 0 to 0.3

• 2nd order polynomial fit data better than power
  fit
• Consistently higher R2
• Increasing lower bound of range above zero for
  power fit (as per Standard (A-10) does not
  necessarily improve either fit
• Trendline power fit in Excel sometimes fails to
  find proper fit solver works better
• Propose for Standard
• Range and convergence criteria need to de
  defined
• Upper bound of range of fit of 0.5 (A-10) is too
  high
• 0.3 is more reasonable, or fraction (80-90?) of
  strain where s-e curve kinks (Relasticmax,
  eelasticmax)
• Skip a(e-b)n from Standard and replace with
  poly

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Conclusions

• Data with Nyilas and Shepic extensometers very
  comparable
• Unreinforced wire sensitive to handling and/or
  sample-sample variation
• Chucks are suitable, require careful handling
• Value of round-robin TBD
• 2nd order polynomial fit of initial slope
• Fits better than linear or a(e-b)n
• Not necessarily better predictor of Eo compared
  to linear
• Discussion needed to define criterion,
• 2nd order polynomial fit of slope to 0.3
• Fits better than a(e-b)n
• Clearly a better choice
• 0 to 0.5 is too large a range for BSCCO
• Some proposals made to adapt Standard

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Miscellaneous proposals

• Test report section 10.2, Optional results
• When reporting elongation to failure, add
  location of failure (at grips, within
  extensometer) to report