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

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 15 th 2009. Outline. Overview of recent testing Curve fitting RRT on Bi-2212

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

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  1. 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

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

  3. 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 • Grips:128 g (zeroed out), pins: 76.5g each (lower pin not zeroed out)

  4. Recent testinggrips and extensometers

  5. Load cell Nyilas extensometer close up

  6. Bi-2223 3-ply Brass“raw” data 1,2 Shepic 3,3 Nyilas

  7. Bi-2223 3-ply stainless steel“raw” data 1,2 Shepic 3,3 Nyilas

  8. Bi2212 round wire“raw” data 1,2 Shepic 3,4 Nyilas Return line slopes more useful than initial slope

  9. 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

  10. Linear and 2nd order poly fit comparison Poly fit has almost always higher R2 value, otherwise equal

  11. 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

  12. Curve fitting of initial slope • 2nd order polynomial fit data better than 1st order (linear) fit • Not surprising, but both fit with R2 > 0.99 • Clearly higher R2 values; linear fit trends down with increasing range for s,e, 2nd order fit doesn’t. • 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

  13. Curve fitting over larger rangeR2 values fit to 0.3% Data for increasing strain only (return lines removed)

  14. 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

  15. 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

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

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