1. UNTF 2010 The behaviour of Lüders bands in ferritic steel David Johnson Nuclear Department HMS Sultan © British Crown Copyright 2010 / MOD Published with the permission of the Controller Of Her Britannic Majesty’s Stationery office

2. Topics Project outline-Aims Lüders bands; brief introduction Digital Image Correlation (DIC) Current work-Two spring system in series (Frame optimizing problem) and Sigmoidal strain in Lüders band Conclusions Future work

3. Project Outline To improve reactor design Current reactors use R6 code during design phase –Leads to costly and over conservative designs –Assumes homogenous deformation RPV (main body) consists of low alloy steel –Deforms in a non-homogenous fashion; Lüders bands. Incorporate Lüders bands into R6 code –Less conservative designs and reduction in costs.

4. Lüders bands

5. Uniaixal tensile test Expect two points of nucleation Lüders bands nucleate top and bottom Propagate throughout specimen

6. Lüders bands Lüders/shear bands occur during the onset of plasticity Plasticity-Dynamical resistance to dislocation flow (Johnston and Gilman) Normally found in body centred cubic structures

7. Dislocations Source:Seeger(1957), dislocations and mechanical properties of crystals.p. 243, Wiley. Sighted:Introductions to dislocations 4th ed-D. Hull, D Bacon

8. Dislocations Source:http://www.geol.ucsb.edu/faculty/hacker/geo102C/lectures/dislocation2.jpg(reproduced with kind permission from Dr Bradley Hacker)‏

9. Experimental Apparatus Denison Tensile rig (uniaxial) Digital image correlation - two 5 Megapixel cameras 0.007% and 0.07% carbon steels Dog bone shaped specimens 0.3% carbon low alloy steel grips

10. Specimen Length: 64 mm Gauge length: 34 mm Width: 4 mm

11. Digital Image Correlation

12. Band Velocity/Strain

13. Modelling Assume-strain proportional to dislocation density; frictionless. Any frictional forces, proportional to strain;small strain displacement in band.

14. Strain vs Time

15. Load - time (frame number) curve Data from analogue channels Frame range 0-300 corresponds to time of 150 seconds

16. Interpretation of gradient (load – frame number) Assume yield point at elastic limit Gradient constant

17. Tools for determining the gradient Gradient of line: Hooke's law: Tensile distance: Spring constant :

18. Results k avg =15.69MN/m (0.07% C steel) Spec Cross head vel(m/s) YP(M Pa) K(MN/ m) K2(MN /m) Ty(s)Predicte d Ty(s) Error% A-Y11e-0623018.7821.7250339.71*26.4% A-L52.5e-0521616.7417.6411.512.769.87% A-L68.3e-621614.8914.944038.43-4.67% *Ferritic steel value

19. Interpretation of k Large gauge length and/or small cross-section results in closer agreement between k and k 2 Consistent with two spring system in series

20. Summary of Results Strain dependent on dislocation distribution; in model dislocations behaves sigmoidally. Gradient of elastic region from analogue channels consistent with two spring model (in series) Predicts when the material would approximately yield Solves the problem of optimizing frame number

21. Future Work Micro-structure affects Lüders bands- comparing ferrite/bainite with tempered martensite Temperature dependence and grain- structure. Incorporate into FE model. Alternative to R6 code.

22. Acknowledgements Dr Ian Giles Dr Michael Edwards Dr Paul Chard-Tuckey, Sean Jarman and Dr Mark Wenman