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
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.
Uniaixal tensile test Expect two points of nucleation Lüders bands nucleate top and bottom Propagate throughout specimen
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
Dislocations Source:Seeger(1957), dislocations and mechanical properties of crystals.p. 243, Wiley. Sighted:Introductions to dislocations 4th ed-D. Hull, D Bacon
Dislocations Source:http://www.geol.ucsb.edu/faculty/hacker/geo102C/lectures/dislocation2.jpg(reproduced with kind permission from Dr Bradley Hacker)
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
Specimen Length: 64 mm Gauge length: 34 mm Width: 4 mm
Digital Image Correlation
Modelling Assume-strain proportional to dislocation density; frictionless. Any frictional forces, proportional to strain;small strain displacement in band.
Strain vs Time
Load - time (frame number) curve Data from analogue channels Frame range 0-300 corresponds to time of 150 seconds
Interpretation of gradient (load – frame number) Assume yield point at elastic limit Gradient constant
Tools for determining the gradient Gradient of line: Hooke's law: Tensile distance: Spring constant :
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
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
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
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.
Acknowledgements Dr Ian Giles Dr Michael Edwards Dr Paul Chard-Tuckey, Sean Jarman and Dr Mark Wenman