Identification of safe hot working

Transcription

1 Identification of safe hot working conditions in cast Zr 2.5Nb 25Nb Rajeev Kapoor Mechanical Metallurgy Division, Materials Group, Bhabha Atomic Research Centre, Mumbai, India Coauthors J.K. Chakravartty, Materials Group, BARC A.Sarkar, Materials Group, BARC V. Kumar, RDCIS, Ranchi SK S.K. Jha, NFC, Hyderabad N. Saibaba, NFC, Hyderabad S. Banerjee, DAE, Mumbai

2 Outline Introduction Motivation of work on cast Zr.5Nb Methodology & Experiments Results Flow stress behavior Strain rate sensitivity map Instability conditions Microstructural verification Comparison with wrought Zr.5Nb Conclusions

3 Introduction Zr.5Nb is the pressure tube material used in Indian pressurized heavy water reactors. At present Zr.5Nb pressure tubes are manufactured by Melting and casting quenching Hot working in + phase or phase then + phase Secondary processing steps Hot working is to be performed in an optimum T and space. Determined through hot deformation studies. Constituti ve behavior f,,, T, S

4 Objectives of hot working Break down the cast microstructure. Shape the ingot. Chemically homogenize the product. Obtain a near desired microstructure. Obtain product without micro / macro defect or flow instabilities. Hot working should be carried out in a strain rate and temperature regime such that the desired microstructure is produced without defects.

5 Motivation Hot deformation studies on wrought Zr alloys have been carried out, where optimum conditions and their deformation mechanisms identified. d However, studies on cast alloys not carried out. Do the optimum conditions change for wrought and cast? Are the kinetics of deformations different? Are the regimes of instability different?

6 Methodology T T log T T 2 T 3 T 4 m log log log

7 Experiments and Analysis Compression tests carried out in Gleeble thermo-mechanical mechanical simulator on samples of mm dia and 5 mm length. Temperature range 7 to o C Strain rate range -3 to s - Strain rate sensitivity calculated in the T and space. Ductility determined through tensile tests carried out on sample with 2 mm gauge diameter and 4 mm gauge length. Check for regimes of flow instabilities - From instability conditions - Verified by microstructure

8 Flow stress behavior True Stres ss (MPa) (s - ) = o C True Plastic Strain True Stres ss (MPa) o C (s - ) = True Plastic Strain True Stres ss (MPa) o C (s - ) = True Plastic Strain 2 2 o C o C True Stres ss (MPa) 5 5 (s - ) = - True Stre ess (MPa) 5 5 (s - ) = True Plastic Strain True Plastic Strain -3

9 Stress strain rate temperature behavior 3 25 Stres ss (MPa) 7 o C 75 o C 8 o C 85 o C 9 o C 95 o C o C o C (MPa) 2 5 (s - ) = - Reduced temperature sensitivity Strain rate (s - ) T ( o C) Stress increases with increasing and decreasing T. Low temperature sensitivity in the phase field

10 Strain rate sensitivity contour plot Dilatometery curve 945 o C 6 o C dl (µm) 25 - ) train Rate / s - Log (St Temperature ( C) High m domain over a wide range of T and Temperature o C

11 Ductility 2 log( / s - )= - 8 o C 5 4 o C Stres ss (MPa) Ductility (%) o C o C 9 o C 8 o C Strain -3 - Strain rate (s - ) Large non-uniform elongation Ductility high at o C and low strain rates

12 Tensile samples Single neck Multiple necks

13 Criteria for flow instability Based on strain hardening and strain rate hardening. Jonas, Holt, Coleman, Acta Metallurgica 24 (976) 9 98 Based on Zeigler s criteria of continuum mechanics and extremum principles. Zeigler, Some extremum principles in irreversible thermodynamics with applications to continuum mechanics, in: I. N. Sneddon (Ed.) Progress in solid mechanics, vol IV, 963, pp Based on Lyapunov function D. G. Schultz, J. L. Melsa, State functions and linear control systems, McGraw Hill, 967.

14 Based on strain hardening and strain rate hardening ln Onset of strain localization Hart, Acta Metallurgica 5 (967) 35. Campbell, Journal of the Mechanics and Physics of Solids 5 (967) 359. Jonas, Holt, Coleman, Acta Metallurgica 24 (976) 9. m ln ln m in compression the sign convention is, and

15 Based on strain hardening and strain rate hardening ln Onset of strain localization Hart, Acta Metallurgica 5 (967) 35. Campbell, Journal of the Mechanics and Physics of Solids 5 (967) 359. Jonas, Holt, Coleman, Acta Metallurgica 24 (976) 9. m ln ln m in compression the sign convention is, and Work hardening Work softening

16 Based on strain hardening and strain rate hardening Instability manifests depending di on rate of flow localization. li rapid strain localization in compression is expected when 5 m - 'm ' ' True Str ress (MPa)

17 Based on strain hardening and strain rate hardening Instability manifests depending di on rate of flow localization. li rapid strain localization in compression is expected when 5 m - 'm If m Since is highly negative from start, it implies 5 ' ' True Str ress (MPa) m certain condition for instability

18 Instability from strain and strain rate hardening 5 7 o C (s - ) = o C o C -3 Alph ha -5 - Alph ha Alph ha Strain Strain Strain 5 5 o C -3 o C Alpha - Alpha Strain Strain

19 Log Stress vs. strain True Stress s (MPa) (s - ) = 8 o C - -3 True Stress s (MPa) (s - ) = - -3 True Stress s (MPa) 9 o C (s - ) = - 7 o C True Plastic Strain True Plastic Strain True Plastic Strain True Stress (MPa) 2 2 o C o C ln (s - ) = - -3 True Stress (MPa) (s - ) = True Plastic Strain True Plastic Strain - -3 m

20 Ziegler s criteria using extremum principles Based on the rate of dissipation of work D during deformation. Deformation is unstable if dd d D d lnd d ln if D is taken as the power input rate d ln d ln d ln d ln D m Condition for instability

21 Ziegler s criteria using extremum principles (D=J) If D J P G d J co content content of the power dissipation. The physical interpretation of J is controversial

22 Ziegler s criteria using extremum principles (D=J) If D J P G d J co content content of the power dissipation. The physical interpretation of J is questionable J P 2 P 2 min m P min d dj J For D=J the Ziegler criteria i becomes d 2m Condition for instability J

23 Instability from Ziegler s criteria using D=J m Log (Strain Rate / s - ) Temperature o C.28.29

24 Use of Lyapunov function Second method of Lyapunov uses a function called Lyapunov function V(x) such that V ( x) with equality if and only if x and defines the stability as, dv ( x) V ( x ) with equality if and only if x dt A physical sense this can be considered as some energy function. Energy of the system decreases with time without being restored thereby eventually reaching itsfinalresting state.

25 Lyapunov function Gegel used and s as the Lyaponov functions with independent variable as ln s T ln ln T lnt Instability condition ln s ln Alexander used m and s as the Lyaponov functions Instability condition m ln s ln s m ln lnt m T

26 Using m and s as Lyapunov functions Eq. (7) Instability condition m ln Log (Strain Rate / s - ) Eq. (6) m m T Temperature o C

27 Macrostructure after deformation Log (Strain Rate / s - ) Temperature o C.29

28 Macrostructure after deformation Log (Strain Rate / s - ) m Temperature o C

29 Macrostructure after deformation Eq. (7) Log (Strain Rate / s - ) m Eq. (6) Temperature o C ln m T

30 Microstructure after deformation Cast Zr 2.5Nb alloys showed a Widmannstätten type of α+β microstructure t m m ln m T Eq. (7) Deformed at 75 o C. /s Log (Strain Rate / s - ) Log (Strain Rate / s - ) Eq. (6) Temperature o C Temperature o C Lamellae structure distorted but remains

31 After deformation at 8 o C,. /s,.6 Overall the lamellae structure remains but cell formation is observed. m m Alpha 5 8 o C Log (Strain Rate / s - ) ln T Eq. (7) Eq. (6) Strain Temperature o C

32 After deformation at 9 o C,. /s, o C m ln m T Eq. (7) Regions of dynamic recrystallization Alpha -5 - Log (Strain Rate / s - ) Eq. (6) Strain Temperature o C

33 After deformation at o C,. /s,.7 Equiaxed grains suggesting dynamic recrystallization Alpha Transformed grains Eq. (7) o C m Strain Log (Strain Rate / s - ) Eq. (6) Temperature o C.92 ln m T.234

34 Comparing maps with wrought Zr 2.5Nb - ) Log (Strain Rate / s Beta quenched wrought Bt hd equiaxed Temperature o C g (Strain Rate / s - ) Log cast ) Log (Strain Rate / s Temperature o C Chakravartty et al. Mater. Sci. Technol. 2 (996) 75. Strain rate sensitivity map of cast and wrought Zr.5Nb similar Temperature o C

35 Microstructure of wrought Zr 2.5Nb () Starting microstructure Log (Strain Rate / s - ) Temperature o C Chakravartty et al. Mater. Sci. Technol. 2 (996) 75.

36 Maps for wrought Zr 2.5Nb comparing in phase field Log (S Strain Rate / s - ).5 Wrought in phase field Temperature o C Log (S Strain Rate / s - ) Cast Temperature o C Kapoor et al. Journal of Nuclear Materials 36 (22) 26.

37 Microstructure of wrought Zr 2.5Nb () Undeformed Log (Strain Rate / s - ) Temperature o C Kapoor et al. Journal of Nuclear Materials 36 (22) 26.

38 5 3 Comparison of deformation kinetics cast wrought A n exp Q RT Z(s - ) 9 )phase phase Q = 27 kj/mol n = 4.84 Q = 25 kj/mol n = 4.7 Z exp Q RT n A Activation energies for diffusion Zr in Zr = 9 kj/mol Nb in Zr 5%Nb = 2 kj/mol Zr in Zr = kj/mol (MPa)

39 Conclusions Hot deformation of cast Zr.5Nb showed a single domain over 8 to C and. to. s -. Peak strain rate sensitivity of.3 at C and -3 s -. Dynamic recrystallization was observed in high m domain. 2m appears to predict flow instability well. Where 2m is satisfied, m is also low. m is low at low temperatures and high strain rates. This regime needs to be avoided. The microstructure of cast Zr.5Nb can be safely broken in both the α+β phase (8-85 o C) and β phase ( o C) when deformed at strain rates of. s - or lower.