Effect of Recovery & Precipitation on Recrystallization of Micro-alloyed Steels

Transcription

1 Effect of Recovery & Precipitation on Recrystallization of Micro-alloyed Steels Md Kashif Rehman Dr Hatem S Zurob McMASTER U N I V E R S I T Y 1280 Main Street West, Hamilton, ON, Canada L8S 4L7 1

2 Presentation Outline 1. Introduction to Micro-alloyed Steels. 2. Literature Review. 3. Critical Aspects of Coupled Model. 4. Recrystallization Model. 5. Summary 6. Future Work. 2

3 1. Introduction: > Microalloyed Steels? These are low carbon steels with small additions of Nb, Ti or V (<0.1%). Micro alloyed steels make 10-15% of the world s total steel production. They are used in the building, automotive and pipeline industries. Micro alloyed steels posses high strength and toughness due to their fine grain-size. 3

4 Temperature 1. Introduction: > Processing of Microalloyed Steels Finish rolling is usually carried out below T NR (no Rex temperature). The retardation of Rex due to micro alloying has been extensively studied. GC T NR A 3 A 1 time 4

5 1. Introduction: > Problem Definition For the most part, the modelling has focussed on the microstructure evolution following a single deformation pass. Very advanced empirical and semi-empirical databases have been developed. For example Sellars and colleagues derived the following relations for a steel containing % Nb: for T 1004 t for 890 T 1004 t for T 890 t o o C C d d d 2 o o 2 o 2 o C exp exp 325,000 RT 780,000 RT 130,000 exp RT 5

6 1. Introduction: > Problem Definition Relations such as these are necessary components of models for industrial hot rolling. Our objective was the development of such equations from being purely empirical to being more physicallybased. This is of great practical importance because the predictive nature of the physically-based model makes it possible to look at new steels and new processes. For example: Near Net-shape products. Hot-working of CSP steels. for T 1004 t for 890 T 1004 t for T 890 t 50 o o C C d d d 2 o o 2 o 2 o C exp exp 325,000 RT 780,000 RT 130,000 exp RT 6

7 Literature Review 7

8 Key Processes The deformation of microalloyed steels sets the stage for three simultaneous processes. Precipitation: Which occurs heterogeneously on dislocations. Recovery: Which gradually reduces dislocation density. Recrystallization: Which replaces deformed regions with deformation-free regions. It is essential to look at the time evolution of these processes with special emphasis on the interactions between the three processes. Recovery Recryst. M(C,N) GC & PT 8

9 Identification of Key Interactions Recrystallization Recrystallization is described by using a modified JMAK equation. Recovery delays Rex progress. Ppt both accelerates and retards Rex progress Recovery Recovery is described in terms of the stress-relaxation model of Verdier et al (acta, 47, 127). Precipitation & Rex both delay Recovery progress. Precipitation Precipitation is described in terms of the nucleation, growth and coarsening model of Dutta and Sellars (acta, 49, 785). Recovery and Recrystallization both delay hetrogeneous precipitation. 9

10 Key Interactions Recovery consumes the driving force. Recryst. 1. Ppt can pin Nucleation & Growth 2. Ppt removes solute Nb thus changing solute drag affecting boundary mobility. Rex consumes the driving force. Recovery 1. Fine Ppt pin dislocation network retarding recovery. Rex reduces dislocation density thus reducing potential nucleation sites for heterogeneous precipitation. M(C,N) Recovery reduces dislocation density thus reducing potential nucleation sites for heterogeneous precipitation. 10

11 Key Interactions Recryst. ρ(σ) N, ρ(σ),c Nb Recovery N, ρ(σ) M(C,N) 11

12 Modelling: > Recrystallization: Classical Model Classically JMAK equation has been used to explain Recrystallization X 1 exp( kt n ) Where k and n are empirical constants. Cahn(1956) calculated n for nucleation at random sites on grain boundaries & found that n varies from 4 to 1 between recrystallized start to finish times. Growth Dimensionality Site Saturation Constant Nucleation Rate 3-D D D

13 Modelling: > Recrystallization: JMAK Assumptions and Limitations Random Nucleation. Generally k and n are taken to be constants, Constant Nucleation Rate Constant Growth Rate Experimentally determined JMAK exponents are usually less than or equal to 2 mainly because growth rate is not constant[2,3]. Relaxed JMAK models have been developed in which growth rate is decreasing function of time[2,3,4]. 13

14 Previous Recrystallization Model [1] Limitations: 1. Site saturation which is not necessarily true. 2. As an input it needs initial number of nucleation sites hence can t predict Recrystallized Grain Size. 3. Nucleation Module absent. 4. Psi factor My today s presentation will focus on a New Recrystallization Model which aims to eliminate these problems. [1] Acta mater. 49 (2001)

15 New Recrystallization Model 15

16 Modelling: > Recrystallization: A New Approach Austenite Nuclei Start of Nucleation 16

17 Modelling: > Recrystallization: A New Approach Austenite Nuclei Site saturation has been achieved. Nucleation stops now and only growth continues. 17

18 Modelling: > Recrystallization: Nucleation The present approach uses SIBM concepts. Nucleation depends on the stored energy. r crit 2SE G( t) The criterion takes into account the progress of recovery. 18

19 Modelling: > Recrystallization: Effect of Precipitation on Nucleation Precipitation will retard the nucleation of recrystallization by pinning the dislocation substructure. This new idea is captured mathematically through the introduction of the Nucleation Probability term Nucleation Probability takes into account 1. Number Density of precipitates. 2. Size of the precipitates. 19

20 Modelling: > Recrystallization: Effect of Precipitates Number Density Its assumed that beyond a certain critical value of precipitates number density nuclei will be pinned. Average number of precipitates per Sub Grain Critical Precipitates Number Density Probability of Pinning 20

21 Modelling: > Recrystallization: Effect of Precipitates Number Density Its assumed that beyond a certain critical value of precipitates number density nuclei will be pinned. N * 4G( t) R 2 3r 3 4 N( t) R 3 3 G(t) is the driving force for recrystallization. R is the sub grain radius. r is the precipitate radius. N(t) is the avg precipitate number density. 21

22 Modelling: > Recrystallization: Effect of Precipitates Size Distribution We believe that all the precipitate sizes are not equally affective in pinning sub grain boundaries. 22

23 Modelling: > Recrystallization: Effect of Precipitates Size Distribution Where, f ( rr) 2 ( r) Ke 2 In the present work r c = 1nm has been assumed. It is the size at which particle bypass becomes preferable to particle shear. 23

24 Probability of Unpinning Modelling: > Recrystallization: Overall Probability of Nucleation Where, Eff pinning is pinning due to size Time P.with Eff_pinning P(N) is Probability of unpinning taking into account only precipitate number density. P*(N) is Overall probability of unpinning considering both the particles number density and size distribution. 24

25 Modelling: > Recrystallization: Effect of Precipitation on Growth Effects of recovery and precipitation on the growth stage of recrystallization is taken into account by modifying the driving force for recrystallization: i 1 β 3 i = β i VN dt i 1 where: 2 G ( t) 1 ( t) b 3 V / r i i 1 R MGdt Driving force for Recrystallization Time dependent dislocation density Zener Drag 25

26 Modelling: > Recrystallization: Effect of Solute-drag Effect of solute-drag on the recrystallization kinetics is taken into account by introducing a concentration-dependent mobility into the recrystallization equation: i 1 β 3 i = β i VN dt i i i 1 R MGdt where: 1 M 1 M Pure C Nb Grain Boundary Mobility Nb Concentration 26

27 Recrystallization Model Austenite 27

28 Recrystallization Model β = Ratio of Vol of deformed grains to original grain volume β i = β i 1 = R i + R i + R i R i i 3 i 1 i 1 R i 1 R 3 MGdt MGdt = R i 1 R i i + K VN dt i = R i 1 R i-1 i i 1 R=D/2 MGdt 28

29 Modelling: > Recrystallization: The Model The overall model then becomes, i 1 β 3 i = β i VN dt i i i 1 R MGdt Where βi is the Normalized Disappearance Rate of deformed grains. All parameters are volumetric/linear ratio hence they inherently capture the non spherical/ellipsoid shape of deformed grains. 29

30 Modelling: > Recrystallization: The Model: Parameter Evolution 30

31 Modelling: > Recrystallization: The Model i 1 β 3 i = β i VN dt i i i 1 R MGdt Following features are incorporated in the above equation: Strain-induced precipitation on the nucleation of recrystallization (new concept). Precipitation on the growth of recrystallization (Zener drag). Effect of solute Nb on recrystallization (solute drag). Effect of recovery on recrystallization. 31

32 Modelling: > Recrystallized Grain Size Recrystallized Grain Size is calculated from Volume Conservation. (No of Nuclei per unit volume) * (Vol of nucleus) = 1 R 3 3 4N Assumption: As Rex completes all the nuclei at start will become a grain. Grain Coarsening will only commences after Rex is over. 32

33 Summary 1. A new recrystallization model has been developed which is able to describe recrystallization. 2. The new model developed which takes into account: 1. Variable Nucleation Rate. 2. Effect of Recovery. 3. Effect of Precipitates 1. Nucleation 2. Growth 3. It s limited to at present softening occurring in isothermal conditions after a finite deformation in austenite. 33

34 Future Work Model Validation, preliminary results are encouraging. Grain Coarsening after finish of recrystallization. Extending the model to Med C steel. Non-isothermal temperature. Multi-pass Rolling. 34

35 Acknowledgement My supervisor Dr Hatem Zurob(McMaster Univ) Dr Yves Brechet(National Polytechnique Grenoble) for lot of stimulating discussions Steel Research Center(McMaster Univ) for funding this project. McMaster Univ and Gov Of Canada for allowing me to pursue my studies. 35

36 References 1. Acta mater. 49 (2001) Recrystallization and Related Annealing Phenomena, Pergomon Press (1996) 3. Material Science and Technology, 6 (1990) R.A.Vandermeer in Recrystallization and Grain Growth: Proceedings of the first joint international conference (2001) J.W.Cahn in Materials Research Society Symposium Proceedings 398, Materials Research Society, (1996) Acta mater. 47 (1999)

37 Thank you for your attention 37