New paradigm for fcc -bcc martensitic transformations Cyril Cayron

1. New paradigm for fcc-bcc martensitic transformations • Cyril Cayron • - Past address: CEA, LITEN, Grenoble, France • - Future address: EPFL, LMTM, Neuchâtel, Switzerland cyril.cayron@gmail.com, and soon cyril.cayron@epfl.ch ICOMAT 2014, Bilbao, Spain, 7-11 July 2014. Tuesday 8, ‐ Topic 1: Fundamental aspects

2. Phenomenological theory of martensitic crystallography (PTMC) • Bain 1924 • Greninger & Troiano 1949 • Wechsler, Lieberman & Read 1953 • Bowles & Mackenzie 1954 • Christian, Bhadeshia and many others... Shear deformation Bain distortion From HKDHBhadeshia

3. R B = P1 P2 PTMC • Rigid body rotation = free parameter • No physical meaning. • Is like the remainder of a division. • It brings the fcc/bcc volume change • The natural* mechanism should be there but: • No physical meaning for the lattice distortion. • It is here to “explain” the shapes. • Depends too much on the alloy and martensite morphology • Crystallographically correct (same number of atoms in the lattices). • A natural* uniaxial compression along a <100> direction seems dubious. • There is no justification to affirm that it is the best distortion (with minimum strains). • Bain OR nearly never observed. • Physically relevant: Slip by dislocation pile-ups or Nanotwinning. • Two much degree of freedom due to the cubic symmetries. Be careful (see Kelly). • Complex multiple shear mode is required to “explain” some habit planes. * Natural = the fcc-bcc transition mechanism of a small stress-free austenitic single crystal • Depends too much on the exact values of the lattice parameters (?) • The PTMC starts by the end (the versatile shapes and HPs). • It was and still is phenomenological .

4. What is the continuous path between the fcc and bcc crystal? • How move the iron atoms? PTMC R B Would a change of paradigm be useful to “solve” the problem? New paradigm? FCC BCC P1 P2 The paradigm shift (keep cool, it is just to explain…) Ptolemy (center= Earth, geocentrism)  complex machinery of epicyles Copernicus (center = Sun, heliocentrism)  no epicyle

5. Automatic reconstruction of the austenitic grains from EBSD data  Odd patterns in the pole figures of the α’ grains inside the prior  grains  Continuity of α’ orientations between KS, NW, PistchORs EM10: Fe - 0,1C, 9Cr, 1Mo, 0,4Si  grains  grains Reconstruction

6. Where are the Pitsch, NW and KS in the EBSD maps • New module in ARPGE: • Pitsch = red, KS = green, NW = blue EM10: Fe - 0,1C, 9Cr, 1Mo, 0,4Si Reconstucted  grains α grains: P-KS-NW in RGB (10°) α grains: P-KS-NW in RGB* (2°) Cayron, C. (2014) Mater. Charact. 94, 93-110.

7. Continuous features in the pole figures are not EBSD artefacts • The continuous features exist in kamacite (meteorite) by X ray diffraction and EBSD • (G. Nolze, Y. He, P Jacques, J. Jonas, HJ Bunge …) • The continuous features are not due to • possible recovery effect • The continuous features are not a property of steels or Fe alloys! Martensite in CuZn brass (Stanford & Bate 2005) Idea : consider them as the (plastic) trace of the martensitic transformation mechanism

8. Simulation of the continuous features with one OR and two continuous rotations A around [11 0]// [111]α of angles a continuous from 0 and 5° B around [-111] // [1-1 0] αof angles b continuous from 0and 5° 24 KS variants+ P = Pitsch // of Close-Packed Directions (CPDs) NW = Nishiyama-Wasserman // of Close-Packed Directions (CPPs) KS = Kurdjumov-Sachs // of CPDs and // of CPPs Structure of variants (P-KS-NW) is close like a nut (crystallographic intricacy).

9. Two-step model of fcc-bcc martensitic transformation (2010)  (fcc)   (hcp)  (bcc) • The rotation part of the    transformation isA (10°) • The rotation part of the    transformation isB (5°) Actually an old theory ! (without the intermediate hcp) • Advantages of the 2-step model / PTMT: • it relies on physical mechanisms • (ii) the intermediate  (hcp) phase and  sequence have already been observed in some alloys • (iii) the maximum strain is lower than for the Bain deformation • the distinction between the NW or KS orientation relationships is done at the last  step and results from the /Pitsch-Schrader or Burgers OR respectively • KSN model (1930, 1934) of fcc-bcc transformation by a shear of 19.5° on the (111) plane on the [11-2] direction followed by a distortion of 10.5° (and shuffle). From Nishiyama 1978. C. Cayron, F. Barcelo & Y De Carlan Acta Mater. 58 (2010) 1395.

10. One-step model of martensitic transformation based on Pitsch OR (1959) Thin TEM lamella  Nearly no stress due to the surrounding austenite  Natural OR Idea: Transform the Pitsch OR into a lattice distortion 0 % -5.8 % +15.5 % Cayron, C. (2013) Acta Cryst. A69, 498-509.

11. One-step model witch Pitsch OR, and the rotations A & B Idea: There is only Pitsch. KS and NW result from Pitsch in a  matrix deformed by Pitsch! Rot A Rot B

12. It is possible to build a modified version of the one-step model based on the KS OR! Idea: Calculate the continuous intermediate states of the fcc/bcc transformation assuming a hard-sphere packing of the atoms Bain Sculpture 80 Balls Stainless steel, Indian artist AnishKapoor, and located at the Guggenheim Museum Bilbao, Spain From =0° to max = arcsin(1/3). Pistch From =0° to max = arcsin(1/3).

13. KS Final state = deformed fcc = bcc. max = 70.5° (X = 1/3) given by:  1, 1 and 1.088 for eigenvalues.  Not diagonalizable.  The eigenvectors associated to 1.088 in the (-111) fcc plane. From =60° (X = ½) to max = 70.5° (X = 1/3)

14. New paradigm: There is no invariant plane shear but a globally invariant plane with internal angular distortion (111)fcc (110)bcc PTMC and shear conception: invariant plane strain (111)fcc (110)bcc dilatation shear 60° 55° 60° 60° 55° 70° Volume change = Volume change = 1.088 = surface of the (55°,55°,70°) triangle divided by the surface of the (60°,60°,60°) triangle with PQ = PR = Cst = 1.088 perpendicularly to the invariant plane

15. With OR = Pitsch or KS

16. Conclusions: The new paradigms for fcc-bcc martensitic transformations • The continuous features in the EBSD and X-ray pole figures are the plastic trace of the transformation history. • There is a unique “natural” distortion mechanism and orientation relationship. The continuous path between the Pitsch, KS, GT and NW ORs can be explained by this unique OR and the deformation field in the surrounding matrix. • The “natural” distortion is probably not Bain. Logical candidates are Pitsch or KS because both imply the existence of a neutral line along the CP direction <110>fcc= <111>bcc • The transformation must respect (in first order) the hard-sphere packing of the iron atoms. • The fcc-bcc mechanism is not of shear type, nor multiple shear type! • Other ideas: • {225}fcchabit planes = {112} bccPitschand {135}fcchabit planes = {112} bccKS • Should apply to bainite (same odd patterns in the pole figures) • Importance of disclinations to explain the angular distortion of planes.

17. Thanks for your attention

18. Bain