Mechanistic Models of Deformation Twinning and Martensitic Transformations. Bob Pond. Acknowledge: John Hirth

Transcription

1 Mechanistic Models of Deformation Twinning and Martensitic Transformations Bob Pond Acknowledge: John Hirth

2 Classical Model (CM) Geometrical invariant plane Topological Model (TM) Mechanistic coherent interfaces, interfacial line-defects

3 CM TM b h s γ = b/h Twinning dislocation: e.g. F.C. Frank, 1949 (disconnection) Twinning : e.g. G. Friedel, 1926 PTMC : WLR and BM, 1953 Bilby & Crocker, 1965 Martensitic Transformations Pond and Hirth, 2003

4 Interfacial defect character and kinetics

5 Admissible interfacial defects Operation characterising defect (W λ, w λ )(W μ, w μ ) 1 white crystal λ n Interfacial dislocations I, b (W μ, w μ ) (W λ, w λ ) h Twinning disconnections b = t λ Pt μ h = n t λ black crystal μ b γ = b/h bicrystal t λ t μ Pond, 1989

6 Thermally activated disconnections activation energy at fixed stress ~ b 2 loop nucleation rate, ሶ N, reasonable for small b defect mobility, ሶ G enhanced by larger core width, w, which is promoted by small h simple shuffles

7 Motion of a twinning disconnection in a twin t λ [10ത10] E i = 0.26 Jm 2 b h t μ [0001] b = nm h = 2d (10 ഥ12) = nm γ = b/h w~6a σ P d = 1 MPa α Ti Braisaz et al. 1966

8 Atom Tracking: Shear and Shuffle Displacements in (10ത12) Twin z y 4 distinct atoms rocking swapping Pond et al., 2013

9 Deformation twins in Ni 2 MnGa inter-variant boundary Disconnection b = ത1 = nm g = 0012 h = d (202) = nm Pond et al γ = b h = 0.34 Zarubova et al g b = 1

10 Twin tip in Ni 2 MnGa E i = 0.01 Jm 2 4 distinct atoms no shuffling h h g = 20ഥ2 Muntifering et al HAADF STEM (Titan PNNL) SF

11 Topological model for type II twinning

12 Classical Model: irrational plane of shear 1 2 Type I 1 α α Type II 1 rational 1 irrational 2φ 2 2 irrational 2 rational 1= 1 2φ 1 1= 2 2 α s s 2 +α s = 2tanα 1 2 1= 1 1= 2 1

13 TiNi μ 000 1ത10 μ 101 λ λ 11ത1 μ Knowles, 1982 (a) (b)

14 ሶ Formation mechanisms for type I and II twins Type I: glide twin 1= 1 s Type II: glide/rotation twin source Nሶ type I 1= 2 Gሶ 2φ type II s type II Type I: glide twin γ = b/h 1 = 1 2 competitive mechanisms: High G/ ሶ Nሶ favours type I Low G/ Nሶ favours type II 2φ 1 1= 2 2α source Nሶ Gሶ

15 disconnection glide plane, k 1 Type II: formation of glide/rotation twin sheared region h b unsheared region twin b/2 1 = 2 b/2 parent 1= 2 h α 1 (a) b g (c) twin parent (b)

16 Type II: growth 1 = 2 2α b g (i) (ii) γ = s = 2ta (α) (b) (i) (ii) twin 1= 2 parent Read and Shockley, 1953 (a)

17 Experimental observations: e.g. α U type b nm h nm γ No. dist. atoms "{17ത6}" 111 1/2 < 512 > II low " 1ത72 " 112 1/2 < 312 > II low 1ത /2 < 310 > compound high ሶ G/ ሶ N 10μm Type II Twinning in Other Systems α U, Cahn 1953 NiTi CuAlNi TiPd devitrite

18 Topological model of martensitic transformations

19 PTMC d martensite TM low energy terraces (coherently strained epitaxial) two defect arrays: disconnections & LID distortion field of defect network accommodates coherency strains motion of all defects produces shape deformation p invariant plane parent Shape deformation P 1 = RBP 2 = (I + dp )

20 Glissile Disconnections Ti 10 wt % Mo Klenov 2002 b h λ h(μ) t μ b n = h λ b t λ h(μ) 2 distinct atoms steps cause habit plane to be inclined to terrace plane b n also produces rotational distortions motion causes one-to-one atomic exchange between phases with different densities

21 Distortion field of a Defect Array d h Z y Lagrangian frame b X b s b e habit plane ξ

22 Equilibrium: superposed coherency and defect array distortion fields D Solve the Frank-Bilby Equation for the defect array with long-range distortion matrix, D ij m, which compensates D ij c.

23 Habit plane orientation Ti : φ = 0.53 θ = 11.4 φ β crystal: Θ - φ α crystal: Θ + φ homogeneous isotropic approximation θ inhomogeneous anisotropic case rotations partitioned according to relative elastic compliances TM solutions for habit plane orientation differ slightly from PTMC, unless b n = 0

24 Cu Partitioning of rotations εc yy = 12.33% Ag molecular dynamic simulation of static Cu(111)/Ag(111) interface, Wang et al Case Cu Ag - Ag / Cu Isotropic, inhomogeneous Anisotropic MD MD (Artificial)

25 Orthorhombic to Monoclinic Transformation in ZrO 2 Principal strains on terrace plane 0 3.8% xx yy considerable shuffling: 8 Zr & 16 O distinct ions

26 Chen and Chiao, 1985 y habit terrace d D synchronous motion of disconnections z D z y x D zz yz xz D m n b b b d y

27 Lath martensite in ferrous alloys 1: terrace plane Mn IF steel: Morito et al. N-W OR

28 TEM: LID slip dislocations ~{575} G-T OR 1/ 2[111] dislocations, ~10 from screw, with spacing nm Fe-20Ni-5Mn (Sandvik and Wayman, 1983)

29 TEM: Disconnections in near screw orientation Moritani et al. Fe-Ni-Mn [-101] γ projection

30 Plate Martensite ~{121} Ogawa and Kajiwara, 2004 Fe-Ni-Mn

31 Conclusions Topological modelling provides insights into mechanisms and kinetics. Twinning: proposed new model of type II twin formation. Martensite: predicted interface structures consistent with observations, predicted habits differ slightly from PTMC.