MT 610Advanced Physical Metallurgy   Session : Phase Transformations             in Solids IV                         Mate...
Contents Diffusional transformations   Long-range diffusion   Short-range diffusion Diffusionless   transformations  ...
Shear transformation Exp.   Martensite can be generated by shear on γ Both shears are possible  and identical to Bain  d...
Shear transformation Shear of cooperative  movements of atoms can  be in different planes rather than (111)γ plane,  depe...
Shear transformation Greninger and Troiano (1949) found   that   Observed shear plane in Fe-22% Ni-0.8% C    was not the...
Double shear transformation The first shear isa macroscopic shear  that contributes the shape change and  change in cryst...
Invariant plane During the martensitic transformation   The interface should be an invariant plane      Undistorted and...
From the Bain distortion α lattice with bcc can be generated from  an fcc γ lattice by    Compression about 20% along   ...
Bain distortion of a sphere Due to the Bain distortion   A unit sphere of the parent crystal    transforms into an oblat...
Bain distortion of a sphere Initial   sphere equation of the parent crystal                     x12 + x2 + x3 = 1        ...
Bain distortion of a sphere Due  to the lattice deformation            x12 + x2 + x3 = 1                                 ...
Bain distortion of a sphere Vectors unchanged in   magnitude during  the lattice deformation    Corresponding to the    ...
Bain distortion of a sphere Allother vectors not involved in the cones  A’OB’ and C’OD’ would be  changed in magnitude. ...
Bain distortion of a sphere Therefore,Bain distortion has no invariant plane.                              14
Lattice-invariant shear Lattice-invariant shear                        must be of such magnitude so as to produce an undi...
Lattice-invariant shear Graphical analysis of a simple shear of slip or twinning of a unit sphere   Shear  on an equator...
Lattice-invariant shear As a result of  shear on K1    Any vector in the plane AK B is                                 2...
Lattice-invariant shear As a result ofshear on K1    The relative positions of     the planes AK2B and AK’2B     depend ...
Lattice-invariant shear As a result ofshear on K1    The relative positions of     the planes AK2B and AK’2B     depend ...
Lattice-invariant shear When     initial sphere → ellipsoid    by lattice deformation using    Bain distortion is distort...
Stereographic projection                           21
Stereographic representationof the Bain distortion Any vector lying on the initial  cone AOB with a semiapex  of φ moves ...
Stereographic representationof the lattice-invariant shear An unextended line C moves to the final position along the cir...
Stereographic representationof the lattice-invariant shear Vectors in K’2 plane do not  change their length due to  shear...
Requirement for habit plane Both Bain   distortion and lattice  invariant shear provide an undistorted  plane for the hab...
3 important components Bain distortion Lattice invariant shear Rigid body rotation                            26
Bain distortion with slip #1 Vectors b and c  are defined  by the intersections of the  initial Bain cone with K1 plane ...
Bain distortion with slip #1 Vectors b and c  are defined  by the intersections of the  initial Bain cone with K1 plane ...
Bain distortion with slip #1    Complementary      shear     b and c to b’ and c’    Bain distortion     b’ and c’ to b’...
Bain distortion with slip #2 To obtainan invariant plane,  must have other extended lines   Ifassumed to know    the she...
Bain distortion with slip #2 Through  the transformation of the complementary shear and the Bain distortion   Sequences ...
Complete transformationprocess Possible invariant planes will  depend on the choice of  combination of b or c  with a or ...
Complete transformation process If theinvariant plane is the  plane defined by vectors a & c Angle btw a & c   = angle b...
Complete transformationprocess   Once a” and c” coincide simultaneously    with a and c, respectively      Angle btw a &...
Complete transformationprocess T = BPR Bain distortion         (B) Lattice invariant shear (P) Rotation operation      (R)...
Bain distortion with twinning Twinned martensite       can take place by having  alternate regions in the parent phase un...
Nucleation and growth It only takes  about 10-5 to 10-7 seconds for a plate  of martensite to grow to its full size. The...
Nucleation and growth Less likely to occur by  homogeneous nucleation  process, but heterogeneous.    Surfaces and grain...
Nucleation and growth Dissociation  of a dislocation  into 2 partials is favorable  → lower strain energy.               ...
Nucleation and growth Growth of  lath martensite with dimension  a > b >> c growing on a {111}γ planes   Thickening    m...
Nucleation and growth In medium and high carbon steels,   Morphology of martensite turns to change    from a lath to a p...
Effect of pressure to martensite As pressure increases   In Fe unary system, the equilibrium    temperature decreases  ...
Effect of alloying element tomartensite Each alloying element will   effect the martensitic  transformation differently....
Effect of external stress tomartensite As martensite prefers to nucleate   and grow  along the dislocation    Expected t...
Effect of external stress tomartensite Once  the plastic deformation occurs   There is an upper limit value of M that th...
Effect of external stress tomartensite If a tensile             stress is applied    M temperature can be suppressed to ...
Effect of external stress tomartensite Plastic  deformation of γ before transformation  will assist on increasing number ...
Shape-memory alloys (SMA) Unique property  of some alloys   After being deformed at one temperature,    they recover the...
Shape-memory alloys (SMA) Unique property   of some alloys    After being deformed at one temperature,     they recover ...
SMA Common     characteristics   Atomicordering transformation from   ordered parent phase to ordered martensite   phase...
SMA Typical   plot of property changes versus temp. A hysteresis is   usually on the order of 20°C                      ...
One-way SMA Sample is cooled from above Af to  below Mf → martensite forms   Sample  has no shape change Sample is defo...
Two-way SMA Sample is cooled from above Af to  below Mf → martensite forms   Sample  has no shape change Sample is defo...
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Mt 610 phasetransformationsinsolids_iv

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Mt 610 phasetransformationsinsolids_iv

  1. 1. MT 610Advanced Physical Metallurgy Session : Phase Transformations in Solids IV Materials Technology School of Energy and Materials
  2. 2. Contents Diffusional transformations  Long-range diffusion  Short-range diffusion Diffusionless transformations  Martensitictransformation  Geometric observation  Mechanism 2
  3. 3. Shear transformation Exp. Martensite can be generated by shear on γ Both shears are possible and identical to Bain distortion if disregarded the rigid body rotation. 3
  4. 4. Shear transformation Shear of cooperative movements of atoms can be in different planes rather than (111)γ plane, depending on alloy composition and transformation temp. Shear does not have to act along the same direction on every parallel atomic plane. 4
  5. 5. Shear transformation Greninger and Troiano (1949) found that  Observed shear plane in Fe-22% Ni-0.8% C was not the {111}γ plane and the shear angle was 10.45°, not 19.5° as predicted by shear mechanism. Theysuggested that another shear had to be added in order to complete the mechanism. 5
  6. 6. Double shear transformation The first shear isa macroscopic shear that contributes the shape change and change in crystal structure. The second shear is a microscopic shear.  Invariant plane  Bain distortion has no invariant plane  Lattice-invariant shear with Bain distortion 6
  7. 7. Invariant plane During the martensitic transformation  The interface should be an invariant plane  Undistorted and unrotated plane Any deformation on the invariant plane will be termed an invariant plane strain. 7
  8. 8. From the Bain distortion α lattice with bcc can be generated from an fcc γ lattice by  Compression about 20% along one principle axis and a simultaneous uniform expansion about 12% along the other two axes perpendicular to the first principle axis 8
  9. 9. Bain distortion of a sphere Due to the Bain distortion  A unit sphere of the parent crystal transforms into an oblate spheroid of the product crystal  Contraction about 20% along the one principle axis  Expansion about 12% along the other two axes perpendicular to the first principle axis 9
  10. 10. Bain distortion of a sphere Initial sphere equation of the parent crystal x12 + x2 + x3 = 1 2 2 12% expansion 20% contraction Ellipsoid equation of the transformed crystal (x ) 2 1 + (x ) 2 2 + (x ) 2 3 =1 ( 1.12 ) ( 1.12 ) ( 0.80 ) 2 2 2 10
  11. 11. Bain distortion of a sphere Due to the lattice deformation x12 + x2 + x3 = 1 2 2 Vectors OA’ and OB’ represent the final position of vectors Vectors OA and OB represent the initial position of the same vectors unchanged in ( x1 ) + ( x2 ) + ( x3 ) = 1 2 2 2 ( 1.12 ) ( 1.12 ) ( 11 ) 2 2 2 magnitude 0.80
  12. 12. Bain distortion of a sphere Vectors unchanged in magnitude during the lattice deformation  Corresponding to the cones AOB and COD and the cones A’OB’ and C’OD’ These vectors are termed unextended lines.  A homogeneous strain would result in an undistorted plane of contact between the initial sphere of austenite and the ellipsoid of martensite. 12
  13. 13. Bain distortion of a sphere Allother vectors not involved in the cones A’OB’ and C’OD’ would be changed in magnitude. Bain distortion would result in no undistorted plane. Hence, there is no invariant plane. Very difficult to obtain a coherent planar interface between the parent and the product crystals only by the Bain distortion. 13
  14. 14. Bain distortion of a sphere Therefore,Bain distortion has no invariant plane. 14
  15. 15. Lattice-invariant shear Lattice-invariant shear must be of such magnitude so as to produce an undistorted plane when combined with the Bain distortion.  Consider slip or twinning  Must not make any change in crystal structure. 15
  16. 16. Lattice-invariant shear Graphical analysis of a simple shear of slip or twinning of a unit sphere  Shear on an equatorial plane K1 as the shear plane  d as the shear direction  α as shear angle Slip 16
  17. 17. Lattice-invariant shear As a result of shear on K1  Any vector in the plane AK B is 2 transformed into a vector in the plane AK’2B, which is unchanged with length although rotated relatively to its original position.  The plane AK B is the initial Slip 2 position of a plane AK’2B, which remains undistorted as a result of the shear. 17
  18. 18. Lattice-invariant shear As a result ofshear on K1  The relative positions of the planes AK2B and AK’2B depend on the amount of shear involved.  The shear plane itself remains undistorted after shear. Slip  Vectors that remain invariant in length (unextended lines) to this shear operation are define as potential habit planes. 18
  19. 19. Lattice-invariant shear As a result ofshear on K1  The relative positions of the planes AK2B and AK’2B depend on the amount of shear involved.  The shear plane itself remains undistorted after shear. Slip  Vectors that remain invariant in length (unextended lines) to this shear operation are define as potential habit planes. 19
  20. 20. Lattice-invariant shear When initial sphere → ellipsoid by lattice deformation using Bain distortion is distorted by simple shear into another ellipsoid + and the lattice is left invariant,  The simple shear is termed a lattice-invariant shear. shear 20
  21. 21. Stereographic projection 21
  22. 22. Stereographic representationof the Bain distortion Any vector lying on the initial cone AOB with a semiapex of φ moves radially onto the final cone A’OB’ with a semiapex of φ’. Vectors in the cones of unextended lines do not change their length, but only the angle ∆φ. 22
  23. 23. Stereographic representationof the lattice-invariant shear An unextended line C moves to the final position along the circumference of the great circle defined by d* (dash line). 23
  24. 24. Stereographic representationof the lattice-invariant shear Vectors in K’2 plane do not change their length due to shear, and the line OC’ in the plane represents the final position of an unextended line. Line OC in K2 plane represents the initial position of OC’. 24
  25. 25. Requirement for habit plane Both Bain distortion and lattice invariant shear provide an undistorted plane for the habit plane. Additional requirement is that the habit plane be unrotated.  A rigid body rotation must be able to return the undistorted plane to its original position before transformation. 25
  26. 26. 3 important components Bain distortion Lattice invariant shear Rigid body rotation 26
  27. 27. Bain distortion with slip #1 Vectors b and c are defined by the intersections of the initial Bain cone with K1 plane 1.Apply a complementary shear  Vectors b and c become b’ and c’ and still lie in the K1 plane and remain unchanged in both direction and magnitude.  They are invariant lines. 27
  28. 28. Bain distortion with slip #1 Vectors b and c are defined by the intersections of the initial Bain cone with K1 plane 2.Apply a Bain distortion  Vectors b’ and c’ become b’’ and c’’ lie on the initial and final Bain cones, respectively, without changing their magnitude. 28
  29. 29. Bain distortion with slip #1  Complementary shear b and c to b’ and c’  Bain distortion b’ and c’ to b’’ and c’’ Angle btw b and c ≠ angle btw b” and c” Appropriate rotation cannot be applied to return b” and c” to initial positions of b and c. Plane defined by b and c cannot be an invariant plane. 29
  30. 30. Bain distortion with slip #2 To obtainan invariant plane, must have other extended lines  Ifassumed to know the shear angle α, vectors a and d obtained from the intersections of the K2 plane change to a’ and d’ along the great circles.  Bain distortion, vectors a’ and d’ become a” and d”, respectively 30
  31. 31. Bain distortion with slip #2 Through the transformation of the complementary shear and the Bain distortion  Sequences of a→a’→a” and sequences d→d’→d” reveal no change in length  However, angle btw a & d ≠ angle btw a” & d” Plane defined by a and d cannot be an invariant plane. 31
  32. 32. Complete transformationprocess Possible invariant planes will depend on the choice of combination of b or c with a or d such as  Vectors a and b  Vectors a and c  Vectors b and d  Vectors c and d 32
  33. 33. Complete transformation process If theinvariant plane is the plane defined by vectors a & c Angle btw a & c = angle btw a’’ & c’’ Let the axis required for rotation be at point u Determine the amount of rotation stereographically by intersection of a great circle bisecting a-a” with another great circle bisecting c-c” 33
  34. 34. Complete transformationprocess Once a” and c” coincide simultaneously with a and c, respectively  Angle btw a & c = angle btw a’’ & c’’ Therefore, orientation relationship btw γ plane (defined by the vectors a and c) and α’ plane (defined by the vectors a” and c”) can be determined for a specific variant of the Bain distortion (B), lattice invariant shear (P), and rotation operation (R). T = BPR 34
  35. 35. Complete transformationprocess T = BPR Bain distortion (B) Lattice invariant shear (P) Rotation operation (R) 35
  36. 36. Bain distortion with twinning Twinned martensite can take place by having alternate regions in the parent phase undergo the lattice deformation along different contraction axes, which are initially at right angles to each other.  In the first region, contraction occurs along the x3 [ 001] f axis.  In the adjacent region, contraction direction can be either x1 [100] f or x2 [ 010] f axis. Two rigid body rotations are also involved in the twinning analysis. 36
  37. 37. Nucleation and growth It only takes about 10-5 to 10-7 seconds for a plate of martensite to grow to its full size. The nucleation during the martensitic transformation is extremely difficult to study experimentally. Average number of martensite is as large as 104 nuclei/mm3  Number of martensite nuclei can be increased by increasing ∆T prior to Ms.  It is too small in term of number of nucleation sites for homogeneous nucleation. 37
  38. 38. Nucleation and growth Less likely to occur by homogeneous nucleation process, but heterogeneous.  Surfaces and grain boundaries are not significantly contributing to nucleation.  Most likely types of defect that could produce the observed density of martensite nuclei are dislocations (> 105 dislocation/mm2). C. Zener (1948): movement of partial dislocations during twinning could generate a thin bcc region of lattice from an fcc region. 38
  39. 39. Nucleation and growth Dissociation of a dislocation into 2 partials is favorable → lower strain energy. r r r To generate b1 = b2 + b3 bcc structure, a a a [ 110] = [ 211] + 121 the requirements are that all 2 6 6  green atoms move (shear) a forward by 12 [ 211] and an additional dilatation to correct lattice spacings. 39
  40. 40. Nucleation and growth Growth of lath martensite with dimension a > b >> c growing on a {111}γ planes  Thickening mechanism would involve the nucleation and glide of transformation dislocations moving on discrete ledges behind the growing front. Due to large misfit between bct and fcc lattice, dislocations could be self-nucleated at the lath interface as the lath moves forward. 40
  41. 41. Nucleation and growth In medium and high carbon steels,  Morphology of martensite turns to change from a lath to a plate-like shape. As carbon concentration decreases,  Decrease lath structure  Decrease martensitic temperature  Increase twinning  Increase retained austenite  Depending on compositions, the habit plane changes from {111}γ → {225}γ → {259}γ 41
  42. 42. Effect of pressure to martensite As pressure increases  In Fe unary system, the equilibrium temperature decreases  In Fe-C binary system, the phase region around γ phase shifts to the left and downward.  Similar to adding austenite stabilizer 42
  43. 43. Effect of alloying element tomartensite Each alloying element will effect the martensitic transformation differently. If initially Hγ = Hα  When adding C  The ē of C will decrease Hα and cause α to be less stable.  ∆H = Hγ – Hα > 0, stabilize the γ  When adding X  Increase Hα and ∆H < 0, stabilize the α 43
  44. 44. Effect of external stress tomartensite As martensite prefers to nucleate and grow along the dislocation  Expected that an externally applied shear stress will assist and accelerate the generation of dislocations and hence the growth of martensite. An external shear stress can aid martensite nucleation if the external elastic strain components play as a part of the Bain strain.  This can also help by raising the M s temperature. 44
  45. 45. Effect of external stress tomartensite Once the plastic deformation occurs  There is an upper limit value of M that the s stress can be applied.  The limit temp. of M is called M (highest s d temperature that stress helps to form martensite)  Too much plastic deformation will suppress the transformation. 45
  46. 46. Effect of external stress tomartensite If a tensile stress is applied  M temperature can be suppressed to lower s temperature  Transformation may be reversed from α’ → γ Presence of large magnetic field may favor the formation of the ferromagnetic phase and therefore raise Ms temp. 46
  47. 47. Effect of external stress tomartensite Plastic deformation of γ before transformation will assist on increasing number of nucleation sites.  Once the transformation occurs  Result in very fine plate size of martensite (Called the ausforming process) Combined effect of very fine martensite plates, 1 2 solution hardening of carbon, and 3dislocation hardening  Very high strength ausformed steel 47
  48. 48. Shape-memory alloys (SMA) Unique property of some alloys  After being deformed at one temperature, they recover the original undeformed shape when heated to a higher temperature. 48
  49. 49. Shape-memory alloys (SMA) Unique property of some alloys  After being deformed at one temperature, they recover the original undeformed shape when heated to a higher temperature. Fundamental to the shape-memory effect (SME) is the occurrence of a martensitic phase transformation and its subsequent reversal. Alloys: Ni-Ti (called NiTiNOL), Ni-Al, Fe-Pt, Cu-Al-Ni, Cu-Au-Zn, Cu-Zn-(Al,Ga,Sn,Si), Ni-Mn-Ga 49
  50. 50. SMA Common characteristics  Atomicordering transformation from ordered parent phase to ordered martensite phase  Thermoelastic martensitic transformation that is crystallographic reversible  Martensite phase that forms in a self- accommodating manner (slip or twinning) 50
  51. 51. SMA Typical plot of property changes versus temp. A hysteresis is usually on the order of 20°C 51
  52. 52. One-way SMA Sample is cooled from above Af to below Mf → martensite forms  Sample has no shape change Sample is deformed below Mf  Sample remains deformed until heated.  Begin shape recovery at A and complete at A s f  No shape change when cooled below Mf Deforming the 52 martensite again will reactivate SME
  53. 53. Two-way SMA Sample is cooled from above Af to below Mf → martensite forms  Sample has no shape change Sample is deformed below Mf  Sample remains deformed until heated.  Begin shape recovery at A and complete at A s f  Returnsto the deformed shape when cooled below Mf 53

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