Physical Metallurgy 12 th Lecture

1. Physical Metallurgy12 th Lecture MS&E 410 D.Ast dast@ccmr.cornell.edu 255 4140

2. Microstructure cm=>mm mm=>microns nanometers

3. How much morphology controls mechanical properties: An excursion into practical Metallurgy Graphite Ferrite Graphite Graphite Spheres Graphite Plates Pearlite Pearlite Ductile Cast IronBrittle cast iron Identical Carbon Content => different graphite morphology!

4. Time => A) Brittle Graphite Flakes in Austenite that later decomposes into Pearlite (a mixture of Cementite and Ferrite) B ) Ductile Graphite Spheres surrounded by Austenite C) Malleable Heat treated spherulictic, Austenite transforms to ferrite, shedding carbon by increasing existing C particle size or nucleating new ones A) Slow cool => Graphite flakes => Crack like => Brittle B) Slow cool + Mg => Graphite spheres (“drill out” ) => Ductile

5. Cementite or Graphite surrounded by Austenite with 2%C Cementite or Graphite surrounded by Austenite with 0.83%C. Austenite decomposes into pearlite or at slow cool: Ferrite plus graphite

6. A part made of ductile cast iron (what it is it ? ) A table on how one can trade of ductility vs tensile strength in ductile cast iron. Note: We can triple the tensile strength by sacrificing ductility ……...An other example of syvs K1c

7. Microstructure Tables Lots of levers to play with!

9. Microstructure Phase MorphologyGrain Structure Lamellar Size distribution Particles Shape distribution Dentritic Orientation Distribution Composition Phases possible Different phases: Phase amount Different crystal structure => GB Phase diagram Different gGB Non equilibrium phases Solidification Determines phases present size, shape, orientation and their distribution Heat Treatment Refined microstructure: Solutionize More off equilibrium Grain Growth Quench Coarsened microstructure Grain Reorientation Annealing More equilibrium e.g preciptation Grain Boundary - Solute interact. Aging

11. Dislocation Structure Point Defect Density, r Vacancies, Interstitials Cells and Grain Boundary Pairs (Frenkel, Divacancy…..) Geometrically necessary Anti-Site Different phases different b, m Different point defects Thermal stress Dislocation movement, multiplication Number and distribution (e.g. Creep) Phase accommodation Misfit dislocations (epi growth) r Reduction due to annealing polygonization quench in defects, vacancy clusters (cop’s) Thermal stress, the byproduct, may reduce defects by annealing out at sinks increase r

12. Most of this is familiar, except perhaps, Geometric Necessary Dislocations • Not formed due to stress but to accommodate geometry • Term invented by Ashby (Harvard): • “they are the dislocations required to support a • particular curvature in the crystallographic lattice at any given point in a deformed structure” M.F.Ashby (1970) Phil. Mag. 21, 339. • Mathematically it’s like this => E. Kroener theory, again ;-) • a = curl ße • where a is the dislocation tensor and ße the elastic distortion tensor. • See my slide in lecture 11

13. Geometric necessary dislocations have no stress field • Geometric accommodation can also come about by stress induced precipitation IC silicon contains 0.001% dissolved oxygen that can precipitate out as SiO2,

14. Familiar examples of geometric necessary dislocations Tilt boundaries (We could make the same deformation elastically) Misfit dislocations at the interface of crystals of somewhat different lattice constant. Common in epitaxial growth of semiconductors

15. More generally, their use is as follows • Deformation of a poly-crystalline material will develop elastic deformation at grain boundaries, because no gap can open up. These deformations are the result of the fact that the incompatibility conditions of continuum theory must hold. On the other hand, glide is limited to glide systems. • To deal with these stresses (which come from the incompatibility equations) we insert geometric necessary dislocations such that their combined strain field exactly cancels the elastic strain we calculated with elastic theory. • And voila, we have modeled plastic deformation stresses with elastic theory plus “dislocations” • E. Kroener’s theory opened up an entire new field in continuums mechanics

17. Mechanical Deformation Phase Grain - rolling*, forging, swaging Distort, break up Change Shape distribution - martensite phases. (Strain induced) superimpose phase strucure - form/destroy grains and cells Phase changes on gr. size, shape, orientation Change size, shape, orientation Recrystallization New defect free grains grow into Radically changes size, shape defective material (metals, Si not) orientation (defect free in both point defects as well!) Need (critical) deformation to drive Right time and temperature Impurities Changebinary to ternary etcSegregate to GB, pin it Object shape Size, shape (1,2, 3-D) interfaces.. Similar to phase dimension : Limits grain size(e.g. in thin Shape change (or reverse if E.g. max grain size in thin shape is fixed)films is ~3 film thickness Affects orientation For lovers of beer cans: rolling generates a strongly preferred direction making deep draw difficult. “Draw quality sheet” is therefore rolled in two directions

18. Excursion into practical metallurgy: Phase memory alloy You may know this from eye glass frames but there is much more How does it work ?

19. Shape the object in the Austenite phase • Cool (forms twinned Martensite) in the shape of its austenitic predecessor. • Deform => change twin structure • Heat => unfolds to its austenitic shape • Typically delta T => 10 to 20oC

20. The start and finish temperature of the martensite (and austenite phase) transformation is load dependent Stress “acts like decreasing temperature” and can drive reversibly a phase transition => Pseudo Elasticity

21. The eye glass frame is pseudo elasticity: • It’s Austenite (don’t go the South Pole with it !) • You (unintentionally) load it => Martensite => deforms (microtwins) • The take the stress off => transforms back to twin free Austenite An example of a “smart” material

22. Excursion in practical metallurgy: TRIP steels Stress driven phase transformations in steel Strain induced phase transformation put to work. During deformation retained austenite deforms continuously in hard martensite

23. Excursion in practical metallurgy cont.: TRIP steels Q&P is quenching and partitioning (processing to control retained austenite. DP are dual phase steels, with a continuous ferrite phase and a hard austenite phase.

24. Increase in flow stress at high extension due to stress induced austenite/martensite transformation Not what we like to make curvy fenders…. Would you know why ? TRIP steels are great for energy absorption but expensive

26. Deformation Dislocations Point Defects r inceases (need dislos!) Dislocation movement Change in organization of r Generation and Absorption (e.g. dislocation cell walls => of point defects metal fatigue ) (creep) Annealing [c]v,i decreases Impurities Segregate to dislocations Impurity point defect Pin dislocation complexes (very well Lomer Cottrell atmosphere studied for dopants in semi Serrated flow…. Lueders bands conductors) (Reduced) dimensions Force dislocations to interact if L = 2 Dt (Big effect in thin films) point defects will sink at Image forces at free surface free surface (hard oxide film on soft copper)

27. One of the fundamental claims of Nanotechnology is that small objects are more perfect having fewer defects than bulk Well… yes But in most circumstance metallurgists want defects! Of the right kind!

28. Dislocation Pinning => Excursion to practical metallurgy The plateau is due to the break away of dislocations from “an atmosphere of carbon”. Once broken free, less stress is required, causing the dip after the upper yield point Mild Steel 0.3% C The negative work-hardening coefficient causes the strain to concentrate in Lueders bands. Called stretch marks and a nuisance in the deep drawing of fenders when cars used mild steel. Modern cars use HSLA, which is much less ductile and can not be deep drawn. This has led to the disappearance of compound curves in modern automobiles

29. It would be difficult to make such a fender with HSLA steel.

30. Opposite dislocations will annihilate each other ….. If they can glide towards each other.

32. Notes • The fraction recrystallized follow the Johnson Mehl Avrami equation. You had this in kinetics and phase transformation. • The activation energy is that of self diffusion of Fe

33. The activation energy for Fe self diffusion is similar to other impurities, in particular with 4delectrons

34. HW 12-1 Extract the activation energy for self diffusion in the fcc and bcc phase of iron from the graphs on the preceding page

35. Once upon a time we had a swaging machine in MS&E..

36. Notes: • Work hardening occurs because of dislocation multiplication. It requires more and more stress to move the dislocations for further deformation. The stress required is inversely proportional to the spacing H. • Work hardening spreads out deformation. It is vital in engineering application of metals • At dislocation densities of ~ 1012 dislocations/cm2, dislocation recombination is equally probable as dislocation generation. • => Cell walls in fatigues specimens • => Metallic glasses (absence of work hardening)

37. Notes, continued • Most (80..90%) of the external work of rolling, swaging etc goes into disputative processes and winds up as heat. Internal energy storage occurs in • Excess point defect concentrations (jog dragging etc) • Increasing total length of dislocations (E = ~ Gb2) • Elastic energy stored in dislocation pile ups.

38. Energy stored in dislocations arrangements decreases with time. A sensitive measure to track the resulting length changes as f(s,t) is the stress relaxation test IF the machine frame is very stiff, a very tiny extension of the specimen will cause a deep drop in the force on the load cell

39. The energy stored in making dislocations is proportional to r, the dislocation density, and the line energy, T, of the dislocation (left calculation, straight line in right plot) The fraction of external energy stored (which can be measured by calorimetry) decreases with increasing r as more and more irreversible changes develop in the material.

40. Heat output with increasing temperature as measured in a scanning calorimeter. The peak temperature , roughly, is 1/2 of Tm (in degree K). Diffusional creep permits dislocations to “untangle” via non-conservative (I.e. non-glide) motion.

41. Ni3Al type super alloy, cold rolled Ni Al.~8wt% Cr~8wt%

42. Microstructure as function of annealing T,t

43. HW 12-2 Consider 1 cm3 of Fe. Starting out as a single crystal, with a dislocation density of 105 cm-2, it has been cold worked to a dislocation density of 1010 cm-2. a) Using the formula E = Gb2 and the measured G for iron (look it up), calculate the increase in internally stored energy due to the generation of dislocations. Give answer in units of milliWatt. c) Using the measured density of Fe (look it up) calculate the internally stored energy in units of mW/gr d) Consulting the lecture notes, compare your answer with the energy stored in a rolled Ni3Al superalloy. Is your answer lower or higher ? Can you think of any reasons (limit yourself to 2 sentences.. No novel, please

44. d) Assume that to generate such a high dislocation density you need to pull the 1x1x1 cm Fe specimen to a strain of 100%. That is to 0.7x0.7x2 cm. Assume that the flow stress is 30 000 psi and that it stays constant during deformation (the cross section goes down but the work hardening goes up - let us assume they cancel) Calculate the energy delivered to the specimen in mW. Calculate the energy delivered per gram Compare with your result in c) . Comments are welcome but limited to two sentences.

45. Annealing summery: + : Increases ductility. Indispensable when an . object is formed by repeated large deformations. + : Permits the growth of Fe single crystals (why ?) - : Destroys work hardening - :Increases grain size. - : Dissolves precipitates

46. With increasing the temperature, several stages can be observed • Annihilation of screw dislocations • Elimination of edge dislocations • Both occur with the activation energy of the mobility of dislocations • Recrystallization. Occurs with the activation of self diffusion

47. THE END