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Plastic deformation and creep in crystalline materials Chap. 11 Lec 2626/03/2014.

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Presentation on theme: "Plastic deformation and creep in crystalline materials Chap. 11 Lec 2626/03/2014."— Presentation transcript:

1 Plastic deformation and creep in crystalline materials Chap. 11 Lec 2626/03/2014

2 Mechanical Properties of Materials Stiffness Strength ductility Toughness Resistance to elastic deformation Young’s modulus Resistance to plastic deformation Yield stress Resistance to fractureEnergy to fracture Ability to deform plastically Strain to fracture

3 Uniaxial Tensile Test (Experiment 6) Gauge length specimen

4 Result of a uniaxial tensile test Slope = Young’s modulus (Y)  UTS Ultimate tensile strength yy Yield strength  (Engineering stress)  (engineering strain)  f (strain to fracture) necking Area = Toughness elastic plastic break Yield point STIFFNESS STRENGTH DUCTILITY

5 If there is a smooth transition from elastic to plastic region (no distinct yield point) then 0.2 % offset proof stress is used

6 During uniaxial tensile test the length of the specimen is continually increasing and the cross-sectional area is decreasing. True stress ≠ Engineering stress (  =F/A 0 ) True strain ≠ Engineering strain (  =  L/L 0 ) True stressA i = instantaneous area True incremental strain True strain Eqn. 11.3 Eqn. 11.4

7 KStrength coefficient nwork hardening exponent Eqn. 11.5

8 What happens during plastic deformation? Externally, permanent shape change begins at  y Internally, what happens?

9 What happens to crystal structure after plastic deformation? ? Plastic Deformation

10 Some Possible answers Remains the same Changes to another crystal structure Becomes random or amorphous

11 How Do We Decide? X-ray diffraction No change in crystal structure ! No change in internal crystal structure but change in external shape!!

12 How does the microstructure of polycrystal changes during plastic deformation? EXPERIMENT 5 Comparison of undeformed Cu and deformed Cu

13 Slip Lines Before Deformation After Deformation

14 Slip lines in the microstructure of plastically deformed Cu Callister Experiment 5

15 Slip

16 Slip Planes, Slip Directions, Slip Systems Slip Plane: Crystallographic planes Slip Direction: Crystallographic direction Slip System: A combination of a slip plane and a slip direction

17 Lec 2728/03/2014

18 Slip Systems in Metallic Crystals CrystalSlipSlipSlip PlaneDirectionSystems FCC {111} 4x3=12 (4 planes)(3 per plane) BCC {110} 6x2=12 (6 planes)(2 per plane ) HCP {001} 3x1=3 (1 plane)(3 per plane )

19 Why slip planes are usually close packed planes? Why slip directions are close-packed directions?

20 Slip Systems in FCC Crystal x y z (111)

21 Tensile vs Shear Stress Plastic deformation takes place by slip Slip requires shear stress Then, how does plastic deformation take place during a tensile test?

22  N D     : Applied tensile stress N: Slip plane normal D: Slip direction   : angle between  and N    =angle between  and D Is there any shear stress on the slip plane in the slip direction due to the applied tensile stress?

23 F N D   F Area=A  = F/ A F D = F cos  2 Area = A s A s = A cos  1 Resolved Shear stress

24 F F F F No resolved shear stress on planes parallel or perpendicular to the stress axis cos  2 = 0 cos  1 = 0

25 Plastic deformation recap No change in crystal structure: slip twinning Slip takes place on slip systems (plane + direction) Slip planes usually close-packed planes Slip directions usually close-packed direction Slip requires shear stress In uniaxial tension there is a shear component of tensile stress on the slip plane in the slip direction: RESOLVED SHEAR STRESS


27 Lec 2801.04.2014

28 If we change the direction of stress with respect to the slip plane and the slip direction cos  1 cos  2 will change. 1.  CRSS changes. To maintain the equality which of the following changes takes place? 2.  y changes Schmid’s Law:  CRSS is a material constant.

29 Anisotropy of Yield Stress Yield stress of a single crystal depends upon the direction of application of load cos  1 cos  2 is called the Schmid factor

30 Active slip system Slip system with highest Schmid factor is the active slip system

31 Magnitude of Critical Resolved Shear Stress Theory (Frenkel 1926) Experiment

32 b d  CRSS Shear stress  b/2 b Potential energy

33 Fe (BCC) Cu (FCC) Zn (HCP) Theory (GPa) 12 7 5 Experiment (MPa) 15 0.5 0.3 Ratio Theory/Exp 800 14,000 17,000 Critical Resolved Shear Stress

34 ?

35  E. Orowan Michael Polanyi Geoffrey Ingram Taylor Solution

36 Not a rigid body slip Part slip/ part unslipped

37 SlipNot-yet-slipped Boundary between slipped and unslipped parts on the slip plane Dislocation Line (One-Dimensional Defect)






43 Movement of an Edge Dislocation From W.D. Callister Materials Science and Engineering


45 Plastic Deformation Summary Plastic deformation slip Slip dislocations Plastic deformation requires movement of dislocations on the slip plane

46 Recipe for strength? Remove the dislocation

47 700 50 Stress, MPa strain Cu Whiskers tested in tension Fig. 11.6

48 Lec 2902.04.2014 crystal structure changes? Mechanism of deformation No slip Nature of stress required for slipShear stress Is there shear during tension?Resolved shear stress Resolved shear stress required for initiating slip Critical resolved shear stress CRSS is independent of the direction of application of tensile stress

49 Lec 2902.04.2014

50 Effect of temperature on dislocation motion Higher temperature makes the dislocation motion easier W FeFe SiSi Al 2 O 3 Ni Cu 18-8 ss Yield stress T/T m 00.7 Fig. 11.8 Eqn. 11.14 11.15 11.16 11.17 11.18

51 Recipe for strength Remove the dislocation: Possible but Impractical Alternative: Make the dislocation motion DIFFICULT

52 Strengthening Mechanisms Strain hardening Grain refinement Solid solution hardening Precipitation hardening

53 Movement of an Edge Dislocation A unit slip takes place only when the dislocation comes out of the crystal

54 During plastic deformation dislocation density of a crystal should go down Experimental Result Dislocation Density of a crystal actually goes up Well-annealed crystal: 10 10 m -2 Lightly cold-worked: 10 12 m -2 Heavily cold-worked: 10 16 m -2 ?

55 Dislocation Sources F.C. Frank and W.T. Read Symposium on Plastic Deformation of Crystalline Solids Pittsburgh, 1950

56 A B P Q b b b  

57 b

58 b b Fig. 11.9 Problem 11.11

59 Strain Hardening or Work hardening Strain,  yy yy

60 During plastic deformation dislocation density increases. Dislocations are the cause of weakness of real crystals Thus as a result of plastic deformation the crystal should weaken. However, plastic deformation increases the yield strength of the crystal: strain hardening or work hardening ?

61 Dislocation against Dislocation A dislocation in the path of other dislocation can act as an obstacle to the motion of the latter Strain Hardening

62 ]110[ 2 1 )111( ]110[ 2 1 )111( )001( ]110[ 2 1 Sessile dislocation in an FCC crystal Eqn. 11.20 ]110[ 2 1 (001) not a favourable slip plane (CRSS is high). The dislocation immobile or sessile. Energetically favourable reaction Fig. 11.10  

63 )111( )111( Sessile dislocation a barrier to other dislocations creating a dislocation pile-up Piled up dislocations Sessile dislocation (barrier) Fig. 11.10

64 Lec 30 04.04.2014

65 Empirical relation for strain hardening or work hardening  Is the shear stress to move a dislocation in a crystal with dislocation density   o and A : empirical constants Eq. 11.21

66 Fig. 11.11

67 Dislocation Motion Plastic Deformation Difficult Dislocation Motion Difficult Plastic Deformation Strong Crystal Easy Dislocation MotionEasy Plastic Deformation Weak Crystal

68 Grain Boundary Grain1 Grain 2 Grain boundary

69 2-D Defect: Grain Boundaries Single Crystal Polycrystal No Grain Boundaries Grains of different orientations separated by grain boundaries

70 Discontinuity of a slip plane across a grain boundary Disloca- tion Slip plane Grain Boundary

71 Grain Boundary Strengthening Slip plane discontinuity at grain boundary A dislocation cannot glide across a grain boundary Higher stresses required for deformation Finer the grains, greater the strength

72 Coarse GrainsFine Grains

73 Grain Size Strengthening Hall-Petch Relation  y  yield strength D: average grain diameter  0, k: constants

74 Science 5 April 2002: Vol. 296 no. 5565 pp. 66-67 POLYCRYSTALLINE MATERIALS Grain Boundaries and Dislocations The hardness of coarse-grained materials is inversely proportional to the square root of the grain size. But as Van Swygenhoven explains in her Perspective, at nanometer scale grain sizes this relation no longer holds. Atomistic simulations are providing key insights into the structural and mechanical properties of nanocrystalline metals, shedding light on the distinct mechanism by which these materials deform. Van Swygenhoven Some recent developments

75 Mixture of two or more metals Solute atoms: a zero dimensional defect or a point defect Two types: –1. Interstitial solid solution –2. Substitutional solid solution Solid Solutions

76 Interstitial Solid Solution Perfect Crystal Distortion caused by a large interstitial atom

77 Substitutional Solid Solution Small solute atomLarge solute atom Solute atom: a zero-dimensional point defect

78 Solid Solution Strengthening Strains in the surrounding crystal Solute atoms Obstacle to dislocation motion Strong crystal Alloys stronger than pure metals

79 Fig 11.13 Solute Concentration (Atom %) → 50 100 150 10 20 30 40 200 0 Matrix = Cu (r = 1.28 Å) Be (1.12) Si (1.18) Sn (1.51) Ni (1.25) Zn (1.31) Al (1.43) (Values in parenthesis are atomic radius values in Å) Figure: Anandh Subramaniam

80 Airbus A380 to be launched on October 2007

81 A shop inside Airbus A380

82 Alfred Wilm’s Laboratory 1906-1909 Steels harden by quenching Why not harden Al alloys also by quenching?

83 time Wilm’s Plan for hardening Al- 4%Cu alloy Sorry! No increase in hardness. 550ºC T Heat Quench Hold Check hardness Eureka ! Hardness has Increased !! One of the greatest technological achievements of 20 th century

84 Hardness increases as a function of time: AGE HARDENING Property = f (microstructure) Wilm checked the microstructure of his age-hardened alloys. Result: NO CHANGE in the microstructure !!

85 Lec 3109/04/2014 Creep

86 Lec 3211/01.2014

87 As- quenched hardness Hardness time Peak hardness Overaging Hardness initially increases: age hardening Attains a peak value Decreases subsequently: Overaging

88  ++  : solid solution of Cu in FCC Al  : intermetallic compound CuAl 2 4 T solvus  supersaturated  saturated +  FCC Tetragonal 4 wt%Cu0.5 wt%Cu54 wt%Cu Precipitation of  in 

89 Stable  unstable  T solvus As- quench ed   start  finsh ++ Aging TTT diagram of precipitation of  in  A fine distribution of  precipitates in  matrix causes hardening Completion of precipitation corresponds to peak hardness

90  -grains As quenched  -grains +  AgedPeak aged Dense distribution of fine  overaged Sparse distribution of coarse  Driving force for coarsening  /  interfacial energy

91 0.1 1 10100 hardness Aging time (days) 180ºC 100ºC 20ºC Aging temperature Peak hardness is less at higher aging temperature Peak hardness is obtained in shorter time at higher aging temperature Fig. 9.15

92 U I T Stable  unstable  As- quenched   start  finsh  +  Aging T solvus 1 hardness 180ºC 100ºC 20ºC 100 ºC 180 ºC

93 Hardness increases as as a function of time No change in microstructure - Wilm! hardness time As-quenched hardness

94 Guinier-Preston Zones, 1938 Numerous fine precipitates form with time Not visible in optical micrograph X-Ray Diffraction (XRD) Transmission Electron Microscopy (TEM)

95 “It seems justifiable at the moment to conclude that the process of age hardening in this alloys is associated with the segregation of copper atoms on the (100) planes of the crystal as suggested by C.H. Desch in The Chemistry of Solids, 1934” Preston, 1938, “The Diffraction of X-rays by Age-Hardening Aluminium Copper Alloys

96 Precipitation Hardening Precipitates are obstacles to the motion of dislocation Solute atoms Pebbles Precipitates boulders Cake with nuts Age-hardening = Precipitation hardening

97 Dislocation-precipitate interaction Dislocation can 1.Either cut through the precipitate particles (small precipitate) 2.Or they can bypass the precipitates

98   beforeafter Precipitate cutting Fig 11.14 a, c

99 Dislocation bypassing the precipitate Fig. 11.14 b and d

100 Movement of one- dimensional defects called dislocations causes plastic deformation Obstacles to the movement of dislocations cause strengthening

101 Strengthening Mechanisms Name Obstacle Type Solid solution hardeningSolute atoms (0-D) Strain hardeningDislocations (1-D) Grain refinementGrain boundaries (2-D) Precipitation hardeningPrecipitates (3-D)

102 102 Q1: How do glaciers move?



105 105 “Genius is one percent inspiration and ninety-nine percent perspiration” -T.A. Edison Q2: How do bulbs fuse? 2. Electric Bulb

106 106 Rolls-Royce Plc Q3: What does the Rolls-Royce plc make?

107 107

108 108 Q: What is common to all the three? Ans: CREEP 1.Glaciers move due to creep of snow. 2. Bulbs fuse due to creep of W filament. 3. Life of jet engine depends of creep of the turbine blades.

109 Creep Creep is time dependent plastic deformation at constant load or stress It is a “high temperature” deformation T m is the m.p. in K. Difference between normal plastic deformation and creep ?


111 Fig. 11.15

112 Creep Dislocation climb Vacancy diffusion Cross-slip Grain boundary sliding Creep Mechanisms of crystalline materials

113 Cross-slip  In the low temperature of creep → screw dislocations can cross-slip (by thermal activation) and can give rise to plastic strain [as f(t)] 1 2 3 b Slip plane 1 Slip plane 2

114 Dislocation climb  Edge dislocations piled up against an obstacle can climb to another slip plane and cause plastic deformation [as f(t), in response to stress]  Rate controlling step is the diffusion of vacancies

115 Diffusional creep  In response to the applied stress vacancies preferentially move from surfaces/interfaces (GB) of specimen transverse to the stress axis to surfaces/interfaces parallel to the stress axis→ causing elongation  This process like dislocation creep is controlled by the diffusion of vacancies → but diffusional does not require dislocations to operate  Flow of vacancies Coble creep → low T → Due to GB diffusion Nabarro-Herring creep → high T → lattice diffusion

116 Grain boundary sliding  At low temperatures the grain boundaries are ‘stronger’ than the crystal interior and impede the motion of dislocations  Being a higher energy region, the grain boundaries melt before the crystal interior  Above the equicohesive temperature grain boundaries are weaker than grain and slide past one another to cause plastic deformation

117 117 Starter: initiates columnar grains as in Directional Solidification (DS) Pigtail: a helical channel which gradually eliminates most columnar grains Single crystal turbine blade Single crystal blade: best creep resistance

118 118 Coarser grains -> Less grain boundaries -> Better for creep application Single Crystal -> No grain boundaries -> Best for creep application Nanocrystalline materials -> not good for creep applications!

119 119 Improvements due to blade manufacturing technique: Show turbine blades

120 120 Improvements due to engineering design: Blade cooling Engineering Materials 1: Ashby and Jones

121 121 NiCrAlY or NiCoCrAlY Thermal Barrier Coating (TBC) Ceramic top coat: Yittria stabilized Zirconia (YSZ) 1.Low thermal conductivity 2. High thermal expansion 3.High M.P Reduction in surface temp 100-300 o C Operating temp > M.P. (~1300 o C)

122 Creep Resistant Materials  Higher operating temperatures gives better efficiency for a heat engine Creep resistance Dispersion hardening → ThO 2 dispersed Ni (~0.9 T m ) Solid solution strengthening High melting point → E.g. Ceramics Single crystal / aligned (oriented) grains

123  Cost, fabrication ease, density etc. are other factors which determine the final choice of a material  Commonly used materials → Fe, Ni, Co base alloys  Precipitation hardening (instead of dispersion hardening) is not a good method as particles coarsen (smaller particles dissolve and larger particles grow  interparticle separation ↑)  Ni-base superalloys have Ni 3 (Ti,Al) precipitates which form a low energy interface with the matrix  low driving force for coarsening  Cold work cannot be used for increasing creep resistance as recrystallization can occur which will produced strain free crystals  Fine grain size is not desirable for creep resistance → grain boundary sliding can cause creep elongation / cavitation ► Single crystals (single crystal Ti turbine blades in gas turbine engine have been used) ► Aligned / oriented polycrystals

124 No Dislocations Ultra Strong Crystals Whiskers Composite Materials

125 Various Crystal Defects Disloca- tions Grain Boundary G-P zone Substitu- tional solute Interstitial solute Stacking fault Vacancy (Diffusion)

126 Moral of the Story Strength depends upon defects

127 Microstructure Structural features observed under a microscope –Phases and their distribution –Grains and grain boundaries –Twin boundaries –Stacking faults –Dislocations

128 Hierarchy of Structures Physics and chemistry Metallurgy and Materials Science Engineering: Civil, Mechanical, etc. 1m 1mm 1m1m 1nm 1A 0

129 Real Moral of the Story Properties depend upon microstructure Structure Sensitive vs Structure Insensitive Properties

130 For true understanding comprehension of detail is imperative. Since such detail is well nigh infinite our knowledge is always superficial and imperfect. Duc Franccois de la Rochefoucald (1613-1680)

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