Plastic deformation and creep in crystalline materials Chap. 11

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Plastic deformation and creep in crystalline materials Chap. 11 Slide 2 Mechanical Properties of Materials Stiffness Strength ductility Toughness Resistance to elastic deformation Youngs modulus Resistance to plastic deformation Yield stress Resistance to fractureEnergy to fracture Ability to deform plastically Strain to fracture Slide 3 Uniaxial Tensile Test (Experiment 6) Gauge length specimen Slide 4 Result of a uniaxial tensile test Slope = Youngs modulus (Y) UTS Ultimate tensile strength yy Yield strength (Engineering stress) (engineering strain) f (strain to fracture) necking Area = Toughness elastic plastic break Yield point STIFFNESS STRENGTH DUCTILITY Slide 5 If there is a smooth transition from elastic to plastic region (no distinct yield point) then 0.2 % offset proof stress is used Slide 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 Slide 7 KStrength coefficient nwork hardening exponent Eqn. 11.5 Slide 8 What happens during plastic deformation? Externally, permanent shape change begins at y Internally, what happens? Slide 9 What happens to crystal structure after plastic deformation? ? Plastic Deformation Slide 10 Some Possible answers Remains the same Changes to another crystal structure Becomes random or amorphous Slide 11 How Do We Decide? X-ray diffraction No change in crystal structure ! No change in internal crystal structure but change in external shape!! Slide 12 How does the microstructure of polycrystal changes during plastic deformation? EXPERIMENT 5 Comparison of undeformed Cu and deformed Cu Slide 13 Slip Lines Before Deformation After Deformation Slide 14 Slip lines in the microstructure of plastically deformed Cu Callister Experiment 5 Slide 15 Slip Slide 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 Slide 17 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 ) Slide 18 Why slip planes are usually close packed planes? Why slip directions are close-packed directions? Slide 19 Slip Systems in FCC Crystal x y z (111) Slide 20 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? Slide 21 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? Slide 22 F N D F Area=A = F/ A F D = F cos 2 Area = A s A s = A cos 1 Resolved Shear stress Slide 23 F F F F No resolved shear stress on planes parallel or perpendicular to the stress axis cos 2 = 0 cos 1 = 0 Slide 24 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 Slide 25 CRITICAL RESOVED SHEAR STRESS N D Slide 26 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 Schmids Law: CRSS is a material constant. Slide 27 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 Slide 28 Active slip system Slip system with highest Schmid factor is the active slip system Slide 29 Magnitude of Critical Resolved Shear Stress Theory (Frenkel 1926) Experiment Slide 30 b d CRSS Shear stress b/2 b Potential energy Slide 31 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 Slide 32 ? Slide 33 E. Orowan Michael Polanyi Geoffrey Ingram Taylor Solution Slide 34 Not a rigid body slip Part slip/ part unslipped Slide 35 SlipNot-yet-slipped Boundary between slipped and unslipped parts on the slip plane Dislocation Line (One-Dimensional Defect) Slide 36 Slide 37 Slide 38 Slide 39 Slide 40 Slide 41 Movement of an Edge Dislocation From W.D. Callister Materials Science and Engineering Slide 42 Slide 43 Plastic Deformation Summary Plastic deformation slip Slip dislocations Plastic deformation requires movement of dislocations on the slip plane Slide 44 Recipe for strength? Remove the dislocation Slide 45 700 50 Stress, MPa strain Cu Whiskers tested in tension Fig. 11.6 Slide 46 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 Slide 47 Recipe for strength Remove the dislocation: Possible but Impractical Alternative: Make the dislocation motion DIFFICULT Slide 48 Strengthening Mechanisms Strain hardening Grain refinement Solid solution hardening Precipitation hardening Slide 49 Movement of an Edge Dislocation A unit slip takes place only when the dislocation comes out of the crystal Slide 50 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 ? Slide 51 Dislocation Sources F.C. Frank and W.T. Read Symposium on Plastic Deformation of Crystalline Solids Pittsburgh, 1950 Slide 52 A B P Q b b b Slide 53 b Slide 54 b b Fig. 11.9 Problem 11.11 Slide 55 Strain Hardening or Work hardening Strain, yy yy Slide 56 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 ? Slide 57 Dislocation against Dislocation A dislocation in the path of other dislocation can act as an obstacle to the motion of the latter Strain Hardening Slide 58 ]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 Slide 59 )111( )111( Sessile dislocation a barrier to other dislocations creating a dislocation pile-up Piled up dislocations Sessile dislocation (barrier) Fig. 11.10 Slide 60 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 Slide 61 Fig. 11.11 Slide 62 Dislocation Motion Plastic Deformation Difficult Dislocation Motion Difficult Plastic Deformation Strong Crystal Easy Dislocation MotionEasy Plastic Deformation Weak Crystal Slide 63 Grain Boundary Grain1 Grain 2 Grain boundary Slide 64 2-D Defect: Grain Boundaries Single Crystal Polycrystal No Grain Boundaries Grains of different orientations separated by grain boundaries Slide 65 Discontinuity of a slip plane across a grain boundary Disloca- tion Slip plane Grain Boundary Slide 66 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 Slide 67 Coarse GrainsFine Grains Slide 68 Grain Size Strengthening Hall-Petch Relation y yield strength D: average grain diameter 0, k: constants Slide 69 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 I did not mention this in the class but in the interest of recent developments of nanotechnology I feel you should at least be aware of this: Slide 70 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 Slide 71 Interstitial Solid Solution Perfect Crystal Distortion caused by a large interstitial atom Slide 72 Substitutional Solid Solution Small solute atomLarge solute atom Solute atom: a zero-dimensional point defect Slide 73 Solid Solution Strengthening Strains in the surrounding crystal Solute atoms Obstacle to dislocation motion Strong crystal Alloys stronger than pure metals Slide 74 Fig 11.13 Solute Concentration (Atom %) 50 100 150 10 20 30 40 200 0 Matrix = Cu (r = 1.28 ) 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 ) Figure: Anandh Subramaniam Slide 75 Airbus A380 to be launched on October 2007 Slide 76 A shop inside Airbus A380 Slide 77 Alfred Wilms Laboratory 1906-1909 Steels harden by quenching Why not harden Al alloys also by quenching? Slide 78 time Wilms Plan for ha