Dislocation Motion Dislocations plastic deformation Cubic hexagonal metals plastic deformation is by plastic shear or slip where one plane of atoms slides over adjacent plane by defect motion dislocations Adapted from Fig 7 1 Callister 7e If dislocations don t move deformation doesn t occur Deformation Mechanisms Slip System Slip plane plane allowing easiest slippage Wide interplanar spacings highest planar densities Slip direction direction of movement Highest linear densities FCC Slip occurs on 111 planes relatively close packed in 110 directions close packed total of 12 slip systems in FCC in BCC HCP other slip systems occur Stress and Dislocation Motion Crystals slip due to a resolved shear stress tR Applied tension can produce such a stress Applied tensile stress s F A A F Resolved shear stress tR Fs A s slip plane tR FS AS tR normal ns AS FS F Relation between s and tR tR tR s cos cos Fcos F FS A cos nS A AS Note By definition is the angle between the stress direction and Slip direction is the angle between the normal to slip plane and stress direction Critical Resolved Shear Stress Condition for dislocation motion tR tCRSS Crystal orientation can make it easy or hard to move dislocation tR s cos cos s tR 0 90 s typically 10 4 GPa to 10 2 GPa s tR s 2 45 45 tR 0 90 Generally Resolved t shear stress is maximum at 45 And tCRSS sy 2 for dislocations to move in single crystals Slip Motion in Polycrystals Stronger since grain boundaries pin deformations s Slip planes directions change from one crystal to another Adapted from Fig 7 10 Callister 7e Fig 7 10 is courtesy of C Brady National Bureau of Standards now the National Institute of Standards and Technology Gaithersburg MD tR will vary from one crystal to another The crystal with the largest tR yields first Other less favorably oriented crystals yield slip later 300 mm After seeing the effect of poly crystalline materials we can say as related to strength Ordinarily ductility is sacrificed when an alloy is strengthened The relationship between dislocation motion and mechanical behavior of metals is significance to the understanding of strengthening mechanisms The ability of a metal to plastically deform depends on the ability of dislocations to move Virtually all strengthening techniques rely on this simple principle Restricting or Hindering dislocation motion renders a material harder and stronger We will consider strengthening single phase metals by grain size reduction solid solution alloying and strain hardening Strategies for Strengthening 1 Reduce Grain Size Grain boundaries are barriers to slip Barrier strength increases with Increasing angle of misorientation Smaller grain size more barriers to slip Hall Petch Equation Adapted from Fig 7 14 Callister 7e Fig 7 14 is from A Textbook of Materials Technology by Van Vlack Pearson Education Inc Upper Saddle River NJ s yield so k y d 1 2 Hall Petch equation Grain Size Reduction Techniques Increase Rate of solidification from the liquid phase Perform Plastic deformation followed by an appropriate heat treatment Notes Grain size reduction also improves toughness of many alloys Small angle grain boundaries are not effective in interfering with the slip process because of the small crystallographic misalignment across the boundary Boundaries between two different phases are also impediments to movements of dislocations Strategies for Strengthening 2 Solid Solutions Impurity atoms distort the lattice generate stress Stress can produce a barrier to dislocation motion Smaller substitutional impurity Larger substitutional impurity A C B Impurity generates local stress at A and B that opposes dislocation motion to the right D Impurity generates local stress at C and D that opposes dislocation motion to the right Stress Concentration at Dislocations Adapted from Fig 7 4 Callister 7e Strengthening by Alloying small impurities tend to concentrate at dislocations on the Compressive stress side reduce mobility of dislocation increase strength Adapted from Fig 7 17 Callister 7e Strengthening by alloying Large impurities concentrate at dislocations on Tensile Stress side pinning dislocation Adapted from Fig 7 18 Callister 7e Ex Solid Solution Strengthening in Copper 400 300 200 0 10 20 30 40 50 Yield strength MPa Tensile strength MPa Tensile strength yield strength increase with wt Ni wt Ni Concentration C 1 2 s C Empirical relation y Alloying increases sy and TS 180 120 60 0 10 20 30 40 50 wt Ni Concentration C Adapted from Fig 7 16 a and b Callister 7e Strategies for Strengthening 3 Precipitation Strengthening Hard precipitates are difficult to shear Ex Ceramics in metals SiC in Iron or Aluminum precipitate Large shear stress needed to move dislocation toward precipitate and shear it Side View Top View Unslipped part of slip plane S Slipped part of slip plane Result 1 sy S Dislocation advances but precipitates act as pinning sites with spacing S which multiplies Dislocation density Application Precipitation Strengthening Internal wing structure on Boeing 767 Adapted from chapteropening photograph Chapter 11 Callister 5e courtesy of G H Narayanan and A G Miller Boeing Commercial Airplane Company Aluminum is strengthened with precipitates formed by alloying H T Adapted from Fig 11 26 Callister 7e Fig 11 26 is courtesy of G H Narayanan and A G Miller Boeing Commercial Airplane Company 1 5mm Strategies for Strengthening 4 Cold Work CW Room temperature deformation Common forming operations change the cross sectional area Forging roll die A o blank Drawing die Ao Rolling force Ad Ao Adapted from Fig 11 8 Callister 7e roll Extrusion force Ad Ad Ao tensile force force die container ram billet container Ao Ad CW x 100 Ao die holder extrusion die Ad During Cold Work Ti alloy after cold working Dislocations entangle and multiply Thus Dislocation motion becomes more difficult 0 9 mm Adapted from Fig 4 6 Callister 7e Fig 4 6 is courtesy of M R Plichta Michigan Technological University Result of Cold Work Dislocation density total dislocation length unit volume Carefully grown single crystal ca 103 mm 2 Deforming sample increases density 109 1010 mm 2 Heat treatment reduces density 105 106 mm 2 s Yield stress increases sy1 s y0 as rd increases large hardening small hardening e Impact of Cold Work As cold work is increased Yield strength sy increases Tensile strength TS increases Ductility EL or AR decreases Lo Carbon Steel Adapted from Fig 7 20 Callister 7e Cold Work Analysis What is the tensile
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