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ENGR-45_Lec-17_DisLoc_Strength-1.ppt 1 Bruce Mayer, PE Engineering-45: Materials of Engineering Bruce Mayer, PE Licensed Electrical.

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Presentation on theme: "ENGR-45_Lec-17_DisLoc_Strength-1.ppt 1 Bruce Mayer, PE Engineering-45: Materials of Engineering Bruce Mayer, PE Licensed Electrical."— Presentation transcript:

1 ENGR-45_Lec-17_DisLoc_Strength-1.ppt 1 Bruce Mayer, PE Engineering-45: Materials of Engineering Bruce Mayer, PE Licensed Electrical & Mechanical Engineer Engineering 45 Dislocations & Strengthening (1)

2 ENGR-45_Lec-17_DisLoc_Strength-1.ppt 2 Bruce Mayer, PE Engineering-45: Materials of Engineering Learning Goals  Understand Why DISLOCATIONS are observed primarily in METALS and ALLOYS  Determine How Strength and Dislocation-Motion are Related  Techniques to Increase Strength  Understand How HEATING and/or Cooling can change Strength and other Properties

3 ENGR-45_Lec-17_DisLoc_Strength-1.ppt 3 Bruce Mayer, PE Engineering-45: Materials of Engineering Theoretical Strength of Crystals  The ideal or theoretical strength of a “perfect” crystal is  E/10 For Steel, E = 200 GPa –Thus the theoretical strength  20 GPa 2,000 MPa is the practical limit for steel and this is an ORDER of MAGNITUDE Less than 20,000 MPa Most commercial steels have a strength  500 MPa - Why is there such differences?

4 ENGR-45_Lec-17_DisLoc_Strength-1.ppt 4 Bruce Mayer, PE Engineering-45: Materials of Engineering Role of Crystal Imperfections  Crystal imperfections explain why metals are weak (relative to the Theoretical) and why they are so ductile In most applications we need ductility as well as strength - so there is a plus side to the presence of imperfections The main task in deciding what strengthening process to use in metal alloys is to chose a method which minimizes the loss of ductility

5 ENGR-45_Lec-17_DisLoc_Strength-1.ppt 5 Bruce Mayer, PE Engineering-45: Materials of Engineering Edge Dislocations  Recall from Chp.4 The Crystal Imperfection of an Extra ½-Plane of Atoms Called an EDGE DISLOCATION  These imperfections are the Source of PLASTIC Deformation in Xtals Extra ½-Plane of Atoms

6 ENGR-45_Lec-17_DisLoc_Strength-1.ppt 6 Bruce Mayer, PE Engineering-45: Materials of Engineering Dislocations vs. Metals  Dislocation Motion is RELATIVELY Easier in Metals Due to NON-Directional Atomic Bonding Close-Packed Crystal Planes allow “sliding” of the Planes relative to each other –Called SLIP Ion Cores Electron Sea Dislocations & Slip (Deformation)

7 ENGR-45_Lec-17_DisLoc_Strength-1.ppt 7 Bruce Mayer, PE Engineering-45: Materials of Engineering Disloc vs. Covalent Ceramics  For CoValent Ceramics Dislocation Motion is RELATIVELY more Difficult Due to Directional (angular) and Powerful Atomic Bonding  Examples Diamond Carbon Silicon Strong, Directional Bonds Dislocations & Slip (Deformation)

8 ENGR-45_Lec-17_DisLoc_Strength-1.ppt 8 Bruce Mayer, PE Engineering-45: Materials of Engineering Disloc vs. Ionic Ceramics  For Ionic Ceramics Dislocation Motion is RELATIVELY more Difficult Due to Coulombic Attraction and/or Repulsion Slip Will Encounter ++ & -- Charged nearest neighbors + Ion Cores − Ion Cores Dislocations & Slip (Deformation)

9 ENGR-45_Lec-17_DisLoc_Strength-1.ppt 9 Bruce Mayer, PE Engineering-45: Materials of Engineering Dislocations vs Matl Type  Metals Allow Xtal Planes to Slip Relative to Each other Relatively Low Onset of Plastic Deformation (Yield Strength, σ y ) Relatively High Ductility: The amount of Plastic deformation Prior to Breaking  Ceramics Tend to Prevent Disloc. Slip Allow for little Plastic Deformation Failure by Brittle-Fracture (cracking)

10 ENGR-45_Lec-17_DisLoc_Strength-1.ppt 10 Bruce Mayer, PE Engineering-45: Materials of Engineering Dislocation Motion  Produces Plastic Deformation In Crystals  Proceeds by Incremental, Step-by-Step Breaking & Remaking of Xtal Bonds  WithOut Dislocation motion Plastic (Ductile) Deformation Does NOT Occur

11 ENGR-45_Lec-17_DisLoc_Strength-1.ppt 11 Bruce Mayer, PE Engineering-45: Materials of Engineering Screw Dislocations  In the EDGE configuration The axis of  is Parallel (||) to the Applied Shear Stress EDGE Dislocation  A SCREW dislocation is Perpendicular to the Applied Force SCREW Dislocation SHEARING Motion TEARING Motion

12 ENGR-45_Lec-17_DisLoc_Strength-1.ppt 12 Bruce Mayer, PE Engineering-45: Materials of Engineering Role of Imperfections in Plastic Deformation

13 ENGR-45_Lec-17_DisLoc_Strength-1.ppt 13 Bruce Mayer, PE Engineering-45: Materials of Engineering Dislocation Motion Analogies  Caterpillar LoCoMotion  Carpet-Layer LoCoMotion Disloc

14 ENGR-45_Lec-17_DisLoc_Strength-1.ppt 14 Bruce Mayer, PE Engineering-45: Materials of Engineering Stress and Dislocation Motion  Crystals slip due to a resolved shear stress,  R  Applied TENSION can Produce This  -Stress slip direction slip plane normal, n s Resolved shear stress: RR =F s /A s A s RR RR F s slip direction F F s Relation between  and RR RR =F s /A s Fcos A/cos  slip direction Applied tensile stress:  = F/A F A F

15 ENGR-45_Lec-17_DisLoc_Strength-1.ppt 15 Bruce Mayer, PE Engineering-45: Materials of Engineering Resolved Shear Stress,  R (in detail)  Consider a single crystal of cross- sectional area A under compression force F   angle between the slip plane normal and the compression (or Tension) axis  angle between the slip direction and the tensile axis.

16 ENGR-45_Lec-17_DisLoc_Strength-1.ppt 16 Bruce Mayer, PE Engineering-45: Materials of Engineering Resolved Shear Stress,  R cont.1  F projected on Slip Direction: Fcos λ AsAs A = A s cos   The Slip Direction Slant Area, A s, Relative to the Compression Area, A

17 ENGR-45_Lec-17_DisLoc_Strength-1.ppt 17 Bruce Mayer, PE Engineering-45: Materials of Engineering Resolved Shear Stress,  R cont.2  Thus the Resolved Shear Stress Fcos λ AsAs A = A s cos   But F/A = σ; the Compression (or Tension) Stress - So

18 ENGR-45_Lec-17_DisLoc_Strength-1.ppt 18 Bruce Mayer, PE Engineering-45: Materials of Engineering Critical Resolved Shear Stress  Condition for Dislocation Motion:  R >  CRSS  CRSS  CRITICAL Resolved Shear Stress  Xtal Orientation Can Facilitate Dicloc. Motion  R = 0  = 90°   R =  /2  = 45°  = 45°  HARD to Slip  R = 0  = 90 °  HARD to Slip EASY to Slip

19 ENGR-45_Lec-17_DisLoc_Strength-1.ppt 19 Bruce Mayer, PE Engineering-45: Materials of Engineering Yield Stress, Yield Stress,  y  An Xtal Plastically Deforms When  To Get Yield Strength, Need  minimum → (cos  cos ) max  Thus  y = 2  CRSS Plastically stretched zinc single crystal.

20 ENGR-45_Lec-17_DisLoc_Strength-1.ppt 20 Bruce Mayer, PE Engineering-45: Materials of Engineering PolyXtal Disloc Motion  Slip planes & directions (,  ) change from one crystal to another   R varies from one crystal, or Grain, to another  The Xtal/Grain with the LARGEST  R Yields FIRST  Other (less favorably oriented) crystals Yield LATER 300  m

21 ENGR-45_Lec-17_DisLoc_Strength-1.ppt 21 Bruce Mayer, PE Engineering-45: Materials of Engineering Summary  Edge Dislocations  Plastic flow can occur in a crystal by the breaking and reattachment of atomic bonds one at a time This dramatically reduces the required shear stress – Consider how a caterpillar gets from A to B  A similar mechanism applies to screw dislocations  Screw & Edge dislocations often occur together

22 ENGR-45_Lec-17_DisLoc_Strength-1.ppt 22 Bruce Mayer, PE Engineering-45: Materials of Engineering 1-Phase Metal Strengthening  Basic Concept Plastic Deformation in Metals is CAUSED by DISLOCATION MOVEMENT  Strengthening Strategy RESTRICT or HINDER Dislocation Movement  Strengthening Tactics 1.Grain Size Reduction 2.Solid Solution Alloying 3.Strain Hardening 4.Precipitation (2 nd -ph)

23 ENGR-45_Lec-17_DisLoc_Strength-1.ppt 23 Bruce Mayer, PE Engineering-45: Materials of Engineering Strengthen-1  G.S. Reduction  Grain boundaries are barriers to slip due to Discontinuity of the Slip Plane  Barrier "Strength“ Increases with Grain MisOrientation  Smaller grain size → more Barriers to slip  Hall-Petch Reln → Where –  0  “BaseLine” Yield Strength (MPa) –k y  Matl Dependent Const (MPa  m) –d  Grain Size (m) grain boundary slip plane grain A grain B

24 ENGR-45_Lec-17_DisLoc_Strength-1.ppt 24 Bruce Mayer, PE Engineering-45: Materials of Engineering Example  GS Reduction  Calc The Hall-Petch Slope, k y, for 70Cu-30Zn (C2600, or Cartridge) Brass  Find the  ’s  Then the Slope

25 ENGR-45_Lec-17_DisLoc_Strength-1.ppt 25 Bruce Mayer, PE Engineering-45: Materials of Engineering Strengthen-2  Solid Solution  Impurity Atoms distort the Lattice & Generate Stress  Stress Can produce a Barrier to Dislocation Motion Smaller substitutional impurity A B Impurity generates local shear at A and B that opposes dislocation motion to the right. Impurity generates local shear at C & D that opposes dislocation motion to the right. C D Larger substitutional impurity

26 ENGR-45_Lec-17_DisLoc_Strength-1.ppt 26 Bruce Mayer, PE Engineering-45: Materials of Engineering Example  Ni-Cu Solid-Soln  Tensile (Ultimate) Strength, σ u, and & Yield Strength, σ y, increase with wt% Ni in Cu  Empirical Relation: σ y ~ C ½  Basic Result: Alloying increases σ y & σ u

27 ENGR-45_Lec-17_DisLoc_Strength-1.ppt 27 Bruce Mayer, PE Engineering-45: Materials of Engineering Strengthen-3  Strain Harden  COLD WORK  Room Temp Deformation  Common forming operations Change The Cross-Sectional Area: -Forging -Drawing -Rolling -Extrusion

28 ENGR-45_Lec-17_DisLoc_Strength-1.ppt 28 Bruce Mayer, PE Engineering-45: Materials of Engineering Dislocations During Cold Work Dislocations entangle with one another during COLD WORK Dislocation motion becomes more difficult  ColdWorked Ti Alloy 0.9  m

29 ENGR-45_Lec-17_DisLoc_Strength-1.ppt 29 Bruce Mayer, PE Engineering-45: Materials of Engineering ColdWorking Consequences  Dislocation linear density, ρ d, increases: Carefully prepared sample: ρ d ~ 10 3 mm/mm 3 Heavily deformed sample: ρ d ~ mm/mm 3  Measuring Dislocation Density OR length, l Volume, V  l 1  l 2  l 3 V  d 40  m d  N A Area, A N dislocation pits (revealed by etching) dislocation pit   σ y Increases as ρ d increases:

30 ENGR-45_Lec-17_DisLoc_Strength-1.ppt 30 Bruce Mayer, PE Engineering-45: Materials of Engineering

31 ENGR-45_Lec-17_DisLoc_Strength-1.ppt 31 Bruce Mayer, PE Engineering-45: Materials of Engineering CW Strengthening Mechanism  Strain Hardening Explained by Dislocation-Dislocation InterAction  Cold Work INCREASES ρ d Thus the Average  -  Separation-Distance DECREASES with Cold Work  Recall  -  interactions are, in general, REPULSIVE  Thus Increased ρ d IMPEDES  -Motion

32 ENGR-45_Lec-17_DisLoc_Strength-1.ppt 32 Bruce Mayer, PE Engineering-45: Materials of Engineering Simulation – DisLo Generator  Tensile loading (horizontal dir.) of a FCC metal with notches in the top and bottom surface  Over 1 billion atoms modeled in 3D block.  Note the large increase in Dislocation Density

33 ENGR-45_Lec-17_DisLoc_Strength-1.ppt 33 Bruce Mayer, PE Engineering-45: Materials of Engineering  -Motion Impedance  Dislocations Generate Stress This Generates  -Traps

34 ENGR-45_Lec-17_DisLoc_Strength-1.ppt 34 Bruce Mayer, PE Engineering-45: Materials of Engineering ColdWork Results-Trends  As Cold Work Increases Yield Strength,  y, INcreases Ultimate Strength,  u, INcreases Ductility (%EL or %RA) DEcreases

35 ENGR-45_Lec-17_DisLoc_Strength-1.ppt 35 Bruce Mayer, PE Engineering-45: Materials of Engineering Cold Work Example Post-Work Ductility is HAMMERED  y =300MPa % Cold Work Cu yield strength (MPa) 300MPa  What is the Tensile Strength & Ductility After Cold Working?

36 ENGR-45_Lec-17_DisLoc_Strength-1.ppt 36 Bruce Mayer, PE Engineering-45: Materials of Engineering WhiteBoard Work


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