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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 & Mechanical Engineer Engineering 45 Dislocations & Strengthening (1)

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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

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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?

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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

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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

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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)

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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)

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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)

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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)

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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

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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

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

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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

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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: RR =F s /A s A s RR RR F s slip direction F F s Relation between and RR RR =F s /A s Fcos A/cos slip direction Applied tensile stress: = F/A F A F

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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.

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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

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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

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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

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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.

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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

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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

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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)

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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

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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

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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

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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

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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

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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

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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:

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

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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

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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

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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

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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

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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?

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

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