Dislocations and Strenghtening

, Dislocations and strengthening mechanisms

Dept. of Production Engineering 1

Dislocations and StrengtheningWhat is happening during plastic deformation?

Chapter Outline

Dislocations and Plastic Deformation Motion of dislocations in response to stress Slip Systems Plastic deformation in single crystals polycrystalline materials

Strengthening mechanisms Grain Size Reduction Solid Solution Strengthening Strain Hardening

Recovery, Recrystallization, and Grain Growth

Not tested: 7.7 Deformation by twinning,Direction and plane nomenclature in 7.4.



How do metals plastically deform?Why does forging change properties?Why deformation occurs at stresses smallerthan those for perfect crystals?

Introduction

Taylor, Orowan and Polyani 1934 :

Plastic deformation due to motion oflarge number of dislocations.

Plastic deformation under shear stress



Top of crystal slipping one plane at a time.

Only a small of fraction of bonds arebroken at any time.

Propagation of dislocation causes top halfof crystal to slip with respect to the bottom.

The slip plane crystallographic plane ofdislocation motion.

Dislocations allow deformation at much lower stress than in a perfect crystal



Direction of Dislocation Motion

Mixed dislocations: direction is in between paralleland perpendicular to applied shear stress

Edge dislocation line moves parallel to applied stress

Screw dislocation line moves perpendicular to applied stress



Strain Field around Dislocations

Edge dislocations compressive, tensile, andshear lattice strains.

Screw dislocations shear strain only.

Strain fields from distortions atdislocations: Drops radially with distance.



Interactions between Dislocations

Strain fields around dislocations causethem to exert force on each other.

Direction of Burgers vector Sign

Same signs Repel

Opposite signs Attract (annihilate)



Dislocation density dislocation length/ volume OR number ofdislocations intersecting a unit area.105 cm-2 in carefully solidified metalcrystals to 1012 cm-2 in heavily deformedmetals.

Where do Dislocations Come From ?

Most crystalline materials have dislocations due tostresses associated with the forming process.

Number increasesduring plasticdeformation.Spawn from

dislocations, grainboundaries, surfaces.

Picture is snapshot fromsimulation of plasticdeformation in a fcc singlecrystal (Cu).

See animation at http://zig.onera.fr/lem/DisGallery/3D.html



Slip SystemPreferred planes for dislocation movement(slip planes)Preferred crystallographic directions(slip directions)Slip planes + directions (slip systems)highest packing density.

Distance between atoms shorter than average;distance perpendicular to plane longer thanaverage. Far apart planes can slip more easily.BCC and FCC have more slip systems compared toHCP: more ways for dislocation to propagate FCC and BCC are more ductile than HCP.



Slip in a Single Crystal

Each step (shear band) resultsfrom the generation of a largenumber of dislocations andtheir propagation in the slipsystem

Zn



Resolving (Projecting) Applied Stress onto Slip System

Dislocations move along particular planesand directions (the slip system) in responseto shear stresses along these planes anddirections Applied stress is resolved ontoslip systems?

= coscosR

Resolved shear stress,R,

Deformation due totensile stress, .



Slip in Single Crystals Critical Resolved Shear Stress

Resolved shear stress increases crystal will startto yield (dislocations start to move along mostfavorably oriented slip system).Onset of yielding yield stress, y .Minimum shear stress to initiate slip:Critical resolved shear stress:

( )MAXyCRSS coscos =

Maximum of (cos cos) = = 45o cos cos = 0.5 y = 2CRSS

( )MAXCRSS

ycoscos

=

Slip occurs first in slip systems oriented close to

( = = 45o) with respect to the applied stress



Plastic Deformation of Polycrystalline Materials

Grain orientations with respect to appliedstress are typically random.Dislocation motion occurs along slipsystems with favorable orientation(i.e. highest resolved shear stress).

Cu




Larger plastic deformation corresponds toelongation of grains along direction ofapplied stress.

Before After




Polycrystalline metals are typicallystronger than single crystals. WHY?

Slip directions vary from crystal tocrystal Some grains are unfavorablyoriented with respect to the applied stress(i.e. cos cos low)

Even those grains for which cos cos ishigh may be limited in deformation byadjacent grains which cannot deform soeasily

Dislocations cannot easily cross grainboundaries because of changes indirection of slip plane and disorder atgrain boundary



Strengthening

The ability of a metal to deform depends onthe ability of dislocations to move

Restricting dislocation motion can makematerial stronger

Mechanisms of strengthening in single-phase metals:

grain-size reduction

solid-solution alloying

strain hardening

Ordinarily, strengthening reduces ductility



Strengthening by grain-size reduction (I)

Small angle grain boundaries are not veryeffective.

High-angle grain boundaries block slip andincrease strength of the material.

Grain boundaries are barriers todislocation motion: slip plane discontinuesor change orientation.



Strengthening by grain-size reduction (II)Finer grains larger area of grain boundaries toimpede dislocation motion: also improvestoughness.Hall-Petch equation:

o and ky constants for particular materiald is the average grain diameter.

d determined by rate of solidification, by plasticdeformation and by heat treatment.

dk y0y +=

70 Cu - 30 Znbrass alloy



Solid-Solution Strengthening (I)

Alloys usually stronger than pure metals

Interstitial or substitutional impuritiescause lattice strain and interact withdislocation strain fields hinder dislocation motion.

Impurities diffuse and segregate arounddislocation to find atomic sites more suitedto their radii:Reduces strain energy + anchors dislocation

Motion of dislocation away from impurities moves it to region where atomic strains are greater



Solid-Solution Strengthening (II)

Smaller and larger substitutional impurities diffuse intostrained regions around dislocations leading to partialcancellation of impurity-dislocation lattice strains.

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Dislocations and Strenghtening