ME 330 Engineering Materials Lecture 9 Dislocations & Strengthening Mechanisms Strengthening Mechanisms Grain boundary Refinement Solid-solution Hardening Precipitation Hardening Strain Hardening Cold Work Annealing and Recrystallization Please read sections 7.8-7.13

Making the Connection We have learned ... Theoretical strengths are not met for engineering materials Dislocations ease deformation of material Carpet ruck, caterpillar locomotion, planking boards …. Allow planes of atoms to move at lower stresses than predicted Results in permanent deformation prior to tensile failure Today, we will look at how we can regain some strength No dislocations, no plastic deformation If dislocations cannot move, no plastic deformation No plastic deformation, close in on theory But … we loose something … deformation How do we get it back?

Strengthening Mechanisms Eliminate dislocations No mechanism for plastic deformation in metals Whiskers and fibers Eliminate dislocation movement If they can’t move, they can’t carry plastic deformation Introduce barriers to movement Grain boundaries Solid-solution strengthening (alloying) Precipitates can pin dislocations Increase dislocation density Solutes cause multiplication Strain hardening Cold work

Dislocation Interactions Dislocations have built-in stress/strain fields Explains interactions (repel, immobilize) Unless dislocations are of opposite sign, on same slip plane, interaction will cause changes in microstructure Same is true if dislocations interact with some other lattice distortion Grain boundary Solid solution particles Precipitates Slip Planegrain2 Grain Boundary Slip Planegrain1 T C C T T C

Grain Boundary Strengthening Slip Planegrain2 Slip Planegrain1 Grain Boundary Remember: Dislocation motion impeded at grain boundaries Dislocation has to change slip planes in different grains Boundaries posses atomic scale disorder - pins dislocation Smaller grains provide more barriers to dislocation motion - stronger, harder, tougher

Hall-Petch (or Petch-Hall) Yield strength related to grain size o = lattice resistance to motion ky =dislocation locking term d = average grain size Empirical fit! May not hold for very large or small grained materials Dislocation pile-up effects also important at: Phase boundaries Twin boundaries As grains get smaller, Strength increases Toughness increases so k Intrinsic lattice resistance is quite a bit higher for BCC than FCC/HCP … that is why BCC is not 4x as ductile. Same for FCC and HCP note we are plotting inverse root of grain diameter … as we move right, grains are getting smaller From: Hertzberg, p.455

Dislocations & Strengthening Dislocation motion limits strength To increase strength Remove dislocations Don’t allow them to move Impede dislocations with point, line, or planar obstacles “whiskers” Cold worked metals Tensile Strength (MPa) Annealed metals Dislocation Density 100 106 1012

“Whiskers” Extremely small, thin, defect free No dislocations to carry plastic deformation Usually metallic or ceramic Single crystal, may be grown around screw dislocation Applications primarily in composites

Solid Solution Hardening Impurity (alloying) elements are incorporated into crystal structure in orderly manner. Can have substitutional or interstitial solid solutions Substitutional alloys formed when Same crystal structure Atomic sizes are similar Often two or more metals Interstitial alloys usually formed when Alloying agent is of much smaller atomic size Carbon, nitrogen, oxygen in metal Common Alloys Steel Iron, <2% Carbon Gold 18K 75% Au 20% Ag 5% Cu 14K 58% Au 22% Ag 20% Cu Brass 60 – 80% Cu 20 – 40% Zn Bronze 60 – 70% Cu 30 – 40% Sn Stainless Steel 74% Fe 18% Ni 8% Cr

Definitions Alloy – metals which are not pure; impurities are added intentionally Solvent – element or compound present in greater amount (host atoms) Solute – element present in minor concentration Solid solution – addition of impurity into metal solute atoms are added to the host material crystal structure is maintained no new structure is formed atoms are intermixed so composition is uniform (liquid analogy: mixing of two liquids) Two types of solid solutions Substitutional solution – solute atoms replace or substitute host atoms Interstitial solution – impurity atoms fill voids or interstices Read Section 4.3

Substitutional solution Atomic size factor – difference in atomic radii is less than 15% Crystal structure – should be same for solute and solvent atoms Example: copper and nickel Radius of copper = 0.128 nm Radius of nickel = 0.125 nm Both have FCC structure Interstitial solution Atomic diameter of intersticial impurity atoms is much smaller that of host atoms Example: Carbon added to iron Radius of carbon = 0.071 Radius of iron = 0.124

Compositions In wt% In at% nm1 = number of moles m1 and m2, weights (or masses) In at% nm1 = number of moles A = atomic weight

Conversion of atom percent to weight percent Eqn 4.7 Conversion of weight percent to atom percent Eqn 4.6

Solid Solution Strengthening Interstitials and solutes distort the lattice Introduce lattice strains Solutes diffuse toward dislocations Stress fields interact with dislocations Lattice strains increase if dislocations are torn from solutes Greater stress necessary to initiate movement (i.e. higher yield) Greater stress to continue deformation (i.e. more hardening) For solid solutions, larger size mismatch  larger induced stresses Solute Tension Compression Interstitial

Effect of Alloying Strength (tensile and ultimate) increases 70 Copper-Nickel Brass (Copper-Zinc) 400 60 UTS, MPa 50 300 Elongation, % 40 30 200 20 25 50 Nickel / Zinc, % 25 50 Nickel / Zinc, % Strength (tensile and ultimate) increases Hardness increases Ductility can increase or decrease Modulus remains unchanged!

Precipitation Hardening Precipitates form when solubility of a particular impurity is low Solubility usually increases with temperature Add second phase to saturation (or less) at high temperature Cool to room temperature and impurity will precipitate out to form a second phase Rate of cooling is critical … need precipitation time (aging) to give ideal properties i.e. aluminum alloys -T4, -T6 indicates different aging conditions Precipitates act to impede dislocation motion If dislocations loop, multiplication occurs (Frank-Reed, Orowan) If dislocation cuts through precipitate, loses a lot of energy Looping and cutting can occur simultaneously

Strain Hardening Metal strengthens and becomes harder through “cold work” Also known as “work hardening” (brass specimen in lab): Self-feeding process Dislocations multiply, Average spacing decreases Motion is impeded Dislocations multiply Stress needed to move dislocations goes up  (MPa) E  (%) Power-law hardening

Strain Hardening in Industrial Processes Cold Rolling: Large change in cross-sectional area Changes size of grains Work hardens material by strain hardening % Cold Work Sheet metal forming Very large strains at corners t r

Cold Rolling Ao Af Equiaxed grains Low dislocation density Elongated Grains High dislocation density

Mechanical Properties & Cold Work 75 1000 Cu 800 1040 Steel 50 600 Brass Elongation, % Tensile Strength, MPa Brass 25 1040 Steel 400 Cu 200 25 50 75 % Cold Work 25 50 75 % Cold Work Cold Work  Higher strength, lower ductility

Strengthening Methods Specifically for Metals & Alloys Adapted from: N.E. Dowling, Mechanical Behavior of Materials, Prentice Hall, 1993, p. 52

Annealing Process Cold work  dislocation interactions  high strain energy Structure wants to reduce total energy Raise temperature  facilitates atomic motion Material is heated to a high temperature and held for time: Atoms to rearrange themselves into a lower energy state Diffusion driven process Governed by both time and temperature: High temperatures and short times Lower temperatures and longer times. Removes the effects of cold work Dislocation density will decrease Grains become equiaxed. Cold work uses mechanical energy to change microstructure. However, this also locks a lot of energy in the material Annealing uses thermal energy to enable the materials to use its own stored strain energy to again reshape microstructure

Stages of Annealing Recovery Stresses around dislocations are relieved Dislocations move to lower energy configurations, annihilate Recrystallization Strained material still has trapped internal energy New equiaxed grains nucleate from dislocations Return to nearly pre-cold worked structure & mechanical properties Recrystallization temperature - complete recrystallization in 1 hour Typically Increased prior cold work will lower this temperature Will not occur unless certain level of prior cold work has been achieved Grain Growth Grains grow to reduce overall grain boundary area Grain boundaries have high energy: less boundaries  less total energy  energetically more favorable Grain boundaries migrate - atoms diffuse from one side to other Grain diameter Dislocation climb is important during recovery … slip planes change, reorient and allow for some annihilation and lower energy states cold work necessary to increase dislocatoin density and cause driving force for recrystallization

Changing Mechanical Properties Temperature/Time Effects As Annealing temperature (time) increases: Increase ductility Decrease tensile strength As temperature (time) continues to increase, grain size increases Strong relation between time & temperature Annealing a Brass Alloy for 1 hour, varying temperature

Micrographs of Annealing Process From: Callister Different materials, but same basic concept Looking at last micrograph, you should be able to tell me what kind of crystal structure this material has. Annealling twins! From: Hull & Bacon, p.178-9