MATSCIE 220: Chapter 7 - Deformation and Strengthening

Dislocation Motion: slip

- A dislocation moves along a slip plane in a slip direction perpendicular to the dislocation line - The slip direction is the same as the Burgers vector direction Edge Dislocation Screw Dislocation

Microstructure after cold working

- Dislocations entangle with one another during cold work. - Dislocation motion becomes more difficult. ρ_d = total dislocation length / unit volume ρ_d: dislocation density Carefully grown single crystals → ca. 10³ mm⁻² Deforming sample increases density → 10⁹-10¹⁰ mm⁻² - Yield stress increases as ρd increases: image: Dislocation structure in Ti after cold working.

Strategies for Strengthening: Solution Hardening lattice distortion

- Impurity atoms distort the lattice & generate lattice strains. - These strains can act as barriers to dislocation motion. Smaller substitutional impurity (+strain) - Impurity generates local stress at A and B that opposes dislocation motion to the right. Larger substitutional impurity (-strain) - Impurity generates local stress at C and D that opposes dislocation motion to the right.

Example Problem: Annealing (L8S15)

A hypothetical metal alloy has a grain diameter of 1.7 ́ 10-2 mm. After a heat treatment at 450°C for 250 min the grain diameter has increased to 4.5 ́ 10-2 mm. Compute the time required for a specimen of this same material (i.e., d0 = 1.7 ́ 10-2 mm) to achieve a grain diameter of 8.7 ́ 10-2 mm while being heated at 450°C. Assume the n grain diameter exponent has a value of 2.1. A: 1110 min B: 10 min C: 0.001 min D: 5.2 x 10-6 min

Question: (L3S7)

A single crystal of zinc is oriented for a tensile test such that its slip plane normal makes an angle of 65° with the tensile axis. Three possible slip directions make angles of 30°, 48°, and 78° with the same tensile axis. (a) Which of these three slip directions is most favored? (b) If plastic deformation begins at a tensile stress of 2.5 MPa (355 psi), determine the critical resolved shear stress for zinc. 30° τ_CRSS = 0.91 MPa

Effect of Cold Working

As cold work is increased - Yield strength (σ_y) increases. - Tensile strength (TS) increases. - Ductility (%EL or %AR) decreases (% elongation you can achieve)

Annealing: Grain Growth - relation

At longer times, average grain size increases. - Small grains shrink (and ultimately disappear) - Large grains continue to grow Empirical Relation: dⁿ - d₀ⁿ = K t d: grain diameter d₀: initial diameter n: if not given assume ≈ 2 K: coefficient dependent on material and T t: elapsed time

Attractive and Repulsive: Dislocation-point Defect Interactions

Attractive: tensile + large impurity under dislocation compressive + small impurity above dislocation Repulsive: compressive + large impurity above dislocation tensile + small impurity under dislocation

Dislocation motion: Covalent Ceramics

Covalent Ceramics (Si, diamond): Motion difficult - directional (angular) bonding

Strategies for Strengthening: Reduce grain size

Grain boundaries are barriers to slip. Barrier "strength" increases with Increasing angle of misorientation. Smaller grain size: more barriers to slip

Length scales!

Grain size hardening: atomic scale Solution hardening: Cold working: atomic in one micron in another Grain: the fraction of micron to big micron to single crystal Precipitate: even bigger

Question: L2S3

If a steel specimen has a grain size of 144 microns and a yield strength of 120 MPa, what is the yield strength of the same material if its grain size decreased to 36 microns? Assume 𝜎₀ = 0. A: 140 MPa (micron)^½ B: 1440 MPa C: 1440 MPa (micron)^½ D: 240 MPa

Example Problem: cold working (L5S7)

What are the values of yield strength, tensile strength & ductility after cold working Cu? look to graphs after computing cold work

Example Problem: cold working cont. (L5S8)

What are the values of yield strength, tensile strength & ductility for Cu for %CW = 35.6%? look to graphs after computing cold work σ_y: 300 MPa TS: 340 MPa %EL: 7%

Question: L2S?

Which of the following would you expect to be a slip system for the BCC structure? A: {111}<110> B: {100}<111> C: {110}<111> D: {100}<010> ask what are closed packed planes and close pack directions

Dislocation Motion & Plastic Deformation

Metals - plastic deformation occurs by slip - an edge dislocation (extra half-plane of atoms) slides over adjacent plane half-planes of atoms. • If dislocations can't move, plastic deformation doesn't occur! When the unit step of slip occurs becomes plastic

Dislocation motion: Ionic Ceramics (NaCl)

Motion is most difficult - need to avoid nearest neighbors of like sign (- and +)

Annealing: Recrystallization

New grains are formed that: - have low dislocation densities - are small in size - consume and replace parent cold-worked grains All cold-worked grains are eventually consumed/replaced.

Strategies for Strengthening: Hall-Petch Equation

σ_yield = σ₀ + k_y d^(−½) σ_yield: yield stress (MPa) σ₀: initial stress k_y: constant-coefficient? d: diameter of the grain (m = micron*10⁻⁶)

Annealing: Recovery - Dislocation Annihilation

Reduction of dislocation density by annihilation. Scenario 1: Results from diffusion - extra half-plane of atoms exist - half plane diffuses to regions of tension - extra half-planes of atoms connect - Dislocations annihilate and form a perfect atomic plane. Scenario 2: 1. dislocation blocked; can't move to the right 2. grey atoms leave by vacancy diffusion allowing disl. to "climb" 3. "Climbed" disl. can now move on new slip plane 4. opposite dislocations meet and annihilate

Stress and Dislocation motion

Resolved shear stress, τR - results from applied tensile stresses τ_R = σ cosλ cosϕ σ = F / A τ_R = F_S / A_S F_S = F cosλ A_S = A / cosϕ σ: tensile stress F: force A: area τ_R: resolved shear stress F_S: shear force in plane A_S: slip plane area n_S: surface normal λ: slip direction (angle between F and F_S) ϕ: slip plane (angle between A_S and n_S)

The dislocation and its strain field

The fundamentals of strengthening: - There are local strain fields around a dislocation - The strain fields interact with other strain fields Compression where line defect added (-stain) Tension opposite due to stretching (+strain) Repulsion: repel if dislocation on same slip plane Attraction: attract if dislocation have opposite side. - Dislocation annihilation occurs when attracts and form perfect crystal

Annealing Cold-Worked Metals

- One hour treatment at Tanneal... decreases TS and increases %EL. - Effects of cold work are nullified! Stages of Annealing 1) Recovery - dislocation motion - annihilation 2) Recrystallize - new grains form - properties are mostly restored 3) Grain Growth - grains combine

Small impurities

- Small impurities tend to concentrate at dislocations (regions of compressive strains) - partial cancellation of dislocation compressive strains and impurity atom tensile strains - Reduce mobility of dislocations and increase strength

Strategies for Strengthening: Solution Hardening

- hardening a material by forming solid solution with it - Solid solution of B in A (ie., random dist. of point defects) Substitutional solid soln. (Cu in Ni) or Interstitial solid soln. (C in Fe)

Example Problem: Processing-property (L9S2)

A cylindrical rod of brass originally 10 mm (0.39 in) in diameter is to be cold worked by drawing. The circular cross section will be maintained during deformation. A cold-worked tensile strength in excess of 380 MPa (55,000 psi) and a ductility of at least 15 %EL are desired. Furthermore, the final diameter must be 7.5 mm (0.30 in). Explain how this may be accomplished. all of lecture just look at Lecture 9 slides...

Annealing

Can we undo irreversible plastic deformation? heating will recover pre-worked properties and alter strength and other properties

Critical resolved shear stress

Condition for dislocation motion: τ_R > τ_CRSS Ease of dislocation motion depends on crystallographic orientation (τ_R = σ cosλ cosϕ) τ maximum at λ=ϕ=45° τ_R: resolved shear stress τ_CRSS: critical resolved shear stress (typically 10⁻⁴GPa to 10⁻²GPa)

Strategies for Strengthening: Cold Working

Deformation at room temperature (for most metals). Adds dislocations to structure. Common forming operations reduce the cross-sectional area: - Forging - Drawing - Rolling - Extrusion %CW = (A₀ - A_d) / A₀ × 100 %CW: degree of cold working A₀: initial area A_d: area deformed/final

Outline

Deformation: Dislocation motion, slip systems, Shear stress. Strengthening: Strain fields around defects, Grain boundaries, Solid solutions, Work hardening, Precipitation hardening. Annealing: Recovery, recrystallization, and grain growth.

Dislocation motion: Metals (Cu, Al)

Dislocation motion easiest in metals - non-directional bonding - close-packed directions for slip

Precipitation Hardening

Hard precipitates are difficult to shear - Ex: Ceramics in metals (SiC in Iron or Aluminum). - The precipitates pin the plane in place making it more difficult to move Large shear stress needed to move dislocation toward precipitate and shear it. Dislocation "advances" but precipitates act as "pinning" sites with spacing S. σ_y ≈ 1 / S σ_y: yield strength S: average spacing between precipitate particles

Precipitation Hardening Example

Internal wing structure on Boeing 767 Aluminum is strengthened with precipitates formed by alloying.

Large impurities

Large impurities tend to concentrate at dislocations (regions of tensile strains)

Deformation Mechanisms: Slip System

Slip plane - plane on which easiest slippage occurs Highest planar densities (and large interplanar spacings) Slip directions - directions of movement Highest linear densities FCC Slip occurs on {111} planes (close-packed) in <110> directions (close-packed) - total of 12 slip systems in FCC For BCC & HCP there are other slip systems. slipsystems = distinct planes × unit vectors

Strategies for Strengthening: Precipitation Hardening

Solid solution of B in A plus particles of a new phase. Second phase particle - different composition - often different structure

Annealing: Grain Growth - temperature

T_R = recrystallization temperature

Annealing: Recrystallization - Temperatures

T_R = temperature at which recrystallization just reaches completion in 1 h. 0.3 T_m < T_R < 0.6 T_m For a specific metal/alloy, T_R depends on: - T_R decreases with increasing %CW - T_R decreases with increasing purity T_R: recrystallization temperature T_m: temperature melt

Effect of Solution Hardening

Tensile strength & yield strength increase with wt% Ni. Empirical relation: σ_y ≈ C^½ Alloying increases σ_y and TS. σ_y: yield strength C: concentration TS: tensile strength

Example: Deformation of a single crystal (L3S5) part a

a) Will the single crystal yield? no

Example: Deformation of a single crystal (L3S5) part b

b) If not, what stress is needed? >= 50.5 MPa

Annealing: Recovery

dislocations move around and annihilate

Annealing: Grain Growth

driving force to make the grains want to become larger in volume