MSE 382- Chp. 5

Aging induced precipitates on WH

Aging of Cu alloys induces greater WH rate

Work (strain) hardening exponent

'n'- n<1. Material's content that is used in calculations for stress-strain behavior in work hardening. 0= plastic solid 1= elastic solid

Microalloyed steels

- Add carbide former elements (Nb, Cr etc.) - Carbide forms along GBs, prohibits grain growth --> smaller d - Strengthening arises from smaller d, and carbides

Small impurity atoms

Attract disl line which reduces disl line energy. Negative interaction energy.

Non-deforming particle hardening

Dislocation bowing mechanism. - Disl bowing occurs when spacing between particles exceeds a certain size or when particle-matrix interface is disordered. - Cutting stress increases with radius, bowing stress decreases with radius

Strain hardening

Ductile materials become harder as it plastically deforms - disl density increases during CW - average distance between disl decreases - repulsion force between dislocations - dislocations form tangles, forest, jogs - disl movement more difficult towards hardening

Deforming particle hardening- Chemical hardening

Due to create of new interfaces between matrix and particle.

Size effect on interactive energy

FOR EDGE DISL solute interactions - Smaller impurity atoms above plane have negative interaction energy because small atoms reduce disl. - On average, interaction energy between edge disl. and small solute atoms is negative

Deforming particle hardening- Coherency hardening

Harmonic, lattice parameter difference between alpha and beta. 3 TYPES of INTERFACES 1. Coherent --> atoms match up one-to-one on boundary. Small lattice distortion (<2% lattice parameter). Highly contrained interface. 2. Incoherent --> no coherency strains. Large distortion, >5% lattice parameter 3. Semi-coherent- coherency trains partially relieved. Misfit disl.

Solid solution hardening

Improving the strength of metal by adding solute atoms to impede dislocation movement. - Solutes increase strength due to solute-disl interactions - Small impurity atoms --> neighbors in tension - larger impurity atoms --> neighbors in compression

Incoherent vs. coherent precipitate

Incoherent- matrix is intact Coherent- matrix is distorted

Impact of Cold Working

Increasing CW: - increased yield strength - increased tensile strength - decreased ductility/ % elongation

Microscopic vs. Macroscopic Yielding

Microscopic-- activation of disl. in one grain, very localized. Macroscopic- activate disl. in neighboring grain

Strong vs. Weak Obstacles

Obstacle strength determines flow stress. Strong- resist disl. penetration Weak- straighter disl. line As obstacle strength decreases, the critical extrusion angle increases.

Strengthening

Resist the migration of dislocations

Deforming particle hardening- Modulus hardening

Origin from modulus mismatch- disl cuts through particle and travels through matrix. Changes disl line energy.

Oxide particles on work hardening

Oxide particles induce significant work hardening due to GNDs. High WH rate beneficial to improve ductility. From Cu to Cu-BeO (non-deformable particle) increased yield strength and WH. From Cu to Be (deformable particle) increases yield strength but not WH

Hall-Petch equation

Says yield strength of a polycrystalline increases linearly with d^-1/2 . Yield strength and grain size inversely proportional, so decreasing grain size will make material stronger. Ky large for BCC, HCP and Ky small for FCC

Screw disl interactions

Screw disl interact very little with impurity atoms. Screw disl generate shear stress

GB strengthening- mechanism 1

Slip discontinuity leads to GB strengthening, activation of disl. source in neighboring grains. Hall-petch relation. - Strengthen materials by changing their average grain size. Grain boundaries influence dislocation movement and can activate dislocations in neighboring grains.

Modulus and interactive energy

Solute atom "softer" than solvent attracts disl. Solute atom "harder" than solvent create repulsion between disl. and solute atom.

Temperature and flow stress

Temperature dependence on flow stress is dependent on the force-distance curve. Lattice vibrations create this temperature dependence on flow stress. Greater temp, the greater reduction in applied force.

Strain-gradient hardening- size effect

Tension of wires show little size dependence Torsion show obvious size effect due to GNDs - Fine wires twisted to the same extent of large diameter wires require significantly higher torque to deform. This is because fine wires have large strain gradient and form geometrical dislocations to accommodate this. Torque-twist curves are dependent on wire size because plastic strain varies linearly from wire axis to perimeter

Why would smaller impurity atoms stay in the upper plane of disl and larger atoms say in the lower plane of disl?

This cancels out the stress field

Deformation of two phase alloys

When t/d is small, the flow stress of brazing materials increases

GB strengthening- mechanism 2

When σ > σy, disl emission from GBs μ - total length of disl per unit area of GB Disl. density at yielding ρc = 3 μ/d In general K is large for bcc, hcp; small for fcc