Why are nanocrystalline materials stronger? Explain answer based on dislocation

activity. 5 points

As grain size decreases, grain boundary density increases which can prevents slip and the ability of the metal to resist movement of dislocations increases. Any produced dislocations will quickly pile up at the boundaries and create dislocation entanglement resulting in increased strength of the metal.

1. What are the five important factors that affect the recrystallization process in metals?

5 points

1. the extent of deformation of the metal prior to recrystallization;

1. the temperature used for the recrystallization process;

1. the length of time of the recrystallization process;

1. the initial grain size of the metal;

1. the composition of the metal, in terms of metal purity.

4. Consider casting a cube and a sphere on the same volume from same metal. Which one would solidify faster? Why? 5 points

For a cube and a sphere of the same volume (4π/3R3=a3)

R = 0.62 a

Radius of the sphere side of the cube

Surface area of the sphere = 4πR2 = 4.82a2

Surface area of the cube = 6a2

Since the cube (of the same volume as the sphere) has a larger surface area, it will lose heat more rapidly and will cool faster.

4. Why is it difficult to improve both strength and ductility simultaneously? 5 points

One can improve strength by i) applying higher %CW, ii) introducing impurities, iii) reducing grain size, iv) applying heat treatment procedures. However, all of the above approaches will result in a reduction of dislocation motion either due to interaction/interference with existing dislocations, grain boundaries, impurity elements in the solvent matrix, and or harder second phase. The ensued reduction in dislocation motion will strengthen the material but at the same time reduces the amount of plastic/permanent deformation in the materials, resulting in brittle fracture behavior upon continued loading.

Bonus questions: –10 points

0. Why are cast metal sheet ingots hot rolled first instead of being cold rolled?

Hot rolling is applied first because it is more efficient in reducing ingot sheet thickness than cold working.

0. Why does slip in metals usually take place on closed packed planes and in closed packed directions?

Slip usually takes place on the most densely packed planes because the atoms on these planes are in close proximity and hence require less shear energy for displacement.

Slip typically occurs along the closest-packed directions because minimal energy is required to force the atoms to change positions.

1. (a) Explain the three stages of annealing treatment in 2-3 sentences each.

(b) Explain any five properties that we can measure using a stress-strain curve under

uniaxial tensile loading. 10 points

1. Recovery: reduction in the dislocation density by annihilation of dislocations; rearrangement of atoms to form perfect crystal lattice; atoms diffuse to regions of tension.

Recrystallization: new strain free and equiaxed grains form that have low dislocation densities and small size; eventually all cold work is consumed; parent cold-work grains are replaced

Grain growth: small grains shrink and ultimately disappear; large grains continue to grow; at longer times, average grain size increases.

1. Modulus of elasticity: stress divided by strain in the elastic region of an engineering stressstrain diagram

Poisson’s ratio: the ratio of lateral strain and axial/linear strain

Yield strength: the stress above which permanent deformation just begins

Ultimate tensile strength: the maximum stress in the engineering stress-strain curve before material fractures

Ductility: it is a measure of degree of plastic deformation that has been sustained at fracture Modulus of resilience: it is the strain energy per unit volume required to stress a material from an unloaded state to point of yielding

Toughness: a material property indicative of its resistance to fracture when a crack is present

2. What are the 4 strengthening mechanisms of metals? Explain each mechanism in 4-5 sentences. 10 points

Reduction in grain size: Grain boundaries are barriers to slip. Barrier “strength” increases with increasing angle of misorientation. Smaller the grain size more the barriers to slip.

Solid solution strengthening: Impurity atoms distort the lattice & generate lattice strains. These strains can act as barriers to dislocation motion. 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. Large impurities tend to concentrate at dislocations (regions of tensile strains).

Precipitation hardening: Hard precipitates are difficult to shear. Large shear stress is required to move a dislocation toward a precipitate and shear it. Dislocation moves around and advances but the precipitate acts as pinning sites.

Work hardening: Deformation at room temperature (for most metals). Common forming operations reduce the cross-sectional area. Processes such as forging, drawing, rolling, extrusion involved in inducing cold work. Dislocation density increases and dislocations accumulate along the defects such as grain boundaries increasing the plastic deformation before fracture thus strengthening the material.