3 Wrought Alloys

Question 1

What temp range is used for hot working

Answer 1

0.5-0.95 Tm

Question 2

What governs the deformation in cold and hot working

Answer 2

Plastic yielding and high strain rate creep respectively

Question 3

What mechanisms do carbon steel and Al alloys undergo in hot working

Answer 3

Dynamic recrystallisation and Dynamic recovery respectively.

Carbon steels undergo dynamic recrystallisation – new grains forming, growing, work hardening, and recrystallising in a continuous cycle: flow stress peaks then falls.

Al alloys (right) undergo dynamic recovery – dislocation accumulation (work-hardening) 
balanced by dislocation annihilation (recovery): flow stress reaches a constant steady-state.  

Dynamic means during forming
Static would be after forming

Question 4

3 steps to age hardening heat treatable Al alloys

Answer 4

1. Solution heat treat in single phase region
2. Quench to get supersaturated solid solution
3. Age at a temp in 150-250 degree range (artificial ageing) or room temp (natural ageing)

Question 5

What is the tresca yield criterion

Answer 5

Yield occurs when the maximum shear stress reaches a critical value.

Question 6

What is the Von misses yield criterion

Answer 6

According to the von Mises criterion, yield occurs when the elastic shear strain energy reaches
a critical value

Question 7

What is the purpose of a yield criterion

Answer 7

The yield criterion defines the limit of elasticity under any possible combination of stresses.

Question 8

What is the principle for finding the forging load with equilibrium analysis

Answer 8

Find pressure distribution at die face p(x) and integrate. Use a force balance element and apply boundary conditions to the integral.

Remember the stress state sigma(x) is non uniform with x

Longer form:

1. Assume a set of (approximate) principal directions.
2. Assume a friction law. The usual choices are : Frictionless (τ = 0), Coulomb
   friction (τ =μp), or sticking friction (τ = k, where k is the shear yield stress.)
3. If the stress state is not uniform, consider the equilibrium of an element to get a
   differential equation relating stresses in the direction of variation.
4. Assume a flow rule and yield criterion. (N.B. the difference between von Mises and
   Tresca amounts to only 15% difference in the predicted stresses for plane strain).
5. Use the flow rule and yield criterion to relate the principal stresses.
6. Decide which principal stress is required for the problem in hand – e.g. for the vertical
   forging load we needed p(x). Thus we eliminated the other unknown stress 
   give a differential equation in the required stress, p.
7. Solve for the variation of this stress in the x direction by integrating subject to
   appropriate boundary conditions.
8. For loads on the tooling, integrate the pressure over the tool area.

Question 9

What is the basis behind the upper bound theorem

Answer 9

Propose any mechanism of plastic collapse of a body and estimate the
load required by equating the internal rate of energy dissipation to the rate at which the external loads do work; the estimated load will then be above or equal to the correct value (i.e. it will represent an upper bound).

Question 10

What are the equations for internal and external power in upper bound analysis

Answer 10

External power - F x V

Internal power: sum at each different interface: Interface area x shear yield stress k x relative sliding velocity at interface. (Found using a velocity diagram)

Remember to use the symmetry of the problem to reduce the number of shear planes to be considered, e.g. in the forging problem, take two mirror planes to split the problem vertically and horizontally – and consider the horizontal mirror plane to be stationary.

Question 11

How do we find the best upper bound

Answer 11

Found when F is minimised with respect to the variable that represents the depth of yielding. Therefore differentiate and set =0