Handout 4: Part 2 Flashcards
For analytical methods, we approximate the uniaxial stress-strain curve as what?
We approximate the uniaxial stress-strain curve as rigid perfectly-plastic (i.e. neglect elastic strain, and assume a constant yield stress).
What is the “hydrostatic” stress defined as
What dictates wether metals yield?
The hydrostatic stress has no effect on yielding in metals (although it does affect yielding in polymers, and also affects fracture). We can separate any stress state into its hydrostatic and deviatoric components:
The yield criterion becomes a condition about the deviatoric stress tensor – i.e. yield occurs when some function of the deviatoric stress tensor reaches a critical value.
Derive and show the relationship between pure shear k and the yield stress for both yield criterias (Von Mises and Tresca’s)
What must the plastic strain increments add up to if plastic deformation conserves volume?
What is the Levy-Mises flow rule?
The Levy-Mises flow rule states that the plastic strain increment in each principal direction is proportional to the deviatoric stress component in that direction i.e.
What are the assumptions made under plane strain conditions?
Use the Levy-Mises flow rule to explain what it tells you about the stresses in the plane strain metal.
In plane strain, one dimension of the deforming geometry is much larger than the others and there is no strain in that direction (giving 2D, in-plane deformation).
Plane strain is a common simplifying assumption in forming, e.g. for rolling, slab extrusion or drawing, some forging problems, and machining.
Explain how back tension on dies helps improve wear of the die.
What are the two rolling mill designs?
Reversing mill: material passes backwards and forwards through the same mill stand, which is incrementally closed before each pass. Used for “breakdown” rolling of ingot/thick slab, and for section rolling.
Tandem mill: several mill stands (typically four) in connected series. Used for strip/sheet/foil, i.e. stock material that is thin enough to be coiled after rolling. The strip accelerates considerably as its thickness is reduced (due to conservation of volume).
What are som tactics to reduce rolling loads?
To reduce rolling loads:
- reduce yield stress Y (i.e. hot rolling)
- reduce friction m (but note that some friction is required to draw in the strip)
- make small reductions per pass hi - ho (and tandem roll)
- reduce roll radius R
What are the effects of front and/or back tension in rolling?
- reducing the pressure needed to cause yielding (as in sheet/wire drawing)
- reducing the magnitude of the friction hill (and shifting the neutral plane)
- reducing the rolling load, torque and power
State upperbound theorem
- 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).
What is the equation that gives an estimation of the temperature rise during deformation processing?
How accurate is this approach?
- The assumption of adiabatic heating will lead to an over-estimate, since there will be some heat loss to the tooling.
- If all of the heating occurs in primary shear zones, through which all the material passes, the temperature rise will be reasonably uniform. But if significant heating occurs in secondary shear zones at the surface (i.e. due to friction on the tooling), a temperature gradient will be set up, and the peak temperature rise will be higher than the average value calculated.
How do you asses weather there is time for temperature gradients to even out in a material during material deformation?
