Questions

Quick questions

You should be able to answer these questions without too much difficulty after studying this TLP. If not, then you should go through it again!

1. A cubic close-packed (cubic F) metal is deformed under tension. The tensile axis lies along [2 -3 1]. What is the primary slip system?

   	a	[0 -1 1] (1 -1 -1)
   	b	[0 1 1] (1 -1 1)
   	c	[1 -1 0] (1 1 -1)
   	d	[1 1 0] (1 -1 1)

2. Cadmium is hexagonal close-packed and slips on <100>{001} slip systems. As dislocations glide in a cadmium single crystal during plastic flow, steps form at the edges of the crystal where the dislocations reach the surface. What height will the slip step arising from the arrival of one single dislocation at the surface of the crystal be, in terms of the lattice parameters a and c?

   	a	a ∗√(3/4)
   	b	a
   	c	c
   	d	a / 2

3. An amorphous solid is deformed under tension. Which of the following statements describes its behaviour best?

   	a	Dislocations glide through the material, resulting in bulk plastic deformation.
   	b	There is virtually no plastic deformation by slip, since dislocation movement through the structure is very difficult.
   	c	There is no plastic deformation by slip, since dislocations cannot exist in an amorphous material.
   	d	Dislocations can move through the solid, but there are no defined slip planes so plastic deformation tends to occur by other mechanisms.

4. In hexagonal and cubic close-packed crystal structures, slip occurs along close-packed directions on the close-packed planes. Body-centred cubic metals are also ductile through the mechanism of slip, but they have no close-packed planes. What slip systems do b.c.c. crystals slip on?

   	a	<1 -1 1>{110}
   	b	<1 -1 1>{111}
   	c	<1 -1 0>{110}
   	d	<001>{110}

Deeper questions

The following questions require some thought and reaching the answer may require you to think beyond the contents of this TLP.

5. Find the Schmid factor for the primary slip system in a cubic close-packed single crystal when the tensile axis is parallel to [3 4 -1].

6. This question refers to the exercise involving deformation of a cadmium single crystal.

   The experimental data from the experiment are given in the table below. The angles φ and λ at the two stages of elongation were measured from the diagrams in the exercise.

   Determine what the values of φ and λ must have been in the crystal before deformation. (Assume that only one slip system operated.) The values of lcosφ and lsinλ have been calculated for you.

   Percent strain	Sample length / mm	φ	lcosφ / mm	λ	lsinλ / mm
   0 %	l0 = 18	φ0	l0cosφ0	λ0	l0sinλ0
   40 %	l1 = 25	φ1 = 60°	l1cosφ1 = 12.5	λ1 = 30°	l1sinλ1 = 9.3
   100 %	l2 = 36	φ2 = 75°	l2cosφ2 = 9.3	λ2 = 15°	l2sinλ2 = 12.5

7. A polycrystalline sample of a cubic close-packed metal is deformed under tension along a tensile axis parallel to [134]. If the critical resolved shear stress τ_c = 95 kPa, estimate the yield stress σ_y of the sample, assuming that there are no obstacles to dislocation motion and that the grains have random orientation relative to one another.

8. Sometimes plastic deformation occurs without slip. Suggest mechanisms by which plastic deformation could occur without slip in the following circumstances:

   1. At elevated temperature with a very low strain rate.
   2. In an h.c.p. polycrystalline sample with only 3 independent slip systems.
   3. In a semi-crystalline polymer sample.