Nanomateriales #1

1.- A FCC Cu single crystal is subjected to a uniaxial load along the [112] direction. What is/are the first slip systems? If CRSS is 50 MPa, what is the tensile stress at which Cu will start to deform plastically?

The smallest stress magnitudes to cause slip (Yielding) in   are -122 and 122 mPa, respectively.[pic 43]

Therefore, the first slip systems (Plane, direction) are then [pic 44]

2.- Sketch the following directions in a cubic unit cell:

[pic 45]

[pic 46]

[pic 47]

3.- Aluminium foil for storing food weighs around . How many Al atoms does one square inch of foil have?[pic 48]

.[pic 49]

4.- An attempt is made to produce an alloy with a yield stress of 3000 psi. Tests performed show, that a grain size of 5 μm gives a resistance of 4000 psi and that a grain size of 100 μm gives a resistance of 1200 psi. Find the alloy optimal grain size.

Using the hall-petch equation:

[pic 50]

Where σy is the yields stress, σ0  is a materials constant for the starting stress for dislocation movement (or the resistance of the lattice to dislocation motion), ky  is a materials constant for the starting stress for dislocation movement (or the resistance of the lattice to dislocation motion), and d is the average grain diameter.

For 5 μm:

[pic 51]

For 100 μm:

[pic 52]

Then we make an equivalence:

[pic 53]

[pic 54]

[pic 55]

K is replaced to obtain :[pic 56]

[pic 57]

Now it’s possible to calculate d:

[pic 58]

5.- Calculate the Schmid factor for a bcc monocrystalline rod oriented with the <100> direction parallel to the loading axis.

Given the following diagram, we know slip may occur on (111) plane and  as noted below:[pic 59]

[pic 60]

The angle between ] and  directions, λ, may be determined using the following equation:[pic 61][pic 62]

[pic 63]

Where (for [100])  and (for  , therefore,  is equal to[pic 64][pic 65][pic 66][pic 67]

[pic 68]

[pic 69]

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