b100 Screw edge b b100 A 20 points Find the distribution of

b(1,0,0) Screw edge b b(1,0,0) (A) (20 points Find the distribution of forces along the length of the screw (xi). [Hint: the figure on the right shows how the stresses change around the edge dislocation.] (B (20 points Plot this distribution. Clearly mark the zeros and maxima/minima (both the values and locations). (C)(10 points Now follow the motion of the screw dislocation and show how the screw will look like after a sufficiently long time. Mark the relevant distance. [Note: If the (originally screw) dislocation segment rotates it becomes mixed (edge and screw). If it rotates by 90 degrees it becomes pure edge.]

Solution

The force is given b the Peach-Koehler equation:

A1= S11b1+S21b2+S31b3

A2 =S12b1 + S22b2+ S32b3

A3= S13b1+ S23b2+s33b3

where S is the stress matrix, bi the components of burger vector

f1= A2t3-A3t2

f2+A3t1-A1t3

f3= A1t2- A2t1

Given that ht eburger vector for both is [b,0,0], tscrew [0,0,1]

tedge= [0,1,0]

Hence force on the screw from the edge depends on t vector of edge

f1 = -A3t2

f2= 0

f3=A1t2

for the screw

A1 = S11b

A2 = S12 b

A3 =S13b

Substitute in the force eqns and knowing the expressions for the force field from the edge, place as S11 S12 S13

You neded to substitute these expressions with appropriate signs, knowing the orientations of b vectors and t vectors.

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