Question

(a) Explain what is meant by the Peach-Koehler force on a dislocation, and state its unit.\ Show that the Peach-Koehler force (f) is given by the resolved shear stress (\tau) times\ the Burgers vector (b), i.e. f = \tau b.\ (5 marks)\ (b) Using the following two ways, prove that the resolved shear stress needed to maintain\ a circular dislocation loop at a radius R is \tau = T/(Rb), where T is the line tension of\ the dislocation:\ (i) Consider a virtual increment of the dislocation loop radius by \delta R as shown in\ Figure Q2(a)(i). Equate the work done by the Peach-Koehler force, to the\ increment in line energy of the dislocation.\ (3 marks)\ (ii) Consider the force equilibrium of an arc of the dislocation loop as shown in\ Figure Q2(a)(ii).\ [You should answer both parts (i) and (ii).] (2 marks)

          (a) Explain what is meant by the Peach-Koehler force on a dislocation, and state its unit.\
Show that the Peach-Koehler force (f) is given by the resolved shear stress (\tau) times\
the Burgers vector (b), i.e. f = \tau b.\
(5 marks)\
(b) Using the following two ways, prove that the resolved shear stress needed to maintain\
a circular dislocation loop at a radius R is \tau = T/(Rb), where T is the line tension of\
the dislocation:\
(i) Consider a virtual increment of the dislocation loop radius by \delta R as shown in\
Figure Q2(a)(i). Equate the work done by the Peach-Koehler force, to the\
increment in line energy of the dislocation.\
(3 marks)\
(ii) Consider the force equilibrium of an arc of the dislocation loop as shown in\
Figure Q2(a)(ii).\
[You should answer both parts (i) and (ii).] (2 marks)

(a) Explain what is meant by the Peach-Koehler force on a dislocation, and state its unit.Show that the Peach-Koehler force (f) is given by the resolved shear stress (τ) timesthe Burgers vector (b), i.e. f = τb.(5 marks)(b) Using the following two ways, prove that the resolved shear stress needed to maintaina circular dislocation loop at a radius R is τ= T/(Rb), where T is the line tension ofthe dislocation:(i) Consider a virtual increment of the dislocation loop radius by δR as shown inFigure Q2(a)(i). Equate the work done by the Peach-Koehler force, to theincrement in line energy of the dislocation.(3 marks)(ii) Consider the force equilibrium of an arc of the dislocation loop as shown inFigure Q2(a)(ii).[You should answer both parts (i) and (ii).] (2 marks)

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