GATE 2020 MT – Question 36
In the shown edge-dislocation configuration, X and Y are fixed 2h apart on one slip plane. Z can glide on a parallel plane h away. All have identical Burgers vectors. Which describes the stability of Z at positions 1, 2 and 3?
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: (A) 1 unstable equilibrium; 2 unstable; 3 unstable.
Explanation
For a same-sign edge dislocation, glide force at relative coordinates (x,h) is proportional to $g(x/h)$, with $g(u)=u(u^2-1)/(u^2+1)^2$. Set X at 0 and Y at 2h. At position 1, x = h, the two forces vanish individually, but the derivative of their sum is positive, so a displacement is amplified: unstable equilibrium. At position 2, x = 2h, the force from X is positive and nonzero; at position 3, x = 3h, it is also positive. Neither is a stable equilibrium. Thus A.