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Derive an expression for force as a function of bar length

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Reference no: EM13947622

Calculate the total force required to plastically deform a metallic nanobar of circular cross section taking into account the surface energy Es in the case that the length y of the nanobar increases and its cross section α2(y) homogeneously decreases.

What are the bulk and surface contributions to this force in terms of critical stress for material flow (yield stress) and surface energy density g ?

The work required for plastic elongation of the cylinder on Δy is:

Ey = Πα2σyΔy, σy = G/30 is the yield stress and the work required to extend the surface is:

αo2(y) = Es = γ2ΠαΔγ, γ ≈ 1 J/m2 G ≈ 30GPa

1588_Determine the length of the bar.png

a. Derive an expression for the force as a function of bar length y if the length and cross section before deformation are yo and αo2 respectively. Hint: use volume conservation of the bar and the expression for the force:

dV/dy = dya2(y)/dy = 0

and the expression of force:

F = -d(Ev + Es)/dy

Determine the length of the bar at which surface contribution to the force is equal to the bulk contribution. What is a equal to in this case?

Reference no: EM13947622

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