A force of 700 N is applied on a sample of polycarbonate with a diameter of 12 m

Question

A force of 700 N is applied on a sample of polycarbonate with a diameter of 12 mm and a length of 123 mm.   a) calculate the engineering and true stress. B) What is the length and diameter of the bar after the load is applied? What is the length and diameter after the force is completely removed? B) The same part is loaded completely in tension until it breaks. The length at the time of fracture is 215.7 mm and the diameter 2.7 mm. Calculate the Cauchy, Hencky, Green and Almansi strains at the point of fracture. Can the Cauchy strain be a good predictor of strain in this case? Explain. C) Did the sample experience significant necking? Explain.

Explanation / Answer

given force F = 700 N

diameter, d = 12 mm = 12*10^-3 m

length, l = 123 mm = 123*10^-3

a) Engineering stress, E = 4F/pi*d^2 = 4*700/pi*(12*10^-3)^2 = 6189358.8980 Pa

let the poission's ratio be v, youngs modulous be Y

then increase in diamter = (dd)

decrease in length = -dl

also, strain = dl/l

so,

stress / strain = Y

E*l/dl = Y

dl = El/Y

hence

v = dd/dl = dd*Y/El

so, true stress = 4F/pi(d - dd)^2 = 2800/pi(12*10^-3 - vE*123*10^-3/Y^2)

where v is poissions ratio

Y is youngs modulus

E is engineering stress

b) after the load is applied

length = l - dl = l - El/Y

diameter = d - dd = d - vEl/Y

c) cauchy strain = (l - l')/l = (215.7 - 123)/123 = 0.7536

hencky strain = ln(l'/l) = ln(215.7/123) = 0.5617

Green Strain = 0.5(l'^2 - l^2)/l^2 = 1.037

Almaansi strain = 0.5(l'^2 - l^2)/l'^2 = 0.337

he logarithmic strain provides the correct measure of the final strain when deformation takes place in a series of increments, taking into account the influence of the strain path

hence hencky strain is thed best spproximation of the true strain

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