Question

Question 2 A 10 mm-thick plate is decreased in thickness according to the following schedule: 5mm, 2mm, 1mm. Calculate the total strain; . once on the basis of initial and final dimensions and • once as the summation of the incremental strains, using: a. Conventional strain and b. True strain. Compare the results and comment on the significance of the differences.

Answer 1

(a) Calculate the strain in corresponding direction. Strain in x-direction. AL & = L; _L, -L - 10-10-5) 10 _ 10-5 10 = 0.5 Strain in y-direction. & = 42 Ig - L L 10-10-2) 10 10-8 = 10 = 0.2

Strain in Z-direction. _13- L 10-(10-1) S 10 10-9 10 = 0.1 Calculate the total engineering strain. &= 0.5 +0.2 + 0.1 = 0.8 (b) Calculate the true strain. True strain = In(1+&T) True strain = ln(1+0.8) = 0.5877