A paper clip is made of wire 1 mm in diameter. If the original material from which the wire is made is a rod 18 mm in diameter, calculate the longitudinal engineering strain and true strain that the wire has undergone during processing.
Solution
The volume stays the same: L_0*A_0=L_1*A_1
Original length L_0 = (A_1*L_1)/A_0
Area A = (?/4)d^2
engineering strain: e = (L_1-L_0)/L_0 = (L1-((A1*L1)/A0))/((A1*L1)/A0) = ((?/4)d_0^2-(?/4)d_1^2)/(?/4)d_1^2 =
d_0^2/d_1^2 - 1 = (18mm)^2/(1.0mm)^2 - 1 = 323
true strain: ? = ln(L_1/L_0) = ln(L1/((A1*L1)/A0)) = ln(A_0/A_1) = ln(d_0^2/d_1^2) = ln((18mm)^2/(1.0mm)^2) = 5.78
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Separation of Lanthanides/ Lanthanides and Actinides
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A paper clip is made of wire 1 mm in diameter- If the original materia.docx
1. A paper clip is made of wire 1 mm in diameter. If the original material from which the wire is
made is a rod 18 mm in diameter, calculate the longitudinal engineering strain and true strain that
the wire has undergone during processing.
Solution
The volume stays the same: L_0*A_0=L_1*A_1
Original length L_0 = (A_1*L_1)/A_0
Area A = (?/4)d^2
engineering strain: e = (L_1-L_0)/L_0 = (L1-((A1*L1)/A0))/((A1*L1)/A0) = ((?/4)d_0^2-
(?/4)d_1^2)/(?/4)d_1^2 =
d_0^2/d_1^2 - 1 = (18mm)^2/(1.0mm)^2 - 1 = 323
true strain: ? = ln(L_1/L_0) = ln(L1/((A1*L1)/A0)) = ln(A_0/A_1) = ln(d_0^2/d_1^2) =
ln((18mm)^2/(1.0mm)^2) = 5.78
