. A strip of metal is originally 1.0 m long. It is stretched in three steps, fir

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Question

. A strip of metal is originally 1.0 m long. It is stretched in three steps, first to

a length of 1.2 m and then to 1.4 m, and finally to 1.6 m. Show that the total

true strain is the sum of the true strains in each step; that is, the strains can

be added. Show that, using engineering strains, the strains for each step

cannot be added to obtain the total strain. Why are these two measures of

strain nearly equal for low values, but differ disproportionately more for

higher values?

i dont know if these equations should be used or not

Young

True strain, TS1 = ln (Current Length/Original Length) = ln 1.2/1 = ln 1.2

TS2 = ln 1.4/1.2

TS3 = ln 1.6/1.4

TS1 + TS2 + TS3 = ln 1.2 + ln1.4 - ln1.2 + ln 1.6 - ln 1.4 = ln 1.6

Total TS = ln 1.6/1 = ln 1.6

so, TS1 + TS2 + TS3 = Total TS

Engineering Strain, ES1 = Change in Length/Original Length = 0.2/1 = 0.2

ES2 = 0.2/1.2 = 0.167

ES3 = 0.2/1.4 = 0.143

ES1 +ES2 +ES3 = 0.51

Total strain = 0.6/1 = 0.6 which is not equal to ES1 +ES2 +ES3

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