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Question on true strain- experimental reading

Question on true strain - experimental reading

I have an experimental set of readings from elsewhere performed on a tension tets on steel specimen.

I have the initial area and final area (area at the point at which specimen just breaks).

I see that true strain = ln (1 + epsilon) where epsilon is engineering/nominal strain

This is through all the set of readings except the last reading.This is fine.

The last reading just befor the specimen breaks has the final area measured.

And the ratio between initial and final area is 2.14

The last reading for true strain is given as formula:ln( 1+1.14)

I guess from reading of all other speciment that 1.14 =  (ratio between initial and final area -1)

I'm sure I'm mssing a basic- can anyone tell how this formula is obtained from mechanics?

Matt Lewis's picture

The assumption is that volume is conserved (incompressibility).  In this case, the true axial strain, defined as ln((final length)/(initial length)), will be equal to ln((initial area)/(final area)) because (final length)*(final area) = (initial length)*(initial area).

Matt Lewis
Los Alamos, New Mexico

Reza Mousavi's picture

Hi!You can refer to http://imechanica.org/node/6797

About your problem: In the section of your element, we have A as primary area and change in area is dA then

A1=A+dA

(A+dA)/A= (1+dx/x) (1+dy/y)

dx/x=dy/y =>  (A+dA)/A=(1+dx/x)2

ln(1+dA/A)=2ln(1+dx/x)=2εxx

ln(2.14)/2=εxx

So, supposing I do not measure the changed area at every instant during an experiment but measure the area at start of the test and at the end of the test-i.e. as Matt Lewis said,I'm assuming icompressibility.

Then can we say (I think we can) that the true stress computed just before failure as :

true stress = nominal_stress*ln(1+{ Initial area - final area/ initial area}) is the realistic stress measure for true stress-considering the assumption of incompressibility?

So, that in true stress vs true strain plot from the point of initiation of necking (wherein the decrease in area is not so large) to the point of failure, I can just draw a straight line (linear).

For all the other points from zero strain to initiation of necking I use: true stress = ln (1+epsilon) where epsilon is engineering strain

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