Strain describes quantitatively the degree of deformation of a body. It is measured most commonly with extensometers and strain gauges. For uniaxial deformation strain can be expressed as:
Where;
L0 is the original length of the undeformed specimen,
Lf is the length of the deformed specimen.
This strain is the engineering strain, or conventional strain or nominal strain. Based on this definition, if a sample were stretched such that Lf = 2L0, the tensile engineering strain would be 100%. On the other hand, if a specimen is compressed to 1/10 times its original length then the engineering strain is: L0 – 10L0 / 10L0 = 90%or if a sample were compressed to the limit such that Lf = 0, the compressive engineering strain would again be 100%.
Awkward! These extreme examples show that for large strain the definition of engineering strain is not meaningful. Because a specimen elongating 2 times its original length has a strain measure of 100 %, a specimen compressing to 10 times smaller its original length has a strain measure of 90 % and a specimen compressing to zero length has a strain measure of 100%! Thus; we make a convenient (as well as logical) conclusion here: engineering strain definition fails for large deformation problems.
To overcome this limitation, we consider that the total deformation is divided into small increments. Considering the uniaxial case, let dL be the incremental change in gauge length and L the gauge length at the beginning of that increment. Then, the corresponding strain increment becomes;
and the total strain for a change of the gauge length from L0 to Lf
The strain defined by the above equation is the true strain or natural strain. It is a more suitable definition of strain and is particularly useful for large strain analyses. In the case of a sample being compressed to zero thickness, equation above would yield
which is a more reasonable value than the compressive strain of100% predicted by Engineering strain definition. True strain and eng
ineering strain are related by :