There is no doubt about the fact that true stain is logarithmic and engineering strain is linear.However it appears to be almost same for small deformation owing to small values in Taylor expansion.Another thing is people use the word "true" or "engineering" with stress as well.Please explain this ambiguity.
As the term 'Engineering' strain suggests, its an engineering approximation of strain. It makes your life easy in comparing mechanical properties in the broad sense. You essentially just look at change in length by original length. Similarly, Engineering stress is load divided by original cross-section area. Note that in reality, the cross section of the specimen changes continuously with application of load. The value of true stress or true strain is calculated from this instantaneous change in cross section area. Later in this answer, I will also describe how engineering stress-strain curves are also useful.
For small displacements, the values of true strain and engineering strains indeed converge. The same is true for true stress and engineering stress. This can be verified by solving some textbook numerical problems.
At large displacements, the values of true stresses and strains start diverging from their engineering counterparts. Md. Shafiqul Islaml is partially correct but his statement is true only for Uniaxial tensile tests. Since the cross section area decreases during tensile tests, the instantaneous value of stress will be consistently higher than the engineering stress for the same value of load. Conversely, since true strain is calculated by integrating the strain over the entire test, it is larger than engineering strain for the same value of displacement.
However, if you perform uniaxial compression, the instantaneous cross section area actually increases and the value of true stress will be lower than the engineering stress. True strain is however always larger than engineering strain! Hence you have to be careful.
The divergence in the values of true stress and engineering stress occurs only at large loads and displacements; or typically when the specimen is undergoing plastic deformation. That is because most materials have a elastic strain limit close to 0.2%. Note that the values of true stresses and strains are similar to their engineering counterparts below 0.2%.
Regarding your question distinguishing between the two if drawn on a piece of paper, you can follow this thumb rule.
If a material that strain hardens is tested in tension, the true stress-true strain curve will keep increasing till the specimen fails as the cross section area keeps decreasing continuously (even during necking). However, the slope of engineering stress-strain curve becomes positive and negative before and after necking respectively. This is because necking reduces the material's ability to harden and hence take larger loads. Hence the load starts dropping but remember that one still measures the stress as the load divided by the original cross section area. If the instantaneous cross section area were taken into account, as was done for true stress, the load drop is compensated by the acute reduction in cross section area.
In compression, the necking instability does not occur and this difference is not stark. the true stress-strain curve and engineering stress strain curve under compression more-or-less converge (unless specimen 'barrelling' is very prominent).
Also, the true stress-strain curves of tension and compression are the same, which is also why the term 'true' is associated with it. The value of strain appears to be independent of the loading geometry.
In retrospect, it is clear that the use of engineering stress helps in deciding how much load a specimen can take under tension before experiencing instability. It helps in detecting the onset of necking very clearly. This is why engineering stresses and strains are quite useful for engineers
Hi,
Please, refer to below book for the better understanding differences and relation between the true stain and the engineering one.
Solid Mechanics Book
by William F Hosford
Bests,
True stress is instantaneous and hence take the reduction in cross-section due to straining into consideration. It makes the true stress to be higher than engineering one. At lower strain, these effects are negligible. If you have these two stress-strain curves on a paper, the one having smaller strain and larger stress is the true one.
As the term 'Engineering' strain suggests, its an engineering approximation of strain. It makes your life easy in comparing mechanical properties in the broad sense. You essentially just look at change in length by original length. Similarly, Engineering stress is load divided by original cross-section area. Note that in reality, the cross section of the specimen changes continuously with application of load. The value of true stress or true strain is calculated from this instantaneous change in cross section area. Later in this answer, I will also describe how engineering stress-strain curves are also useful.
For small displacements, the values of true strain and engineering strains indeed converge. The same is true for true stress and engineering stress. This can be verified by solving some textbook numerical problems.
At large displacements, the values of true stresses and strains start diverging from their engineering counterparts. Md. Shafiqul Islaml is partially correct but his statement is true only for Uniaxial tensile tests. Since the cross section area decreases during tensile tests, the instantaneous value of stress will be consistently higher than the engineering stress for the same value of load. Conversely, since true strain is calculated by integrating the strain over the entire test, it is larger than engineering strain for the same value of displacement.
However, if you perform uniaxial compression, the instantaneous cross section area actually increases and the value of true stress will be lower than the engineering stress. True strain is however always larger than engineering strain! Hence you have to be careful.
The divergence in the values of true stress and engineering stress occurs only at large loads and displacements; or typically when the specimen is undergoing plastic deformation. That is because most materials have a elastic strain limit close to 0.2%. Note that the values of true stresses and strains are similar to their engineering counterparts below 0.2%.
Regarding your question distinguishing between the two if drawn on a piece of paper, you can follow this thumb rule.
If a material that strain hardens is tested in tension, the true stress-true strain curve will keep increasing till the specimen fails as the cross section area keeps decreasing continuously (even during necking). However, the slope of engineering stress-strain curve becomes positive and negative before and after necking respectively. This is because necking reduces the material's ability to harden and hence take larger loads. Hence the load starts dropping but remember that one still measures the stress as the load divided by the original cross section area. If the instantaneous cross section area were taken into account, as was done for true stress, the load drop is compensated by the acute reduction in cross section area.
In compression, the necking instability does not occur and this difference is not stark. the true stress-strain curve and engineering stress strain curve under compression more-or-less converge (unless specimen 'barrelling' is very prominent).
Also, the true stress-strain curves of tension and compression are the same, which is also why the term 'true' is associated with it. The value of strain appears to be independent of the loading geometry.
In retrospect, it is clear that the use of engineering stress helps in deciding how much load a specimen can take under tension before experiencing instability. It helps in detecting the onset of necking very clearly. This is why engineering stresses and strains are quite useful for engineers
Book: Solid Mechanics Book as well as Fundamentals of Engineering Plasticity by William F Hosford
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