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I'm confused as to what is the difference between the above said stresses and their corresponding strains. If possible can anybody explain in detail what is engineering stress

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  • $\begingroup$ A source of where you have read "engineering stress" and " true stress" may help. $\endgroup$ – Solar Mike Apr 22 '19 at 15:40
  • $\begingroup$ Actually I didn't really it anywhere, I was taught from my class , couldnt recollect it $\endgroup$ – user20200 Apr 22 '19 at 15:42
  • $\begingroup$ So, you want us to come up with what your professor said when he or she was explaining stress... $\endgroup$ – Solar Mike Apr 22 '19 at 15:43
  • $\begingroup$ Not exactly what he said, but how would you explain it in layman's terms $\endgroup$ – user20200 Apr 22 '19 at 15:54
  • $\begingroup$ See engineeringarchives.com/… $\endgroup$ – Solar Mike Apr 22 '19 at 15:56
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A tensile test of a steel rod is typically used to demonstrate the difference. Necking occurs due to the lateral contraction according to poissons ratio. Because of this, the cross section changes in area. Because the load is constant, the true stress is increases in the area where necking occurs.

Engineers base calculations off of the original cross section to keep things uniform.

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In many ductile alloys like A36 steel, the real stress versus strain curve is different by the fact that as gradually the test machine increases the tension they measure the new reduced area, due to the Poisson effect, of the sample and calculate the stress based on this reduced area. $$\sigma= \frac{Tension}{A_{reduced}}$$

But in engineering stress strain curve they assume the area of the sample stays constant as the original area and graph the apparent stress versus strain.

therefore the engineering, apparent, plot bends down after a stage called hardening while the real graph keeps rising until the rupture point.

Her is a comparison graph from Wikipedia page on Stress versus strain of A36 steel which is similar to many other ductile alloys.

stress strain by Slashme (david Richfield) Wikipedia

Graph by, Wikipedia: [User:Slashme] (David Richfield) - Own work

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As a body, say a bar, is being subjected to a load, say a tensile load, there is an extensional strain induced due to the load. This changes the cross-section of the bar due to Poisson effect. Now, stress induced in the bar is dependent on its cross sectional area (as stress = $\frac{\text{Tensile load}}{\text{Cross-sectional area}}$). Engineering stress is when we calculate stress taking the cross-sectional area of the bar before it is loaded. True stress is when we calculate stress taking the current cross-sectional area of the bar as it extends due to the load. Both of them differ only in the choice of cross-sectional area.

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