Interview Tech Tip!! We Previously covered the stress-strain curve for ductile materials so before bouncing around to another critical mechanical engineering interview question topic, it is worth touching on one more stress-strain curve question asked especially often.
Look back at our previous post if you need a refresher on what the regions or points on this curve signify. Here, we will briefly cover the difference between the engineering stress-strain curve, which is more prominently covered in academics, vs. the true stress strain curve. The engineering stress-strain curve is based on an initially measured cross-section, which means that at each data point along the curve, stress is calculated using the instrument force and the initial cross-sectional area. But wait a minute, as we move left to right along the stress-strain curve, the longitudinal extension strain is increasing so by Poisson’s Ratio, the transverse contraction strain must be increasing too. This implies that the cross-sectional area is not constant but rather decreasing as we move left to right along the curve and elongate the material. So, while the engineering stress-strain curve stress values are entirely based upon the initial cross section, the true stress-strain curve recomputes the new cross-section at each data point collected. The engineering stress-strain curve might suggest that the material itself weakens after reaching the ultimate strength point but in reality, the decreased force required to induce strain after this point is simply a product of the extreme cross-sectional decrease during necking.
Although the true stress strain curve better captures the true mechanics of materials at play, it is much more challenging to calculate and is not supported by most tensile test machines. In addition, the curve differences are very statistically insignificant during the elastic regime, which we often design to exclusively exist within. If is almost always the case that at least up to the yield strength point, the intrinsic variation between samples of the same material is greater than the engineering vs true stress strain curve values. Like all things engineering or other, it all comes down to a cost benefit tradeoff. So while the true stress-strain curve might arise infrequently in practical engineering, it is valuable to understand and very worthwhile to know for interviews!
