Engineering stress is axial force divided by the initial cross-sectional area :It uses a fixed geometric reference even as a specimen stretches. The axial Cauchy stress tensor, by contrast, is for a uniform current cross-section . During extension with decreasing area, the two quantities diverge.
For uniform deformation at approximately constant volume, . With engineering strain , the relation is . It assumes a uniform axial stress state and fails as a local conversion after pronounced necking unless the local geometry is measured. In a tensile modulus experiment, engineering stress versus engineering strain gives the initial Young's modulus. Its later maximum identifies a maximum load per original area, rather than a universal local failure stress.
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