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Consider this hypothetical ideal scenario:

If I have a test coupon in a tensile test that has a constant cross-sectional area throughout its length (i.e. along the tensile loading direction) and there are no flaws or imperfections at all, where does necking occur?

In this case stress is uniform throughout the volume of the coupon (no stress concentrations).

Thanks.

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    $\begingroup$ Wherever the biggest local imperfection is. Imperfections are likely to be introduced at the clamp locations by the act of clamping, therefore necking directly adjacent to one of the clamps seems likely. $\endgroup$
    – AndyT
    May 19, 2017 at 9:16

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According to theories of failure, necking begins as small voids near the largest imperfection present in the specimen. But, as far as the case you proposed is concerned, the specimen has no imperfections at all. Then the clamping used to fix the specimen will induce stresses perpendicular to the axis of elongation. This will cause formation of imperfections near the clamps. Thus the necking will occur in close proximity of one of the clamps.

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If you have a tensile test bar with shoulder fillets, the grips will not be a problem. Then as the metal plastically deforms ( assuming it is ductile) , dislocations will pile-up - work harden. This will eventually produce a local stress concentration > necking.

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