Why is the tensile test sample dumbbell shape?

The specimen's shape is usually defined by the standard or specification being utilized, e.g. , ASTM E8 or D638. Its shape is important because you want to avoid having a break or fracture within the area being gripped.So, standards have been developed to specify the shape of the specimen to ensure the break will occur in the "gage length" (2 inches are frequently used) by reducing the cross sectional area or diameter of the specimen throughout the gage length. This has the effect of increasing the stress in the gage length since stress is inversely proportional to the cross sectional area under load.

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