The Condition for the Appearance of Necking under Tensile Tests

When a necking appears in a specimen under a tensile test, the strain rate at the necking region must become larger than the other region of the specimen. Generally, the flow stress of the material increases with strain rate. Taking these factors into account, the condition for the appearance of a nicking in a specimen was calculated. It was shown that a necking can not appear in a specimen if the size and the local work-hardening rate are ideally uniform in the specimen. The cause for the appearance of a necking in a real specimen is the inhomogeneities of the cross-sectional area or the local work-hardening rate in the specimen. Comparisons of the calculated results with experiments are described.