What occurs to a specimen's cross-sectional area as it elongates up to the ultimate stress?

As a specimen is subjected to tensile stress up to the ultimate stress, the cross-sectional area typically decreases rather than remains constant. This phenomenon occurs due to the material undergoing necking, where localized deformation leads to an increase in length and a reduction in the cross-section of the material. As force is applied and the material elongates, the internal molecules are pulled apart, contributing to a reduction in area directly in the region where the most stress is concentrated. The ultimate stress point represents the maximum stress that a material can withstand before failure, and by this point, material changes in geometry reflect significant elongation and a decrease in cross-sectional area.

In contrast, maintaining a constant cross-sectional area would indicate no deformation, and an increase would be indicative of different material behavior not typical to standard tensile testing. Fluctuations could imply variable material properties or measurement errors rather than the consistent behavior expected as materials approach their ultimate stress.