Why true stress higher than the nominal stress?

True stress is higher than the nominal stress because it takes into account the actual area over which the load is applied, which decreases as the material deforms. Nominal stress, on the other hand, is calculated using the original cross-sectional area before deformation.

As a material undergoes plastic deformation, its cross-sectional area decreases, causing the load to be distributed over a smaller area. This results in a higher true stress compared to the nominal stress, which is based on the initial, larger cross-sectional area.

The relationship between true stress and nominal stress can be understood through the concept of engineering strain and true strain. Engineering strain is defined as the change in length divided by the original length, while true strain considers the actual change in length relative to the instantaneous length of the material.

True stress is defined as the load divided by the true cross-sectional area, which takes into account the reduction in area due to deformation. Nominal stress, however, is calculated as the load divided by the original cross-sectional area, which remains constant throughout the deformation process.

As the material undergoes deformation, the true strain increases at a faster rate compared to the engineering strain. This is because the true strain considers the actual deformation, while the engineering strain is based on the original length.

The difference between true stress and nominal stress becomes more significant as the material undergoes larger plastic deformation. In the initial stages of deformation, the difference may be small, but as the material continues to deform, the true stress deviates more and more from the nominal stress.

Therefore, true stress provides a more accurate representation of the actual stress experienced by the material during plastic deformation, taking into account the reduction in cross-sectional area and the true strain.