When original calculated, the breaking stress appears as a _____ value than ultimate stress

 Explanation :

• Once the material reaches the yield point, it starts well, yielding. In many materials, yielding is accompanied by work hardening (strain hardening ).
• As deformation increases, the cross-section is reduced. But when we draw the stress-strain diagram we are still using the original cross-section of the material because keeping track of the cross-section as the material deforms is not easy.
• True stress (sometimes called scientific stress) is defined as the force divided by the smallest cross-sectional area as the sample necks down when you stretch it.
• The true stress keeps going up as you stretch the material toward ultimate failure.
• The engineering stress uses the original full area for convenience in the calculation. It's just that as the force is increasing, you are still dividing by the original full area even though the real area is decreasing.
• That is why we see the plotted value of stress decreasing toward ultimate failure
• Once the material passes the Ultimate stress region, the deformation is drastic which is called necking.
• Until necking starts the distribution of strain and hence stress is uniform throughout the cross-section of the material. But, at some point, when the hardening at one local point decreases compared to the rest of the cross-sectional area, the strain becomes concentrated in that area.
• The deformation then becomes localized (necking).
• This neck propagates through the whole area, and it finally ruptures. 
• ​So, to sum it up, if you consider the actual cross-sectional area at the time of breaking, the stress at which breaking occurs is more than the Ultimate stress.
• So originally calculated, the breaking stress appears as a less value than ultimate stress.