tension engineering stress vs true stress

To cover these situations, the maximum shear stress theory of failure has been incorporated into the ASME (The American Society of Mechanical Engineers) Boiler and Pressure Vessel Code, Section III, Rules for Construction of Nuclear Pressure Vessels.

For components that have to withstand high pressures, such as those used in pressurized water reactors (PWRs), this criterion is not adequate. In many situations, the yield strength is used to identify the allowable stress to which a material can be subjected. However, if the loading is displacement-controlled, the deformation of the material may relieve the load, preventing rupture. If a ductile material reaches its ultimate tensile strength in a load-controlled situation, it will continue to deform, with no additional load application, until it ruptures. Ductile materials have a fracture strength lower than the ultimate tensile strength (UTS), whereas in brittle materials the fracture strength is equivalent to the UTS. At this point, the strain reaches its maximum value and the material actually fractures, even though the corresponding stress may be less than the ultimate strength at this point. The fracture point is the point of strain where the material physically separates. The following points describe the different regions of the stress-strain curve and the importance of several specific locations.

In this case we have to distinguish between stress-strain characteristics of ductile and brittle materials. To clarify, materials can miss one or more stages shown in the figure, or have totally different stages. There are several stages showing different behaviors, which suggests different mechanical properties. A schematic diagram for the stress-strain curve of low carbon steel at room temperature is shown in the figure.

Tension engineering stress vs true stress