Ductile vs Brittle behavior The behavior of materials under loading can be classified as ductile or brittle depending on if the material undergoes gross plastic deformation. The following figure represents the stress-strain curve for ductile and brittle materials. As we can see that a brittle material almost fails at elastic limit. But brittleness is not an absolute property of a material. For example, tungsten is brittle at room temperature and is ductile at high temperatures. The three factors contributing to brittle fracture are : triaxial state of stress, low temperature and high strain rate. All these factors need not be present for a material to show brittle cleavage. A triaxial stress which is present at notch along with low temperature may lead to brittle fracture. Also high strain rate assists those two factors. For most of the engineering materials ductility is an important criteria. Thus, little amount of ductility is needed for most of the mater

                   True Stress-Strain Curve (or) Flow Curve : The conventional engineering stress-strain curve for ductile material is based on original cross-sectional area. Thus, it doesn’t explain the deformation characteristics of a metal properly. Whereas the true stress-strain curve is based on instantaneous cross-sectional area of the material. In engineering stress-strain curve we can see that the curve drops after maximum load(necking). This is due to the fact that the stress is based on the original area. This stress is known as engineering stress and is given by : After necking the load required to deform the material decreases and area being constant the stress also decreases, thus the curve drops until fracture. But here in true stress-strain curve the stress is based on instantaneous area during the application of load. Thus, during necking we know that the area decreases and in turn the stress increases since the stress and area are inversely