Final answer:
Ductile materials fail after high tensile stress due to their ability to plastically deform, while brittle materials fracture under relatively low tensile stress without significant plastic deformation.
Step-by-step explanation:
The kind of failure a material undergoes depends on its response to stress. Ductile materials, such as metals, typically undergo ductile failure due to high tensile stress. This happens because they are able to deform plastically before fracturing; hence, they can absorb a lot of energy. In the stress-strain curve, ductile materials show a characteristic plastic deformation region before reaching the point of fracture. On the other hand, brittle materials fail under relatively low tensile stress because they lack the plastic deformation phase and tend to break suddenly and without much warning.Ductile failure happens when the tensile stress in a material exceeds the yield point, leading to significant plastic deformation followed by a necking process and eventually a fracture. Brittle failure occurs with minimal plastic deformation and a sudden fracture. Therefore, the correct option is 1) Ductile failure due to high tensile stress and brittle failure due to low tensile stress.