Final answer:
Brittle materials exhibit a steep linear stress-strain relationship that ends abruptly at fracture without significant plastic deformation. Ductile materials have a linear elastic region followed by a plastic deformation area before fracture, seen as a curve with a plateau or dip indicating permanent deformation.
Step-by-step explanation:
To graphically represent the behavior of a brittle material and a material that deforms plastically, one must understand the stress-strain diagram. A brittle material's stress-strain curve rises sharply to its elastic limit then fractures without significant plastic deformation, resembling a steep linear relationship followed by an abrupt break. In contrast, a ductile material's graph starts with a linear region where Hooke's law applies (elastic deformation), followed by a yielding point where plastic deformation starts. The curve then transitions into the plastic region, indicating permanent deformation, and finally reaches a fracture point.
The elastic limit, also known as the yield point, separates the linear elastic behavior from permanent, plastic deformation. Beyond the yield point, the ductile material will not return to its original shape, even when the load is removed. Graphically, this is illustrated with a curve that plateaus or dips following the initial elastic region for a ductile material. A brittle material does not have a distinct plastic region and will break once its fracture stress is reached. Toughness is represented by the area under the stress-strain curve; ductile materials with larger areas under the curve are tougher and can absorb more energy before fracturing.