The stress-strain relationship in ductile materials such as structural steel or aluminium is intricate and progresses through several stages. When a specimen is loaded, it initially exhibits a linear length increase, depicted by a steep straight line on the stress-strain diagram. It indicates the material is elastically deforming and will return to its original shape once unloaded. However, when a critical stress value is reached, plastic deformation begins. This stage sees substantial deformation with little increase in the applied load, primarily due to shearing stresses facilitating slippage along the material's oblique surfaces. As the load increases, there's a decrease in the material's diameter at a certain point, known as necking. After necking, even a minor load increment significantly stretches the specimen until it ruptures.

In this context, yield strength is the stress-initiating plastic deformation. Ultimate strength is the maximum load the material can bear before necking, and breaking strength is the stress leading to rupture. Interestingly, structural steel's stress-strain diagram remains steady post-yield due to strain-hardening, unlike aluminium, which sees non-linear stress increase after yield. Finally, ductility, indicating significant plastic deformation before rupture, is measured by percent elongation or reduction in cross-sectional area. Under compression, stress-strain curves of ductile materials diverge at high strains as necking doesn't occur.