(e) stress–strain graphs for typical ductile, brittle and polymeric…

The idea

Stress–strain graphs reveal how materials deform. A ductile material such as copper or mild steel shows an initial straight elastic region obeying Hooke's law, then yields and undergoes large plastic strain before breaking; it may show a yield point and ultimate tensile stress. A brittle material such as glass or cast iron is stiff and strong but fractures with little plastic strain, so its graph is almost linear to breaking. A polymeric material such as rubber shows a curved, non-linear response with a low Young modulus, large elastic strain and hysteresis: loading and unloading curves differ, and the area between them represents energy dissipated per unit volume. The gradient of the initial linear region gives the Young modulus; the area under the curve up to a strain gives energy stored per unit volume.

What earns the marks

• Identifies the initial linear region as elastic behaviour where the gradient equals the Young modulus.
• Describes ductile behaviour: yield point, significant plastic deformation and a clear breaking point.
• Describes brittle behaviour: little or no plastic deformation, fracture soon after the elastic limit.
• Describes polymeric behaviour: non-linear curve, low gradient, large elastic strain and hysteresis between loading and unloading.
• Interprets the area under a stress–strain graph as energy per unit volume and the area between hysteresis loops as energy dissipated.

Common mistakes and how to put them right

• Assuming all materials have a straight-line stress–strain graph.

  Put it right: Recognise polymers curve and brittle materials may fracture before much strain.

• Confusing strength with stiffness.

  Put it right: Note that strength relates to breaking stress while stiffness relates to the gradient, the Young modulus.

• Thinking the area under a stress–strain graph is force.

  Put it right: It represents energy per unit volume because stress times strain is energy per unit volume.

• Treating the breaking point as the same as the elastic limit.

  Put it right: The elastic limit is where plastic deformation begins, while the breaking point is where fracture occurs.

Exam tips

• Sketch the three curve shapes and label elastic region, yield point, plastic region and breaking point.
• Use the gradient of the linear portion to compare stiffness, and the breaking stress to compare strength.
• For polymers, mention hysteresis and explain that the enclosed area represents energy dissipated per unit volume.