Stress-strain graphs and breaking stress

Why stress and strain?

A force-extension graph depends on the sample's length and thickness. Stress (F/A) and strain (Δx/x) remove those effects, so a stress-strain graph is the same for every sample of a material. (See the lesson on stress, strain and the Young modulus for the definitions.)

Features of the graph

• Straight-line section: gradient = Young modulus E
• Limit of proportionality and elastic limit, as on force-extension graphs
• Yield point(s): large strain for little extra stress
• Ultimate tensile stress (UTS): the maximum stress the material can take
• Breaking stress: the stress at which the material breaks (fractures)

Types of material

• Brittle (glass, cast iron, ceramics): a straight line almost to the breaking point; little or no plastic deformation, so it snaps suddenly.
• Ductile (copper, mild steel): large plastic deformation before breaking; can be drawn into wires.
• Polymeric (rubber): large strains, with a non-linear graph.

A material is strong if its breaking stress is high and stiff if its Young modulus is high.

(Brittle, ductile and ultimate tensile stress are useful background but are not named in the IAL specification; exam questions focus on breaking stress.)

Worked example

A wire of cross-sectional area 2.0 x 10^-7 m² breaks under a tension of 90 N. Find its breaking stress.

1. Breaking stress = breaking force / area
2. = 90 / (2.0 x 10^-7)

Answer: Breaking stress = 4.5 x 10⁸ Pa

Check yourself

1. A steel wire of diameter 0.50 mm breaks under a tension of 200 N. Find its breaking stress in GPa, to 3 s.f.
   Show answer

   1.02 GPa. A = π(0.25 x 10^-3)² = 1.96 x 10^-7 m²; stress = 200 / 1.96 x 10^-7 = 1.02 x 10⁹ Pa = 1.02 GPa.

2. A wire of cross-sectional area 1.0 x 10^-6 m² has a breaking stress of 4.0 x 10⁸ Pa. Find the largest tension it can take, in N.
   Show answer

   400 N. F = stress x area = 4.0 x 10⁸ x 1.0 x 10^-6 = 400 N.

3. On a stress-strain graph, the straight section passes through a stress of 1.2 x 10⁸ Pa at a strain of 0.0016. Find the Young modulus in GPa.
   Show answer

   75 GPa. E = 1.2 x 10⁸ / 0.0016 = 7.5 x 10¹⁰ Pa = 75 GPa.

4. Which describes a brittle material?
   • It can be drawn out into long wires
   • It breaks with little or no plastic deformation
   • It has a very low Young modulus
   • It stretches a lot before breaking
   Show answer

   It breaks with little or no plastic deformation. Brittle materials such as glass snap without first deforming plastically.

5. Which material is ductile?
   • Glass
   • Cast iron
   • Concrete
   • Copper
   Show answer

   Copper. Copper undergoes large plastic deformation and can be drawn into wires.

6. What is the ultimate tensile stress of a material?
   • The stress at the limit of proportionality
   • The maximum stress it can withstand
   • The stress at which it starts to deform
   • Its Young modulus
   Show answer

   The maximum stress it can withstand. UTS is the highest point on the stress-strain graph.

7. Why do engineers compare materials using stress-strain graphs rather than force-extension graphs?
   • Force-extension graphs cannot show the elastic limit
   • Stress-strain graphs are always straight lines
   • Force cannot be measured accurately
   • Stress-strain graphs do not depend on the size of the sample
   Show answer

   Stress-strain graphs do not depend on the size of the sample. Dividing by area and original length removes the effect of sample dimensions.

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Sources

• Pearson Edexcel International Advanced Subsidiary/Advanced Level in Physics specification (XPH11/YPH11), Issue 3
• Pearson qualifications: International Advanced Levels Physics (2018)

Last updated 7 November 2026. Spotted a mistake? Tell us.