## Episode 229: Stress-strain graphs

Lesson for 16-19

- Activity time 100 minutes
- Level Advanced

A stress-strain graph includes a great deal of information about a material. Your students may need to learn to extract this information, and to compare one material with another by comparing their graphs.

Lesson Summary

- Discussion: Interpreting stress-strain graphs (15 minutes)
- Student questions: On stress-strain graphs (30 minutes)
- Discussion: Energy stored in a stretched material (20 minutes)
- Student activity: Calculating energy stored (15 minutes)
- Discussion: Correct terminology (20 minutes)

#### Discussion: Interpreting stress-strain graphs

So far, we have considered elastic behaviour, as characterized by stiffness and the Young modulus. Now we go on to plastic behaviour and fracture (breaking).

Show a selection of stress-strain graphs and discuss various examples to show how different materials behave, and to identify yield point, breaking stress. Your syllabus may refer to three different measures of the strength of a material:

- Yield stress: the stress at the yield point
- Breaking stress: the stress at fracture (the end of the graph)
- Ultimate tensile stress: the maximum stress withstood by a material (the highest point on the graph)

#### Student questions: On stress-strain graphs

Graphs for five different materials, for interpretation.

Episode 229-1: Analysis of tensile testing experiments (Word, 63 KB)

#### Discussion:Energy stored in a stretched material

The stress-strain graph can tell you about the energy stored in a stretched wire.

Work is done on the sample as it is stretched. When under tension, this energy is stored elastically. When the load is released, energy can be recovered. If the behaviour is elastic, no energy is stored thermally after stretching. If the behaviour is plastic, some energy *is* stored thermally. If the sample shows *hysteresis* , it returns to its original shape, but does not follow the same load extension graph when being unloaded).

Work done = force × distance

Work done = load × extension

Work done = area under a load-extension graph

This result is valid for *any* shape of force extension graph. For Hookean materials the area required is a triangle.

Area of a triangle = 12 × base × height

Work done = 12 × load × extension

so,

Work done = 12 *F* Δ *x*

or,

Work done = 12 *k* Δ *x*^{ 2}

For a material, energy stored per unit volume = 12stress × strain

#### Student activity: Calculating energy stored

Students can calculate values for the materials used in their measurements of the Young modulus.

#### Discussion: Correct terminology

Since much of the terminology used in this topic can cause confusion, it is worth ensuring that students have grasped the different concepts. You could ask them to define the following terms in their own words: stiff, strong, weak, elastic and plastic.

Extend this to include the following:

brittle (cracks or breaks without plastic deformation); ductile (can be deformed under tension); malleable (hammerable

– can be deformed under compression).

Finish by looking at some charts which summarize how various properties of materials are related to one another, and which are used by engineers in selecting materials for particular applications.

Episode 229-2: Introduction to materials selection chart (Word, 262 KB)