Strength, ductility and toughness are three very important and distinct material properties, but understanding the differences between them can sometimes be confusing. This page and the video below should help clear things up!

Material Strength

Strength is a measure of the stress a material can withstand. Two different measurements are used to define the strength of a material:

• The ultimate strength, which is the maximum stress the material can withstand before fracturing.
• The yield strength, which is the stress at which the material begins to deform plastically (meaning that permanent deformation remains after the applied load is removed).

Both the ultimate strength and the yield strength express how much force the material can withstand per unit area, so they have the same units as stress, which is force/area. In the SI system strength and stress have units of pascals ($1 \mathrm{Pa} = 1 \mathrm{N} / \mathrm{m^2}$), but are often expressed in megapascals (MPa).

Yield and ultimate strengths can be determined from the stress-strain curve of a material, that is obtained by performing a tensile test.

Many structures and components are design to ensure that they only deform elastically (i.e. there is no permanent deformation after the applied load is removed). This makes the yield strength a commonly used criterion for defining failure in engineering design codes. The failure theories page goes into more detail about the different ways failure is defined.

Here are some typical strength values for a few different materials.

Determining the Yield Strength from a Stress-Strain Curve

The transition from elastic to plastic deformation is not always easy to identify on a stress-strain curve. For this reason standard methods have been developed to determine the yield strength from tensile test data. One of the more common methods that is often used for metals is the 0.2% offset method. Here’s how it works:

• Step 1 – draw a line with a slope equal to the Young’s modulus of the material
• Step 2 – shift this line 0.2% to the right on the stress-strain curve
• Step 3 – the intersection between this line and the stress-strain curve gives you the material’s 0.2% offset yield strength (also called 0.2% proof stress)

This process is illustrated in the image below. This material has a 0.2% offset yield strength of 330 MPa.

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Material Ductility

Ductility is a measure of the ability of a material to deform plastically before fracturing.

• A material is ductile if it undergoes a large amount of plastic deformation before it breaks. These materials fracture at very large strains. Examples of ductile materials include mild steel, aluminium, and gold.

• A material is brittle if it fractures at low strains with little or no plastic deformation. Examples of brittle materials include glass and ceramics.

The differences between ductile and brittle materials can be seen in the stress-strain curves shown below.

Ductile and brittle materials have very different stress-strain curves, with brittle materials exhibiting little or no plastic deformation before fracturing. Because they don’t deform plastically, the concept of yield strength is irrelevant for brittle materials.

Typically a material that has a strain at fracture of less than 5% is considered to be brittle.

Compressive vs Tensile Loading

Another interesting difference between ductile and brittle materials is how the behave under compressive versus tensile loading.

For ductile materials like mild steel the yield and ultimate strengths are very similar in the tensile and compressive directions. Compression tests are more difficult to carry out than tensile tests because buckling can be an issue, so compression tests aren’t often performed for ductile materials.

For brittle materials like concrete and ceramics the material strength is much larger in compression than in tension. Separate tensile and compression tests usually need to be carried out to properly characterised these materials.

Ductility vs Temperature

The ductility of a material can vary with temperature. A lot of different types of steel for example are ductile are room temperature but become brittle when the temperature drops to below the ductile-to-brittle transition temperature. This is an important design consideration because ductile failure is normally preferred to brittle failure.

Material Toughness

Toughness is the ability of a material to absorb energy up to fracture. Materials that can absorb a lot of energy before fracturing have high toughness.

Toughness can be thought of as the area under the stress-strain curve. If the area is large, the material will have high toughness and will be able to absorb a large amount of energy before fracturing.

For a material to have high toughness it should have a good balance of both high strength and high ductility. Low strength and brittle materials tend to have low toughness.

Strength vs Ductility vs Toughness

Strength, ductility and toughness are separate but linked material properties. The five boxes below summarise the definitions of these properties, and a fifth parameter, resilience, is introduced.

These five properties can be identified on the stress-strain curve, as shown below.

Related Topics

Young's Modulus

Young's modulus is a measure of the stiffness of a material – it describes the relationship between stress and strain.

Learn more

Stress and Strain

Stress and strain are fundamental concepts that relate to the internal forces and deformations within a body in response to applied loads.

Learn more

Young’s modulus is a really important material property that appears all the time in engineering and physics. It’s used for everything from calculating when a column will buckle to determining how much a beam will deflect when forces are applied to it. So let’s learn more about it!

What is Young’s Modulus?

Young’s modulus, also called the elastic modulus, is a material property that describes how much a material will deform when a load is applied to it. It is essentially a measure of how stiff a material is.

The easiest way to visualise Young’s modulus is on a stress-strain curve, shown in the image below, that can be obtained by performing a tensile test on a sample. The curve can be divided into two regions, an elastic region and a plastic region. If the applied stress is low and we remain in the elastic region – the original dimensions of the material will be completely recovered when the applied load is removed. For larger stresses that take us into the plastic region, permanent plastic deformation will remain after the applied load is removed.

The stress-strain curve is a straight line in the elastic region for most materials. The slope of this curve is equal to Young’s modulus, which is denoted using the letter $E$. Young’s modulus describes the relationship between stress and strain in the elastic region. The higher the Young’s modulus of a material, the smaller the elastic deformations (strain) will be for a given applied load (stress).

Hooke’s law gives us the relationship between stress and strain in the linear elastic region of the stress-strain curve.

Since strain is dimensionless, Young’s modulus has the same units as stress. Steel has a high Young’s modulus of around 200 GPa, whereas Polystyrene has a low Young’s modulus of around 3 GPa.

Check out the video below if you want to watch an animated summary of all of this information about Young’s modulus. If not, just keep reading!

Applications of Young’s Modulus

Young’s modulus is very important when it comes to engineering, because so often engineering design and analysis involves determining how much something will deform. A high Young’s modulus value is good if you want deformations to be very small – you wouldn’t want a bridge to deform much when a car passes over it, for example, so it would make sense to construct the bridge from materials with a high Young’s modulus.

Because it defines the relationship between stress and strain, Young’s modulus appears in all kinds of different equations that are commonly used in mechancal and civil engineering. Here are a few examples:

How to Determine Young’s Modulus

If you have data from tensile tests performed for a particular material, it’s easy to figure out what the Young’s modulus for that material is. All you have to do is take two points in the linear elastic part of the stress-strain curve, and use those points to measure the slope of the curve. This is illustrated in the figure below.

Young’s Modulus Values for Different Materials

The image below shows stress-strain curves for a few different materials. Material 1 has the steepest slope in the elastic region, which means that it has the largest Young’s modulus – you will need to apply a much larger force to deform Material 1 than you would to deform Materials 2 or 3 by the same amount. The stress-strain curve for Material 1 is typical of diamond, for example, whereas Material 2 is more like steel, and Material 3 is typical of a material like rubber.

The table below shows typical Young’s modulus values for a few different materials. Ceramics and metals generally tend to have quite high Young’s modulus values, meaning that they are quite stiff. Polymers on the other hand have much lower values.

Understanding Young’s Modulus Using the Ball-and-Spring Model

The Young’s modulus of a material is closely related to the strength of the bonds between its atoms. We can think of these interatomic bonds as small springs connecting adjacent atoms, represented by balls.

When a force is applied to the material, deformation of the material is resisted by the stiffness of the interatomic bonds. Young’s modulus is a measure of how strong the interatomic bonds are, or in other words it is a measure of how stiff the springs between the atoms are. When the force is removed the atoms return to their initial position – this is elastic deformation.

The mechanism behind plastic deformation is very different, because it involves the breaking of bonds and the re-arrangement of the position of the atoms.