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# Failure and strength of materials

## The properties of matter

The strength of a material is defined as the stress (the force per unit cross-sectional area) that it can withstand. Strength is measured in newtons per square metre (N·m−2).

Stiffness is a measure of how flexible a material is. In Science we measure the stiffness of a material by calculating its Young's Modulus. The Young's modulus is a ratio of how much it bends to the load applied to it. Stiffness is measure in newtons per metre (N·m−1).

Hardness of a material can be measured by determining what force will cause a permanent deformation in the material. Hardness can also be measured using a scale like Mohs hardness scale. On this scale, diamond is the hardest at 10 and talc is the softest at 1.

### Interesting Fact:

Remembering that the Mohs scale is the hardness scale and that the softest substance is talc will often come in handy for general knowledge quizzes.

The toughness of a material is a measure of how it can resist breaking when it is stressed. It is scientifically defined as the amount of energy that a material can absorb before fracturing.

A ductile material is a substance that can undergo large plastic deformation without fracturing. Many metals are very ductile and they can be drawn into wires, e.g. copper, silver, aluminium and gold.

A malleable material is a substance that can easily undergo plastic deformation by hammering or rolling. Again, metals are malleable substances, e.g. copper can be hammered into sheets and aluminium can be rolled into aluminium foil.

A brittle material fractures with very little or no plastic deformation. Glassware and ceramics are brittle.

## Structure and failure of materials

Many substances fail because they have a weakness in their atomic structure. There are a number of problems that can cause these weaknesses in structure. These are vacancies, dislocations, grain boundaries and impurities.

Vacancies occur when there are spaces in the structure of a crystalline solid. These vacancies cause weakness and such materials often fail at these places. Think about bricks in a wall, if you started removing bricks the wall would get weaker.

Dislocations result in weakened bonding between layers of atoms in a crystal lattice and this creates a critical boundary. If sufficient force is applied along the boundary, it can break the weakened bonds, allowing the two sides of the crystal to slide against one another. The two pieces of the crystal keep their shape and structure.

Impurities in a crystal structure can cause a weak region in the crystal lattice around the impurity. Like vacancies, the substance often fail from these places in the lattice. This you can think of as bricks in a wall which don't fit properly, they are the wrong kind of bricks (atoms) to make the structure strong.

## Controlling the properties of materials

There are a number of processes that can be used to make materials less likely to fail. We shall look at a few methods in this section.

## Cold working

Cold working is a process in which a metal is strengthened by repeatedly being reshaped. This is carried out at a temperature below the melting point of the metal. The repeated shaping of the metal results in dislocations which then prevent restrict the motion of dislocations in the metal. Cold working increases the strength of the metal but in so doing, the metal loses its ductility. We say the metal is work-hardened.

## Annealing

Annealing is a process of heating and cooling a material to relax the crystal structure and reduce weakness due to impurities and structural flaws. During annealing, the material is heated to a high temperature that is below the material's melting point. At a sufficiently high temperature, atoms with weakened bonds can rearrange themselves into a stronger structure. Slowly cooling the material ensures that the atoms will remain in these stronger locations. Annealing is often used before cold working.

## Introduction of impurities

Most pure metals are relatively weak because dislocations can move easily within them. However, if impurities are added to a metal (e.g., carbon is added to an iron sample), they can disturb the regular structure of the metal and so prevent dislocations from spreading. This makes the metal stronger.

## Alloying

An alloy is a mixture of a metal with other substances. In other words, alloying involves adding impurities to a metal sample. The other substances can be metal or non-metal. An alloy often has properties that are very different to the properties of the substances from which it is made. The added substances strengthen the metal by preventing dislocations from spreading. Ordinary steel is an alloy of iron and carbon. The carbon impurities trap dislocations. There are many types of steel that also include other metals with iron and carbon. Brass is an alloy of copper and Zinc. Bronze is an alloy of copper and tin. Gold and silver that is used in coins or jewellery are also alloyed.

## Tempering

Tempering is a process in which a metal is melted then quickly cooled. The rapid cooling is called quenching. Usually tempering is done a number of times before a metal has the correct properties that are needed for a particular application.

## Sintering

Sintering is used for making ceramic objects, among other things. In this process a substance with a very high melting point is heated so that its particles stick together. The resulting product is often very pure and can be formed into a desired shape during the process. Unfortunately, sintered products are brittle.

### Exercise 1: Failure and strength of materials

List the similarities and differences between the brittle and ductile modes of failure.

Brittle material fractures with little or no plastic deformation, whereas ductile material can undergo large plastic deformation without fracturing.

What is meant by the following terms:

1. vacancies

2. dislocations

3. impurities

4. grain boundaries

1. The term vacancies refers to when there are spaces in the structure of a crystalline solid.

2. Dislocations are where weakened bonding between layers of atoms in a crystal lattice create a critical boundary.

3. Impurities in a crystal structure can cause a weak region in the crystal lattice around the impurity.

4. Grain boundaries are where two grains (chrystallites) in a crystal lattice meet.

What four terms can be used to describe a material's mechanical properties?

Toughness, malleable, hardness and stiffness.

What is meant by the following:

1. cold working

2. annealing

3. tempering

4. introduction of impurities

5. alloying

6. sintering

1. Cold working is a process in which a metal is strengthened by repeatedly being reshaped. This is carried out at a temperature below the melting point of the metal.

2. Annealing is a process of heating and cooling a material to relax the crystal structure and reduce weakness due to impurities and structural flaws. During annealing, the material is heated to a high temperature that is below the material’s melting point.

3. Tempering is a process in which a metal is melted then quickly cooled. The rapid cooling is called quenching.

4. Most pure metals are relatively weak because dislocations can move easily within them. However, if impurities are added to a metal (e.g., carbon is added to an iron sample), they can disturb the regular structure of the metal and so prevent dislocations from spreading. This makes the metal stronger.

5. An alloy is a mixture of a metal with other substances. In other words, alloying involves adding impurities to a metal sample. The other substances can be metal or non-metal. An alloy often has properties that are very different to the properties of the substances from which it is made. The added substances strengthen the metal by preventing dislocations from spreading.

6. Sintering is used for making ceramic objects, among other things. In this process a substance with a very high melting point is heated so that its particles stick together.