# Introduction to mechanical testing

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## Aims

On completion of this tutorial you should:

• understand the general shape of the tensile stress-strain curve
• understand how the microstructure of a material can effect its properties, in particular the yield-strength and stiffness
• understand some ways that the microstructure can be controlled

## Introduction

While it is very common to associate properties with a metal, it is possible to produce a wide range of properties from the same material, by varying the composition slightly, or by varying its processing. The different ways of processing a metal include how it has been cooled and worked, and any heat treatments it has been subjected to.

These processes and compositional changes affect the microstructure of the material, in particular the grain shape and size and the dislocation density, as well as phase structure and precipitates.

In this package changes in microstructure will be studied for two different materials. The first is aluminium, which will demonstrate how the phase structure and the precipitates caused by the addition of small amounts of copper can effect mechanical properties, in particular in the tensile test.

The second material is copper, which will demonstrate how the grains and the dislocation density are affected by work hardening and by heat treatments. This will be shown with both the tensile test and with three-point bending.

## Theory 1: Tensile testing

In a tensile test, a sample is extended at constant rate, and the load needed to maintain this is measured. The stress (σ) (calculated from the load) and strain (ε) (calculated from the extension) can either be plotted as nominal stress against nominal strain, or as true stress against true strain (definitions). The graphs in each case will be different:

Graphs illustrating the difference between nominal stress and strain and true stress and strain.

There are two main types of strain - elastic strain and plastic strain. Elastic strain is the stretching of atomic bonds, and is reversible. Elastic strain can be related to the stress by Hooke's law :

σ = Eε

where E is the Young's modulus .

Plastic strain, or plastic flow, is irreversible deformation of a material. There is no equation to relate the stress to plastic strain.

Several points on the graph can be defined:

A - limit of proportionality - the point beyond which Hooke's Law is no longer obeyed. This is the point at which slip (or glide ) due to dislocation movement occurs in favourably oriented grains. The graph is linear up to this point, and begins the transition from elastic to plastic deformation above this.

B - yield stress - the stress at which yielding occurs across the whole specimen. The stress required for slip in a particular grain will vary depending on how the grain is oriented, so points A and B will not generally be coincident in a polycrystalline sample. At this point, the deformation is purely plastic.

C - proof stress - a third point is sometimes used to describe the yield stress of the material. This is the point at which the specimen has undergone a certain (arbitrary) value of permanent strain, usually 0.2%. The stress at this point is then known as the 0.2% proof stress. This is used because the precise positions of A and B are often difficult to define, and depend to some extent on the accuracy of the testing machine.

D - ultimate tensile strength (UTS) - the point at which plastic deformation becomes unstable and a narrow region (a neck) forms in the specimen. The UTS is the peak value of nominal stress during the test. Deformation will continue in the necked region until fracture occurs.

E - final instability point - the point at which fracture occurs, ie the failure point

F - fracture stress - The stress at which fracture occurs - only obtainable from the true stress-strain curve. See fracture toughness .

## Theory 2: Precipitation hardening in alloys

Duralumin is an aluminium alloy containing 4wt% copper, as well as smaller amounts of other elements. The impurities in the material changes its properties by changing the microstructure, and since the distribution of the copper atoms can be varied using heat treatments, a variety of microstructures, and hence properties can be produced.

In the samples used in this experiment, the copper forms precipitates of CuAl2 within an aluminium matrix - see image below. These precipitates hinder the movement of dislocations and substantially strengthens the alloy. This process is widely used to make strong aluminium alloys for structural purposes, and is known as precipitation hardening .

## Method

The tensometer apparatus shown below extends a sample at a constant rate, and electronically measures the displacement and the load. In order to work out the stress and strain the diameter and gauge length of the samples needs to be recorded before the test is carried out.

Tensometer apparatus

The specimens load into the machine as shown in the photographs below, and the machine begins to extend the specimens at a rate of approximately 3.5 mm per minute. The load and cross head displacement are recorded directly into graph form using the pen-plotter. This gives continuous data so it is easier to see the yield point than if using data from the meter at particular time intervals.

Assembly of specimen, clamp, collar and pin

Specimen installed in tensometer

To record the data given in the results in this package a more sophisticated machine was used, which recorded the data straight onto a computer, taking readings every second, from which graphs were produced.

## Results 1

It can be seen from the graph that both the aluminium and the duralumin have the shape of the typical graph shown in Theory 1. However, the values for the yield stress and the ultimate tensile strength are very different for the two specimens.

The yield stress for aluminium is about a quarter that for duralumin, because there is far less resistance to the movement of the dislocations in pure aluminium. In the alloy the precipitates hinder the motion of the dislocations and a much higher stress is required to initiate slip.

Once slip has started the stress required for further plastic deformation increases a little, due to work hardening in the material. (For information on work hardening see Theory 3). However, as there is still greater resistance to dislocation movement in the duralumin due to the precipitates, the pure aluminium specimen necks for longer.

The ductility in the pure aluminium specimen is so high that the specimen only breaks once the neck has become very narrow, as seen in the photos below, the narrow neck allowing the load to drop to almost zero before failure occurs.

In contrast, the duralumin specimen begins to neck, but then fails with a brittle fracture, resulting in a cup and cone fracture surface - pictured below.

 Duralumin (cone) Duralumin (cup) Pure aluminium

Fracture surfaces from tensile tests. (Click on image to view larger version.)

The fracture in the duralumin is initiated at microvoids, which can be seen in the SEM image below. These coalesce, to form an internal crack. Final failure occurs when the shear stress causes the remaining cross section to tear. The shear stress is greatest at 45° to the applied load, and hence forms the angled walls, resulting in the distinctive cup and cone profile.

SEM image of the fracture surface of duralumin. (Click on image to view larger version.)

## Theory 3: Heat treatment of copper

Work hardening: The process of plastically deforming a sample by rolling or drawing the material at low temperatures (less than half the melting temperature, Tm), which increases the number of dislocations and the amount that they are entangled, resulting in reduced ductility and increased hardness and strength.

Annealing is a heat treatment process that brings about a softer or more relaxed state in worked materials. There are three main stages - recovery, recrystallisation and grain growth, which are temperature dependent processes.

Stage 1 - Recovery - some restoration of original properties (eg hardness, ductility, resistivity) is achieved by the rearrangement of dislocations at temperatures around 0.3 Tm, to lower the overall strain energy. The dislocation density is lowered slightly, and the strength, grain shape and grain size are largely unchanged.

Stage 2 - Recrystallisation - at a temperature above 0.4 Tm, new crystals begin to grow at certain points in the deformed metal and eventually absorb the deformed crystals. The new crystals are more equiaxed and contain far fewer dislocations than the deformed ones, with the dislocation density reduced approximately from 1015 m-2 to 1010 m-2.

Stage 3 - Grain growth - holding the metal at recrystallisation temperature for an extended period of time, or at a higher temperature, allows the average grain size of the metal crystals to increase. This occurs because the grain boundaries have a higher energy than a perfect lattice, so there is a driving force to reduce the area of grain boundaries by increasing the grain size.

Samples that have been annealed have very different properties to those that are work hardened.

The resistance to the movement of dislocations can be separated into a contribution from the lattice and a contribution from other obstacles, such as impurities and grain boundaries. Any increase in dislocation density will have a large effect on how easily the material can be deformed. More ... In addition an increase in grain size can lower the yield stress. More...

In the annealed sample the contribution from the lattice dominates, as the density of dislocations is low. Slip occurs at a relatively low stress, yielding almost immediately, and slip will continue until there is a large extension. It is possible to see shear bands forming on the surface - the appearance becomes more matt as the shear bands roughen the surface on a very small scale. As the sample is extended, the dislocation density increases, and extensive work hardening takes place.

In contrast, the work hardened copper already has a high dislocation density, meaning that it takes a much larger stress for slip to begin. This means that the yield point will be much higher, and so the elastic region is much longer.

## Results 2

You can view the following 'speeded up' QuickTime video clips of the tensile tests:

You can also view image sequences of the tensile tests which also display the growth of the stress-strain graph:

As with aluminium, the tensile test graphs for the copper specimens exhibit the shape as the typical stress against strain graph in Theory 1, although the difference in properties can clearly be seen between the two specimens. The annealed specimen has been heat treated at 800°C for two hours, so recovery, recrystallisation and grain growth all take place.

While the annealed specimen yields almost immediately, the work hardened specimen yields at a stress many times higher, as predicted in the theory. The difference in ductility between the two specimens is apparent, with the annealed specimen straining to almost three times that of the work hardened.

Once the annealed specimen begins to yield, work hardening occurs, which is why the stress required to deform the specimen continues to increase for a long time. The full extent of this can be seen in the photo below, However, the other specimen has already been work hardened, so once yielding starts no further work hardening can occur, so the stress does not increase.

The fracture mechanism for both of the copper samples is similar to that of duralumin discussed in Results 1, in that there is microvoid formation and coalescence as seen here:

(Click on image to view larger version.)

There is also a less pronounced cup and cone profile:

(Click on image to view larger version.)

There is also the formation of shear bands , which causes the change in colour seen in the photograph of unstretched and full stretched specimens above, as the oxide layer on the surface mixes with fresh layers from the shear bands, resulting in the brighter but matt finish seen once deformation has occurred.

## Notes on tensile testing

Although the tensile test previously discussed gives a good idea of the shape of the stress-strain curve, it is not very accurate for strain readings. The graph above shows the two measurements of strain on a duralumin specimen. The purple set of measurements come from the test machine via the displacement of the cross head. This is assumed to be the extension of the specimen, and then converted to a nominal strain by dividing the extension by the initial length. The grey set of measurements were recorded by a strain gauge, pictured below

 Strain gauge on specimen (Click on image to view larger version) Close up of strain gauge (Click on image to view larger version)

The graph shows the difference beteween the two sets of measurements. The strain gauge measures the actual strain, but only works up to relatively small strains. The cross head displacement records the correct shape of the curve, up to large strains as needed, but is not particularly accurate in giving actual strain due to the method of measuring. As can be seen above, the machine readings do not have a very straight line initially, and this is due to slack within the machine being taken up gradually as the clamps tighten onto the specimen.

As the displacement transducer measures the total displacement of the machine and the specimen, the apparent displacement is much larger than expected. This is because as a stress is applied, many other parts of the machine stretch slightly, and so increase the displacement. As a result when the Young's modulus is caluculated, the displayed strain results in a value of around 20GPa (on the steepest part of the graph), while the strain gauge gives a value of 80GPa. The real value for aluminium is 70GPa, and it can be seen that the strain gauge gives a more accurate result.

For the test used here, the interest was in the plastic deformation of the specimen, and so it was appropriate to use the displacement measurement. However, it should always be remembered that if accurate strain readings are required, they must be acquired using a strain gauge.

## Results 3

The changes in properties due to each stage of the annealing process are demonstrated by the three-point bending graphs. Apparatus and method for this technique are covered in the The structure and mechanical behaviour of wood TLP.

These results show that at higher annealing temperatures, the work for plastic deformation decreases. However, it is difficult to see from the graph how much the microstructures have changed during the annealing.

Referring to the micrographs below, it can be seen that the microstructure of the work hardened copper specimen has small grains, and there is a directionality to the grains - they are relatively long and thin. In the specimen annealed at 350°C, the material has recovered and recrystallised, as seen by the slightly larger, equiaxed grains. The specimens which have been heated at 500°C and 800°C have a similar shape of grain, but grain growth has occurred, and as such, the grains are larger as the temperature of anneal increases.

Relating this to the graph, it can be seen that recrystallisation reduces the yield stress. This is because there has been a large reduction in dislocation density. As a result the remaining dislocations are much more mobile since there are not as many pinning points, and so slip occurs at a much lower stress. Grain growth also has a significant effect on the plastic flow, with the increase in size reducing the flow stress.

In this experiment it has not been possible to observe the effects of recovery to the properties of a material. It is likely that the work hardened specimen has already recovered at room temperature due to the high purity of the copper.

 Work hardened copper Copper annealed at 350°C Copper annealed at 500°C Copper annealed at 800°C (Click on an image to view a larger version.)

## Summary

You should now be familiar with the tensile test and the stress-strain graphs produced from the data it provides, as well as the various terms used to describe the mechanical behaviour of materials. You have also seen how similar materials can have very different properties dependent on the microstructure.

Pure aluminium is very soft and rarely used, its most common use being aluminium foil. The addition of just a small percentage of foreign atoms, such as copper as demonstrated in this package, can have a profound effect on the mechanical properties, and aluminium alloys are very common. The range of alloys is large, with various elements that can be added to alter its properties.

The effect that work hardening and heat treatments have on the properties of copper can also be profound effect on the yield stress, without the composition being altered. Pure copper is also seldom used, except as an electrical conductor, and is much more commonly used as an alloy.

## Questions

### Quick questions

You should be able to answer these questions without too much difficulty after studying this TLP. If not, then you should go through it again!

1. On a typical tensile stress-strain curve, how is the elastic region represented?

 a By a horizontal straight line b By a curved region of increasing gradient c By a straight line of positive gradient d By a parabolic region

2. The presence of a small amount of copper in aluminium significantly strengthens the alloy by ...

 a Forming CuAl2 precipitates which hinder dislocation motion b Increasing its Young's Modulus c Binding atoms together, thus preventing slip d Rearrangement of the crystal structure resulting in fewer dislocations

3. Work hardening strengthens an alloy by ...

 a Removing internal defects in the crystal structure b Increasing the dislocation density c Decreasing the grain size of the alloy d Increasing the lattice resistance to dislocation motion

4. Annealing ...

 a Softens an alloy by thermally activating dislocation slip b Strengthens an alloy by means of thermal stresses c Softens an alloy by reducing the dislocation density d Does not affect a material's strength

5. What causes grain growth?

 a Thermal expansion of the grains b Larger grains can contain more defects, making them entropically favourable c Rearrangement of the grain boundaries into lower energy crystallographic positions d Reduction in grain boundary area, since grain boundaries are high energy features

### Deeper questions

The following questions require some thought and reaching the answer may require you to think beyond the contents of this TLP.

1. Why is it not possible to obtain the fracture stress of a material from a nominal stress-strain curve?

 a Due to the accuracy of the testing machine, the precise fracture stress is impossible to define on a nominal stress-strain curve. b The nominal stress is calculated from the initial sample dimensions and does not take into account the change in cross-sectional area as the tensile test proceeds. c Because the nominal strain does not pinpoint the breaking point accurately d Because the load on the sample varies throughout this type of test

2. In a polycrystalline sample, why do the points A (limit of proportionality) and B (yield point) on a graph of true stress against true strain tend not to coincide?

 a Because at A the grains are slipping past one another whereas at B they begin to yield internally. b At A, slip begins to take place by means of dislocations, whereas at B there is sufficient stress for whole planes of atoms to slide, without need for defects. c Because as the stress increases, the grain size changes. d At A, slip begins, but only in certain grains which are favourably orientated.B is the point at which yielding occurs across the whole specimen, and is therefore at a slightly higher stress.

3. Which of the following factors affects yield stress?

 Yes No a Sample geometry Yes No b Lattice resistance Yes No c Dislocation mobility/interactions Yes No d Grain size Yes No e Ultimate tensile strength Yes No f Presence of precipitate particles

## Going further

### Books

• Dieter G E Mechanical Metallurgy, McGraw-Hill 1988.
• Ashby M F and Jones D R H Engineering Materials: An introduction to their properties and applications (vol 1), Pergamon 1996.
• Smallman R E and Bishop R J Metals and Materials, Butterworth Heinemann 1995.

### Websites

• Microstructures of Copper and Copper Alloys
A site displaying micrographs of commercially important and/or metallurgically interesting copper and copper alloys and processings.
• aluMATTER
A site developed in partnership with the European Aluminium Association offering educational resources on the applications, materials science and processing of aluminium, including:
• Aluminium and Aluminium Alloys - Designations
An article on the AZoM (A to Z of Materials) website.
• Ductile Fracture
A page by David Bailey at the Materials Science and Engineering department of Virginia Tech, including photographs and micrographs of aluminium and steel fracture surfaces.

## Definitions of stress and strain

Nominal stress: the force on the object divided by the original area.

True stress: the force on the object divided by the actual area. E.g., when necking occurs the true stress is the force applied divided by the area of the neck.

The unit for stress is Nm-2, or Pa.

Nominal strain: change in dimension / original dimension

This is also known as the engineering strain, and is strictly only true for very small displacements. For large displacements, true strain should really be used.

True strain: loge [deformed length / original length]

True strain is applicable for larger strains, but tends to be more difficult to apply than nominal strain. Is also be known as the logarithmic strain. This remains a ratio, and so does not have any units.

There are no units for strain since it is a pure ratio.

## Resistance to motion of dislocations

In pure materials the main source of resistance to the motion of dislocations other than the lattice resistance is from other dislocations that intersect the glide plane (picturesquely known as forest dislocations).

If a glide dislocation has its path blocked by forest dislocations that are separated by an average distance λ, then the dislocation must bow between these pinning points. The stress required to do this is given by

τ = Gb/ λ

If the dislocation density, ρ, is known, then the flow stress can be estimated, since ρ is related to λ by

ρ = 1/λ2

The difference in dislocation density between annealed and work-hardened crystals can be as much as 105 m-2, meaning that the difference in stress required to move the dislocation can vary by a factor of 300.

## The effects of grain size on yield strength

A change in grain size affects the yield strength due to the dislocations interacting with the grain boundary as they move. The boundaries act as obstacles, hindering the dislocation glide along the slip planes. As subsequent dislocations move along the same slip plane the dislocations pile-up at the grain boundaries.

The dislocations repel each other, so as the number of dislocations in the pile-up increases the stress on the grain boundary increases. In fact, if there are n dislocations in the pile-up, the stress at the grain boundary will be n times the applied stress.

If the grain boundary in a sample gives way at a stress τ, there needs to be a stress of τ/n applied to the sample in order to cause the boundary to collapse.

In a larger grain there will be more dislocations within the grain, so there will be more dislocations in the pile-up. Therefore a lower applied stress is required to produce a local stress great enough to cause the grain boundary to collapse. Accurate modelling is difficult, but it is found that the tensile yield stress, σy, is related to grain diameter, d, by the Hall-Petch equation:

where σi is the 'intrinsic' yield stress, and k is a constant for a particular material.

Academic consultant: Tom Matthams(University of Cambridge)
Content development: Matt Charles, Mark Wharton and Heather Scott
Photography and video: Brian Barber and Carol Best
Web development: Dave Hudson

This TLP was prepared when DoITPoMS was funded by the Higher Education Funding Council for England (HEFCE) and the Department for Employment and Learning (DEL) under the Fund for the Development of Teaching and Learning (FDTL).

Additional support for the development of this TLP came from the Armourers and Brasiers' Company and Alcan.