# The Ductile-Brittle Transition

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## Aims

On completion of this tutorial you should:

• understand how materials' resistance to crack propagation can be determined using the notched bar impact method
• understand the difference between brittle and ductile fracture, and how the energy absorbed in each differs
• understand how temperature can influence the resistance to crack propagation

## Introduction

Materials used to build load-bearing structures must be able to survive all the possible conditions that will occur during service. The toughness of the material is very important and there are many factors which will affect the material's ability to resist fracture. These include:

• low temperatures
• extra loading and high strain rates due to wind or impacts
• the effect of stress concentrations such as notches and cracks

all of which tend to encourage fracture.

To some extent, the complex interaction of these factors can be understood by using fracture mechanics theory. However, in some circumstances where safety is extremely critical, full scale engineering components may be tested in their worst possible service condition.

Such full scale tests are extremely expensive and are very rarely conducted. Fracture mechanics is also a fairly recent development in engineering design, and measurement of the fracture toughness parameters (such as K1c) is quite time-consuming and expensive.

Notched-bar Impact Tests are methods for evaluating the relative toughness of engineering materials. They measure the energy absorbed by the high strain rate fracture of a standard notched specimen, and can be used as an economical quality control method to assess the notch sensitivity and impact toughness of engineering materials.

In the test a notched specimen is broken by the impact of a pendulum hammer falling from a fixed height. From the starting height, the initial gravitational potential energy, and hence the kinetic energy with which the hammer impacts the specimen can be calculated. By recording the height to which the hammer rises after impact, the energy loss can be calculated. This is the energy absorbed by the fracture of the specimen.

Charpy Test and the Izod Test exist as 'standard' notched-bar tests. Variables including the size and shape of the specimen and notch, the orientation at which the specimen is impacted, and the range of speeds at which the bar is impacted are specified so that test results will always be comparable.

## Notched bar impact testing

In these tests the fracture energies for a number of materials are measured at a range of temperatures. Specimens are 3 mm in diameter and 30 mm long, and all are notched in an identical way.

Specimens for the notched bar impact test

To create the notches, the specimen to be tested is placed in the test apparatus and marked to show where the notch must be cut. Shown by the blue line in the diagram below.

A notching block is used to ensure the notch is cut to a consistent depth in all the samples.

Notching of specimen

Impact test apparatus.

The specimen is placed in the apparatus, shown above, so that the notch is facing the hammer and is located below the point of impact.

Specimen in place.

The initial and final gravitational potential energies are calculated from the maximum angle of swing of the pendulum, which is recorded electronically.

To calculate the energy absorbed:

The energy absorbed is equal to the loss in potential energy of the system, according to the equation:

Potential energy lost = MgH ( sin (q1 - 90) + cos (q2) )

This does not take into account any energy lost through friction in the bearings and air resistance. This energy loss can be estimated by measuring the loss of energy when no specimen is in place.

## Results

The test was performed at a range of temperatures. Liquid nitrogen and propanol were used to cool the specimens to temperatures between -196 °C and 0 °C. Water heated using a controllable hot plate was used to heat the samples to temperatures between room temperature (20 °C) and 100 °C.

The videos of the notched bar impact tests are in QuickTime format and require your browser to have the QuickTime plugin installed (version 5 or above). If necessary download the plugin from the QuickTime download site.

The following video clips shows room temperature impact testing of:

In each clip, note the angle the hammer starts at, and then the maximum angle it reaches after the impact. These values are shown on the display in the bottom left hand corner of the video clip.

Impact tests were performed on six materials at seven temperatures. The results are shown in the graph below.

The higher the points on the graph, i.e. the greater the impact energy, the more ductile the material.

• It can be seen that copper remains ductile at all temperatures in the range covered by this experiment.
• Nylon can be seen to be going through its glass transition at above 50 °C, and hence shows a brittle to ductile transition.
• In contrast, acrylic remains brittle, as seen from the consistently low impact energies.
• Zinc becomes more ductile at temperatures above room temperature.
• Mild steel shows a ductile-brittle transition at around -60 °C.
• Results for aluminium show that it become slightly less ductile as the temperature is increased, and all the values for impact energy lie between the ductility of copper and the brittleness of acrylic. Flow is always easier than cleavage in aluminium so there is never a ductile-brittle transition observed. The decrease of overall ductility with temperature seen in aluminium arises from dynamic recovery.

## Impact energy

The energy absorbed in fracture can be split into two components:

• the plastic work done during yielding as a plastic zone develops at the notch
• the work done to create the fracture surface.

The work done to create the fracture surface is the energy required to overcome the cohesive forces between the atoms on either side of the crack path. The energy associated with brittle fracture consists primarily of this work required to break the atomic bonds.

In ductile fracture, as plastic deformation occurs, the plastic zone work-hardens, increasing the stress and strain in this area until the specimen fractures. It is the amount of plastic work done before fracture that is the main cause of the difference in total energy absorbed between specimens.

The total impact energy also depends on the sizes of the test specimen and the notch, and a standard specimen size is used to allow comparison between different materials. The impact energy is affected by a number of factors, such as:

## Ductile-to-brittle transition

The notched-bar impact test can be used to determine whether or not a material experiences a ductile-to-brittle transition as the temperature is decreased. In such a transition, at higher temperatures the impact energy is relatively large since the fracture is ductile. As the temperature is lowered, the impact energy drops over a narrow temperature range as the fracture becomes more brittle.

The transition can also be observed from the fracture surfaces, which appear fibrous or dull for totally ductile fracture, and granular and shiny for totally brittle fracture. Over the ductile-to-brittle transition features of both types will exist.

While for pure materials the transition may occur very suddenly at a particular temperature, for many materials the transition occurs over a range of temperatures. This causes difficulties when trying to define a single transition temperature, and no specific criterion has been established.

If a material experiences a ductile-to-brittle transition, the temperature at which it occurs can be affected by the variables mentioned earlier, namely the strain rate, the size and shape of the specimen and the relative dimensions of the notch.

The ductile-brittle transition is exhibited in bcc metals, such as low carbon steel, which become brittle at low temperature or at very high strain rates. Fcc metals, however, generally remain ductile at low temperatures.

In metals, plastic deformation at room temperature occurs by dislocation motion. The stress required to move a dislocation depends on the atomic bonding, crystal structure, and obstacles such as solute atoms, grain boundaries, precipitate particles and other dislocations. If the stress required to move the dislocation is too high, the metal will fail instead by the propagation of cracks and the failure will be brittle.

Thus, either plastic flow (ductile failure) or crack propagation (brittle failure) will occur, depending on which process requires the smaller applied stress.

In fcc metals, the flow stress, i.e. the force required to move dislocations, is not strongly temperature dependent. Therefore, dislocation movement remains high even at low temperatures and the material remains relatively ductile.

In contrast to fcc metal crystals, the yield stress or critical resolved shear stress of bcc single crystals is markedly temperature dependent, in particular at low temperatures. The temperature sensitivity of the yield stress of bcc crystals has been attributed to the presence of interstitial impurities on the one hand, and to a temperature dependent Peierls-Nabarro force on the other. However, the crack propagation stress is relatively independent of temperature. Thus the mode of failure changes from plastic flow at high temperature to brittle fracture at low temperature.

## Summary

It should now be clear why an energy is required to cause a material to fracture, and how the magnitude of this energy can vary for different materials. The amount of energy used in plastic deformation influences whether a material is ductile or brittle.

The energy is easily calculated using a notched-bar impact test, such as the one demonstrated in this package, or using a recognised standard such as the Charpy test or the Izod test.

The energy required for fracture is effected by the material, but also by the test parameters such as the notch size and the strain rate. The temperature also has an effect, as can be seen by the ductile-brittle transition

## Questions

### Deeper questions

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

1. Which of the following can affect a material's resistance to crack growth, i.e. the toughness?

 Yes No a Temperature Yes No b Strain rate Yes No c Applied stress Yes No d Notches and cracks Yes No e Grain size and shape

2. A high impact energy is associated with:

 Yes No a large strain energy at yielding Yes No b cleavage failure mechanism Yes No c high surface energy

3. A steel sample of stiffness 200 GPa is loaded until failure at a strain of 0.01. Assuming a yield strength of 1.2 GPa, and perfect plastic deformation (stress remains constant once yielding occurs), and that 90 % of the applied energy is lost to heat, how much energy per unit volume goes into deforming the steel?

a) 0.60 MJ m-3
b) 0.84 MJ m-3
c) 1.20 MJ m-3
d) 7.56 MJ m-3

4. Impact tests were carried out for three materials over a variety of temperatures, and the results plotted, as shown below.

Impact Energies for Copper, Mild Steel and Nylon

Using this data, suggest which of the three would be best suited for the following applications:

1. Shock absorbers for low temperature use
2. A "break-before-bend" component at room temperature

### Open-ended questions

The following questions are not provided with answers, but intended to provide food for thought and points for further discussion with other students and teachers.

1. Why were the hulls of the infamous Liberty Ships of the Second World War prone to fracture in the North Atlantic, but not in the warmer waters of the South Pacific?

2. Why do plastics show a brittle to ductile transition upon heating?

## Going further

### Books

• Newey C and Weaver G, Materials: Principles and Practice, Open University and Butterworths, 1990 (ch.2,3,6)
• Weidmann G, Lewis P and Reid N, Structural Materials, Open University and Butterworths, 1990 (ch. 1,2,4)
• Anderson J C, Leaver K D, Rawlings R D and Alexander J M, Materials Science, Van Nostrand Reinhold, 3rd ed. 1985 (ch. 5,6,8,9)

## Yield strength and ductility

Most structures are designed so that the materials used will only undergo elastic deformation. It is therefore necessary to know the stress at which plastic deformation (yielding) begins. For metals which experience a gradual elastic-plastic transition, the yield stress may be taken to be the point at which the stress-strain curve is no longer linear. A more precise way of determining the limit is to use the stress at a strain of 0.002, this value is known as the yield strength.

Ductility is a measure of the degree of plastic deformation which has occurred prior to fracture. A material that undergoes very little plastic deformation is brittle.

The area under the stress-strain curve gives the fracture energy of the material. A ductile material has a greater fracture energy.

The total fracture energy can be broken into that required to produce elastic deformation (shown by the pink shaded region) and that required to produce plastic deformation (green shaded region).

Increasing the yield strength of a metal by processes such as work-hardening , precipitation hardening and solid solution strengthening generally decreases the ductility. They, therefore, decrease the notched-bar impact energy since less plastic work can be done before the strain in the plastic zone is sufficient to fracture the test specimen.

## Notches

The notch in the test specimen has two effects:

1. Stress concentration around the notch causes plastic deformation to occur in this area. The decrease in area caused by the notch increases the stress to a value above the yield stress for the material, while the rest of the specimen may still be at a stress below the yield stress. This plastic hinge which develops at the notch reduces the total amount of plastic deformation in the test specimen.
2. The plastic deformation at the notch is constrained by the surrounding material and this increases the tensile stress in the plastic zone. The degree of constraint depends on the severity of the notch (depth and sharpness). The increased tensile stress encourages fracture and reduces the work done by plastic deformation before fracture occurs.

Some materials are more sensitive to notches than others, and a standard notch tip radius and notch depth are therefore used to enable comparison between different materials.

## Fracture Mechanisms

### Ductile fracture

The propagation of a ductile crack involves substantial plastic flow and ductile fracture usually gives a characteristic rough fracture surface. Fracture occurs by a process known as microvoid coalescence.

First, plastic strain causes small microvoids to form in the material, most often at sites of inclusions . As the process proceeds, these microvoids grow and begin to join together (coalesce). Final failure occurs when the walls of material between the growing voids finally break..

### Brittle fracture

Brittle fracture takes place by rapid crack propagation and very little plastic deformation, and yields a relatively flat fracture surface.

For most brittle crystalline materials, crack propagation corresponds to the successive and repeated breaking of atomic bonds along specific crystallographic planes, this is known as cleavage.

Cleavage is essentially a low temperature phenomenon, which can be eliminated if a sufficiently high deformation temperature is used. See the section on the ductile-to-brittle transition. The occurrence of brittle fracture is also associated with certain crystal structures, in particular BCC. Where it is more pronounced in the presence of impurities which form interstitial solid solutions in metals of this structure.

Academic consultant: Cathie Rae (University of Cambridge)
Content development: Jacqui Capes, Mark Wharton and Chris Shortall
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.