Materials Science

Tensile Testing Masterclass

Truncated Notes

Glossary of TermsTerm Explanation

BrittleCracks easily. A crack is started (initiated) and rips through the material with little energy used.Opposite = Tough

DuctileThe property that allows a material to undergo a large permanent shape change due to the application of a tensile force. Plasticine is a definitive material to illustrate this property.The equivalent property for compressive forces is malleable.

ElasticThe property that allows a material to regain its original shape once a deforming force is removed. A metal spring is an excellent material to illustrate this property.Opposite = Plastic

Elastomer A rubbery, polymeric material that exhibits approximate elastic properties.

Engineering Stress

If stress is given by Load / Cross Sectional Area, as necking occurs and area decreases then localised stress also increases. However, this is difficult to measure in-situ and does not provide additional useful material (since the useful limits of the material as a structural material have been far exceeded). To simplify matters, the “Engineering Stress” is defined as Load / original cross sectional area.Also see Stress and True Stress

HardA material property that describes the resistance of a material to being deformed.Opposite = Soft

Load The Force in Newtons applied to the specimen.

Necking The localised deformation and characteristic thinning of a specimen during ductile flow.

PlasticThe ability of a material to undergo permanent shape changeOpposite = Elastic

Stiffness The resistance of a material to elastic deformation.

Engineering Strain The ratio of extension to original length: usually expressed as a percentage. The quantity is dimensionless so has no units.

Strain RateHow fast the strain increases. This should be a constant for tensile tests. Since strain is dimensionless, the strain rate has the curious unit of s-1. Pupils would find this curious and it could open a route to discussing units with a link to speed for revision purposes.

Stress

The Force per unit area – same as a reduction in pressure (negative pressure) – and has the effect of standardising the load to be comparable to specimens of any cross sectional area: again, this is a useful discussion point to discuss units – with a link to pressure for revision purposes.Compression would be the equivalent of an increase in positive pressure.

ToughA material that resists cracking by absorbing a large amount of energy before it breaks. Ductile materials are tough.Opposite = Brittle

True Stress

If the stress at the site of necking is determined from in-situ measurements of cross sectional area, then the True Stress at that point would be known. As load decreases, the area decreases even faster, so that the True Stress continues to rise up to failure.Also see Stress and Engineering Stress

UTS Tensile Strength (or Stress). This corresponds to the maximum (if there is one) of the test material.

Yield Point /Yield Stress /

The point, just above the linear region of the stress v strain curve, at which plastic deformation results in permanent change in shape of the material.

Elastic Limit

Stress-Strain Diagrams Recorded on a Tensometer

The shape of the curves can be misleading due to a combination of the design of the Tensometer, which is designed to provide a constant strain rate, and the behaviour of the ductile specimen being tested. The following refers to specimen charts illustrated in the Excel file, Tensile Tests.xls, on the OxMAT CD ROM (Reprinted for reference in the Appendix).

An overview of the properties of a ductile metal can be explained below. This is most closely represented by Copper in the data provided in the spreadsheet, but all ductile metals show some of these characteristics. Difference corresponding to carbon steel are considered later.

In the case of the three metals shown in the chart, all follow the following general patterns:-

In the diagram (right)

O = Initial originOO1 = Permanent elongationA = Elastic limitOA = Linear regionB = General point beyond ABO = Relaxation if stress removed(Note: O1B is parallel to OA)C = Maximum StrengthAC = Region of plastic DeformationX = FailureCA = Plastic Flow(Note: This is the region where “necking” or localised thinning of the specimen takes place.)

The overall shape (not values) of the curve would be the same for a plot of Force v length. However, plotting (Engineering) Stress v Strain standardises the curve to an initial cross sectional area of 1m2 by dividing by the initial cross sectional area.

Problems: The plot assumes that the initial cross sectional area and length are constant throughout. This is not the case.

• The volume of material remains constant, therefore as the length increases, the cross sectional area decreases. This effect is minute and is generally ignored over the elastic region.

• Once necking takes place, however, reduction in the cross sectional area at that point becomes marked. This is not normally allowed for in these plots and can

A

B

OO

1

C

Engineering Stress (Nm-2)

Strain (No dimensions)

X

give rise to misleading observations. Since the Stress is determined by Load/Area, as localised area decreases, the stress will, in fact increase at this point. As the Tensometer cannot measure the decrease in cross sectional area, it is not actually measuring the “True stress”, but the stress assuming a constant cross-sectional area, referred to as the “Engineering stress”.

Engineering stress is generally used for simplicity, since once this starts to happen, any safe loading has been exceeded by far, and few structures are designed to fail in such a precise way. Exceptions may include safety bolts that are designed to fail under dangerous loading conditions.

Line OA: The line is linear and the material follows Hooke’s Law. Relieving stress returns the specimen to its original, unstretched length.Beyond A: the stress is such that dislocations (later) in the crystal start to move. This changes the spatial arrangement of some of the atoms relative to each other, hence a permanent change in length is observed and the line is no longer linear.Relaxing the specimen of all stress at this point allows the Stress v Strain line to follow a path parallel to the line OA, as the slope is a property of the material (Young’s Modulus = Stress/Strain), but returns to point O1 where OO1 indicates the permanent extension resulting from the movement of dislocations.

Carbon SteelsThe above applies to carbon steels also, but the alloying element carbon affects the behaviour of the dislocations.

Carbon atoms are small compared to iron and tend to fit between iron atoms in the crystal lattice (interstitial alloy), as opposed to occupying the site of an iron atom in the crystal as happens with metal-metal alloys (substitutional alloys).

The position of carbon atoms increases the local stress (same dimensions as pressure) in the crystal. If the atoms could be positioned in a region where the crystal lattice is imperfect, and greater gaps between iron atoms are found, then the stress will be reduced. Placing the interstitial atoms in these spaces (see dislocations, later) forms a lower energy situation than having the carbon distributed within a perfect crystal lattice. Such imperfections occur at grain boundaries (where crystals of different orientation meet) and at dislocations. Natural systems adjust from high to low energy systems, therefore, to minimise the energy of the system, carbon atoms diffuse to these sites – that is, grain boundaries and dislocations.

Carbon atoms occupy the larger than usual gap at a dislocation. This prevents the dislocation from moving and is said to “pin” the dislocation.

If the dislocations in iron are pinned, then they cannot move, preventing plastic deformation at

C SteelPure Iron

NOT TO SCALE

Stress

Strain

stress values that would otherwise result in plastic deformation. This extends the useful range of the iron by extending the elastic region of the stress v strain curve. There is a limit, however, and once it is reached, the dislocation is forced past the carbon atom that has been pinning it. This results in a slight relaxation and an initial peak at the end of the elastic region. More dislocations are pinned, preventing further deformation, hence the line rises again. This stress and relaxation pattern repeats a number of times giving the series of peaks observed in the graph.

Elastic Limit and Limit of Proportionality – A Closer Look

In the detail of a stress strain diagram…

EL = Elastic Limit

LP = Limit of Proportionality

From origin to LP, the metal obeys Hooke’s Law. That is:-

Stress ∝ Strain

Furthermore, extension is not permanent, and removing the load will return the metal to its original size and shape

Beyond the point LP, but NOT coincident with it, is a point at which plastic flow starts to occur, EL.

Beyond EL, there are two components to the extension, such that if the load is removed and elastic component will result in the material trying to regain its original size and shape, but also there will be a plastic deformation, resulting in a permanent increase in length.

The region BETWEEN LP and EL is also purely elastic, with full recovery on the unloading of the metal, but is NOT linear.

To explain this feature, we need to consider the Potential Energy between metal atoms as the separation of the atoms changes. As the atoms approach, the PE changes:-

1. Decreases (-) due to electronic / bonding effects (inverse square law).

a. Over relatively large distances, the attractive force dominates.

b. Approaching from infinity (moving right to left in figure 2a on the next page), the PE increases to a large negative value (- for attraction) as the extent of electronic / orbital overlap increases.

c. The PE increases as the square of the distance.

2. Increases (+) due to repulsive forces between nuclei (inverse cubic).

a. Over very short distances, the repulsive force dominates

b. As the nuclei approach (moving right to left), electrostatic repulsion increases the PE (+ for repulsion) between the atoms

c. The PE varies as the cube of the distance.

3. There is an equilibrium position where the forces balance and the PE is at a minimum value referred to as the Potential Energy well illustrated in Fig 2b on the next page. This corresponds to the bond length, or lattice parameter in the case of a cubic metal crystal.

EL

LP

Path taken on unloading

BEFORE ELPath taken on

unloading AFTER EL

Strain

Stress

4. The PE well is not symmetrical. To the left, repulsive forces (varied as 1/distance cubed) dominate and to the right, attractive forces (varied as 1/distance squared) dominate.

5. Compressing the material is, therefore harder than extending the material.

6. In extending the material, the atomic distance is increased. Over a short period of time, this approximates to a linear relationship.

7. Larger distances reduce the attraction between neighbouring atoms making it easier for bonds to break and reform, e.g. at a dislocation, where a strained bond breaks but reforms with a closer neighbour. Hence we get plastic deformation.

8. Between the linear, elastic region and the onset of plastic deformation is a region in which

a. The relationship between force and distance is NOT linear, but…

b. The attractive forces do not allow for bonds to break, hence…

c. A non-linear, elastic region is recognised.

Stress-Strain Plots for Different Carbon Contents

0.00E+00

1.00E+02

2.00E+02

3.00E+02

4.00E+02

5.00E+02

6.00E+02

7.00E+02

8.00E+02

9.00E+02

1.00E+03

0.00E+00 5.00E-02 1.00E-01 1.50E-01 2.00E-01 2.50E-01 3.00E-01 3.50E-01 4.00E-01 4.50E-01 5.00E-01

Millions

Strain

Stress /

Pa

0.02% C 0.18% C 0.41% C 0.54% C 0.8%C 3%C

Variation of Stress-Strain charts with increasing carbon content

Steel Samples Compared

A medium carbon steel (top) compared to a high carbon steel (below).

Note the relatively large extent of necking and permanent increase in length of the medium carbon specimen compared to that of the high carbon specimen.

Both steels are compared with an untested original specimen to allow for relative measurements to be made.

Low Carbon Steel Fracture Surface.

Note the dimpled interior structure indicating ductile failure and a surrounding smoother “shell” which denotes a brittle failure across crystal planes. Most metals will exhibit this mixed failure pattern in varying degrees.

Medium Carbon Steel

High Carbon Steel

Glossary of Metallurgical terms used

There are different structures that occur depending on the amount of carbon present and the heat treatment that the steel has been subjected to. The different structures are readily identified by observing the microstructure. The terms used to explain these images are explained briefly, below. The explanations relate to the text of this resource and should not be considered to be exhaustive.

Austenite: Gamma (γ) iron (not magnetic). Austenite is a face-centred-cubic (fcc) lattice of iron which is the thermodynamically stable form of steel at high temperatures. Carbon can dissolve in austenite interstitially. On cooling, transformations to other phases take place, the exact structure (and hence properties) being dependent on cooling rate. Cementite: Iron carbide (Fe3C). Orthorhombic crystalline structure which forms in low carbon steel as lamellae in pearlite. As carbon content increases, the amount of ferrite decreases and the amount of pearlite increases. At ~0.80 to ~0.85%C all of the microstructure is pearlite but once the carbon content exceeds ~0.85%C cementite forms as a distinct phase with no ferrite present (other than that within the pearlite). Ferrite and cementite look very similar in micrographs and experience is needed to identify them in a steel of unknown carbon content.

Ferrite: Alpha (α) iron (magnetic). For most practical purposes, ferrite can be considered as ‘pure’ iron, being soft, ductile and of relatively low strength. Ferrite typically contains a maximum of 0.03% carbon. The iron forms a body-centred cubic lattice with carbon atoms dispersed interstitially. The magnetic properties of iron are due essentially to ferrite.

Normalise: This is a preliminary heat treatment in order to allow all carbon to dissolve interstitially and relieve internal stresses from working etc. The temperature is raised to 860˚C for one hour before allowing the steel to cool in still air.

Pearlite: This is found in all slowly cooled structures of carbon steels and consists of alternate layers of ferrite and cementite. As the carbon content of the steel increases, the amount of pearlite increases with a consequent reduction of ferrite content. At appropriate magnification the pearlite structure has a fingerprint-like appearance. When etched, a striped appearance is given to the microstructure. The separation of lamellae depends on the angle with which the crystal strikes the surface. At small angles, the lamellae can behave as a diffraction grating and produce a “mother of pearl” impression in white light - hence the term pearlite.

Surface of the steel

Lamellae viewed from above

Lamellae approaching the surface at different angles

Work: In the context of applying a force which brings about a mechanical change, Work is done to move dislocations, induce internal stress, cause fractures etc.

Summary of the microstructures%C Low Mag High Mag

0.02

Very low Carbon. Little or no pearlite.

0.18

Once the iron is “saturated”, pearlite starts to appear.

0.40

Increasing carbon content results in increasing pearlite formation.

0.54

Pearlite is easily resolved in the optical microscope.

0.80

More pearlite forms with increasing C content. Pearlite is clearly visible as “zebra” stripes within a grain.