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**How to Choose the Right Material**

1E10 Lecture by David Taylor Mechanical Engineering Dept

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What’s It About? This lecture is about the mechanical properties of materials… …how to measure them and use them. It’s important for any material which is going to be subjected to mechanical forces in use. These forces cause the material to deform (i.e. change shape) and may cause it to fail (i.e. break).

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**Mechanical Properties in Design**

Designers need to know about mechanical properties… …to choose the right material for a given component (e.g. a car’s crankshaft) or structure (e.g. a dam). They need to make sure that there won’t be too much deflection under load, and that the forces won’t be high enough to cause failure.

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Examples of Failures A 737 engine; one of the turbine blades broke away and exited through the engine casing, nearly taking someone’s head off!

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Examples of Failures X-ray showing an artificial hip joint, made of metal, which broke in two whilst inside someone’s leg. As an engineer, you don’t want to be famous for designing a component that failed.

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**Defining and Measuring Mechanical Properties**

There are lots of mechanical properties; in this lecture we are just going to look at the simplest (and most important) ones, which we call the “static” properties. These can be measured using very simple tests, conducted on samples of the material. The most important test is the tensile test…

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**The Tensile Test FORCE F Take a sample of material**

Pull on the ends to stretch it Measure the force needed You can also apply other types of loads, such as compression or torsion, but we’ll stick to tension here. Original Length Lo Stretch to new length L

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Some Practicalities You can use any size and shape of sample provided it has parallel sides… …so the cross section is the same throughout. The shape of the cross section doesn’t matter, it can be rectangular (as here), square, circular, etc. Its area is A. Normally we make the ends of the specimen bigger so it’s easy to grip in the testing machine Cross Section of Sample, area A

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**The Stress/Strain Curve**

We want to see how much the sample stretches for a given applied force. So we could plot the force, F, against the stretch (L-Lo). But it’s better to normalise these quantities, so that the overall size of the sample doesn’t matter. We do this by calculating the STRESS, s, which is F/A and the STRAIN, e, which is (L-Lo)/Lo.

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Typical Results The stress/strain curve has different shapes in different materials; below are some examples. As strain increases, stress can go up or down X indicates the point at which the sample breaks X X X (units N/m2 = Pa) Stress s X Strain e (no units)

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**The stress/strain curve in more detail…**

First Stage: Elastic Deformation In this part of the curve, the material behaves like a spring. If you remove the stress, the strain goes back to zero. Stress is (usually) proportional to strain. Stress s X Strain e

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Stiffness The material’s “stiffness” is the slope of the stress/strain curve in the elastic region. Called Young’s modulus (or the elastic modulus), symbol E. If the line is straight then E = stress/strain at any point on the line.

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Using Stiffness You can use E to calculate the strain for a given stress, and therefore work out how much the structure will deflect under load… …e.g. how much a car’s suspension will move when six people get in. Also used to find the stress in the material for a given amount of deformation… …if this stress is too high it may fail.

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**Using Stiffness Also used to prevent buckling.**

Buckling is what happens when you have a long, thin, structure loaded in compression… …like a straw or a drinks can when you push on the ends. It suddenly “gives” – this is buckling. The analysis of buckling is complex – the important thing is that the only material property it depends on is E.

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Elastic Energy If you load up a material in its elastic region, to some stress s… …then the area under the line is a measure of the energy you used to do it. This area is actually the energy per unit volume of material in the sample This energy is stored in the material and will be released if you unload it. This is very useful in a mangonel, for example! Stress s X Strain e

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**Non-Linear Elasticity,Hysteresis**

In some materials (e.g. some polymers) the stress/strain line is curved in the elastic region… …and sometimes the loading and unloading lines are different. Loading Unloading

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**Non-Linear Elasticity,Hysteresis**

In that case E is not constant… …and some energy is lost, (given by the area between the lines). This is called hysteresis. Loading Unloading

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**Plastic Deformation, Damage and Failure**

Above a certain stress, sy, the stress/strain line becomes flatter and curved, and unloading gives you a permanent deformation. e.g. if you load up from O to point A and then unload, you get back to B, not O. The distance OB is the plastic strain left in the material A sy X Stress s O B Strain e

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**Plastic Deformation, Damage and Failure**

Why does this happen? It depends on the material. In metals, plastic strain occurs because the atoms in the material can flow over each other. In other materials, such as concrete and wood, it’s due to damage in the material; small cracks and splits which weaken it. The important thing is that we can’t use the material at a stress greater than sy, so for engineering purposes it’s the maximum allowable stress.

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**Plastic Deformation, Damage and Failure**

Two other points from the stress/strain curve: The maximum point in the curve is called the Ultimate Tensile Strength (UTS). We used to use this as a measure of the strength of a material but these days we normally use sy. The strain and stress at the failure point X (ef, sf) are also useful to know. ef is called the “ductility”; it tells you how much deformation the material can take without failing, which is useful for manufacturing operations like forging and wire-drawing.

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**Energy Again, Toughness**

The area under the whole stress/strain curve is the energy (per unit volume) needed to make it fail. But you get some energy back in elastic recoil (the black triangle). The remaining area is the energy absorbed by the material in failing. This is one measure of the “toughness” of the material. Stress s X O Strain e

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More About Toughness Toughness is a property which is difficult to define. One definition is the energy to failure (as above)… …but these days we normally use the so-called “fracture toughness” which is a measure of how easily the material cracks. You’ll learn more about toughness (and other mechanical properties) in the materials course next year.

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Summary We’ve seen that the simple tensile test can tell you a lot about how a material performs under load… …how much it deforms, both temporarily (elasticity) and permanently (plasticity)… …how much energy it can store and release… …and how much stress and energy are needed to break it.

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What’s the stress? This material information is useful only if you know what stress (or strain) is going to arise in the component or structure that you’re designing. In the tensile test the stress is simply found by F/A, but that’s not the case for a real structure, where the stress will depend on the shape and forces it sees, and will vary from place to place in the structure. Stresses can be calculated for any structure; these days we mostly use computer models (such as finite element analysis) but you can use analytical equations for simple structures like beams and arches, and to get a rough estimate in more complex cases. You will learn more about stress analysis in other lectures and other courses.

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**More Information If you want to learn more, try…**

Textbooks by Ashby & Jones: Engineering Materials books 1 and 2. We use these books in courses in 2nd and 3rd year. Materials by Ashby, Shercliff and Cebon Lots of information on line, in Wikipedia, company databases, etc

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Elasticity and Strength of Materials

Elasticity and Strength of Materials

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