# Materials

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## 11.3 Deformation of Solids

• The elasticity of a solid material is its ability to regain its shape after it has been deformed or distorted, and the forces that have deformed it have been released.
• Deformation that stretches an object is tensile.
• Deformation that compresses an object is compressive
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## 11.3 Deformation of Solids (cont)

• A tension/extention graph shows how easily stretched certain materials are.
• A material is held at its upper end and loaded by hanging weights at its lower end.
• Weights are added and extention is measured with each load increase.
• Extention measured with a set-square.
• The weights are then removed until there is zero tension.
• Tension is equal to weight
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## 11.3 Deformation of Solids (cont)

• Tensile stress is the tension per unit cross-sectional area, = T / A. Its units are pascals, or Newtons per square metre.
• Tensile strain is the extention per unit length, change in L / L. It is a ratio and therefore has no units
• In all materials, stress is proportional to strain until the limit of proportionality is reached.
• Until then, the stress/strain value is a constant, known as the Young's Modulus of a material.
• The Young's Modulus of a wire material can be measured using Searle's apparatus.
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## 11.3 Deformation of Solids (cont)

• Two wires of the same material are attached and hung at a rigid support. One of the the wires is a control wire, the other is the test wire.
• Further down on the wires, a spirit level is attached across the two wires, and hinged on the control wire.
• A micrometer is attached so that when the spirit level is moved about the hinge, the extension can be accurately measured.
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## 11.3 Deformation of Solids (cont)

• Measure the initial length of the control/test wire (same) several times using a ruler and take an average
• Measure the diameter at several points along the wire using a micrometer, and take an average.
• Calculate the cross-sectional area from this data.
• Record the micrometer reading when the spirit level is horozontal. Add test weights to the test wire, and record the new micrometer reading. Subtract the old micrometer reading from this. Calculate the stress and strain from your data. Repeat and plot a graph
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## 11.3 Deformation of Solids (cont)

• Beyond the limit of proportionality is the elastic limit, which is the point beyond which the material is perminantly stretched and suffers plastic deformation.
• The breaking point is the point where the material breaks. Just before this is the ultimate tensile stress (breaking stress), where the wire loses its stength  and becomes narrower (drops in stress).
• The stiffness of a material is shown by its Young's Modulus. Greater Young's Modulus means material is more stiff
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## 11.3 Deformation of Solids (cont)

• The strength of a material is its maximum stress, which is its ultimate tensile stress/breaking stress.
• A brittle material snaps without noticable yield.
• A ductile material can be stretched/drawn into a wire easiliy.
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## 11.4 More about Stress and Strain

• If a metal wire is stretched beyond its elastic limit, the unloading line is parallel and to the right of the loading line.
• When the wire is completely unstretched it will be slightly longer, so it will have a perminant extention
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## 11.4 More about Stress and Strain (Cont)

• The rubber band returns to its original length, so it has a high elastic limit.
• However, the line is proportional for a very small load; it has a small limit of proportionality
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## 11.4 More about Stress and Strain (Cont)

• A polythene ***** is the same as a rubber band, except it has a low elastic limit as well as a low limit of proportionality.
• As a result, there is a perminant extention as the polythene undergoes plastic deformation
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## 11.4 More about Stress and Strain (Cont)

• The area under a force-extention graph is equal to the work done to stretch the wire.
• The work done to deform an object is referred to as the strain energy.
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