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Deforming Solids

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Stretching a spring Strain energy Stretching materials Describing deformation

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Stretching a Spring

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Hookes Law states that The extension is proportional to the force The spring will go back to its original length when the force is removed So long as we do not exceed the elastic limit

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Graphs

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Interpreting Graph Strain Energy

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Stored ability to do work due to stretching or compression or displacement

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Combination of Springs

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Deformation of Rubber Band Hysteresis

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Deformation of Rubber Band Hysteresis

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Elastic versus Plastic Elastic Behaviour Material has the ability to go back to its original shape Elastic Limit A point where beyond it the material is permanently deformed

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Elastic versus Plastic Plastic Behaviour Material has been permanently deformed but not broken

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Describing Deformation Stress Measure of force required to cause a particular deformation Force per unit area Pressure Units: Nm 2 Pascal

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Describing Deformation Strain Resulting deformation Extension divided by original length Dimensionless quantity

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Testing Materials

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Describing Deformation Young Modulus, Y Ratio of tensile stress to tensile strain Units: Nm - 2 Pascal

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Some interesting values of Young Modulus DNA ~ 10 8 Pa spaghetti (dry) ~ 10 9 Pa cotton thread ~ 10 10 Pa plant cell walls ~ 10 11 Pa carbon fullerene nanotubes ~ 10 12 Pa

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Materials

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Graph

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Interpreting Graph Slope = Young Modulus Ultimate Tensile Stress Maximum stress a material can withstand before breaking

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Measuring Young Modulus

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Describing Deformation Curve A shows a brittle material. Strong The fracture of a brittle material is sudden and catastrophic Example: cast iron

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Describing Deformation Curve B is quite brittle and slightly ductile Brittle but deforms before breaking Example: steel

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Describing Deformation Curve C is a ductile material Deforms permanently Drawn into thin wires Examples are copper and gold

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Describing Deformation Curve D is a plastic material. Deforms permanently Deformation is not proportional to stress applied Example is polyethylene

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Materials