Materials

Materials

1. Density

   • Density is the mass per unit volume of a substance in kgm-3
   • Density depend on what the object is made of, not the shape. It also determines whether it floats or sinks.

2. Hooke's Law

   • The extension of a stretched wire is proportional to the load/force
     • F=kΔL
       • k = the stiffness constant (force needed to extend the wire by 1m)
   • A metal spring also changes length when a pair of forces are applied
     • For springs, k = spring constant
     • Hooke's law works the same for compressive and tensile (stretching) forces
   • The Limit of Proportionality is the point beyond which the force is no longer proportional to the extension, Hooke's Law tops being true
   • If you increase the load beyond the Elastic Limit, the material will be permanently stretched.
     • Stretching beyond the elastic limit shows Plastic Deformation
   • If a deformation is elastic, the material returns to its original shape once the forces are removed.
     • Atoms don't actually change positions, just move relative to their equilibrium position.
     • For a metal, elastic deformation happens as long as Hooke's Law is obeyed.

3. Stress and Strain

   • Tensile Stress is force applied divided by cross sectional area, measured in Pascals
     • Stress pulls the atoms apart from each other. Eventually the stress becomes so great that the atoms separate completely.
       • This is called breaking stress/fracture stress
   • A stress causes a strain. Tensile strain is the change in length divided by the original length, it has no units.
   • Tensile forces = positive Compressive forces = negative
   • Ultimate Tensile Stress (UTS) is the maximum stress te material can withstand.
   • Work done in stretching is stored as potential energy in the material called elastic strain energy
     • On a load/extension graph, this is equal to the area under the graph
     • E=0.5FΔL >>> (F=kΔL) >>> E=0.5k(ΔL)^2

4. The Young Modulus

   • E=tensile stress/tensile strain
   • Below the Limit of Proportionality, stress divided by strain is constant. This constant is Young Modulus (E).
   • THE EXPERIMENT
     • 1. As long as possible (over 1m) to reduce percentage uncertainty. 2. As this as possible wire to get higher extension for the same force.
     • 3. Measure the distance between the fixed end of the wire and the marker using a ruler to find the unstretched length. The marker will move when you increase the weight.
     • 4. Increase the weight by steps, recording the marker reading each time. The extension is the difference between this reading the unstretched length.
     • 5. Once taking a range of readings (possibly repeat for accuracy), use a micrometer to measure the diamerter of the wire in several places. Take and average of this and use it to work out the cross sectional area of the wire.
     • 6. Calculate stress and strain for each weight and use this to plot a stress vs. strain graph. Find the gradient of this graph, which will equal the Young Modulus of the wire.
   • The area under a stress vs. strain = energy per unit volume = 0.5stressstrain

5. Interpreting Stress-Strain Curves

   • Yield Point is where the material suddenly starts to stretch without any extra load. A large amount of plastic deformation takes place.

6. Brittle Materials

   • Stress strain graph for a brittle material starts with a straight line through the origin, so it obeys Hooke's Law
     • But it doesn't begin to deform plastically. When stress reaches a certain point the material fractures.
   • Examples of brittle materials include pottery, glass and chocolate.
   • Ceramics have a crystalline structure which makes them very rigid. This makes them highly brittle.
     • When stress is applied, tiny cracks form at the surface and get bigger until the material snaps completely. The cracks grow due to the rigid structure.
     • Metals are ductile because the atoms can move to prevent cracks growing big enough to fracture.

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