Unit 6: Deformation of Solids

• Load is the force that a body is subjected to as a result of a mass being added
• Extension: Tensile forces act away from the centre of the object, causing extension

  Compression: Compressional forces act towards the centre of the object, causing compression
• When tensile forces are exerted on a spring, it undergoes 'tensile deformation'; when compressive forces are exerted, it undergoes 'compressive deformation'
• Stress (σ) is the force per unit area that a body is subjected to
• Strain ( 𝝴 ) is the extension of a body following subjection to a load, divided by its original length
• Hooke’s law states that the strain experienced by a solid is directly proportional to the stress applied up until the limit of proportionality for that material
• The limit of proportionality is the load beyond which the extension of a body is no longer directly proportional to the magnitude of the load
• When hanging masses are suspended from a spring, the spring extends proportionally to the mass added up to the limit of proportionality for the spring
• Elastic deformation: the object returns to its original shape when the force is removed

  Plastic deformation: the object does not return to its original shape after the force is removed
• Energy stored during elastic deformation is transferred and stored as elastic potential energy
• Breaking stress is the amount of stress a material can take without breaking
• A brittle material breaks without any noticeable yield
• The elastic limit is the point after which plastic deformation occurs
• If no further load is added beyond the elastic limit, the material will continue to extend by plastic deformation
• The area underneath a force-extension graph represents the work done
• Elastic strain energy is calculated using the equation: E = ½ k ΔL^2
• Young’s modulus = tensile stress / tensile strain
• Young’s modulus is found from a stress-strain graph using the gradient of the line
• A material described as brittle tends to break rather than deform plastically shortly after the limit of proportionality is overcome
• Measurements required to determine Young modulus of a wire: Initial length, extension (initial and final lengths), weight (calculated from mass x g)
• Equipment necessary to determine Young modulus of a wire: Micrometer or vernier calliper, ruler, travelling microscope, scales, Newton meter
• To determine Young modulus from measurements: Stress = force / cross-sectional area, Strain = extension / original length, Young’s Modulus = Stress / Strain, Equal to the gradient from the stress-strain graph
• Graph B shows plastic deformation

  
• The material in the graph is brittle. There is no plastic deformation (it is elastic) and returns to the same length when the stress is removed. It obeys Hooke’s law

  
• Material is a polymer. It is elastic and returns to the same length when the stress is removed. It does not obey Hooke’s law.

  
• Diagram of apparatus to determine Young's modulus

  A) G-Clamp

  B) Wooden blocks

  C) Wire

  D) Workbench

  E) Pulley

  F) Masses