Materials

Materials

1. Hooke's Law

   • The extension of a stretched object is proportional to the load or force applied to it, up to the limit of proportionality
     • The graph of a material which obeys Hooke's law will start with a straight line through the origin
   • F=kΔL
     • K=stiffness constant. An objects stiffness constant is the force needed tot extend it by 1m
   • The limit of proportional/Hooke's law limit is the point beyond which force is no longer proportional to extension
     • The elastic limit is the force beyond which a material will be permanently stretched
   • An elastic material returns to its original shape/length once the forces acting on it are removed
     • A plastic material is permanently stretched once the forces acting on it are removed

2. Density

   • The mass per unit volume of a material or object
   • ρ=m/v
   • A solid object will float on a fluid if it has a lower density than the fluid

3. Stress and Strain

   • Tensile stress
     • stress=F/A
       • Unit for stress=Nm^-2 or Pa
   • Tensile strain
     • strain=ΔL/L
       • Strain has no unit
   • Breaking stress is the lowest stress that's big enough to break a material
   • Ultimate tensile stress(UTS) is the maximum stress that a material can withstand
   • Elastic strain energy is the energy stored in a stretched material
     • E=1/2FΔL
       • E=1/2k(ΔL)^2
   • Work done=1/2F x ΔL
     • Area of triangle orarea underneath the straight line on a force-extension graph
   • Yield point (or yield stress) is the stress at which a large amount of plastic deformation takes place with a constant or reduced load

4. Young Modulus

   • Young modulus, E, = tensile stress/tensile strain
     • E=F/A/ΔL/L
       • E=FL/AΔL
   • The stress-strain graph is a straight line provided that Hooke's law is obeyed
     • The gradient will give you the Young Modulus
     • The area underneath = strain energy per unit volume
       • Energy per unit volume=1/2 x stress x strain

5. Brittle Materials

   • A brittle material doesn't deform plastically, but snaps when the stress on it reaches a certain point
   • Brittle fracture is when a stress applied to a brittle material causes tiny cracks at the material's surface to get bigger until the material breaks completely
   • Examples: chocolate bar, ceramics (glass, pottery)