3.4.2 Materials

3.4.2 Materials

1. Bulk properties of solids

   • density, symbol - ρ
     • ρ = mass / volume
       • unit - kg m^(-3)
   • Hooke's Law
     • F = kΔL
       • k - stiffness of spring, spring constant
       • doesn't apply after elastic limit has been exceeded
         • plastic deformation
     • Spring combinations
       • two in parallel
         • total spring constant is individual spring constants added together
         • same ΔL
       • series
         • 1/k = 1/kp + 1/kq
         • ΔL = ΔLp + ΔLq
     • elastic potential energy stored in a stretched sping, Ep = FΔL/2 = kΔLΔL/2
       • area under force-extension graph
   • tensile stress
     • σ = T / A
     • unit - Pascal (Pa)
     • max. tensile stress= ultimate tensile stress = breaking stress
       • beyond breaking stress, wire loses strength, extends, and becomes narrower at its weakest point
   • tensile strain
     • ε = ΔL / L
       • ratio therefore no units
   • material descriptions
     • strength = UTS
     • stiffness = gradient of stress-strain line
     • brittle = snaps without any noticeable yield
     • ductile = material can be drawn into a wire

2. The Young modulus

   • Young modulus = tensile stress / tensile strain = FL/(AΔL)
     • therefore Young modulus is the gradient of the line on a stress-strain graph
   • elastic energy stored in a stretched wire = TΔL/2
   • work done to deform an object is referred to as strain energy

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