Stress, Strain and Young's Modulus
Stress is force per area - strain is deformation of a solid due to stress
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Stress
Stress is defined as "force per area".
Stress normal to the plane is usually denoted "normal stress" and can be expressed as
σ = Fn / A (1)
where
σ = normal stress ((Pa) N/m2, psi)
Fn = normal component force (N, lbf)
A = area (m2, in2)
Stress parallel to the plane is usually denoted "shear stress" and can be expressed as
τ = Fp / A (2)
where
τ = shear stress ((Pa) N/m2, psi)
Fp = parallel component force (N, lbf)
A = area (m2, in2)
Strain
Strain is defined as "deformation of a solid due to stress" and can be expressed as
ε = dl / lo = σ / E (3)
where
dl = change of length (m, in)
lo = initial length (m, in)
ε = unitless measure of engineering strain
E = Young's modulus (Modulus of Elasticity) (Pa, psi)
Modulus of Elasticity (Young's Modulus or Tensile Modulus)
Most metals have deformations that are proportional with the imposed loads over a range of loads. Stress is proportional to load and strain is proportional to deformation expressed by the Hook's law like
E = stress / strain = (Fn / A) / (dl / lo) (4)
where
E = Young's modulus (N/m2) (lb/in2, psi)
Modulus of Elasticity or Young's Modulus are commonly used for metals and metal alloys and expressed in terms 106 lbf/in2, N/m2 or Pa. Tensile modulus are often used for plastics and expressed in terms 105 lbf/in2 or GPa.
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