Calculating Young's Modulus of Elasticity

Calculating Young’s Modulus of Elasticity

Understanding Young’s Modulus of Elasticity

  • Young’s modulus, also known as the modulus of elasticity, gauges a material’s ability to withstand changes in length when under lengthwise tension or compression.
  • It has the symbol E and is measured in units of pressure (Pascal, Pa), typically gigapascals (GPa) or megapascals (MPa) in engineering.
  • Young’s modulus represents the stress-to-strain ratio in the linear elastic part of a material’s stress-strain curve.
  • A higher modulus means the material is stiffer, or more resistant to deformation, whereas a lower modulus indicates a more flexible material.

Calculating Young’s Modulus

  • The calculation for Young’s modulus is E = σ / ε, where E is Young’s modulus, σ is stress, and ε is strain.
  • Stress (σ) is the force applied per unit area. It can be calculated as σ = F / A, where F is force in newtons (N) and A is the area in square metres (m²).
  • Strain (ε) measures the deformation produced by the stress. It is the ratio of change in length to the original length and has no units – ε = ΔL / L, where ΔL is the change in length and L is the original length of the material.
  • For example, if a 100N force is applied to a 0.05m² sample causing it to change length from 1m to a final length of 1.01m, stress would be 100N / 0.05m² = 2000 Pa, and strain would be (1.01m - 1m)/1m = 0.01. Thus, Young’s Modulus would be 2000 Pa / 0.01 = 200,000 Pa or 200 kPa.

Interpreting Young’s Modulus

  • Materials with a higher Young’s modulus have a steep stress-strain curve, indicating that they deform less for a given applied force, compared to materials with a lower modulus.
  • Different materials require different amounts of stress to cause them to yield or rupture. Hence, Young’s modulus alone cannot be used to predict material failure.
  • Knowledge of the modulus helps engineers and scientists to predict how a material will perform under load and to select materials for specific applications. For example, materials with a higher modulus could be used when rigidity is necessary.
  • It’s important to note that the considered material must follow Hooke’s Law: the strain in the material is proportional to stress. If the material does not obey this rule, Young’s modulus cannot be accurately calculated.