Which factors affect the modulus of elasticity?

• A. Bonding and Temperature
• B. Bonding only
• C. Temperature only
• D. Grain size

Answer: (C)

Modulus of elasticity reflects how stiff a material is, which comes from the stiffness of the interatomic bonds in the crystal lattice. The factor among the options that can be varied for a given material is temperature. As temperature increases, atoms vibrate more, and the effective bond stiffness (the force constants) decreases, so the material becomes less stiff and the modulus drops. Bonding type is an intrinsic property of the material and won’t change without changing the material itself, so it isn’t a tunable factor here. Grain size affects many properties, but its influence on the elastic modulus is typically small, so it doesn’t play a major role in determining E. Hence, temperature is the factor that changes the modulus for a given material, making it the best answer.