What is defined as the ratio of modulus of toughness to modulus of resilience?

The ratio of the modulus of toughness to the modulus of resilience is known as the ductility factor. Ductility factor is a measure that assesses the material's ability to deform plastically before fracturing, reflecting its toughness relative to its ability to absorb energy in the elastic range.

Modulus of toughness represents the total energy a material can absorb prior to failure, while the modulus of resilience indicates the energy absorbed during elastic deformation. By taking the ratio of these two moduli, the ductility factor provides insight into how well a material can withstand and deform under stress without breaking, offering a valuable parameter for evaluating material performance in engineering applications.

The other options represent different material properties but do not pertain to the specific relationship of toughness and resilience.