By summarizing over seven hundred elastic constants of materials with various crystal structures, we have found that the so-called ductile-to-brittle transition originates from the bonding type transition. This can be reflected well by a universal linear relation between Cauchy pressure/bulk modulus (CP/B) and shear modulus/bulk modulus (G/B). In general, G/B of a material will gradually decrease with increasing pressure and temperature, while a significant change in G/B against increasing temperature often corresponds to a certain phase transition, such as magnetic transition, spin flipping, structural phase transition and so on. The present work suggests that the value of G/B for materials can serve as an indicator of bonding type. Importantly, this linear relation is robust for materials under temperature, pressure and with defects. Here we propose that damage tolerance properties can be experimentally measured from the elastic constants of a given material. It is suggested that a material with a value of G/B that varies little with temperature, pressure and defect concentration, potentially exhibits high damage tolerance. These observations shed light on the ductile-to-brittle transition. They may provide a potential tool towards the design of materials, particularly under extreme conditions.