Simple and accurate model of fracture toughness of solids

Fracture toughness $KIC$ plays an important role in materials design. Along with numerous experimental methods to measure the fracture toughness of materials, its understanding and theoretical prediction are very important. However, theoretical prediction of fracture toughness is challenging. By investigating the correlation between fracture toughness and the elastic properties of materials, we have constructed a fracture toughness model for covalent and ionic crystals. Furthermore, by introducing an enhancement factor, which is determined by the density of states at the Fermi level and atomic electronegativities, we have constructed a universal model of fracture toughness for covalent and ionic crystals, metals, and intermetallics. The predicted fracture toughnesses are in good agreement with experimental values for a series of materials. All the ingredients of the proposed model of fracture toughness can be obtained from first-principles calculations or from experiments, which makes it suitable for practical applications.