In this book the authors focus on the description of the physical nature of cleavage fracture to offer scientists, engineers and students a comprehensive physical model which vividly describes the cleavage microcracking processes operating on the local (microscopic) scale ahead of a defect. The descriptions of the critical event and the criteria for cleavage fracture will instruct readers in how to control the cleavage processes and optimize microstructure to improve fracture toughness of metallic materials. - Physical (mechanical) processes of cleavage fracture operating on the local (microscopic) scale, with the focus on the crack nucleation and crack propagation across the particle/grain and grain/grain boundaries - Critical event, i.e., the stage of greatest difficulty in forming the microcrack, which controls the cleavage fracture - Criteria triggering the cleavage microcracking with incorporation of the actions of macroscopic loading environment into the physical model - Effects of microstructure on the cleavage fracture, including the effects of grain size, second phase particles and boundary - Comprehensive description of the brittle fracture emerging in TiAl alloys and TiNi memory alloys