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This lecture discusses the concept of crack-tip energy dissipation in brittle and ductile materials, emphasizing the role of dissipative processes in crack growth. It introduces the Cohesive Zone concept, explaining how tractions and crack openings are interdependent. The Atomistic Cohesive Zone Law is presented, detailing the procedure to determine surface stress and tractions along the crack plane. The lecture explores how crack growth evolves with increasing applied stress, from no growth to maximum toughening, considering the energy dissipation and damage zones. Fracture at the atomistic scale is analyzed, highlighting the cohesive zone associated with surface energy. The importance of understanding cohesive zones in fracture mechanics is underscored.