Abstract: Starting with the nonlocal continuum theory, a new rational mechanics method is applied to study logically the cohesive stress law of ahead of a crack tip. First, the equivalence between the cohesive stress and the surface-induced traction (nonlocal surface residual) within the cohesive zone is established by introducing nonlocal stress boundary conditions on the crack surface. Then, by means of the energy balance relation, a new cohesive stress law of Mode I crack is obtained which is only concerned with the surface energy density within the cohesive zone. On the basis of the results, a concrete example of brittle balance is calculated to investigate the distribution of surface energy and cohesive stress which changes with the variation of crack opening displacement (COD). Finally, a summary of the study is provided and several conclusions are made. The results show that the stress singularity at the crack tip is removed, and the maximum stress may occur within the cohesive zone away from the crack tip.

Key words: nonlocal stress boundary condition, cohesive crack model, energy balance, surface energy, surface-induced traction, crack tip opening displacement, brittle fracture