Line singularity near the tip of a crack and of a fixed rigid line: unified treatment.

The elastic interaction between a line singularity and ei¬ther a single-ended crack or a single ended fixed rigid line (FRL), in generalized plane stress or plane strain condi¬tions, is considered. A single equation, representing the boundary condi¬tion for both the crack and the FRL problem, is written, and a unified treatment, based on the mapping by a complex differen¬tiable function and on the image method, is proposed. Formulas yielding the elastic potentials, the near tip elastic field, the stress singularity coefficients, and the J integral are de¬duced.