Tight crack modeling for the finite element simulation of inspection tools in pipelines

Tight crack numerical modeling is of importance to the gas transmission industry for the prediction of inspection tool responses to stress corrosion. The presence of a crack is modeled by corresponding changes in electromagnetic values σ and μ of the pipe wall material. These changes can be approximated by some general rational polynomials for implementation in a finite element formulation in Cartesian, cylindrical, and polar coordinates. To minimize the mesh density, these changes in electromagnetic values only in elements adjacent to the crack wall are modeled, thus allowing these values to vary within single elements. Special shape functions in the finite element formulation must be used to achieve high accuracy. These special shape functions are derived from the governing partial differential equations and the crack criteria model, corresponding to analytical solution of the properly chosen 1-D differential equations. Examples of the computed distribution of the magnetic field around cracks in a pipe, as well as corresponding NDT signals are, shown.