TIGHT CRACK MODELING FOR THE FINITE-ELEMENT SIMULATION OF INSPECTION TOOLS IN PIPELINES

Tight crack numerical modeling is of importance to the gas transmissio n industry for the prediction of inspection tool responses to stress c orrosion. The presence of a crack is modeled by corresponding changes in electromagnetic values sigma and mu of the pipe wall material. Thes e changes can be approximated by some general rational polynomials for implementation in a finite element formulation in Cartesian, cylindri cal, and polar coordinates. To minimize the mesh density, these change s in electromagnetic values only in elements adjacent to the crack wal l are modeled, thus allowing these values to vary within single elemen ts. Special shape functions in the finite element formulation must be used to achieve high accuracy. These special shape functions are deriv ed from the governing partial differential equations and the crack cri teria model, corresponding to analytical solution of the properly chos en I-D differential equations. Examples of the computed distribution o f the magnetic field around cracks in a pipe, as well as corresponding NDT signals are, shown.