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Abstract. Calculation of a stress intensity factor becomes more difficult when crack are subjected to a complicated stress distribution profile. A standard procedure called influence coefficients is inadequate because a stress profile may not be accurately represented by a polynomial function. This paper applies a piecewise linear approximation of stress profile and a weight function method to overcome that restriction. However, the typically adopted weight function, i.e. universal weight function, is replaced by a weight function, in which its form coincides with the analytical form. Although a new weight function consists of lesser number of terms, it is proved to be accurate when applies to a cracked-cylinder problem, e.g. internal part-through circumferential crack and internal fully circumferential crack under various complicated weld residual stress profiles. Using this simpler weight function and linearized approximation scheme led to a closed-form stress intensity factor solution, which is convenient for programming.

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