Fatigue life estimation for planar cracks, e.g. part-through surface cracks or embedded cracks is very important because most of fatigue cracks found in welded built-up structures show planar crack morphologies. Although authors had proposed the estimation procedure of crack shape evolution for a planar crack based on the fracture mechanics approach, this method cannot apply if the values of stress intensity factor at the vertices of the surface crack approximated as an ellipse cannot calculated. Then, development of the shape evolution procedure of a planer crack under the stress field with arbitrary gradient, because fatigue cracks in welded built-up structures exist near the stress concentrated region. A Practical estimation formula the shape evolution of a surface crack under stress field with the gradient is proposed in this study. This formula is established by considering the stress field under no crack condition and some former proposed formulae under uniform and pure bending stress fields. The validity of the proposed formula are confirmed by comparing some measured surface crack shape evolutions under some stress gradient conditions.
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