An approximate and simple expression is presented to calculate the crack face displacements of collinear cracks and center cracks by use of only one reference stress intensity factor. The crack face displacement and its partial derivative determined by the present method are in good agreement with their exact solutions. Calculations of weight functions for the center crack are reduced to the simple quadrature of the correction function and of the partial derivative of the crack face displacement. Based on the weight function method, the relationships between the stress intensity factor of the rotating blade with a center crack to the crack length, crack location, rotating speed and angular acceleration are studied. The critical rotating speed of the blade is evaluated based on the fracture law.