Taking a double cantilever beam (DCB) as a representative of one dimensional fracture, a unique pair of pure fracture modes I and II are successfully found in the absence of axial forces, which are orthogonal to each other with respect to the coefficient matrix of the energy release rate. Although the pair are pure modes there still exist interactions between them. The interactions result in energy flow between the two modes and are successfully determined. With the presence of axial forces, there are two independent pure modes I and two independent pure modes II, which are orthogonal to each other as well. They are found and used to partition the total energy release rate.