Some remarks upon fracture mechanics

This work studies the basics of fracture mechanics. The theory proposed by Griffith is derived starting from the examination of the momentum and moment of momentum principles. A condition for crack growth is formulated. This equation also contains the influence of kinetic energy and continuum dissipation. The condition is expressed in the rate form i.e. it describes the response of a continuum in the case of a running crack. In the special case, the derived condition reduces to that proposed by Griffith. The present investigation derives 7 sufficient conditions for the path independency of the J-integral. The mathematical treatment of unbounded functions (due to the crack tip) is also considered, This study examines the relation between the J-integral and the potential energy. The present work brings out a new result: If a pure elastic deformation and crack tip singularity is assumed a previously not derived term has to be added to the above mentioned relationship. A computed example which studies the mode I of cracking and assumes a linear elastic, isotropic material behaviour shows that the value of this new term equals that of the J-integral.