1 Separation of the Energy Release Rate of Fracture Tianmin Guo Siemens AG, Duisburger Straße 145, 47829 Krefeld, Germany e-mail: tianmin.guo@gmail.com _____________________________________________________________________________________________ Abstract Formally, the Griffith's energy release rate, the Irwin's integral expression of crack closure energy and the Rice's J-integral give same results for linear elastic material. But let us ask a question: do these three approaches really give an exact mathematical equality and an identical physical meaning? For this purpose, a uniform equation was therefore introduced into our new investigation. Thus, not only the Irwin's integral expression of crack closure energy and the Rice's J-integral can be derived from this uniform equation, but a very important result has been also obtained from them: the energy release rate is separable into two parts. The first part describes the extension of the crack front surface and the second the distortion. Keywords the Griffith's energy release rate, the Irwin's integral expression of crack closure energy, the Rice's J-Integral and the new found Sk-Integral und Tk-Integral _____________________________________________________________________________ 1. Introduction Cracks and fractures are known natural phenomena and occur everywhere in our daily lives. They are mostly associated with catastrophic consequences. Therefore attempts have been made for a long time to understand and finally to master them. As a pioneer, Griffith (1920) [2] has laid a foundation through examining these phenomena energetically. Based on the Inglis (1913) [1] identified stress and displacement field for an elliptical crack-like hole in an infinite plate, he has considered the energy balance and introduced a new quantity "energy release rate" into the fracture mechanics. His mind was so fundamental that it has always been of great importance for the further development of fracture mechanics. But his theory was limited only on linear elastic material behavior and mode I loading case. Irwin (1957, 1964) [3, 4] expanded the Griffith's thought on complicated load cases and established a relationship between the energy release rate and the stress intensity factor. So the stress intensity factor for linear elastic material has been widely used. A path-independent integral, the well-known J-integral was introduced by Cherepanov (1967) [11] and Rice (1968a) [7] into the fracture mechanics. Rice in particular has derived a connection between the Griffith's energy release rate and the J-integral and interpreted the J-integral as an extended energy release rate. Since that time, the J-integral rapidly disseminated and was used for elastic-plastic material in the fracture mechanics. All this shows a significant development in the classical fracture mechanics and is the foundation of the fracture mechanics. The classical fracture mechanics has found variety applications for many different areas. However, it must be clearly mentioned that it can only describe the crack problem in relatively simple cases and under certain conditions. It is not yet able to handle and exactly describe complicated crack problems in both natural events as well as in everyday life and eventually to solve. This situation can certainly not satisfy us and the problems mentioned above let us thoroughly think whether the foundation of the fracture mechanics is consistent and where and what has not
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