| The thesis for doctoral degree consists of two part, while, the research of integral about elastic-plastic fracture mechanics and fracture criterion for mixed mode crack propagation. Now we describe it as follow:It is well known that the principle ofintegral is one of the classical theories of elastic-plastic fracture mechanics. As Irwin put forward stress intensity factor in the linear elastic fracture mechanics, Rice proposed a line integral , which has identical value for all paths encircling the tip of a crack, andintegral is a measure of singularities amplitude of stress and strain field near crack tip in elastic-plastic situation. The conservation ofintegral was given by Rice in 1967. Meanwhile, the critical value ofintegral JIC was determined by text method and is independence of the kind and size of specimens. The relation of J≤JIC can be considered as the criterion of elastic-plastic fracture. Rice, Rosengren and Hutchison made respectively approximate analysis of elastic-plastic deformation field with the aid of integral, furthermore, they drew the same conclusion: the stress and strain field near crack-tip possess the HRR singularities. Therefore, integral act as an important research tool of elastic-plastic fracture mechanics.On the basis of Orowan's investigation about the crack propagation in metal material, we realize that a yielding zone is formed in the vicinity of crack tip before crack growth. The system must supply enough energy for crack propagation, which is used for supplying the necessary surface energy of the incremental surface and plastic work caused such a plastic deformation. According to Orowan's investigation results, the amount of plastic work Γ is three orders larger than that of surface energy. However, the yielding of metal material is only associated with the deviator strain energy. A path independent line integralof the deviator strain energy is proposed by the authors. Meanwhile, the conservation of integral is proved strictly. Under the linear elastic situation, the relation of integral and stress intensity factor KI is derived. As application examples, mode-I stress intensity factors of cracked beams are obtained with present approach, the results are shown to agree well with those of Tada's handbook. The physical illustration of deviator strain energy release rate aboutintegral is given in this paper.In the end of part one, we found the formulas of calculatingintegral with aid of the finite element method. The method avoids the defect that the stress tensor can not be resolved into the spherical stress tensor and the deviator stress tensor at boundary. Fracture criterion for mixed mode crack propagation will be discussed in the thesis of part two. In practical engineering structures, due to unsymmetry of load distributed, crack direction and anisotropic of material. Crack subjected to a complex case of stress state. There are very important theoretical and practical values for research of fracture criterion relative to mixed mode crack propagation. The true cause and motive force of crack growth in all kinds of structures and materials have being investigated by researchers all the time. On the basis of same reason with part one of this dissertation, we think that true motive force of crack growth comes form the deviator strain energy release. So we put forward fracture criterion of the deviator strain energy density factor and fracture criterion of the deviator strain energy for the mixed-mode crack propagation, simplifies as criterion and criterion respectively. It denote the fact the distortion energy plays a major rule during the crack propagation in metallic materials, while the whole strain energy does not. As application examples, criterion and criterion predict successfully crack initiation angle and critical load for mixed-crack several problems. The results gained by using the present approach make coherence with experimental data in predicting crack initiation angles and it is better than S-criterion. Meanwhile...
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