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1 2004

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Local and global instabilities in ductile failure

Wnuk M. P.

Eksploatacja i Niezawodność

2004

nr 3

40-51

Catastrophic fracture in ductile solids is usually preceded by a certain amount of quasistatic crack growth that occurs as a result of void expansion and coalescence process associated with large deformations localized in the narrow zone adjacent to the crack leading edge. This zone is subject to a tri-axial state of stress, and its local properties may vary from those of the bulk material. To describe this condition a modified cohesive crack model is suggested based on the mesomechanical law of the S-stress distribution and equipped with the "fine structure" feature that is lacking in the standard model. Subcritical crack growth may be likened to the phenomenon of "preliminary displacements" known in the studies encountered in the physics of tribology. Microscopic sliding of a solid block placed on an elastic-plastic substrate located on the inclined plane is observed to begin at angles somewhat smaller than the critical angle q = tan-1(m), where m denotes the coefficient of friction. With careful observational techniques these displacements can indeed be measured. Likewise, in the course of the early stages of ductile fracture, quasistatic crack growth is detected between the lower bound KI = Kini' , tantamount to the onset of stable growth, and the upper bound KI = Kf. equivalent to occurrence of the catastrophic failure. While Kini' is believed to be a material constant, the other quantity, Kf is determined not only by the material properties, but it also depends on specimen geometry, crack configuration and type of the external loading. The exact shape of the terminal instability locus represented in the plane (load, crack length) must be established by employment of the R-curve technique, in which the second variations of the energy terms are involved. When the Liapunov criterion is invoked, then it appears that the propagation of a stable crack should be viewed as a sequence of local instability states, while transition to an unstable propagation becomes equivalent to the loss of global stability, as then the entire component breaks up. A moving quasistatic crack is described on the basis of the Wnuk criterion of final stretch, which leads to the nonlinear differential equations governing the resistance curves for various materials. Both the ductile and brittle limits of material response are discussed. One of the essential results of this study is the partition of energy available for fracture within the end zone, accomplished by means of considerations of the pre-fracture states developed at the mesa-level. This, in turn, leads to a discovery of the energy screening effect, which manifests itself by a significant enhancement of material fracture toughness prior to the catastrophic failure state. Such phenomena are being confirmed by the brilliant experimental work of the Panin group in Tomsk, and Popov's team in Berlin.