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Bifurcation and stability of structures with interacting propagating cracks

Abstract

A general method to calculate the tangential stiffness matrix of a structure with a system of interacting propagating cracks is presented. With the help of this matrix, the conditions of bifurcation, stability of state and stability of post-bifurcation path are formulated and the need to distinguish between stability of state and stability path is emphasized. The formulation is applied to symmetric bodies with interacting cracks and to a halfspace with parallel equidistant cooling cracks or shrinkage cracks. As examples, specimens with two interacting crack tips are solved numerically. It is found that in all the specimens that exhibit a softening load-displacement diagram and have a constant fracture toughness, the response path corresponding to symmetric propagation of both cracks is unstable and the propagation tends to localize into a single crack tip. This is also true for hardening response if the fracture toughness increases as described by an R-curve. For hardening response and constant fracture toughness, on the other hand, the response path with both cracks propagating symmetrically is stable up to a certain critical crack length, after which snapback occurs. A system of parallel cooling cracks in a halfspace is found to exhibit a bifurcation similar to that in plastic column buckling.

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Bazant, Z.P., Tabbara, M.R. Bifurcation and stability of structures with interacting propagating cracks. Int J Fract 53, 273–289 (1992). https://doi.org/10.1007/BF00017341

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  • DOI: https://doi.org/10.1007/BF00017341

Keywords

  • Fracture Toughness
  • Tangential Stiffness
  • Symmetric Body
  • Tangential Stiffness Matrix
  • Stability Path