Fracture and stability of strain-softening materials and structures - Tabbara, Mazen (1990)
The principal object of investigation is the behavior of structures with softening load-displacement curves. The study deals with three interrelated areas: (1) a model for fracture of aggregate composites, (2) stability analysis of structures with interacting cracks, and (3) stability analysis of strain-softening columns. A particle model for brittle aggregate composites materials such as concretes, rocks or ceramics is presented. The model is shown to realistically simulate the evolution of cracking and its localization. For direct tension specimens, the model predicts a development of asymmetric response after the peak load. This asymmetric response, which has also been observed in experiments, deserves more attention and is a problem that lies in the realm of inelastic stability theory. To study stability, a general method to calculate the tangential stiffness matrix of a structure with a system of interacting propagating cracks is formulated. The need to distinguish between stability of state and stability of path is emphasized. The formulation is applied to symmetric bodies with interacting cracks and to a halfspace with parallel equidistant cooling or shrinkage cracks. As examples, specimens with two interacting crack tips are analyzed numerically. It is found that in 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. As another practically important application of stability theory, a simple method for calculating column interaction diagrams taking into account slenderness effects is formulated. The method consists of an incremental loading algorithm which traces the load-deflection curve at constant eccentricity of the axial load. The peak loads of columns with small eccentricities are compared to Shanley''s tangent modulus load and to Engesser-von Karman''s reduced modulus load for a perfect column.