Mechanical damage and crack growth in concrete

Abstract

Structural elements can fail in many different ways. The ultimate load condition may be reached by a combination of plastic flow, slow or fast crack propagation, depending on the material strength, ductility and toughness, and the size of the structural components. Highly constrained and/or brittle materials may result in sudden crack formation and unstable crack propagation, whereas less constrained and/or more ductile materials are more likely to fail progressively by plastic yielding. In those situations, the presence of initial cracks do not play an important role in the failure process. In many cases, however, the terminal condition is preceded by slow crack growth that continues even into the stage of global structure failure. There are other situations where slow crack growth may occur simultaneously with plastic flow and the final failure can still be catastrophic. The current fracture mechanics literature contains a multitude of ideas, concepts, and criteria, that are not always consistent one with the other. Plastic Limit Analysis and Linear Elastic Fracture Mechanics are two theories that address failure of structural components with very ductile and very brittle behavior, respectively. They are unable to account for the slow crack growth and the softening behavior in concrete structures aside from the effect of material heterogeneity that is connected with the brittleness of concrete. Remarkable scale effects have been found in fracture toughness testing of cementitious materials. The mechanical behavior can change from the very ductile to the very brittle simply by altering the size of geometrically similar specimens. Large specimens can fail by rapid crack propagation within the linear elastic range before softening takes place. On the other hand, small specimens tend to fail in a ductile manner with slow crack growth and softening leading to a complete stress relaxation. In this book, a crack growth and material damage model is used in conjunction with the strain energy density theory of Sih to analyze the integrity of concrete structural members. A bilinear softening constitutive law is applied while the progressive damage of material is accounted for by changing the material elastic modulus and crack growth for each load step. The finite