1 Department of Civil Engineering, Technical University of Denmark2 Section for Structural Engineering, Department of Civil Engineering, Technical University of Denmark
Experimental Investigations of Material Modeling
Cracks are a natural part of concrete and concrete structures. The cracks influence the general structural behavior in terms of e.g. the stress distribution and the stiffness. A direct inclusion of the cracks in the design will result in a more precise description of the structural behavior and a better basis for the assessment of the service life of the structure. The constitutive relation between Mode I crack opening and the normal stresses across the crack is well described through the Fictitious Crack Model (FCM) and related models. However, after a crack in concrete is initiated, the crack may open in mixed mode, i.e. a combination of opening and sliding. To get a thorough description of the structural consequences it is important to include the stress transferring effects related to the mixed mode opening. The existing constitutive mixed mode models either have a rather extensive model formulation or are based on one or more model parameters which are difficult to conceive and give a mechanical interpretation. To some extent this may be explained by the sparse experimental basis for the mixed mode cracking in concrete. In this thesis a series of new mixed mode experiments are presented. An experimental basis for the interpretation of the mixed mode crack behavior is achieved through the experimental results. Based on an elasto-plastic model a constitutive mixed mode model is formulated. By a direct inclusion of the actual crack topography, the model gives a consistent and purely mechanical based interpretation of the crack behavior. A stiff biaxial test set-up is applied to the mixed mode measurements. The relative opening and sliding of the crack is used as the control signals in a new enhanced closed control loop. The opening and the sliding of the crack are measured by clip gauges using a pair of custom made orthogonal gauge rails mounted on the specimen. The precise orthogonal gauge rails entail a direct interpretation of the mixed mode crack opening process, ensuring that the achieved response over the ligament is equal to the prescribed mixed mode displacement. After a crack is initiated in a double notch specimen, the crack is exposed to mixed mode opening. The experiments may be used in a direct interpretation of the mixed mode behavior. The elliptic yield surface in the associated elasto-plastic material model is controlled by two hardening parameters, which represent the actual compressive and tensile strength of the concrete, respectively. The constitutive behavior is based on the relation between normal opening and normal traction. For an opening of the crack the material softens, for a closure the material hardens, and for a large closure the material crushes described as a softening. The crack surface is measured through an optical laser scanix ner. In the model, the included topographic description consists of a series of average contour lines describing the average trends of the topography. Compared with experiments and without any tuning the constitutive model based on the plasticity model and the topographic description gives a convincing description of both Mode I opening, crushing and mixed mode cracking. The experimental investigations, and the topographic description together with the constitutive model provide an interpretation of the mixed mode crack behavior.