Incremental displacement collocation method for the determination of fracture properties of quasi-brittle materials

Abstract

This thesis presents experimental and numerical investigations on the fracture properties of quasi-brittle materials, including mortar, concrete and graphite. Fracture toughness in terms of the critical stress intensity factor K_IC and fracture energy G_F of the materials were determined through three-point bending tests on centre-notched beams. Furthermore, full-field displacement of the beams subjected to bend was obtained using Electronic Speckle Pattern Interferometry (ESPI) technique.

In order to verify the accuracy of the displacement data measured using the ESPI technique and to obtain reliable deformation information, the displacement and strain errors induced by the rigid-body motions of the specimen were quantified. This study found that the displacement errors were negligible whereas the strain errors were notable and must be eliminated. The influence of different rigid-body motions was analyzed. It was found that the out-of-plane movement of the specimen was critical and affected considerably the accuracy of strain data. Thus the experimental setup was improved accordingly to eliminate the influence of critical rigid-body motions.

Quasi-brittle materials have a finite stress region near the crack tip, known as the fracture process zone (FPZ). The materials exhibit nonlinear fracture behaviour in the FPZ. The cohesive crack model (CCM) is widely used to characterize the nonlinear fracture behaviour of quasi-brittle materials. According to the CCM, all the nonlinear behaviours in the FPZ can be represented by a cohesive crack, and the crack propagation is controlled by the relationship between the cohesive stress and crack opening, namely, the tension softening curve (TSC). Thus an accurate estimation of the TSC is essential.

In order to determine the TSC of quasi-brittle materials, an incremental displacement collocation method (IDCM) was originally developed in this study. In the IDCM, the deformation data measured by the ESPI sensor was analyzed to obtain the crack opening displacement (COD) of the notched specimens. The experimental COD profiles together with the CCM were then integrated into a finite element model to simulate the nonlinear fracture response of the specimen. By minimizing the difference between the computed and measured displacements at selected collocation points, the cohesive stress corresponding to certain crack opening was determined. The entire TSC was constructed in a step-by-step manner following the loading steps.

The IDCM was first applied to estimate the TSC of mortar. By using the estimated TSC, the displacements of the specimen under certain loading levels were computed. By comparing the computed displacements with the experimental data, the reliability of the IDCM and the accuracy of the estimated TSC were verified.

The application of the IDCM was further extended to the determination of the TSCs of concrete and graphite. The parameters used to define the shape of the TSC of the materials were determined using regression analysis. The applicability of those parameters was verified by comparing the TSCs estimated in the present study with those derived by other researchers. Recommendations were put forward to choose appropriate tensile properties of quasi-brittle materials in the numerical simulations. Furthermore, by using the ESPI technique, fracture phenomena of quasi-brittle materials were observed and reported. Such records can greatly enhance the understanding of crack initiation, growth and arrest in quasi-brittle materials, and lead to improvements to the existing fracture models.