Scaling of Failure and Time Dependent Behavior of Brittle Heterogeneous Materials: Composite, Concrete and Bone

Quasibrittle materials such as concrete, rocks, composites, bones and sea ice are brittle heterogeneous materials characterized by a fracture process zone (FPZ) size that is not negligible compared to the characteristic size of the structure. The present focus is on the bone and fiber-polymer composite. For these materials, the classical approach of linear elastic fracture mechanics is not applicable because it implies the FPZ to be a point. Neither is the ductile yielding fracture mechanics, in spite of the large size of the yielding zone. In quasibrittle fracture, the essential aspect is the progressive softening damage within the FPZ, which requires the use of cohesive crack model, crack band model or nonlocal model.;For the cohesive crack simulation, a bilinear form of traction-separation law is adopted. Fitting the size-effect test data by Bazant's size-effect law yields the initial fracture energy and the tensile strength of the cohesive crack model, but cannot provide the total fracture energy of the bovine bone. On the other hand, similar to previous study of concrete, it is shown that the initial fracture energy and tensile strength cannot be identified from complete pre-and post-peak load-deflection curves of specimens of one size. It is demonstrated that the same limitation applied to the human bone tests of Yang et al. (2006). The reason is that, without size-effect data, the problem of identification of fracture parameters is ill-conditioned—i.e., the parameters obtained by optimizing the data fit are not unique. Bilinear cohesive traction-separation laws in which the initial fracture energy and tensile strength differ by as much as 72.4% and 100%, respectively, are found to fit the same experimental complete load-deflection curve with post-peak softening quite closely, with deviations much smaller than the inevitable statistical scatter of experiments. Further it is demonstrated that the non-uniqueness in identifying the cohesive traction-separation law can be eliminated when the tests of complete load- deflection curves of one-size specimens are supplemented by the tests of size effect on the nominal strength. Finally, an optimal size range for the size-effect tests of bovine bone is shown to exist and is identified.;Recently, the size effect in fatigue lifetime, which is an important aspect of quasibrittle materials, has been investigated experimentally. Generally, Paris law, which relates the crack growth rate to the stress amplitude, is normally contingent on the small fracture process zone. For quasibrittle or cohesive fracture, this assumption is no longer valid. The Bazant size-effect law is shown to be effective to adjust the size dependence by introducing the brittleness number of the structure, a number that represents the ratio of the structure size d to the transitional size d0. For woven composite, the test results are found to be highly scattered, because the thickness effect did not average out, due to too small a number of plies. For unidirectional laminates, the failure has been found to take place near the tab region, due to high stress concentration, which deviated from conventional test results. Also, the strength capacity has been found to be too high for the testing machines in the departmental laboratory. The lessons learned have fundamentally contributed to further planned investigations.;Finally, both theoretical and experimental investigations by Ulm et al. have shown that scratching is a fracture dominated process. Using dimensional analysis, they derived a model that relates quantities measured in the scratch tests to the fracture properties of material. Examples of paraffin wax, cement paste, and Jurassic limestone show that linear elastic fracture mechanics (LEFM) is valid for a sufficiently large scratching blade. Determination of material characteristic size and transitional quasibrittle size effect can be extended to the scratch test theory. It is concluded that this is possible if tests of a broad size range is made. This conclusion is supported by simulation using the new microplane M7 which gives superior characterization of quasibrittle behavior. (Abstract shortened by UMI.).