Crack-tip parameters in polycrystalline plates with compliant grain boundaries.

摘要

The design of cost-effective and reliable offshore structures and bridge piers subjected to ice-flows requires a better understanding of the fracture behavior of ice. A specific issue that needs to be resolved is whether the limited available experimental strength and fracture toughness data of this polycrystalline material shows a dependence on structural size as a result of nonlinear material behavior, or whether the statistical nature of the data is size independent. To address this problem, the statistics of the local stress intensity factor of a cracked polycrystalline plate is investigated using two micromechanical models. The first is a finite element based Monte Carlo procedure where the plate's microstructure, which includes a finite number of crystals (or grains) separated by a finite thickness interphase (referred to as grain boundaries in this thesis), is approximated as a Poisson-Voronoi tessellation. The statistics of the effective elastic moduli of the uncracked plate are calculated as well as the local stress intensity factors of the corresponding cracked plate. This is done for selected values of the parameters that quantify the ratio of elastic mismatch between the crystals and the grain boundaries, and the expected number of grains in the plate. The results indicate that the average values and standard deviations of the local stress intensity factors are independent of the number of grains in the plate, and imply that the initiation fracture toughness of polycrystalline plates does not depend on structural size.; The results of the Monte Carlo model suggest that the crack tip parameters of cracked polycrystalline plates could be calculated using an efficient alternative analytical model involving a long crack penetrating a circular inhomogeneity. This problem is solved using the method of continuously distributed dislocations, which relies on the Green's functions of dislocations interacting with a circular inhomogeneity, derived using complex variable techniques. The traction-free condition along the crack surfaces is written as a system of singular integral equations, which are solved numerically. The results demonstrate that as long as the elastic mismatch between the inhomogeneity and the surrounding material is interpreted correctly, then the approximate analytical model is associated with averaged stress intensity factors that are in excellent agreement with those of the polycrystalline microstructure.; An attempt is made to apply the developed models to interpret experimental data obtained from warm lake ice. It is concluded that proper interpretation of data obtained from polycrystalline plates with compliant grain boundaries necessitates stress analyses that incorporate explicitly the stochastic microstructure. However, additional experimental data is required to resolve the issue that motivated the present study. Monte Carlo finite element models such as the ones developed in this thesis could be extended to study crack propagation in polycrystalline plates, and in turn processes such as the break up of an ice flow as it comes into contact with a structure.