Fracture Near Interfaces of Disparate Length Scales

Abstract

Fracture often occurs near interfaces, whether the interface is within a material or between different materials. Interfaces exist across disparate length scales, from microscopic to macroscopic, which leads to a wide range of fracture phenomena. For example, within a single material, fracture near a microscopic interface can set its bulk fracture behavior. In a system of different materials, even when a crack is contained in one material, the mechanics near an interface can govern the driving force of the crack. This thesis studies fracture near interfaces in fiber-matrix composites, soft materials, and thin films. Applications include wind turbines, soft adhesives, and microchips. We show how the rate-dependent interactions at an interface affect the fracture behavior of a ceramic fiber and a ceramic matrix composite. We formulate a boundary value problem in which a crack runs through the matrix, with the fibers being intact and bridging the crack. The composite is subject to a tensile load normal to the crack. Both the fibers and the matrix are elastic, and the sliding stress between them is linear in their relative velocity. When the loading rate is low, the sliding stress is low, so that tension in each fiber is distributed over a long length. Breaking the fiber dissipates elastic energy over a long length of the fiber, leading to high toughness. When the rate of the applied load is high, the sliding stress is also high, so that tension in the fiber is concentrated in a short length. This concentration of stress leads to low toughness. We model this rate-sensitive toughness using a shear lag model. We demonstrate how the interactions near the interface dictate the fracture behavior of the composite at various loading rates. Next, we show how fracture of hydrogels relates to the interface between polymer chains and water. Because water has a low viscosity and lubricates polymer chains, we find that the stress-stretch curve of the hydrogel is rate-independent and has negligible hysteresis. However, we report that the toughness of the hydrogel is rate-dependent when the polymer chains are long. We invoke a shear lag model to explain how the interactions at the interface of a polymer chain dictate the length along which stress is transmitted and consequently, the toughness. We find that the scaling of our analytical model agrees well with our experimental data. We next consider the interface between a hydrogel adhesive and a rigid adherend. Experimentally, we find that fracture initiates near the corner between the adhesive and adherend interface. To investigate the conditions for fracture, we numerically compute the non-linear elastic field around the interface. We find that for a 90-degree corner the elastic field is finite. We simulate various material models and use the near-corner elastic field to correlate the conditions for fracture. We analyze fracture in a brittle thin film near a ductile layer and show that plastic deformation in the ductile material affects fracture in the brittle material. We use a model structure common in many semiconductor devices: a metal line encased by a silicon substrate and a brittle oxide layer. In the triaxially constrained metal, the stresses readily exceed the yield strength of the metal. We compute the stress in the oxide, as well as the energy release rate of a crack. We demonstrate how the proximity of the crack to the metal interface markedly affects cracking behavior. We discuss strategies to avert cracking in the oxide. Much of the work in this thesis was motivated by experimental findings. A combination of analytical and numerical modeling is used to interpret those findings. It is hoped that the analyses developed in this thesis will assist future scientists in understanding a variety of fracture phenomena. Furthermore, it is hoped that this inspires future scientists to do a deep dive whenever they come across an interesting experimental finding in fracture mechanics.