Cracks are inherently unstable and propagate until they strike a 90? reflection plane or an obstacle such as a defect or a numerical boundary. Cracks do not generally proceed through a large change in direction but occasionally rebranch wildly. This is often the result of reorientation of existing branches at the tip during crack propagation, but the equations of point-plane fracture are time dependent and permit this behaviour. As a result, it is possible to simulate unstable crack propagation with sufficient accuracy by applying slip to the crack faces. The stress distribution around the crack is a localised distribution, which can be achieved by the application of a slip boundary condition, along the crack faces. Slip is the tangential component of the stress acting perpendicular to the crack surface.
Our objective was to develop a computational strategy based on a simple level set function for the representation and tracking of the progressive propagation of cracks in two dimensional rounded crack tip geometries. Because it is based on the originally frame-by-frame acquired image sequence, it is amenable to large scale processing, notably the integration of multiple image sequences, and is ideally suited to the development of high-resolution crack measurements. In this initial testing of an approach, a known branch geometry has been incorporated into the benchmark. The Douglas spar or known geometry is selected for its simplicity and because it is an idealised crack tip geometry. It is also compatible with the crack growth profiles we have used in our earlier software development and any crack evolution analysis. Initial crack was simulated to grow until it reached the established endpoint; it was defined as the point at which the local interface between the cracks becomes steep and less than 1.5 µm. The full forward simulation of the next level set relates the two different level sets. To perform this fundamental advancement, the level set function is first developed, which is followed by a description of the explicit equations used to perform this advancement. These equations were developed from the fundamental equations governing point-plane fracture. They were derived from the first order equations of point-plane stress fracture. They are completely explicit and can therefore be used for all crack patterns, and for their evolution during external loading. The equations were then modified to explicitly account for the introduction of a curved crack boundary and consequently simulate a rounded crack tip geometry. The level set functions used here are robust and efficient and there are no difficulties in introducing arbitrary crack geometries and directly imaging the evolving crack borders. 7211a4ac4a