Research conducted jointly between Cornell University and the Georgia Institute of Technology and sponsored by the National Science Foundation (NSF), Project #CMS9625406, Scheduled for 3 years with a start date of January 1, 1997. The principal investigators are: Dr. Leonid Germanovich, Dr. Anthony Ingraffea, and Dr. Bruce J. Carter.
The principal objective is to understand the mechanisms underlying rock fracture in compression and to formulate and test, through unique experiments and computer simulation, evolution rules for the stable growth of three-dimensional cracks of arbitrary shape in brittle and rock materials.
The principal scientific benefit is formulation and testing, through both experiments and simulation, of evolution rules for the stable growth of three-dimensional cracks of arbitrary shape. Practical, long-standing problems in rock fracture mechanics which will benefit from knowledge of such rules include: primary rock cutting for tunneling and mining via drag bit or roller cutter wherein multiple, interacting, non-planar cracks are responsible for chip formation; borehole breakouts and hydraulic fracture propagation from inclined, cased, perforated wellbores. Multiple interacting non-planar cracks also occur in such increasingly common situations in hydrocarbon wells.
The growth and interaction of cracks fundamentally controls the response of three-dimensional rock structures loaded in compression. However, the most basic questions regarding how cracks under such conditions change shape, and how they intersect or coalesce, as a result of a change in boundary conditions, are currently unanswered. The primary objective of the proposed research is to develop and to test models for crack growth and interaction. The approach will be to:
* perform unique experiments on brittle materials containing internal cracks of controllable size, orientation, and distribution;
* observe shape evolution and mechanisms of interaction;
* hypothesize fracture propagation criteria and models that could explain these observations;
* program these models into a fully three-dimensional numerical simulator which can freely accommodate arbitrary crack growth and interaction;
* simulate the experiments;
* compare the simulation results with the experimental observations, and
* draw conclusions regarding the accuracy of the models.
The primary objective of the proposed study is to determine the underlying mechanisms of fracture of brittle rock subjected to uniaxial and polyaxial compression. The intention is to obtain the relationship between crack dimensions and load in order to develop an accurate mathematical model and to ensure its verification. It is intended to obtain a better understanding of the mechanical mechanism(s) of brittle fracture in solids in order to facilitate the derivation of improved models for the simulation of failure. This will then form the basis of the micromechanical model for macroscopic deformation and failure of brittle materials containing propagating and interacting microcracks.
The second objective is to develop the laser technique of crack initiation in brittle transparent materials to the level of standard conventional laboratory method. Such a technique provides the means of viewing fracture generation and propagation helping to simulate the phenomena that are very difficult to view in reality, difficult to perform, and difficult to verify in models. For example, an advantage of the laser technique is that it makes it possible to obtain transparent samples containing several internal cracks. It therefore allows the study of 3-D crack interaction, in particular, crack coalescence in compression. Understanding the mechanism of laser-induced cracking in transparent organic and non-organic glasses is important by itself but, regarding this proposal, also in order to establish a controlled and stable procedure for the preparation of the test samples. Moreover, it is necessary to better understand those mechanisms governing crack propagation that rule the introduction of disk-like cracks. Generating disc-shaped cracks in transparent brittle silica glass samples will occur by focusing a high energy laser pulse at the sample. This shape is favored for theoretical modeling of the resulting fracture propagation because of the mathematically simple geometry. Naturally formed cracks are not perfect in their shape, neither are they flat. However, the main feature of this investigation is to determine the principles of the 3-D crack growth and interaction. Therefore, it is desirable to have a simple shape of the initial crack in order to concentrate on the major features of the process of crack growth.
The third objective of the proposed research is to develop a three-dimensional mathematical model of crack growth and interaction in compression. At the present time there is no code that can adequately simulate crack growth under compression in 2-D or in 3-D. Indeed, crack propagation in compression is very much different compared to tension and the available codes at Cornell cannot be used without modification. The achievement of this goal, coupled with the previous ones, will allow one to attack numerous longstanding problems in rock mechanics, of significance to a range of customers, with increased physical rigor. Examples include:
* primary rock cutting via drag bit or roller cutter: multiple, interacting, non-planar cracks are responsible for chip formation in such systems. However, despite substantial progress in the understanding of rock fracture mechanisms, ubiquitous mechanical systems which cut rock using these approaches are still designed by experience. Fully 3D simulations of machine-rock interaction, necessary to optimize cutter/roller design and applied forces, have not been performed to date.
* hydraulic fracture propagation from inclined, cased, perforated wellbores: again, multiple interacting non-planar cracks occur in such increasingly common situations in hydrocarbon wells.
* borehole breakouts caused via crack growth parallel to the borehole walls.
The connection between the proposed research and these situations wherein compressive mechanical loading and/or in situ stresses dominate crack behavior should be apparent. Nevertheless, to avoid misunderstanding we would like to mention that silica glass and PMMA are not at all structurally like any geological material of engineering interest. Much more work will need to be done before any of the research in this proposal will contribute to immediate engineering advances and immediate practical benefits. Indeed, although we propose a real structural approach to the material analysis, the methodology proposed treats rock structure only at the highest level. This is, however, the necessary first step.
In accordance with these objectives, the proposed research will have 4 major tasks:
Task 1. Development of a process for using a laser to induce internal three-dimensional cracks of given number, size, and orientation within specimens of transparent brittle materials.
Task 2. Testing these specimens under compressive loading to induce initially stable growth of these cracks so that evolving shapes, interactions with each other, and with structural boundaries, and structural instabilities can be easily observed.
Task 3. Formulating 3-D fracture propagation criteria based on the performed testing.
Task 4. Application and extension of a existing computer simulator for fully 3D crack growth and interaction. Based on the experimental observations and existing theories, possible evolution rules will be programmed into this simulator, which allows arbitrary trajectories of single internal cracks, cracks interacting with free surfaces, and with each other. The hypothesis to be tested within this objective is that, using computer simulation, an acceptable rule is one which will be able not only to reproduce the experimental observations, but also to predict evolving crack shapes in additional proof tests before performing them.