ATOMISTIC BASIS OF FRACTURE IN MATERIALS J. J. Mecholsky, Jr. Department of Materials Science & Engineering, University of Florida, Gainesville, FL 32611-6400 ABSTRACT The fundamental question in fracture is “How do bonds break?” To answer this question a combination of modeling and experiment is needed. The modeling should be able to suggest the correct energy criterion to describe the geometric change in atomic and molecular positions before and after bond separation. The experimental verification should be robust enough to test quantitatively the tenants of the model. The novel aspect of this research is the application of fractal geometry to explain observed and predicted behavior during fracture. A model based on fractal geometry is suggested as providing the atomic basis of fracture that will fit experimental observations as a result of brittle fracture. The atomic model is based on molecular orbital theory. Molecular dynamics provides the details of the surface created during fracture. It is hypothesized that the fundamental unit of fracture at the atomic scale is a quantity known as a 0 . In turn, a 0 can be related to the fracture energy, γ, and the elastic modulus, E, through a scaling parameter, the fractal dimensional increment, D*, i.e., γ = ½ a 0 ED*. It is suggested that a 0 is a measure of the strain at the crack tip just before fracture and is related to the available free volume for fracture in materials. The characteristic markings of mirror, mist and hackle observed on the fracture surfaces of glasses, ceramics and polymers are related to the fractal dimensional increment: (Y/ Y j ) 1/2 c/ r j = D*, where c is the crack size, r j , is either the mirror-mist radius (j = 1), mist-hackle radius (j = 2) or crack branching boundary (j = 3), Y and Yj are constants related to the initial and propagating crack geometry, respectively. The combination of atomistic modeling, experimental measurements and the application of fracture mechanics and fractal geometry leads to a suggested sequence and organization of the brittle fracture process. Brittle fracture, i.e., bond breaking, is a series of bond reconfiguration events at the crack tip dictated by minimum energy configurations. This reconfiguration leads to an increase in free volume all along the crack front. As the crack moves, some of these regions will move either approximately above or below the fracture plane. Nearest neighbor regions of free volume will either add or annihilate. The regions that add, will grow in size. The ones that annihilate each other will return to their approximate original positions. The grown regions will then become nearest neighbors to other regions and the process continues as long as energy is supplied to the system. The addition of regions of free volume will create what is observed on fracture surfaces as mirror, mist and hackle. Macroscopic crack branching is also a fractal process dictated by the energy supplied and the far- field stress. Crack branching patterns are fractal in nature and will provide a description of the size and number of particles created during fracture. 1 INTRODUCTION The fracture of materials that fail in a brittle manner is a complicated phenomenon that needs the application of several different methodologies in order to better understand the process. Both experimental and analytical approaches are necessary. Within those categories several different techniques need to be applied. Analytically, atomic and molecular models need to be examined. At macroscopic length scales, finite element models and fracture mechanics equations need to be compatible with the atomic and molecular predictions. Modelling has to explain the existence of the fracture surface topography observed, e.g., mirror, mist and hackle in inorganic and organic glasses. Experimentally and analytically, the fracture surfaces needs to be examined at many length scales along with measurements of particle emissions and non-linear crack velocity during propagation. In addition, there are several fundamental questions that need to be answered in order to understand the nature of fracture. How does a bond break? Once a bond breaks, how do the ensembles of bonds, at the tip of a crack, propagate? What are the energetic and geometric steps to fracture? How does energy scale? Is roughness a meaningful parameter for fracture