The same conclusion also has been suggested for a mode II crack's limiting speed because the “forbidden velocity zone” between the Rayleigh and shear wave speeds acts as an impenetrable barrier for the shear crack to go beyond the Rayleigh wave speed. From these theoretical solutions, it has been concluded that a mode I crack's limiting speed is clearly the Rayleigh speed. Whereas the energy release rate remains zero for a mode I crack, it is positive for a mode II crack over the entire range of intersonic velocities. However, the predictions for the two loading modes differ for crack velocities greater than the shear wave speed. A mode II (shear) crack behaves similarly to a mode I crack in the subsonic velocity range i.e., the energy release rate monotonically decreases to zero at the Rayleigh wave speed and remains zero between the Rayleigh and shear wave speeds. For a mode I (tensile) crack, the energy release rate vanishes for all crack velocities in excess of the Rayleigh wave speed, implying that the crack cannot propagate at a velocity greater than the Rayleigh wave speed. Predictions of continuum mechanics ( 5, 6) suggest that a brittle crack cannot propagate faster than the Rayleigh wave speed. In order of increasing magnitude, they are the Rayleigh wave speed, or the speed of sound on a solid surface, the shear (transverse) wave speed, and the longitudinal wave speed. In this problem, there are three important wave speeds in the solid. First Study: Supersonic Crack Propagation In Brittle Fracture How Fast Can Cracks Move? For a visual description of ASCI White, we refer the reader to Scientific American's special issue entitled Extreme Engineering ( 1). This is exactly the increase in the number of atoms that we could simulate over the last 35 years. For 35 years, that translates into a computer speed increase of 10 million.
Moore's Law states that computer speed doubles every 1½ years. The present record is well over a few Teraflops for optimized performance, and we have now simulated over 1,000,000,000 atoms in a work-hardening study at the Lawrence Livermore National Laboratory by using the ASCI White 12-teraflop computer. The communication is done through message passing procedures. A modern parallel computer is made up of several (tens, hundreds, or thousands) small computers working simultaneously on different portions of the same problem and sharing information by communicating with one another. Before that time, computational scientists were concerned that the speed of scientific computers could not go much beyond 4 Gigaflops, or 4 billion arithmetic operations per second and that this plateau would be reached by the year 2000! That became forgotten history with the introduction of concurrent computing. In the mid-1960s, a few hundred atoms could be treated. These features may be external forces, initial conditions, boundary conditions, and the choice of the interatomic force law. A simulation study is defined by a model created to incorporate the important features of the physical system of interest. Beyond two atoms, this is impossible except for a few very special cases, and we must resort to numerical methods. We learn in beginning physics that the dynamics of two atoms can be solved exactly.
MD predicts the motion of a large number of atoms governed by their mutual interatomic interaction, and it requires the numerical integration of the equations of motion, force equals mass times acceleration or F = ma. Our simulation tool is computational MD ( 2), and it is very easy to describe. Using our “computational microscope ,” we can see what is happening at the atomic scale. Atomistic simulations yield ab initio information about materials deformation at length and time scales unattainable by experimental measurement and unpredictable by continuum elasticity theory. With the present-day supercomputers, simulation is becoming a very powerful tool for providing important insights into the nature of materials failure.