Our simulation tool is computational molecular dynamics, and it is very easy to describe. Molecular dynamics 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." We learn in beginning physics that the dynamics of two atoms can be solved exactly. Beyond two atoms, this is impossible except for a few very special cases, and we must resort to numerical methods. A simulation study is defined by a model created to incorporate the important features of the physical system of interest. These features may be external forces, initial conditions, boundary conditions, and the choice of the interatomic force law.
In the mid 1960s, a few hundred atoms could be treated. In 1984, we reached 100,000 atoms. 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. 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. The communication is done through message passing procedures. 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 LLNL using the ASCI White 12-teraflop computer. Moore's Law states that computer speed doubles every one and one-half years. For 35 years, that translates into a computer speed increase of ten million. This is exactly the increase in the number of atoms that we could simulate over the last 35 years.
What Distinguishes Brittle From Ductile Behavior?
If brittle fracture were the sole mechanism for materials failure, our world would be quite fragile. However, there are two generic types of materials failure: brittle fracture and ductile bending. In the first case, atomic bonds are broken, and such a failure is easily recognized when you see glass shatter. For ductile failure, such a catastrophic event does not occur. Tough materials like metals do not shatter; they bend because plastic deformation occurs by the motion of rows of atoms sliding passed one another on preferred slip-planes (dislocations).
We briefly review some basic fundamentals of fracture mechanics. They are simple to understand even though we all know that fractured glass can look very complicated. That is because there are lots of cracks when glass shatters. As a matter of fact, micocracks are the seeds for both brittle and ductile failure. In order to understand the failure of solids, we must go to an atomic picture of matter. It is because a solid is made up of atoms, and not a continuum, that a solid can break. Fracture is a consequence of breaking atomic bonds by separating atoms from their neighboring atoms, and this can happen because the bonds have a limited strength, the strength depending on the particular material. The solid is said to be brittle when this happens; this has the special meaning that the solid fails by the permanent breaking of atomic bonds.
Solids can fail a second way; by rows of atoms slipping pass their immediate nearest neighbors much like a "ripple in a rug" being pushed across a stationary floor. However, the atomic-level ripple is now called a line dislocation. Also, while atomic bonds are broken by stretching the solid, the sliding between planes is achieved by shearing the solid. The ease of the atomic slip depends on the atomic arrangement of the slip planes. The more compact (less bumpy) planes slip best. When the solid fails by atomic sliding through dislocation motion, the solid is described as ductile. The face-centered-cubic (fcc) packing is known to have a strong propensity toward ductility; body-centered-cubic (bcc) much less so. Glasses do not have extended crystallinity because atoms are packed randomly. They have no slip-planes and hence no ductility. Glasses exhibit brittle failure. These descriptions are over simplified, and there are clear exceptions to them.
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