Materials Science and Engineering for the 1990s Maintaining Competitiveness in the Age of Materials (1989) / Chapter Skim
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Appendix E: Analysis and Modeling
Appendix E: Analysis and Modeling
Pages 269-280
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From page 269... ...
Complementing these technology push factors is the pulling force of the technological demand for increasingly complex materials. Underlying all of these developments are advances in our theoretical understanding of the properties of materials and in our mathematical ability to devise accurate numerical simulations.
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From page 270... ...
· New support is needed both to make high-level computational facilities available for materials research and to develop validated data bases, algorithms, and numerical simulations. · Special attention should be paid to the need for accurate models of nonequilibrium phenomena, particularly processes relevant to manufacturability and performance of materials.
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From page 271... ...
(Here the quantum theory of metallic binding does turn out to be of practical importance, but the basic statistical methods remain relevant.) Research in the area of phase transitions was placed on a much firmer footing in the mid-1970s, when the classic problem of critical phenomena was solved by means of what has come to be known as the "renormalization group" method.
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From page 272... ...
In recent applications of this technique, total energy differences between alternative crystalline structures have been obtained accurately to within a few tenths of an electron volt per atom, structural parameters to within tenths of angstroms, and bulk moduli and phonon frequencies to within a few percent. Note, however, that the method described above pertains only to zero-temperature ground states of regular crystalline arrays of atoms and not to irregular configurations or to alternative phases that might occur at higher temperatures.
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From page 273... ...
For example, it recently has turned out to be possible to perform an ab initio calculation of the atomic positions at a twist grain boundary in germanium. In comparison to what would have happened if the atoms had been kept frozen in their bulk crystalline positions, the relaxed configuration determined computationally exhibits substantial distortions and the formation of many new covalent bonds.
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From page 274... ...
In order to describe the implications of some of these recent developments, two broad classes of continuum problems that are part of the traditional core of materials research microstructural solidification patterns in alloys and fracture mechanics are discussed below. These are by no means the only areas of materials research where analysis and modeling at continuum length scales are appropriate.
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From page 275... ...
Initially smooth shapes naturally develop grooves and fingers, the fingers split or develop side branches, the side branches split or develop tertiary side branches, and so on. What has been discovered only very recently is that the patterns generated by this process are controlled by an extremely delicate interplay between a basic diffusional instability and a number of ostensibly much weaker effects, most notably surface tension, but also crystalline anisotropy, interracial attachment kinetics, and even ambient noise.
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From page 276... ...
Our aspiring modeler may start out as a computational physicist or a theoretical metallurgist, but he or she will have to master some very subtle mathematical concepts in order to write sensible computer codes, and then will have to learn the language of technology in order to translate numerical results into useful rules of procedure for the processing of materials. Fracture Mechanics Research in fracture mechanics is described in Appendix C
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From page 277... ...
We have no quantitative understanding of what controls the extent of plastic deformation near the tip of a moving crack, how fast the crack will move under given external stresses, or what governs the path along which the crack will move in a heterogeneous medium. Note that all of these problems, like solidification theory, inescapably involve nonequilibrium phenomena; irreversible, dissipative processes play essential roles.
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From page 278... ...
In the example of the turbine disk, the microstructure could be optimized for creep strength at the rim and for low cycle fatigue and ultimate tensile strength in the bore. The same detailed simulations might also address issues of technical feasibility and economics.
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From page 279... ...
l APPENDIX E: ANALYSIS AND MODELING 279 occasionally will turn out to be very different from what was expected. When that happens, the technological impact is apt to be very great indeed.
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