Vol.3, No 13, 2003 pp. 559-572
UDC 539.421:539.422:537.226.86:531.64
POTENTIAL ENERGY STATE DURING CRACK  PROPAGATION IN DISCRETE MODEL OF MATERIAL
Dragan B. Jovanović
Faculty of Mechanical Engineering, University of Niš, Beogradska 14, 18000 Niš
E-mail: jdragan@masfak.masfak.ni.ac.yu
The theory of fracture mechanics has two main approaches to the problem of crack propagation: the continuum mechanics, and the atomic approach. They are presented in classical literature of fracture mechanics listed in [3], [4], [5], [9], [10], [11], [15], [18] and [19]. Expecting that duality of approaches will be over passed by integrative theory in the future, this paper deals with the atomic approach of cracks inside a discrete model of material (atomic lattice).  Solids may be represented as systems of discrete masses linked by interacting forces, interatomic forces or simple bonds. Not only mechanical loads are involved in crack growth, but also chemical, thermo-mechanical, electro-mechanical, acoustic and other physical phenomena are also involved. Ability of a discrete model to explain crack healing, slow subcritical crack growth, sound generation during crack propagation, effects of chemical processes at the tip of the crack, nonlinearity of stress, strain and energy distribution in the crack tip region, influence of temperature on crack propagation and gives great advantage to procedures based on model of discrete masses (atomic lattice). Two intrinsic interatomic force functions are used to represent mechanical interaction between the neighboring atoms (discrete masses) in lattice. Released potential energy, as a result of crack propagation through the lattice, by breaking interatomic bonds is presented. One- and two-dimensional models of lattice and relations for total potential energy of selected models of lattice are presented.
Key words:  crack, mathematical form of localized energetic structure, discrete model of material, atomic lattice, functions of interatomic forces, potential energy of atomic bond, total potential energy of lattice, activation energy, strain energy surfaces.
STANJE POTENCIJALNE ENERGIJE
U TOKU NAPREDOVANJA PRSLINE
U DISKRETNOM MODELU MATERIJALA
Teorija mehanike loma ima dva osnovna pristupa problemu napredovanja prsline:
- mehanika kontinuuma i
- atomistički pristup.
Oni su prikazani u klasičnoj literaturi mehanike loma [3], [4], [5], [9], [10], [11], [15], [18], [19]. Očekujući da će dualnost ovih pristupa biti prevaziđena integrativnom teorijom mehanike loma u budućnosti, ovaj rad se bavi atomističkim stanovištem. Atomistički pristup razmatra prsline unutar diskretnog modela materijala (atomska mreža). Čvrsta tela se mogu prikazati kao sistemi diskretnih masa povezanih silama uzajamnog dejstva, međuatomskim silama ili jednostavno (vezama). Nisu samo mehanička opterećenja uključena u rast prsline, već takođe hemijske, termo-mehaničke,elektro-mehaničke, zvučne i druge fizičke pojave. Sposobnost diskretnog modela da objasni zarastanje prsline, spori podkritični rast prsline, stvaranje zvuka u toku napredovanja prsline, uticaje hemijskih procesa na vrh prsline, nelinearnost rasporeda napona, deformacija i energije u oblasti vrha prsline, uticaj temperature na napredovanje prsline, daje veliku prednost postupcima zasnovanim na modelu diskretnih masa (atomska mreža).
Dve svojstvene funkcije međuatomskih sila su korišćene da prekažu mehaničku interakciju između susednih atoma (diskretnih masa) u mreži. Prikazana je oslobođena potencijalna energija kidanjem međuatomskih veza, kao posledica napredovanja prsline kroz mrežu. Prikazani su jedno dimenzionalan i dvodimenzionalan model mreže i relacije za totalnu potencijalnu energiju izabranih modela mreže.
Ključne reči:  prslina, matematička forma lokalizovane energetske strukture, diskretni model materijala, atomska mreža, funkcije međuatomskih sila, potencijalna energija atomske veze, totalna potencijalna energija mreže, energija aktiviranja, površine energije deformacije.