Компьютерное имитационное моделирование роста трещины с помощью метода молекулярной динамики

Abstract

В работе выполнено детальное изучение процессов нелинейного деформирования и разрушения с помощью вычислительного компьютерного имитационного эксперимента. Среди современных подходов моделирования роста трещины особыми преимуществами обладает метод молекулярной динамики, широко используемый в настоящее время. Проведено моделирование роста трещины в образцах из кристаллической меди и алюминия при смешанном деформировании в полном диапазоне смешанных форм нагружения от чистого нормального отрыва (тип I) до чистого поперечного сдвига (тип II). Перспективным представляется использование пакета LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator). The study is focused on the application of the different approaches for the determination of the initial crack propagation angle. Copper plate with the central crack under complex mechanical stresses (Mode I and Mode II loading) is studied by extensive molecular dynamics simulations based on the EAM potential. On the other hand, the complete Williams expansion for the crack tip fields containing the higher-order terms is used. The crack propagation angle is obtained by 1) the multi-parameter fracture mechanics approach based on three fracture mechanics criteria, MTS, maximum tangential strain and SED; 2) atomistic modeling for the mixed-mode loading of the plane medium with the central crack. From our simulations we can get crack propagation directions and crack angles. Calculations of MD method were run for three different values of e M : 0.4, 0.5 and 0.6. Calculated values of crack angles were -51.5°, -46.6° and -42.2° accordingly. All the fracture criteria tested give similar values of the crack growth angle for different values of the mixity parameter. It is shown that the initial crack propagation angles given by the both approaches are very close especially for the case when the higher order terms of the Williams series expansion for the stress/ displacement field description are taken into account. Thus one can conclude that the criteria of classical continuum mechanics MTS and SED can give satisfactory predictions for crack initiation direction. The crack propagation direction angles given by the conventional fracture mechanics reasonably agree with the angles obtained from molecular dynamics simulations.