A Micro Instability Criterion Based On The Change Of The Energy

The traditional macro instability criterion is established on consecutive medium mechanics, which has been widely applied to project. Meanwhile, the microstructural mechanics performance and the deformation behavior get more attention with the in-depth research on nano technology. However, it is quit different of plastic forming theory and method between micro-scale and macro-scale. The traditonal theories of consecutive medium mechanics is no longer applicable. Therefore, in order to evaluate the plastic deformation and further explore the nature and mechanism of various phenomenons of the nano material plastic forming procsss, it has to estabilish a micro criterion.In the paper, a micro instability crition of arbitrary atomic structure is established by the change of potential energy of the whole system, which is rigorously considered by taking into account the degree of the atoms in the system. The instability criterion is given as positiveness of the minimum eigenvalue of the matrix, which consists of second order differential of potential energy with respect to atomic coordinates.The interaction between atoms is descriped by Morse potential energy function and the conjugate gradient method is used to minimize the energy of the system. The crystal defects is analized by centrosymmetry parameter. Molecular dynamics simulations are used to establish various models, including 2d crack tention model, 3d crack tention model, half-curled crystal tensile model, symmetrical double crystal tensile model, asymmetrical double crystal tensile model, nano-indetation model, ect. After that, the micro instability criterion is applied to capture the models'initial instability deformation. Meanwhile, we have a lot nano indentation experiments to study the applicability and accuracy of the instability criterion.The results show that, we could have a accurate prediction of the initial unstable deformation by the micro instability criterion under 0 K. And it is also adapted to the unstable deformation of single crystal under low temperature.