13th International Conference on Fracture June 16–21, 2013, Beijing, China -3- 2.1. The effect of crystal plasticity on crack growth It has been known that the strength of metallic materials of various structures at extreme temperatures has a strong relationship with crystal plasticity generated by thermally activated microscopic mechanisms, which is usually controlled by elementary dislocation mechanisms. In order to understand and predict the crack growth and fracture behaviors of materials, it is extremely important to know what determine dislocation mobility and how it changes under the influence of stress and temperature. Based on thermal activation theory the derivation expression of the strain rate can be written by[18] / ) exp( 0 G kT = −Δ γ γ& & with id m A b A l ν ρ γ ( '/ ) 0&= , (1) where A is a geometrical coefficient, ρm is the mobile dislocation density, b is the Burger' s vector, A’ is the area swept by segment l between two successive obstacles, l is the wavelength of the vibration scales depending on the conditions, νid is the vibration frequency of the dislocation segment, k is the Boltzmann constant and T the absolute temperature. Here ΔG is the change of Gibbs free energy of the sample as the dislocation moves along dislocation coordinate. ΔG is used to characterize the energy barrier opposing dislocation motion. In terms of fracture mechanics the crack growth is related with strain rate. Considering the above and from the point of view in engineering it prompts us to introduce a factor Cm(T) referring to thermally activated energy to take the effect of temperature on crack growth into account. Factor Cm(T) is defined as a function in form of kT mC T e m/ ( ) − ∝ . (2) where m is a constant which can be determined by molecular simulation. 2.2. Radial distribution function (RDF) In statistical mechanics, the radial distribution function or pair correlation function g(r) in a system of particles describes how the density varies as a function of the distance from a reference particle. It can also be determined experimentally, by radiation scattering techniques or by direct visualization for large enough particles via traditional or confocal microscopy. The radial distribution function is of fundamental importance in thermodynamics because the macroscopic thermodynamic quantities can usually be determined from g(r). It is a primary reference for theory verification by experiments and also a fundamental function characterizing non-sequential system. For an ideal crystal structure the value and location of peaks at different near neighbour position indicates effect of temperature. Therfore it gives us an idea about whether it has realtionship with crack growth by means of thermal activation energy in different temperature. Based on the simulation results the atomic radial distribution function g(r) and the corresponding number integral are calculated and over a given trajectory. 3. Molecular simulaton modeling 3.1. Interatomic potential An appropriate description of potential functions is essential in a molecular dynamics simulation. It concerns the accuracy and reliability of simulation results. Lots of potentials have been proposed to approximate the interactions of atoms, such as Lennard – Jones, Tersoff, embedded atom method (EAM) and etc. The steels studied for the crack growth simulation belong to amorphous metal model and is assumed to be made from Fe. The EAM potential for describing interatomic interaction in a semi-empirical form is used to study the crack growth of steels. It is suitable for characterizing metals and alloys with FCC, BCC and HCP structures. In a simulation, the EAM
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