PSI - Issue 23

Stepanova Larisa et al. / Procedia Structural Integrity 23 (2019) 322–327 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

323

2

1. Introduction

Modelling particle interactions at the nanoscale requires approaches that can account for the complex, nonlinear constitutive behavior at this length scale (Roy and Roy (2019)). Molecular dynamics method has been proven effective in capturing the typical phenomena related to fracture at the nanoscale (Roy and Roy (2019), Chowdhury et al. (2019), Liu et al. (2019)). MD approach is a powerful tool in characterizing the inception and evolution of plastic deformation and associated fracture mechanism at the atomic scale. Applied to the problem of crack propagation and growth, the method has been used extensively to analyze the fundamental mechanisms of material’s fracture in the past (Tang et al. (2010), Sung et al. (2015), Tang et al. (2014), Wu et al. (2015), Chandra et al. (2016)) and at present (Zhou et al. (2019), Han et al. (2019), Roy and Roy (2019), Chowdhury et al. (2019), Singh et al. (2019), Belova and Stepanova (2018)) . The study is aimed at the determination of the crack propagation direction angle in a wide range of mixed-mode loading using 1) molecular dynamics simulation of the crack propagation behavior under mixed mode loading; 2) the multi-parameter strain energy density criterion; 3) the multi-parameter maximum tangential strain criterion; 4) the multi-parameter maximum tangential stress criterion in a full range of the mixity parameter which is defined as       22 12 2/ arctan , 0 / , 0 . e M r r         The mixity parameter equals 0 for pure mode II; 1 for pure mode I, and 0 1 e M   for different mixities of modes I and II. There are several methods of simulating crack behavior, including conventional fracture mechanics analysis, molecular mechanics, molecular dynamics, finite element method and methods based on density functional theory (DFT). Focus of this study is comparison of molecular dynamics and continuum fracture mechanic approach. Atomistic simulations of the central crack growth process in an infinite plane medium under mixed-mode loading using LAMMPS, a classical molecular dynamics code, are performed. In the framework of MD approach two types of materials are considered. The first one is hcp-copper and the second one is fcc - aluminum. The inter-atomic potential used in this investigation is Embedded Atom Method potential. The plane specimens with initial central crack were subjected to Mixed-Mode loadings. The simulation cell contains from 300000 to 800000 atoms. The crack propagation direction angles under different values of the mixity parameter in a wide range of values from pure tensile loading to pure shear loading in a wide range of temperatures (from 0.1 К to 800 К ) are obtained and analyzed. Periodic boundary conditions were implemented in all three directions of the cell. To neglect the effect of neighbouring cells we choose the size of the central crack to be relatively small (1:10 ratio) to the size of the simulation cell. Furthermore, we added small non-interacting boundaries to the edge of the plane. Before mixed loading is applied, plate is optimized to the minimal energy with conjugated gradient method. When minimum energy state is achieved, we apply mixed strain. During all 50000 steps of simulation, we collect data of the state of all atoms in the cell. The results of simulations for Mode I loading in the copper plate with the central crack are shown in Figs. 1-8, color coding is obtained by OVITO tool. Brighter colors correspond to higher stress. Figs. 1-3 show the distribution of the stress component 11  in the copper plate with Mode I crack at different times. Figs. 3-6 show the distribution of the stress component 22  in the copper plate with Mode I crack at different times. Figs. 6-8 show the temperature distribution in the copper plate with Mode I crack at different times. The temperature distributions and temperature values obtained via the molecular dynamics method are in a good agreement with the experimental data (Bui (2006)). It can be seen from Figs. 6-8 that the temperature rise in the vicinity of the crack tip is very high for crack propagation. The hot region near the crack tip is observed. This hot zone is due to inelastic dissipation distributed over a small, but non vanishing area around the moving crack tip. From MD simulations one can get crack propagation directions angles for different values of the mixity parameter. Calculations of MD method have been performed for seven different values of the mixity parameter e M : 0.2, 0.3, 0.4, 0.5, 0.6, 0.7 and 0.8. Calculated values of crack direction propagation angles were -51.6 ° , -44 .5° , -40.7 ° , -36 .5° , -30.3 °, -24.5 ° and -20 .2° respectively. 2. Approaches of crack growth simulation: molecular dynamics