Particle Modeling Based on Interatomic Potential and Crystal Structure: A Multi-Scale Simulation of Elastic-Plastic Deformation of Metallic Material

Abstract

We formulate a macroscopic particle modeling analysis of metallic materials (aluminum and copper, etc.) based on theoretical energy and atomic geometries derivable from their interatomic potential. In fact, particles in this framework are presenting a large mass composed of huge collection of atoms and are interacting with each other. We can start from cohesive energy of metallic atoms and basic crystalline unit (e.g. face-centered cubic). Then, we can reach to interparticle (macroscopic) potential function which is presented by the analytical equation with terms of exponent of inter-particle distance, like a Lennard-Jones potential usually used in molecular dynamics simulation. Equation of motion for these macroscopic particles has dissipative term and fluctuation term, as well as the conservative term above, in order to express finite temperature condition. First, we determine the parameters needed in macroscopic potential function and check the reproduction of mechanical behavior in elastic regime. By using the present framework, we are able to carry out uniaxial loading simulation of aluminum rod. The method can also reproduce Young’s modulus and Poisson’s ratio as elastic behavior, though the result shows the dependency on division number of particles. Then, we proceed to try to include plasticity in this multi-scale framework. As a result, a realistic curve of stress-strain relation can be obtained for tensile and compressive loading and this new and simple framework of materials modeling has been confirmed to have certain effectiveness to be used in materials simulations. We also assess the effect of the order of loadings in opposite directions including yield and plastic states and find that an irreversible behavior depends on different response of the particle system between tensile and compressive loadings.