# ICME Overview for Polycarbonate

## Contents |

#### Structural Scale

At the structural scale, all of the problems and requirements must be defined in order to direct the lower scales. Generally, solid mechanic simulations require information about how damage evolves, how stiff the material is, how the material creeps, how history effects performance, and how the environment interacts with the materials. In order to get there, lower scales are needed. The side figure gives an overview about what all the polymer ISV continuum requires as well as how each scales works which each other. For PC, the macroscale needs the following information: Elastic modulus, high rate versus low rate effects, PC density, temperature dependence for both elasticity and plasticity, the bonding and mobility which defines plastic deformation, particle–polymer interactions, and particle–crack interactions. The following sections give a brief description of how that information is found and communicated to the other scales.#### Fracture Mechanics

As the dawn of fracture mechanics for metals occurred in 1948 with Irwin^{[1]}, the polymer community has had ample time to follow along and apply it to polymers. The literature is replete with examples of this. One recent work by Pasta^{[2]} investigates the effect of cracks and particles, which is information the macroscale needs. However, the fracture mechanics scale needs to know how particles and void interact. This information is found at one scale lower.

#### Micromechanics

Micromechanics simulations prove helpful when quantifying how particles, voids, and the surrounding matrix interact. In particular, the debonding characteristics are of value. Socrate^{[3]} ran numerical studies to show how the void distribution as well as the triaxial loading conditions affect stress–strain behavior. This information is fed up to the macroscale. However, the particle interactions are governed at a lower length scale—coarse graining.

#### Coarse Graining

In the polymer community, coarse graining can refer to sever length scales. It can refer to a conglomeration of chains interacting, much like the molecular dynamic word by Leon^{[4]}, yet it can also refer to nanoparticle interactions with the surrounding matrix as documented in Glotzer^{[5]}. The general idea is getting down to multiple PC chains and then showing energies relating to their movements. In order to run such calculations, the mobility of the chains are needed. This information must be found from the next lower level—atomistic calculations.

#### Atomistics

At the atomistic length scale, high rate mechanisms and mobility causes are realized. Through molecular dynamic codes such as MEAM or LAMMPS, the stress–strain behavior can be found in Hossain^{[6]}. However, the interatomic potentials (elasticity) and the interfacial energies are need for these calculations which are determined at the final lower level—electron principles.

#### Electron Principles

Currently in ICME, the electron scale is the lowest scale. Density functional theory (DFT) is a common theory used to return the elasticity values needed at atomistic simulations as well as at the continuum scale. A DFT study of PC, performed by Montanari^{[7]}, is a good example of how the energies and vibration frequencies are found.

#### References

- ↑ G.R. Irwin. Fracture dynamics. In
*Fracturing of Metals*, pages 147–166. American Society for Metals, Cleveland OH, 1948. - ↑ S. Pasta. Fatigue crack growth through particulate clusters in polycarbonate material.
*Engineering Fracture Mechanics*, 78(2):397–411, 2011. - ↑ Socrate and M.C. Boyce. Micromechanics of toughened polycarbonate.
*Journal of the Mechanics and Physics of Solids*, 48(2):233–273, 2000. - ↑ S. León, N. van der Vegt, L. Delle Site, and K. Kremer. Bisphenol a polycarbonate: Entanglement analysis from coarse-grained md simulations.
*Macromolecules*, 38(19):8078–8092, 2005. - ↑ Sharon C. Glotzer and Wolfgang Paul. Molecular and mesoscale simulation methods for polymer materials.
*Annual Review of Materials Research*, 32(1): 401–436, 2002. - ↑ D. Hossain, M.A. Tschopp, D.K. Ward, J.L. Bouvard, P. Wang, and M.F. Horstemeyer. Molecular dynamics simulations of deformation mechanisms of amorphous polyethylene.
*Polymer*, 51(25):6071–6083, 2010. - ↑ B. Montanari, P. Ballone, and R.O. Jones. Density functional study of polycarbonate. 2. crystalline analogs, cyclic oligomers, and their fragments.
*Macromolecules*, 32(10):3396–3404, 1999.