Multiscale Modeling of the Fracture Behavior in Semicrystaline Polymers
BackgroundThe range of length scales involved in the mechanical behavior of polymers makes polymeric engineering a prime candidate for an multisclae modeling approach. For amorphous polymers, the random structure prohibits long-range order, as observable in crystalline systems, and thus does not involve dislocations based fracture mechanisms but rather mechanisms such as crazing, shear band formation, and crack propagation. Lower length scale characteristics, such as entanglement density, chain slippage, chain rupture, and crystal morphology can be useful in quantifying the macroscale fracture behavior.
With the end goal of polymer fracture behavior in mind, we can downscale to capture the microscale phenomenon and relate it to a constitutive internal state variable model (ISV). While amorphous polymers have been well described by ISV models, the micromechanisms of the fracture behavior in semicrystalline polymers are not as well characterized. Additional work is required to completely bridge all length scales especially regarding the complex crystal morphologies seen in semicrystalline polymers. Figure 1 illustrates the required information bridges between the continuum model and lower length scale simulations as well as the information bridges between length scales.
Macroscale ISV Continuum
A macroscale description of the fracture behavior in polymers is difficult due to the underlying micromechanisms involved and their dependence on temperature, strain rate and stress state. A comprehensive model must include details from all the various length scales and all the interactions involved. The ISV continuum model must describe all the amorphous phase interactions such as chain slippage, entanglements, void formation and growth, and chain rupture. Additionally, the crystalline interactions such as crystallographic slip, amorphous-crystalline interfaces, and spherulite interactions must be accounted for in the model.
Spherulite Interactions (FEA)
Microscale finite element simulations (FEA) of spherulite interactions shows a strong deformation field dependence on the spherulite distribution. Interlammelar interactions within each spherulite complicate such interactions and is thus a key parameter in the determination of spherulite distribution effects on the deformation gradient. Lower length scale simulations on interlamellar slip can be bridged to spherulite interactions.
Crystallographic Slip (FEA)
Crystallographic slip between the amorphous and crystalline regions of polymers plays a large role in the fracture behavior of polymers. Much like dislocations in metals, crystalline regions can dislocate and glide past amorphous regions, usually when a preferred slip direction. The preferred slip direction can be found using molecular simulations on the chain tilt interface region.
The nanoscale is an information rich length scale for the quantification of polymer fracture behavior. Along with the interface energy passed to microscale FEA simulations, molecular interactions like chain entanglement, deformation induced chain alignment, and chain rupture can be passed directly to the ISV continuum model. Atomistic simulations require the use of a potential function to describe the energy of the system. While many potentials functions are empirically based, electronic level simulations can be used to parameterize such functions.
At the electronic scale we can use the density functional theory (DFT) to calculate the lattice parameter and elastic constants of some polymers. DFT calculations can be used as a parameterization tool for atomistic potential functions.
- ↑ J. L. Bouvard, D. K. Ward, D. Hossain, E. B. Marin, D. J. Bammann, and M. F. Horstemeyer, “A general inelastic internal state variable model for amorphous glassy polymers,” Acta Mech., vol. 213, no. 1–2, pp. 71–96, Jun. 2010.
- ↑ J. L. Bouvard, D. K. Francis, M. A. Tschopp, E. B. Marin, D. J. Bammann, and M. F. Horstemeyer, “An internal state variable material model for predicting the time, thermomechanical, and stress state dependence of amorphous glassy polymers under large deformation,” Int. J. Plast., vol. 42, pp. 168–193, Mar. 2013.
- ↑ M. Uchida, T. Tokuda, and N. Tada, “Finite element simulation of deformation behavior of semi-crystalline polymers with multi-spherulitic mesostructure,” Int. J. Mech. Sci., vol. 52, no. 2, pp. 158–167, Feb. 2010.
- ↑ S. Gautam, S. Balijepalli, and G. C. Rutledge, “Molecular Simulations of the Interlamellar Phase in Polymers: Effect of Chain Tilt,” Macromolecules, vol. 33, no. 24, pp. 9136–9145, Nov. 2000.
- ↑ 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, vol. 51, no. 25, pp. 6071–6083, Nov. 2010.