Fracture of polymers

Polymer-based nanocomposites are very important engineering materials since their properties may be tailored for a huge range of applications. One of the most challenging fields of research is the investigation of mechanisms in nanocomposites which improve the fracture toughness, even at very low filler contents [1]. Several failure processes may occur like crack pinning, bi-furcation, deflections, and separations [2]. However, these processes take place at very small scales and are thus hardly accessible by mechanical testing. Since the nanofiller particles’ size is comparable to the typical dimensions of the monomers of the polymer chains and thus processes happen at the level of atoms and molecules, continuum-based descriptions and fracture mechanical characteristics are not straightforward to obtain.

To model such processes at atomistic scale with high accuracy, particle-based simulation tools as Molecular Dynamics (MD) have been established. As a so called “ab initio” approach, MD is a promising tool to model fracture in polymer nanocomposites as it provides constitutive relations not available from mechanical testing. However, a pure particle-based description becomes computationally prohibitive for system sizes relevant in engineering. To overcome this, only e.g. the crack tip shall be resolved to the level of atoms or, if a coarse-grained approach is used, of superatoms.

Hence, multiscale techniques seem to be a promising tool. Several of concurrent multiscale schemes have been proposed and applied to various problems [3,4], but most of them are limited to crystalline materials or highly simplified problems. By implication, a tool specifically designed for multiscale simulation of fracture in polymers considering crack initiation, development, and propagation (see Figure 1) is still a vision.

Figure 1: Crack at MD level propagating through FE domain

Thus, we will extend the multiscale Capriccio method [5,6,7] to adaptive particle regions moving within the continuum. With such a tool at hand, only the vicinity of a crack tip propagating through the material during fracture has to be described at molecular level, whereas the remaining parts may be treated continuum-based with significantly less computational effort.

To resolve the crack tip by MD at its current position, an MD calculation must be activated if a certain load threshold is reached. For this purpose, an MD system must be predeformed according to the instantaneous deformation state. By utilizing a hybrid molecular dynamics-continuum mechanical technique recently proposed by our group [8], the efficiency of the corresponding MD computation can be increased markedly. Upon switching back to FE when crack tip has moved forward and the load threshold is undercut again, the deformation state is transferred to the continuum by employing the Murdoch-Hardy procedure [9]. In [10], we have presented first MD-FE coupled fracture simulations using the Capriccio method and obtained promising results. Currently, we are advancing the MD framework to cover bond rupture in an appropriate manner (see Particle-based material description).

–Christof Bauer (M. Sc.) and Felix Weber (M. Sc.)

[1] M. H. Wichmann, K. Schulte and H. D. Wagner, “On nanocomposite toughness”, Composites Science and Technology, vol. 68, pp. 329-331, 2008

[2] S. Chandrasekaran, N. Sato, F. Tölle, R. Mülhaupt, B. Fiedler and K. Schulte, “Fracture toughness and failure mechanism of graphene based epoxy composites”, Composites Science and Technology, vol. 97, pp. 90-99, 2014

[3] R. E. Miller and E. B. Tadmor, “A unified framework and performance benchmark of fourteen multiscale atomistic/continuum coupling methods”, Modelling and Simulation in Materials Science and Engineering, vol. 17, p. 053001, 2009

[4] P. T. Bauman, J. T. Oden and S. Prudhomme, “Adaptive multiscale modeling of polymeric materials with Arlequin coupling and Goals algorithms”, Computer Methods in Applied Mechanics and Engineering, vol. 198, pp. 799-818, 2009

[5] S. Pfaller, “Multiscale Simulation of Polymers”, Erlangen, 2015

[6] S. Pfaller, M. Rahimi, G. Possart, P. Steinmann, F. Müller-Plathe and M. C. Böhm, “An Arlequin-based method to couple molecular dynamics and finite element simulations of amorphous polymers and nanocomposites”, Computer Methods in Applied Mechanics and Engineering, vol. 260, pp. 109-129, 2013

[7] S. Pfaller, A. Kergaßner and P. Steinmann, “Optimisation of the Capriccio Method to Couple Particle- and Continuum-Based Simulations of Polymers”, Multiscale Science and Engineering, vol. 1, pp. 318-333, 2019

[8] C. Bauer, M. Ries and S. Pfaller, “Accelerating molecular dynamics simulations by a hybrid molecular dynamics-continuum mechanical approach”, Soft Materials, vol. 20, pp. 428-443, 2022

[9] W. Zhao and S. Pfaller, “A concurrent MD-FE coupling method towards simulations of fracture of thermoplastic polymers”, Proceedings of XVI International Conference on Computational Plasticity. Fundamentals and Applications 2021, submitted manuscript

[10] R. J. Hardy, “Formulas for determining local properties in molecular-dynamics simulations: Shock waves”, The Journal of Chemical Physics, vol. 76, pp. 622-628, 1982