Peridynamic Models for the Fracture of Graphene Sheets

石墨烯斷裂破壞的近場動力學模型

Student thesis: Doctoral Thesis

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Award date20 Aug 2019

Abstract

Graphene sheet, a one-atom thick two-dimensional nano-structure with sp2 bonded carbon atoms arranged in a hexagonal lattice, has shown superior mechanical, thermal, electrical and optical properties. Because of these remarkable properties, graphene sheet shows the potential in designing micro- and nano-electromechanical devices and composites. Especially as a thin sheet, graphene is of great significance in engineering applications of membrane structures. Therefore, it has gained increasing attention from all over the world. Because fracture propagation is one of the most common failure modes, understanding the fracture of graphene sheet is of great importance to its applications.

Generally, it is a challenge to carry out experimental studies on the mechanical characteristics of single layer graphene sheets (SLGS). Then theoretical predictions are necessary to understand the properties of SLGS. First principle based calculations can be well employed for the prediction of mechanical properties of SLGS, but they are only applicable to the systems with a few hundred of atoms at most because of the highly computational cost. Although molecular dynamics (MD) simulation can save the computational cost through reducing the computational accuracy slightly compared with first principle calculations, it remains computationally expensive for relatively large nanoscale systems and cannot satisfy the requirements in engineering. With calibrating against atomistic calculations, continuum mechanics models such as finite element (FE) models can be used to predict the nonlinear mechanical behaviors of graphene. However, such continuum mechanics based methods are very limited when discontinuities such as vacancies and cracks exist. The newly proposed continuum based peridynamic (PD) theory has absolute advantages over the classical continuum mechanics (CCM) based methods in solving the discontinuity related problems such as the crack propagation. However, its application in the mechanical investigation of graphene sheets has not been reported in detail in the open literatures.

This thesis presents the development of effective and efficient PD models for the fracture analysis of SLGS and systematic investigations on the dynamic fracture of SLGS based on the developed PD models. Main parts of the work are presented as follows.

A nonlinear ordinary state based PD (OSPD) coarse-grained (OSPD-CG) model is developed based on the nonlinear continuum elastic constitutive relation of SLGS under homogeneous and isotropic assumptions in which the PD parameters are derived through calibrating the PD strain energy density against the one of the fully atomistic SLGS system obtained by MD simulations. However, the isotropic assumption makes the OSPD-CG model only applicable to armchair or zigzag SLGS. Then a bond-based PD-CG (BPD-CG) model is further developed by considering the nonlinear and anisotropic properties and the effect of chirality of SLGS. In the BPD-CG model, the PD parameters are determined by comparing the PD stress-strain relation with the one derived from the analytical molecular structural mechanics (MSM) model, which is simpler than the strain energy density calibration method. The parameters in the PD models are related with the interatomic potential at atomic scale, thus providing a multiscale modeling insight in the single PD framework. To improve the computational efficiency, coarse-graining techniques are employed in the PD simulations, in which several atoms in SLGS are coarse-grained as a material point. Especially, one four-atom basic cell in SLGS is coarse-grained as a material point in the BPD simulation by considering micro chiral structures in SLGS.

Based on the OSPD-CG model, the fracture of pre-cracked zigzag SLGS is studied. The obtained results agree well with those from MD simulations, including the stress-strain relations, the crack propagation patterns and the average crack propagation velocities. The interaction effect between edge and center pre-cracks on the crack propagation of the pre-cracked SLGS is discussed in detail. Then the fracture mechanisms at atomic level in SLGS are revealed through analyzing the bond stretching, the bond rotation and the local stress state around the moving crack tip by MD simulation for the reason that the PD-CG methods may lose the information at atomic sale. The effect of crack size and structure of initial crack tip on the fracture of SLGS is discussed. Finally, the fracture of SLGS with different chirality is investigated based on the BPD-CG model. The results are consistent with the current published results and show the dependence of fracture on the chirality of SLGS. The fracture propagation of SLGS with single and multiple pre-cracks is modeled. The interaction between the initial center crack and different defects is investigated as well. The crack propagation can be significantly affected and even arrested by the vacancies properly arranged around the crack tips. Numerical results show the advantages of PD-CG models over the CCM methods and MD simulation in solving large nanoscale complex fracture problems with good effectiveness and high efficiency. With the rapid development of nanoengineering, the present results of the fracture in SLGS can provide significant guidance in the design of graphene based devices in nanoengineering.