The fracture behavior of a graphene sheet, containing a center crack (length of 2a) was characterized based on the atomistic simulation and the concept of continuum mechanics. Two failure modes, i.e., opening mode (Mode I) and sliding mode (Mode II), were considered by applying remote tensile and shear loading, respectively, on the graphene sheet. In the atomistic simulation, the equilibrium configurations of the cracked graphene subjected to applied loadings, before and after the crack extension of 2Da, were determined through molecular dynamics (MD) simulation, from which the variation of the potential energy and the strain energy release rate of the discrete graphene sheet because of crack extension was calculated accordingly. It is noted that because of the discrete attribute, there is no stress singularity near the crack tip, and thus, the concept of stress intensity factor that is generally employed in the continuum mechanics may not be suitable for modeling the crack behavior in the atomistic structures. For the sake of comparison, the continuum finite element model with the same geometric parameters and material properties as the atomistic graphene sheet was constructed, and the corresponding strain energy release rate was calculated from the crack closure method. Results indicated that the strain energy release rates obtained from the continuum model exhibit good agreement with those derived from discrete atomistic model. Therefore, it is suggested that the strain energy release rate is an appropriate parameter, which can be employed in the atomistic model and the continuum model for describing the fracture of cova-lently bonded graphene sheet.
The stress distribution of CNTs embedded within polyimide matrix subjected to applied loading was investigated using molecular dynamics simulation. The purpose of evaluating the stress distribution of CNTs is to characterize the loading transfer efficiency between the nano-reinforcement and surrounding polyimide matrix, which basically is an essential factor controlling the mechanical properties of nanocomposites. Three different interfacial adhesions between the CNTs and polyimide molecular were considered, that is, vdW interaction, CNTs with surface modification, and covalent bond. The stress distribution of the CNTs was calculated by using the Lutsko atomistic stress formulation1,2 and by taking the derivative of the potential functions as well. Results revealed that when the CNTs surface was modified, the higher load transfer efficiency from the polyimide to the CNTs was observed resulting in the higher modulus of the nanocomposites. It is noted that, if no surface modification on CNTs, the load transfer efficiency which basically depends on the intensities of the vdW interaction is relatively low. As a result, the surface modification on CNTs is an effective manner to improve the load transfer efficiency as well as the modulus of nanocomposite, which should be suggested in the fabrication of CNTs nanocomposites.
In this study, the mechanical properties of graphene and single walled carbon nanotubes (SWCNTs) were investigated based on molecular dynamics (MD) simulation. During the characterization of the mechanical properties, the atomistic interactions of the carbon atoms were described using the bonded and non-bonded energies. The bonded energy consists of four different interactions: Bond stretching, bond angle bending, dihedral angle torsion, and inversion. On the other hand, the non-bonded interaction between the carbon atoms within the cut-off ranges was regarded as the van der Waals (vdW) force. The effect of vdW force on the mechanical properties of graphene and SWCNTs would be mainly of concern. Simulation results indicated that the Young's modulus of the graphene with vdW force included is 15% higher than that without considering any vdW interaction. The same tendency also was observed in the armchair and zig-zag SWCNTs. Furthermore, it was revealed that the increment of moduli caused by the vdW force could be primarily attributed to the 1-4 vdW interaction. The influence of the vdW interactions on the mechanical properties of graphene and SWCNTs was then elucidated using the parallel spring concept.
This research is aimed to fabricate the nano and micron particle reinforced composites as well as to understand the particulate size effect on the mechanical behaviors of the composites. The stiffness, strength and fracture toughness were investigated in this study. Spherical alumina particles with diameters of 5 microns and 10-20 nano meters were dispersed respectively into the epoxy resin using the mechanical mixer followed by the sonication. To measure the stiffness and strength of the composites, coupon specimens were prepared and then tested in tension. On the other hand, the fracture toughness was evaluated by performing three point bending tests on the single edge notch bending specimens. Experimental results revealed that the Young’s modulus of composites basically is not affected by particulate size; while, the tensile strength of the composites containing nano particles is higher than that with micron particles. From the fracture tests, it was indicated that the composites containing nano particles possess superior fracture toughness than the composites with micron inclusions.
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