Narrow Results

We extend our analysis of the gauging of rigid symmetries in bosonic two-dimensional sigma models with Wess–Zumino terms in the action to the case of world-sheets with defects. A structure that permits a non-anomalous coupling of such sigma models to world-sheet gauge fields of arbitrary topology is analyzed, together with obstructions to its existence, and the classification of its inequivalent choices.

We develop a rigorous framework for modeling the geometry equilibration of crystalline defects. We formulate the equilibration of crystal defects as a variational problem on a discrete energy space and establish qualitatively sharp far-field decay estimates for the equilibrium configuration. This work extends [V. Ehrlacher, C. Ortner and A. Shapeev, Analysis of boundary conditions for crystal defect atomistic simulations, Arch. Ration. Mech. Anal.222 (2016) 1217–1268] by admitting infinite-range interaction which in particular includes some quantum chemistry based interatomic interactions.

The fatigue strength of components is affected by loading and environmental conditions, their geometry, the material and the manufacturing process adopted for their production. As a consequence of local stress concentrations, fatigue cracks can propagate to failure from the defects created by the manufacturing processes or introduced during the service life, as occurs in impact-damage. Ti6Al4V titanium alloy is commonly used in the aeronautical sector and other engineering applications due to its high specific strength. The study of the fatigue behavior of Ti6Al4V is therefore critical for designing reliable and durable structures. The work reports a synthesis of the results present in the literature for the fatigue behavior of Ti6Al4V in inert and aggressive environments, in the presence of a deposited coating, in the case of impact-damage, when components are produced by additive manufacturing and in the absence of solution treatment and over-aging.

We report on the structural stability of ideal (defect-free) and structurally and morphologically degenerate carbon nanotubes and nanotube junction systems under axial loading based on the finite element method. We estimated the values for critical buckling load for uncapped and capped single-walled carbon nanotubes (SWCNTs) and linear and angle-adjoined SWCNT heterojunctions in ideal and structurally degenerate systems containing single-, double-, triple-, pinhole- and pentagon–heptagon (i.e., 5–7) structural defects and also containing a substitutional nitrogen (N) atom inclusion under compressive loading. Absolute atomic vacancy (defect) concentration in studied SWCNTs models was assumed to be nil for ideal systems, and was up to 3.0 at.% for structurally and morphologically degenerate systems. It was found that all types of structural defects and the morphological N-defect had reduced the load carrying capacity and mechanical strength in all SWCNT systems studied. The SWCNT models containing physically large vacant sites, such as triple- and pinhole-defects, displayed significantly lower critical load values compared to the systems that contained only a single-, double- or triple-vacancies. In addition, we found that capped SWCNTs performed marginally better in critical load carrying capacity compared to uncapped SWCNT systems. Furthermore, majority of the investigated structures displayed reduced load in SWCNTs with narrower tube widths, proportional to the size and the type of the defect investigated. The effects of chirality, such as zigzag- versus armchair-type, on the structural stability of the investigated SWCNT models were also investigated.

This study aims to build a new bridge between configurational stress/force and material fracture. The migrating control volume and thermodynamics are used to develop the Eshelby relation, and the relationship between the conservative integral in fracture mechanics and configurational stress/force for elastic or elastic-plastic materials is further clarified. Additionally, the configurational stresses, including circumferential configurational stress at the crack tip taking T-stress into consideration, are determined, and the $J$ integral vector is then calculated further. The results indicate that $J_1$ integral is path-independent while $J_2$ is path-dependent when T-stress is considered. We preliminarily present the relationship between the configurational stress and crack initiation and the zero circumferential configurational stress fracture criterion (ZCCS) is proposed based on the local properties of the crack-tip configurational stress tensor and fracture mechanics. To estimate the fracture loads, we also develop two fracture criteria based on the critical area of crack-tip plastic zone determined by the Mises configurational stress (MCSPA) and the principal configurational stress difference (PCSDPA), respectively. It is found that the initiation angle assessed by the ZCCS fracture criterion is in good agreement with that by both the MTS fracture criterion and experimental observations, as well as T stresses could affect the initiation angles for mixed-mode cracks under tension-shear loads. Furthermore, the fracture loads evaluated by the MCSPA and PCSDPA fracture criteria are consistent with that by both the MTS fracture criterion and experimental results. Finally, the initiation angles determined based on the characteristics of crack-tip plastic zone by configurational stress coincide with that by MTS and ZCCS fracture criteria.

A molecular structural mechanics method has been implemented to investigate the vibrational characteristics of single-layer graphene (SLG) with defects. By adopting the lumped mass unit to replace carbon atoms, and the beam element with circular cross-section to mimic C–C covalent bonds, SLG is modeled as a space framework. The simulation results show that the chirality almost has no effect on the natural frequency and the vibration mode of SLG, while boundary conditions have great influences. The influences of defects with different number and location on the natural frequencies are also studied. It is concluded that vibration mode is insensitive to the vacancy defect, small hole and short flaw, but large holes and long flaws can affect the vibration characteristics. So the graphene sheet even with small defect effects might be selected as the nanosensor material as well as pristine graphene. The conclusions in this paper may provide some references for the design of nanosensor.