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Description
Fracture phenomena have been extensively studied in the last several decades. Continuum mechanics-based approaches, such as finite element methods and extended finite element methods, are widely used for fracture simulation. One well-known issue of these approaches is the stress singularity resulted from the spatial discontinuity at the crack tip/front. The requirement of guiding criteria for various cracking behaviors, such as initiation, propagation, and branching, also poses some challenges. Comparing to the continuum based formulation, the discrete approaches, such as lattice spring method, discrete element method, and peridynamics, have certain advantages when modeling various fracture problems due to their intrinsic characteristics in modeling discontinuities.
A novel, alternative, and systematic framework based on a nonlocal lattice particle model is proposed in this study. The uniqueness of the proposed model is the inclusion of both pair-wise local and multi-body nonlocal potentials in the formulation. First, the basic ideas of the proposed framework for 2D isotropic solid are presented. Derivations for triangular and square lattice structure are discussed in detail. Both mechanical deformation and fracture process are simulated and model verification and validation are performed with existing analytical solutions and experimental observations. Following this, the extension to general 3D isotropic solids based on the proposed local and nonlocal potentials is given. Three cubic lattice structures are discussed in detail. Failure predictions using the 3D simulation are compared with experimental testing results and very good agreement is observed. Next, a lattice rotation scheme is proposed to account for the material orientation in modeling anisotropic solids. The consistency and difference compared to the classical material tangent stiffness transformation method are discussed in detail. The implicit and explicit solution methods for the proposed lattice particle model are also discussed. Finally, some conclusions and discussions based on the current study are drawn at the end.
A novel, alternative, and systematic framework based on a nonlocal lattice particle model is proposed in this study. The uniqueness of the proposed model is the inclusion of both pair-wise local and multi-body nonlocal potentials in the formulation. First, the basic ideas of the proposed framework for 2D isotropic solid are presented. Derivations for triangular and square lattice structure are discussed in detail. Both mechanical deformation and fracture process are simulated and model verification and validation are performed with existing analytical solutions and experimental observations. Following this, the extension to general 3D isotropic solids based on the proposed local and nonlocal potentials is given. Three cubic lattice structures are discussed in detail. Failure predictions using the 3D simulation are compared with experimental testing results and very good agreement is observed. Next, a lattice rotation scheme is proposed to account for the material orientation in modeling anisotropic solids. The consistency and difference compared to the classical material tangent stiffness transformation method are discussed in detail. The implicit and explicit solution methods for the proposed lattice particle model are also discussed. Finally, some conclusions and discussions based on the current study are drawn at the end.
ContributorsChen, Hailong (Author) / Liu, Yongming (Thesis advisor) / Jiao, Yang (Committee member) / Mignolet, Marc (Committee member) / Oswald, Jay (Committee member) / Solanki, Kiran (Committee member) / Arizona State University (Publisher)
Created2015
Description
A new class of layered materials called the transition metal trichalcogenides (TMTCs) exhibit strong anisotropic properties due to their quasi-1D nature. These 2D materials are composed of chain-like structures which are weakly bound to form planar sheets with highly directional properties. The vibrational properties of three materials from the TMTC family, specifically TiS3, ZrS3, and HfS3, are relatively unknown and studies performed in this work elucidates the origin of their Raman characteristics. The crystals were synthesized through chemical vapor transport prior to mechanical exfoliation onto Si/SiO¬2 substrates. XRD, AFM, and Raman spectroscopy were used to determine the crystallinity, thickness, and chemical signature of the exfoliated crystals. Vibrational modes and anisotropic polarization are investigated through density functional theory calculations and angle-resolved Raman spectroscopy. Particular Raman modes are explored in order to correlate select peaks to the b-axis crystalline direction. Mode III vibrations for TiS3, ZrS3, and HfS3 are shared between each material and serves as a unique identifier of the crystalline orientation in MX3 materials. Similar angle-resolved Raman studies were conducted on the novel Nb0.5Ti0.5S3 alloy material grown through chemical vapor transport. Results show that the anisotropy direction is more difficult to determine due to the randomization of quasi-1D chains caused by defects that are common in 2D alloys. This work provides a fundamental understanding of the vibrational properties of various TMTC materials which is needed to realize applications in direction dependent polarization and linear dichroism.
ContributorsKong, Wilson (Author) / Tongay, Sefaattin (Thesis advisor) / Wang, Liping (Committee member) / Green, Matthew (Committee member) / Arizona State University (Publisher)
Created2017