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This work introduces a semi-analytical formulation for the simulation and modeling of curved structures based on the Scaled Boundary Finite Element Method (SBFEM). This approach adapts the fundamental idea of the SBFEM concept to scale a boundary to describe a geometry. Until now, scaling in SBFEM has exclusively been performed along a straight coordinate which enlarges, shrinks or shifts a given boundary.
In this novel approach, scaling is based on a polar or cylindrical coordinate system such that a boundary is shifted along a curved scaling direction. The derived formulations are used to compute the static and dynamic stiffness matrices of homogeneous curved structures. The resulting elements can be coupled to general SBFEM or FEM domains. For elastodynamic problems computations are performed in the frequency domain. Results of this work are validated using the Global Matrix Method and Standard Finite Element analysis.
The elastic constants are the most basic mechanical properties of a material and are needed for any structural analysis of a component. For example, they have a major influence on the eigenfrequencies of vibrating parts. Single crystals of Ni-base superalloys are strongly anisotropic, which means that the observed properties are orientation dependent. Tensor algebra is then required to mathematically formulate the elastic properties and their relations to the crystal orientation. Hence, this chapter first summarizes some basic definitions and calculation rules for Rotation matrices, including the definition of the Euler angles, which are most commonly used to define the relative orientations of the crystal and the component. Parts of this chapter closely follow the lines of the excellent exposition of the topic by Olschewski.
We obtained concomitant dimorphic forms of Anthracene Schiffbase (N-(anthracen-9-yl methylene)-2,5- dichloroaniline) from hexane solvent. Two polymorphs can be differentiated by their morphology and mechanical properties. One form is long acicular type and elastically bendable while another form is block shaped and brittle in nature. Mechanical property is attributed to underlying crystal packing. Hirsh- feld analysis and energy framework calculations were done to corroborate structure-property correlation of two forms.
Experimental and phase field studies of age hardening response of a high purity Al‐4Cu‐1Li‐0.25Mn‐alloy (mass %) during isothermal aging are conducted. In the experiments, two hardening phases are identified: the tetragonal θ′ (Al₂Cu) phase and the hexagonal T1 (Al₂CuLi) phase. Both are plate shaped and of nm size. They are analyzed with respect to the development of their size, number density and volume fraction during aging by applying different analysis techniques in TEM in combination with quantitative microstructural analysis. 3D phase‐field simulations of formation and growth of θ′ phase are performed in which the full interfacial, chemical and elastic energy contributions are taken into account. 2D simulations of T1 phase are also investigated using multi‐component diffusion without elasticity. This is a first step toward a complex phase‐field study of T1 phase in the ternary alloy. The comparison between experimental and simulated data shows similar trends. The still unsaturated volume fraction indicates that the precipitates are in the growth stage and that the coarsening/ripening stage has not yet been reached.
This work addresses the computation of stiffness matrices for general prismatic structures with an arbitrary cross section. The presented approach is based on the scaled boundary finite element method (SBFEM), a semi-analytical method, which can be used to model structures by only discretizing the boundary of a domain. For prismatic structures, the process is further simplified, as only the cross section of the structure has to be discretized. Thus, a particular semi-analytical finite element is constructed for bounded and unbounded domains. The proposed approach leads to a frequency-dependent stiffness matrix. This stiffness matrix can easily be coupled to other prismatic SBFEM domains or general SBFEM domains. Necessary modifications to include forces along the scaling direction, such as body loads, are addressed. The results of the proposed approach are compared to those of traditional FEM models obtained using commercially available software.
Simulation of the θ′ Precipitation Process with Interfacial Anisotropy Effects in Al-Cu Alloys
(2021)
The effects of anisotropic interfacial properties and heterogeneous elasticity on the growth and ripening of plate-like θ′-phase (Al2Cu) in Al-1.69 at.% Cu alloy are studied. Multi-phase-field simulations are conducted and discussed in comparison with aging experiments. The precipitate/matrix interface is considered to be anisotropic in terms of its energy and mobility. We find that the additional incorporation of an anisotropic interfacial mobility in conjunction with the elastic anisotropy result in substantially larger aspect ratios of the precipitates closer to the experimental observations. The anisotropy of the interfacial energy shows comparably small effect on the precipitate’s aspect ratio but changes the interface’s shape at the rim. The effect of the chemo-mechanical coupling, i.e., the composition dependence of the elastic constants, is studied as well. We show that the inverse ripening phenomenon, recently evidenced for δ’ precipitates in Al-Li alloys (Park et al. Sci. Rep. 2019, 9, 3981), does not establish for the θ′ precipitates. This is because of the anisotropic stress fields built around the θ′ precipitates, stemming from the precipitate’s shape and the interaction among different variants of the θ′ precipitate, that disturb the chemo-mechanical effects. These results show that the chemo-mechanical effects on the precipitation ripening strongly depend on the degree of sphericity and elastic isotropy of the precipitate and matrix phases.