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Integration Scales and Coordinate Systems
Published in William G. Gray, Anton Leijnse, Randall L. Kolar, Cheryl A. Blain, of Physical Systems, 2020
William G. Gray, Anton Leijnse, Randall L. Kolar, Cheryl A. Blain
The microscopic scale is typically interpreted as the length scale at which the molecular structure of matter is disregarded such that it may be conceptualized as without gaps or empty spaces. Functions describing the system may be defined at this scale that are continuous and have continuous derivatives Malvern, 1969]. At this scale, the behavior of individual molecules is accounted for only in an average, continuum sense. In the example of figure 4.1, the microscopic characteristic length, l, is associated with a mean pore diameter. For river flow (figure 4.2), l is related to identification of a collection of fluid molecules such that they form a continuum or parcel.
Static solution of two-dimensional decagonal piezoelectric quasicrystal laminates with mixed boundary conditions
Published in Mechanics of Advanced Materials and Structures, 2022
Chao Liu, Xin Feng, Yang Li, Liangliang Zhang, Yang Gao
In Figure 7, the state variables distributions in different boundary condition laminates are presented under Loading Case 1. By comparing u1 and u2 in Figure 7(a) and (b), it can be found u1 is equal to u2 when the boundary conditions are SSSS and CCCC, while u1 is smaller than u2 with other boundary conditions. By changing the boundary conditions change, the stiffness of the laminate changes accordingly, and then u3 in Figure 7(c) gradually decreases with the increase of the number of clamped-supported boundaries. The direction of w2 in Figure 7(d) changes when the x2-direction is clamped boundary condition, which implies boundary conditions have a certain effect on the degree of atomic rearrangement. the atom vibration and rearrangement at the microscopic scale play the dominant role in the overall mechanical behavior of QCs at the macroscopic scale.
Stochastic dynamics of veering modes in a symmetric coupled system
Published in Ships and Offshore Structures, 2022
The development of computing resources has improved prediction capability of the theoretical model. This has paved path towards the development of complex finite element model to replicate the behaviour of the actual system. However, there are still problems associated with these complex models. Developing a theoretical model includes isolating a certain part of the reality. The isolated part could be the problem of significance or interest. For example, the response in the lateral direction is isolated in the theoretical model and the interaction with other dof, such as the coupling between the lateral and axial direction is ignored. Another issue is the scale of modelling, a deterministic system under microscopic scale could become uncertain in a macroscopic scale. This could be due to the prohibitive number of experimental measurements required to the quantify variables under consideration. Hence the enhancement of computational tools need not necessarily resolve the problem of identification of the uncertainties associated with their estimation.
Effect of HIP post-treatment on the HIPed Ti6Al4V powder compacts
Published in Powder Metallurgy, 2019
Xina Huang, Lihui Lang, Gang Wang
The densification, microstructure and mechanical properties of Ti6Al4V powder compacts fabricated using HIP with and without HIPPPT were studied. The major conclusions can be summarised as follows. The relative density of region II in HIPed powder compact is improved from 91.5 to 96.8% after HIPPT.The microstructure of powder compact before HIPPT are composed of lamellar α phases, equiaxed grains, and PPBs. After HIPPPT, the interlayer spacing of the lamellar α phase is increased, PPBs disappear and equiaxed grains coarsen. In addition, the average grain size of the powder compact is increased by 27.2% and the number of a high-angle grain of powder compact is reduced after HIPPT.The elongation of powder compact after HIPPT is improved 12.8%, while the strength and yield strength are almost not changed. The fracture morphologies before and after HIPPT show the features of cup-and-cone in the macroscopic scale and ductile fracture in the microscopic scale. However, the dimples of powder compact after HIPPPT are larger and deeper, indicating a better ductility.