The critical influence of some “tiny” geometrical details on the stress field in a Brazilian Disc with a central notch of finite width and length

The role of some geometrical characteristics of the notches ma­chined in circular discs, in order to determine the mode-I fracture tough­ness of brittle materials, is discussed. The study is implemented both analyti­cally and numerically. For the analytic study advantage is taken of a recently intro­duced solution for the stress- and displacement-fields developed in a finite disc with a central notch of finite width and length and rounded corners. The vari­ation of the stresses along strategic loci and the deformation of the peri­me­ter of the notch obtained analytically are used for the calibration/validation of a flexible nu­mer­ical model, which is then used for a parametric investiga­tion of the role of geometrical features of the notched disc (thickness of the disc, length and width of the notch, radius of the rounded corners of the notch). It is con­cluded that the role of the width of the notch is of critical im­port­ance. Both the ana­lytic and the numerical studies indicate definitely that ignoring the ac­curate geo­metric shape of the notch leads to erroneous results concerning the actual stress field around the crown of the notch. Therefore, it is possible that misleading values of the fracture toughness of the material of the disc may be obtained.

Thermo-mechanical stress analysis of rotating fiber reinforced variable thickness disk

Circumferentially fiber reinforced composite disk, which has a variable thickness, is modeled via analytical approaches. The disk is subjected to rotation in traction free conditions and decreasing, constant, and increasing steady state radial temperature gradients along the disk radius. Limit angular velocities are calculated by operating Tsai-Wu and Norris failure indexes to the problem. Subsequently, these limit velocities are gradually decreased to examine the stress and displacement fields. Acquired results show that as the angular velocity drops, the effects of temperature gradients become more visible. At lower angular velocities, these gradients may even alter the stress field directions. Also, different failure criteria implementation may change the calculated limit velocities to a considerable degree. Therefore, the failure index should be chosen attentively to procure conservative results. In the investigation, the influence of disk geometry on the directional stresses is studied as well. Without further ado, it can be expressed that the geometry causes slight alterations in stresses and displacements.

Modeling and Simulation of the Casting Process with Skeletal Sand Mold

The author-proposed skeletal sand mold, which mainly includes a shell, air cavities and a truss support structure, has been experimentally proven to be very useful in controlling the cooling of casting at local areas and at different periods of the casting process. The modeling and simulation of the casting process using a skeletal sand mold were systemically analyzed. Complicated casting/mold and mold/air boundaries, and the thermal and mechanical behavior of the skeletal sand mold during the casting process were highlighted. A numerical simulation of the casting process of a stress frame specimen using a skeletal sand mold was performed. The temperature, stress and displacement fields of the casting and skeletal sand mold were obtained and compared with those using a traditional sand mold. The simulated results were validated with experiments. Using the skeletal sand mold, the cooling rate of the casting can be greatly improved due to the significant heat release from mold surface to environment. The residual stress and deformation of the casting can be reduced because of the decreased stiffness of this kind of mold. Although the skeletal sand mold is susceptible to cracking, it can be avoided by filleting in the conjunctions and increasing the shell thickness.

Theory of the flow-induced deformation of shallow compliant microchannels with thick walls

Long, shallow microchannels embedded in thick, soft materials are widely used in microfluidic devices for lab-on-a-chip applications. However, the bulging effect caused by fluid–structure interactions between the internal viscous flow and the soft walls has not been completely understood. Previous models either contain a fitting parameter or are specialized to channels with plate-like walls. This work is a theoretical study of the steady-state response of a compliant microchannel with a thick wall. Using lubrication theory for low-Reynolds-number flows and the theory for linearly elastic isotropic solids, we obtain perturbative solutions for the flow and deformation. Specifically, only the channel's top wall deformation is considered, and the ratio between its thickness t and width w is assumed to be ( t / w ) 2 ≫1. We show that the deformation at each stream-wise cross section can be considered independently, and that the top wall can be regarded as a simply supported rectangle subject to uniform pressure at its bottom. The stress and displacement fields are found using Fourier series, based on which the channel shape and the hydrodynamic resistance are calculated, yielding a new flow rate–pressure drop relation without fitting parameters. Our results agree favourably with, and thus rationalize, previous experiments.

Analytical Solutions for Stress and Displacement Fields in Disks under Arbitrarily Distributed Loads

The general series solution (GSS) approach is presented, in order to determine the stress and displacement fields in disks under arbitrarily distributed normal and tangential loads. An Airy stress function in series form is selected. Stresses are expressed by infinite coefficients. Thus displacements are expressed by the infinite stress coefficients. And self-equilibrated loads acting on the side edge are extended to Fourier series. Stress coefficients are related to loading coefficients by stress boundary conditions. Then five examples show the validity of this approach. The GSS approach might lead to industrial applications in rock mechanics, petroleum and mining engineering, etc.