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At least 235 records · Page 13

Analyses of composite fuselage structure under various loading conditions

With the characteristics of high strength/weight and stiffness/weight ratios in advanced composite materials, composite plate structures have been successfully applied to secondary load-carrying structural components in the aerospace industry for the past two decades. Recently, filament wound composite shells are being considered for design of primary fuselage structures. To implement the design the structural response under various loading conditions needs to be predicted accurately. Therefore, it is essential to establish a rigorous analytical solution in the area of composite laminated shells. A closed form solution is presented that predicts the response of a composite shell subjected to internal pressure, axial tension, bending, and torsion. The material of the shell is assumed to be general cylindrically anisotropic. Based on the theory of cylindrical anisotropic elasticity coupled partial differential governing equations are developed using Lehknitskii's stress function approach. The general expressions for the stresses and displacements in the composite cylinders under these loading conditions is discussed. Three examples (45) off-axis unidirectional, (45/45) unsymmetric, and (45/45)(sub s) symmetric angle-ply fiber-reinforced laminated shells are shown to illustrate the effect of radius-to-thickness ratios, coupling, and stacking sequence.

Yuan, Fuh-Gwo↗

A kinematically driven anisotropic viscoelastic constitutive model applied to tires

Aircraft tires are composite structures manufactured with viscoelastic materials such as carbon black filled rubber and nylon cords. When loaded they experience large deflections and moderately large strains. Detailed structural models of tires require the use of either nonlinear shell or nonlinear three dimensional solid finite elements. Computational predictions of the dynamic response of tires must consider the composite viscoelastic material behavior in a realistic fashion. We describe a modification to a nonlinear anisotropic shell finite element so it can be used to model viscoelastic stresses during general deformations. The model is developed by introducing internal variables of the type used to model elastic strain energy. The internal variables are strains, curvatures, and transverse shear angles which are in a one-to-one correspondence with the generalized coordinates used to model the elastic strain energy for nonlinear response. A difference-relaxation equation is used to relate changes in the observable strain field to changes in the internal strain field. The internal stress state is introduced into the equilibrium equations by converting it to nodal loads associated with the element's displacement degrees of freedom. In this form the tangent matrix in the Newton-Raphson solution algorithm is not modified from its form for the nonlinear statics problem. Only the gradient vector is modified and the modification is not computationally costly. The existing finite element model for the Space Shuttle nose gear tire is used to provide examples of the algorithm. In the first example, the tire's rim is displaced at a constant rate up to a fixed value. In the second example, the tire's rim is enforced to follow a saw tooth load and unload curve to generate hysteresis loops.

Johnson, Arthur R.↗

Solute effects upon dislocation motion and recovery in Mg alloys (Final Report)

The objective the research was to develop a firmer understanding of the interactions between substitutional solute atoms and dislocations within Mg alloys. These interactions govern the absolute and relative mobilities of various types of dislocations in Mg (e.g., basal < a>, non-basal < a>, and pyramidal < c+a>). Furthermore, they have an impact on dislocation recovery processes (e.g., cross-glide, climb, rearrangement, and annihilation). Ultimately, solute-dislocation interactions strongly impact a) strain hardening, b) strain rate sensitivity, c) plastic anisotropy of textured polycrystals, d) texture evolution, e) dislocation substructures evolution, and even f) recrystallization behavior. It is broadly known that Mg alloys exhibit poor low temperature formability. Since formability is largely governed by properties (a) – (c) in this list, it is critical to develop a better understanding of solute-dislocation interactions, if one hopes to improve the situation. While the theory of static solute strengthening is well developed, especially for alloys with face centered cubic (FCC) crystal structures, there are outstanding questions related to applications to hexagonal close packed (HCP) crystal structures and dynamic strain aging (DSA) in materials of various structures. DSA has far-reaching implications for metal formability and, in the case of Mg alloys, appears to correlate with the so-called rare-earth (RE) texture which has been shown to benefit formability. The Portevin-Le Chatelier (PLC) effect, and associated negative strain rate sensitivity, occur at higher temperatures (>100℃) in Mg alloys as compared with similar Al alloys, even though they have similar melting points and solute diffusivities. Our preliminary research has shown that modern, physics-based models of DSA can be tuned to describe the behavior of Mg alloys if a rather higher activation enthalpy is assumed for cross-core diffusivity. While this partially explains the delay in DSA to higher temperatures, it is also hypothesized that this delay is due in part to the intrinsically more thermally activated (rate sensitive) nature of non-basal < a> dislocation motion which is required for macroscopic flow of Mg alloys, whereas octahedral slip in many FCC metals like aluminum is essentially athermal at room temperature. It was originally proposed to employ a combination of in-situ diffraction-based experimental characterization to validate existing theory. It was envisioned to perform in-situ transmission electron microscopy (TEM) to assess individual dislocation behavior and in-situ high-energy X-ray diffraction (HEXRD) techniques which were showing great promise for elucidating collective dislocation behavior, 2 including recovery, especially if the contributions to various forms of diffraction peak broadening (𝜂𝜂,𝜔𝜔,and 2𝜃𝜃) can be effectively integrated. Finally, it was envisioned to perform discrete dislocation dynamics (DDD) modeling approaches to aide in the interpretation of both TEM and HEXRD experiments. In the end, mechanical tests were performed on more complex Mg alloys which exhibited evidence of dynamic strain aging, and this led to the establishment of another project. Mechanical test data obtained at McMaster University served as the basis of an assessment of the applicability of Bazinski’s “stress equivalence” theory of solute strengthening to polycrystalline alloys of Mg. Although we did not succeed in applying the approach to Mg alloys, we did develop expertise with the HEXRD approach using a BCC, β-Ti alloy and demonstrated numerous new capabilities that may be applied to any polycrystalline material in collaboration with researchers at CHESS and around the world: (1) assessment of details of the elastoplastic transition (yielding) using a combination of HEXRD and full-field polycrystal plasticity modeling, (2) the first-ever experimental observation of strong stress rotation within the individual grains of a polycrystalline material, and (3) a comprehensive analysis of the grain-level dislocation density evolution based upon diffraction peak broadening along 𝜂𝜂,𝜔𝜔,and 2𝜃𝜃 directions. This final aspect allowed us to confirm that dislocations were gliding on multiple plane types and not restricted to {110} type planes, and it also provided clues as to why some grains were unloading during straining, with surprising implications for our understanding of the effects of geometrically necessary dislocations (GNDs). Finally, graduate student, Mohammed Shabana, developed a MATLAB code which confirmed the conclusions of Prof. Catalin Picu (Rensallear Polytechnic Institute, RPI) regarding the effect of solute-trapped, forest dislocations on the breaking stress of Lomer lock junctions in FCC metal alloys. He applied the same anisotropic line-tension model to a variety of dislocation junction configurations and found an inconsistency in the widely cited results of Dupuy and Fivel regarding the Hirth Lock, and he outlined an approach to extend these finding to HCP Mg alloys that we are still pursuing with discretionary fundings at UVA.

36 MATERIALS SCIENCE↗

Yeh-Stratton Criterion for Stress Concentrations on Fiber-Reinforced Composite Materials

This study investigated the Yeh-Stratton Failure Criterion with the stress concentrations on fiber-reinforced composites materials under tensile stresses. The Yeh-Stratton Failure Criterion was developed from the initial yielding of materials based on macromechanics. To investigate this criterion, the influence of the materials anisotropic properties and far field loading on the composite materials with central hole and normal crack were studied. Special emphasis was placed on defining the crack tip stress fields and their applications. The study of Yeh-Stratton criterion for damage zone stress fields on fiber-reinforced composites under tensile loading was compared with several fracture criteria; Tsai-Wu Theory, Hoffman Theory, Fischer Theory, and Cowin Theory. Theoretical predictions from these criteria are examined using experimental results.

Yeh, Hsien-Yang↗

Computation of turbulent rotating channel flow with an algebraic Reynolds stress model

An Algebraic Reynolds Stress Model has been implemented to modify the Kolmogorov-Prandtl eddy viscosity relation to produce an anisotropic turbulence model. The eddy viscosity relation becomes a function of the local turbulent production to dissipation ratio and local turbulence/rotation parameters. The model is used to predict fully-developed rotating channel flow over a diverse range of rotation numbers. In addition, predictions are obtained for a developing channel flow with high rotation. The predictions are compared with the experimental data available. Good predictions are achieved for mean velocity and wall shear stress over most of the rotation speeds tested. There is some prediction breakdown at high rotation (rotation number greater than .10) where the effects of the rotation on turbulence become quite complex. At high rotation and low Reynolds number, the laminarization on the trailing side represents a complex effect of rotation which is difficult to predict with the described models.

Warfield, M. J.↗

Self-Organized Stress Distributions in Polycrystalline Materials [Dissertation]

Understanding stress distributions in solid materials is complicated by the fact that most materials are polycrystalline in nature, with each crystal having an elastically anisotropic reaction to force. This study is to gain a better understanding on how external forces placed on a polycrystal are related to internal reactions within and between the grains. The hypothesis is that the stress distribution in porous to fully dense materials are self-organized based on strong contacts between and within the individual grains created by force chains. Force chains, commonly known in loaded granular materials, and could be the phenomenon that connect micro to macro deformation. Scale bridging measurements conducted through Raman spectroscopy, Atomic Force Microscopy, and Digital Image Correlation will be used to create stress maps, modulus maps, and elastic strain maps across a variety of geological and pharmaceutical polycrystals. When possible, the resulting maps will be compared to current homogenization schemes and a full field models. Finite element modeling will be used to assess whether the patterning seen in the experimental map is a reasonable approximation based on the orientation data of the samples used. A minimum of three publications is projected to be accomplished focusing each on a different method to experimentally test and analyze stress distributions.

36 MATERIALS SCIENCE↗

Cytosine monohydrate under mechanical stress

We report nanoindentation performed with a conospherical tip on the (100) face of cytosine monohydrate (CM) revealed a highly anisotropic response over a range of loads. Post-indent atomic force microscopy images identified an asymmetric deformation response owing to the pro-chiral structure of the surface. Activation of low rugosity slip planes induces movement of π-stacks rather than their displacement along the 1-dimensional hydrogen bonded ribbon direction. Anisotropy arises because slip can only propagate to one side of the indent, as the tip itself imparts a barrier to slip on the preferred plane thereby forcing the activation of secondary slip systems and pileup. The anisotropic deformation is of interest in relation to previous work which proposed a ribbon–rotation model to account for the topotactic conversion between CM and the product of its dehydration. The asymmetry in the nanomechanical properties exhibited by CM provides further support for the rotational model put forth and also serves to underscore the inherent relationship between a hydrate's mechanical properties and its solid state dehydration mechanism.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

On various mechanisms of shear wave generation from underground chemical explosions in hard rocks

Significant shear waves observed during underground explosions can make them look similar to natural earthquakes. In the near field, they can be caused by the source geometry and emplacement conditions, heterogeneous and anisotropic properties of the rock mass, relaxation of a non-uniform in situ stress around the source after the departure of the shock wave as well as by activation of nearby faults. Here, the stress relaxation mechanism is important at depth when the difference in main principal stresses becomes significant. Another mechanism of shear motion generation is due to explosive gas flow from the source cavity into the cracks initiated by the shock wave and joints connected to the cavity. Also, the shock wave from the explosion can cause weakening of the rock either due to permanent damage or shock-induced liquefaction at saturated joints. Numerical modelling of underground chemical explosions in hard rock at various confinement stresses has been conducted to compare various mechanisms of shear wave generation and their seismic characteristics with that of a simple fault rupture process observed during an earthquake.

58 GEOSCIENCES↗

Exact solutions for laminated composite cylindrical shells in cylindrical bending

Analytic elasticity solutions for laminated composite cylindrical shells under cylindrical bending are presented. The material of the shell is assumed to be general cylindrically anisotropic. Based on the theory of cylindrical anisotropic elasticity, coupled governing partial differential equations are developed. The general expressions for the stresses and displacements in the laminated composite cylinders are discussed. The closed form solutions based on Classical Shell Theory (CST) and Donnell's (1933) theory are also derived for comparison purposes. Three examples illustrate the effect of radius-to-thickness ratio, coupling and stacking sequence. The results show that, in general, CST yields poor stress and displacement distributions for thick-section composite shells, but converges to the exact elasticity solution as the radius-to-thickness ratio increases. It is also shown that Donnell's theory significantly underestimates the stress and displacement response.

Yuan, F. G.↗

A normal stress subgrid-scale eddy viscosity model in large eddy simulation

The Smagorinsky subgrid-scale eddy viscosity model (SGS-EVM) is commonly used in large eddy simulations (LES) to represent the effects of the unresolved scales on the resolved scales. This model is known to be limited because its constant must be optimized in different flows, and it must be modified with a damping function to account for near-wall effects. The recent dynamic model is designed to overcome these limitations but is compositionally intensive as compared to the traditional SGS-EVM. In a recent study using direct numerical simulation data, Horiuti has shown that these drawbacks are due mainly to the use of an improper velocity scale in the SGS-EVM. He also proposed the use of the subgrid-scale normal stress as a new velocity scale that was inspired by a high-order anisotropic representation model. The testing of Horiuti, however, was conducted using DNS data from a low Reynolds number channel flow simulation. It was felt that further testing at higher Reynolds numbers and also using different flows (other than wall-bounded shear flows) were necessary steps needed to establish the validity of the new model. This is the primary motivation of the present study. The objective is to test the new model using DNS databases of high Reynolds number channel and fully developed turbulent mixing layer flows. The use of both channel (wall-bounded) and mixing layer flows is important for the development of accurate LES models because these two flows encompass many characteristic features of complex turbulent flows.

Horiuti, K.↗

Stability and natural vibration analysis of laminated plates by using a mixed element based on a refined plate theory

A mixed shear flexible finite element, with relaxed continuity, is developed for the geometrically linear and nonlinear analysis of layered anisotropic plates. The element formulation is based on a refined higher order theory which satisfies the zero transverse shear stress boundary conditions on the top and bottom faces of the plate and requires no shear correction coefficients. The mixed finite element developed herein consists of eleven degrees of freedom per node which include three displacements, two rotations and six moment resultants. The element is evaluated for its accuracy in the analysis of the stability and vibration of anisotropic rectangular plates with different lamination schemes and boundary conditions. The mixed finite element described here for the higher order theory gives very accurate results for buckling loads and natural frequencies.

Putcha, N. S.↗

Fracture of composites using singular finite elements

Six noded quarter point natural isoparametric triangular elements are employed to obtain displacement and stress distributions around the crack tip in unidirectional graphite epoxy. The performance of the quarter point element for predicting crack growth direction in unidirectional composite materials is studied for different loading conditions and fiber orientations. The finite element results are compared to analytical solutions of anisotropic elasticity where available. Notched Iosipescu shear specimens are analyzed to study fracture behavior under shear loading. Two methods for determining stress intensity factors are presented.

Choksi, G. N.↗

Consequences of plane-strain and plane-stress assumptions in fully coupled chemo-mechanical Li-ion battery models

In Li-ion battery research, it is common to simulate chemo-mechanical phenomena in reduced dimensions (e.g., 2-D) as opposed to fully resolve these complex physics in 3-D. It is common to assume either (1) the out-of-plane strain is negligible (commonly referred to as plane-strain), or (2) the out-of-plane stress is negligible (commonly referred to as plane-stress). However, there is typically little consideration as to the quantitative consequences of these approximations. Furthermore, the influence of these out-of-plane assumptions can be compounded and convoluted when chemo-mechanics models implement so-called “fully coupled” formulations, where the local species concentrations influence the stress-state and the stress-state influences the local species fluxes. Here, the present manuscript explores the implications of using plane-stress and plane-strain assumptions in 2-D as compared to simulating a full 3-D electrode particle. This comparative study includes simulating both isotropic and anisotropic particle intercalation where the particles can be surrounded by either a liquid or solid electrolyte. Additionally, common Li-ion battery-model metrics such as the state-of-stress, intercalation fraction distribution, and specific capacity are compared, while also considering the effects of particle size and C-rate. As alternatives to the pure plane-strain and plane stress approximations, two modified plane-strain assumptions are found to better approximate the fully coupled chemo-mechanical 3-D behavior.

25 ENERGY STORAGE↗

Short and medium range structure in elastic deformation of metallic and covalent glasses

Here, we present a concise methodology to analyze structural response to the applied stress in amorphous solids, including metallic glasses (MG), glassy selenium, silica and polycarbonate, using high energy x-ray diffraction and atomic pair distribution function (PDF) analysis. To assess the structural anisotropy induced by applied axial stress, diffraction data were expanded into spherical harmonics. Using Bessel transformation, components of the structure function were converted into isotropic and anisotropic PDFs. The PDFs were compared to the expected model behavior for ideal elastic deformation to separate homogeneous affine strain from local non-affine strains. In metallic glass the range of non-affine deformation is limited to the nearest neighbor shell, suggesting local strain relaxation under stress that occurs even in the elastic regime. Beyond the second atomic shell strain is uniform. However, in glassy silica, polycarbonate and selenium strong local bonding inhibits local displacements and strain in short range order is accommodated by rotation of local units. Interestingly, beyond a molecular unit, deformation in covalent systems is similar to MG, and response of the medium range order scales with the macroscopic stress.

glassy structure↗

Impact on multilayered composite plates

Stress wave propagation in a multilayer composite plate due to impact was examined by means of the anisotropic elasticity theory. The plate was modelled as a number of identical anisotropic layers and the approximate plate theory of Mindlin was then applied to each layer to obtain a set of difference-differential equations of motion. Dispersion relations for harmonic waves and correction factors were found. The governing equations were reduced to difference equations via integral transforms. With given impact boundary conditions these equations were solved for an arbitrary number of layers in the plate and the transient propagation of waves was calculated by means of a Fast Fourier Transform algorithm. The multilayered plate problem was extended to examine the effect of damping layers present between two elastic layers. A reduction of the interlaminar normal stress was significant when the thickness of damping layer was increased but the effect was mostly due to the softness of the damping layer. Finally, the problem of a composite plate with a crack on the interlaminar boundary was formulated.

Kim, B. S.↗

Note on the effect of transverse shear deformation in laminated anisotropic plates

The paper describes the development of some computer methods in applied mechanics. It begins with a distribution of primary stresses in laminated plates, followed by a determination of the associated statically consistent transverse shearing stress. The last section deals with the use of an energy principle for the utilization of these expressions for primary and transverse stresses. The purpose of this is to obtain two-dimensional constitutive equations involving transverse shear deformations and transverse shear stress resultants.

Reissner, E.↗

New insights on carbon black suspension rheology—Anisotropic thixotropy and antithixotropy

We report a detailed experimental study of peculiar thixotropic dynamics of carbon black (CB, Vulcan XC-72) suspensions in mineral oil, specifically the observation of sequential stress increase then decrease at a fixed shear rate in a step-down test. We verify that such dynamics, though peculiar, come from a true material response rather than experimental artifacts. We also reveal how this long-time stress decay is associated with antithixotropic structural change rather than viscoelastic stress relaxation by using orthogonal superposition (OSP) rheometry to probe viscoelastic moduli during the step-down tests. The orthogonal storage and loss moduli are present, showing this two-timescale recovery then decay response, which demonstrates that this response is antithixotropic, and it involves shear-induced structuring. We further show a mechanical anisotropy in the CB suspension under shear using OSP. Based on the rheological results, a microstructural schematic is proposed, considering qualitatively thixotropic structure build-up, antithixotropic densification, and anisotropic structure evolution. Our observation for these CB suspensions is outside the standard paradigm of thixotropic structure-parameter models, and the elastic response provides us with new insight into the transient dynamics of CB suspensions.

Mechanics↗

Functional Nanomaterials with Tunable Plasmonic and Emittive Properties (Final Project Report)

The goal of the project is on understanding the principles of non-covalent assembling of tunable functional materials with various nanocrystals in order to control light-matter interactions by changing localized interfacial refractive properties, coupling parameters, or the ionic environment of surrounding media. We explore novel soft functional matrices with controlled physical properties via the application of light, mechanical stresses, ionic environment, and electrical potential. These functional matrices is used in conjunction with novel anisotropic inorganic nanostructures such as noble metal/metal alloy anisotropic nanostructures with complex optical properties (multiple LSPR modes) and quantum dots with light-emissive or absorbing properties in a broad spectral range from the UV to the NIR for efficient solar energy absorption and light conversion.

36 MATERIALS SCIENCE↗