The problem of thermal-expansion stresses in reinforced plastics
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RESINS, SYNTHETIC↗
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Hard tissue as a composite material. I - Bounds on the elastic behavior.
Recent determination of the elastic moduli of hydroxyapatite by ultrasonic methods permits a re-examination of the Voigt or parallel model of the elastic behavior of bone, as a two phase composite material. It is shown that such a model alone cannot be used to describe the behavior of bone. Correlative data on the elastic moduli of dentin, enamel and various bone samples indicate the existence of a nonlinear dependence of elastic moduli on composition of hard tissue. Several composite models are used to calculate the bounds on the elastic behavior of these tissues. The limitations of these models are described, and experiments to obtain additional critical data are discussed.
Katz, J. L.↗
Estimation of single crystal elastic constants in low symmetry materials using neutron diffraction
The use of constrained global optimization appears to be a potential way to estimate single crystal elastic constants for low symmetry materials from diffraction measurements
36 MATERIALS SCIENCE↗
Analytical model for laser-induced transient grating measurements of thermal diffusivity in non-opaque materials
The thermal transport and elastic properties of materials are often measured using the laser-induced transient grating spectroscopy (TGS) technique. The analysis of the TGS signal usually involves fitting well-known expressions, derived assuming the limiting cases of opaque or transparent materials, to the measured data. In this paper, the system of thermoelastic equations is analytically solved for an isotropic homogeneous material assuming finite laser penetration depth, which is an important consideration when the penetration depth is on the order of the acoustic wavelength. The need to use such a solution is discussed and compared to the expression for opaque material. The solution is benchmarked against TGS signal measured on single-crystal silicon with {100} surface orientation and is found to significantly improve the accuracy of the calculated thermal diffusivity as compared to using the expression for opaque material.
36 MATERIALS SCIENCE↗
The Applicability of the Generalized Method of Cells for Analyzing Discontinuously Reinforced Composites
The paper begins with a short overview of the recent work done in the field of discontinuous reinforced composites, focusing on the different parameters which influence the material behavior of discontinuous reinforced composites, as well as the various analysis approaches undertaken. Based on this overview it became evident that in order to investigate the enumerated effects in an efficient and comprehensive manner, an alternative approach to the computationally intensive finite-element based micromechanics approach is required. Therefore, an investigation is conducted to demonstrate the utility of utilizing the generalized method of cells (GMC), a semi-analytical micromechanics-based approach, to simulate the elastic and elastoplastic material behavior of aligned short fiber composites. The results are compared with simulations using other micromechanical based mean field models and finite element (FE) unit cell models found in the literature given elastic material behavior, as well as finite element unit cell and a new semianalytical elastoplastic shear lag model in the inelastic range. GMC is shown to definitely have a window of applicability when simulating discontinuously reinforced composite material behavior.
Pahr, D. H.↗
The Applicability of the Generalized Method of Cells for Analyzing Discontinuously Reinforced Composites
The paper begins with a short overview of the recent work done in the field of discontinuous reinforced composites, focusing on the different parameters which influence the material behavior of discontinuous reinforced composites, as well as the various analysis approaches undertaken. Based on this overview it became evident, that in order to investigate the enumerated effects in an efficient and comprehensive manner, an alternative approach to the computationally intensive finite-element based micromechanics approach is required. Therefore, an investigation is conducted to demonstrate the utility of utilizing the generalized method of cells (GMC), a semi-analytical micromechanics-based approach, to simulate the elastic and elastoplastic material behavior of aligned short fiber composites. The results are compared with (1) simulations using other micromechanical based mean field models and finite element (FE) unit cell models found in the literature given elastic material behavior, as well as (2) finite element unit cell and a new semianalytical elastoplastic shear lag model in the inelastic range. GMC is shown to definitely have a window of applicability when simulating discontinuously reinforced composite material behavior.
Pahr, D. H.↗
On elastic behaviour of fibre reinforced materials of arbitrary transverse phase geometry.
Bounds for plane strain bulk modulus and shear moduli of multiphase fiber reinforced materials of arbitrary transverse phase geometry
BULK MODULUS↗
Faster, Easier Finite-Element Modeling Of Weld Offsets
In faster, easier technique, material in weld zone fictitiously softened to negligibly low modulus of elasticity, and material considered deformed to specified offset. Displacements caused by deformation computed by analysis of static stresses and strains in fictitiously deformed material, using specified offset as displacement boundary condition. Resulting displacements added to coordinates of corresponding nodes of original (nonoffset) mathematical model of welded part. Technique used to modify large finite-element mathematical model to any desired weld offset configuration in short time.
Hong, C. Chen↗
Stress and strain concentration at a circular hole in an infinite plate
The theory of elasticity shows that the maximum stress at a circular hole in an infinite plate in tension is three times the applied stress when the material remains elastic. The effect of plasticity of the material is to lower this ratio. This paper considers the theoretical problem of the stress distribution in an infinitely large sheet with a circular hole for the general case where the material may have any stress-strain curve. The plate is assumed to be under uniform tension at a large distance from the hole. The material is taken to be isotropic and incompressible. (author)
THEORIES - ELASTICITY↗
First principles calculations in support of Pu aging: calculating the effects of lattice imperfections on thermodynamics
Plutonium (Pu) has, in theory, well defined crystal structures: its atoms are arranged in regular spatial patterns. But Pu is radioactive, and as its nuclei decay those regular spatial patterns are interrupted. The interruptions are lattice imperfections, which are known to affect how materials respond to their environment. To adequately model Pu, we need to know which lattice imperfections are present, how they interact with each other, and how they affect the material’s response to its environment. The work presented here aims to use density functional theory (DFT) calculations to begin to answer the latter, in particular, how individual lattice imperfections affect measurable effects including thermal expansion (the change in volume in response to a change in temperature), heat capacity (the amount of thermal energy needed to change a material’s temperature), and elastic moduli (a material’s resistance to applied stresses). Pu poses many computational challenges. The $\textit{f}$ electrons require special attention. Of all the elements, Pu has the largest number of electrons that must be included in the calculations. Thermal effects require calculating the phonons (the lattice vibrations), which for systems containing lattice imperfections demand large, complex computational cells - but computational resources limit the size and complexity. With careful restructuring of how the calculations are performed, all these challenges have been met to enable calculations that provide insight into how lattice imperfections affect Pu’s response to its environment. Reported here are the computational challenges and the advances developed to meet them, along with the first results showing the strong effect that one prototype lattice imperfection (an interstitial Pu atom in a delta-phase Pu lattice) has on Pu’s response to its environment.
36 MATERIALS SCIENCE↗
3D mapping of residual stresses in growing grains of partially recrystallized Gum Metal
The crystallographic orientations and residual stresses within recrystallizing grains in partially recrystallized beta titanium-Gum Metal-were examined non-destructively in 3D using synchrotron Differential Aperture X-ray Microscopy. Contrary to common assumptions, significant local stresses and stress variations are observed within the recrystallizing grains. The results reveal that the development of these local residual stresses depends on the plastic deformation mode and material's elastic constants, rather than grain properties such as size and orientation, or even the material's yield stress. This work provides insights valuable for the design of advanced materials with heterogeneous microstructures.
36 MATERIALS SCIENCE↗
Vibration and wave propagation characteristics of multisegmented elastic beams
Closed form analytical solutions are derived for the vibration and wave propagation of multisegmented elastic beams. Each segment is modeled as a Timoshenko beam with possible inclusion of material viscosity, elastic foundation and axial forces. Solutions are obtained by using transfer matrix methods. According to these methods formal solutions are first constructed which relate the deflection, slope, moment and shear force of one end of the individual segment to those of the other. By satisfying appropriate continuity conditions at segment junctions, a global 4x4 matrix results which relates the deflection, slope, moment and shear force of one end of the beam to those of the other. If any boundary conditions are subsequently invoked on the ends of the beam one gets the appropriate characteristic equation for the natural frequencies. Furthermore, by invoking appropriate periodicity conditions the dispersion relation for a periodic system is obtained. A variety of numerical examples are included.
Nayfeh, Adnan H.↗
Anisotropic structure and optical engineering of strontium titanate and zirconia responding to sequential hydrogen and helium irradiation
Unraveling the correlation between strain engineering with anisotropic optical properties via nanoscale defects gradually evolved into a strategy for fundamental studies and technological applications, yet it remains understudied in functional complex oxides compared to metals and semiconductors. Here, the methodology of strain engineering for the determination of the lattice parameters, parallel/normal to the sample surface, in the individual layers of single-crystalline superlattices is derived, which is based on analysis of high-angle X-ray diffraction measurements in combination with diffraction reciprocal space mapping. With modeling that takes into account the effect of elastic properties, two elastically anisotropic materials, SrTiO 3 and ZrO 2 , have been compared in terms of defect-induced elastic strain caused by individual and sequential H + and He 2+ irradiation. The anisotropic lattice swelling with corresponding refractive index, and obstructive behavior of elastic strain recovery are demonstrated in SrTiO 3 , while approaching strain behaviors accompanied by isotropic refractive index distribution in both orientations are confirmed in ZrO 2 . Under sequential He 2+ /H + irradiation, pre-existing He-vacancy complexes acted as vacancy traps, preferentially capturing H + clusters to induce lattice distortion and enhance absorption. Nanohardness increments (ΔH) calculated by the DBH model matched nanoindentation results, confirming that sequential irradiation generated higher indentation yield stress than individual irradiations.
Anisotropic expansion↗
Rapid method for computing the mechanical resonances of irregular objects
A solid object's geometry, density, and elastic moduli completely determine its spectrum of normal modes. Solving the inverse problem—determining a material's elastic moduli given a set of resonance frequencies and sample geometry—relies on the ability to compute resonance spectra accurately and efficiently. Established methods for calculating these spectra are either fast but limited to simple geometries, or are applicable to arbitrarily shaped samples at the cost of being prohibitively slow. Here, we describe a method to rapidly compute the normal modes of irregularly shaped objects using entirely open-source software. Our method's accuracy compares favorably with existing methods for simple geometries and shows a significant improvement in speed over existing methods for irregular geometries.
Acoustics↗
Fracture analysis of surface- and through-cracked sheets and plates.
The Neuber stress-concentration relation for notches in an elastic-plastic material subjected to shear loading was generalized for a crack in a finite plate subjected to tensile loading. An equation was derived which related the linear elastic stress-intensity factor, the applied stress, and two material parameters. The equation was then used as a two-parameter fracture criterion for surface- and through-cracked specimens. Fracture data from the literature on surface- and through-cracked sheet and plate specimens of steel, titanium alloy, titanium weldment, and aluminum alloy tested at room and cryogenic temperature were analyzed according to the proposed equation. For surface cracks, wide ranges of crack-depth to crack-length ratio and crack-depth to specimen-thickness ratio were considered. For through cracks, wide ranges of crack length and specimen width were also considered.-
Newman, J. C., Jr.↗
Effects of internal swelling on residual elasticity of a quasi-brittle material through a composite sphere model
This work describes the development of a micromechanical-based constitutive model accounting for the effect of internal expansion on the residual elasticity of a Hashin composite material. This material is made of spherical inclusions that are subjected to gradual swelling within a quasi-brittle matrix. The main focus of this work is to describe and analyze the material mechanical response, with an additional focus on the internal swelling’s effect on the stress–strain response and residual elasticity. Microstructural features and parameters of major importance for the mechanical responses were identified. The innovative characteristics of the proposed approach are summarized as follows: (1) a full determination of the physics of a complete-damage problem throughout the whole process of inclusion swelling with upscaling techniques, which transfers the microcrack-related properties from the lower scale to upper scale; and (2) an evolution of the mechanical fields and the corresponding residual elasticity for various inclusion swelling levels. Concerning the matrix–inclusion composite, it was hypothesized that only the matrix was susceptible to cracking, with varied degrees of damage, whereas the inclusions behave elastically and the elastic modulus of the expanding inclusions remains constant. It is to emphasize that the gradual swelling of inclusions is modeled by an increasing strain in the current micromechanical-based constitutive model, and the microcracks are represented by a set of randomly oriented penny-shaped microcracks with identical radii (namely, closed cracks). The main contribution of the current research is to establish the exact mathematical solutions for the mechanical fields (stress, strain) caused by the swelling of the inclusions (mechanical loading) and derive the effective residual elasticity of a composite (structural response) subject to internal expansion and quasi-brittle damage. Based on the assumption of closed cracks that could be extended to open cracks in the upcoming work, the results proposed by the present paper help to understand the non-linear mechanical behavior of quasi-brittle materials subject to microcracking and provide a theoretical framework to be used as academical benchmark for numerical simulations.
36 MATERIALS SCIENCE↗
Fully flooded elastohydrodynamic lubricated elliptical contacts
Emphasis is on fully flooded, elastohydrodynamic lubricated, elliptical contacts. A fully flooded conjunction is one in which the film thickness is not significantly changed when the amount of lubricant is increased. A brief description of the relevant equations used in the elastohydrodynamic lubrication of elliptical contacts is given. The most important practical aspect of the elastohydrodynamic theory is the determination of the minimum film thickness within the contact. The maintenance of a fluid film of adequate magnitude is an essential feature of the correct operation of lubricated machine elements. The results presented show the influence of contact geometry on minimum film thickness as expressed by the ellipticity parameter and the dimensionless speed, load, and materials parameters. Film thickness equations are developed for materials of high elastic modulus, such as metal, and for materials of low elastic modulus, such as rubber. In addition to the film thickness equations that are developed, plots of pressure and film thickness are presented. These theoretical solutions for film thickness have all the essential features of previously reported experimental observations based on optical interferometry. Correlation between theory and experiments is also presented.
Hamrock, B. J.↗
Elastohydrodynamic lubrication of elliptical contacts
Fully flooded, elastohydrodynamically lubricated, elliptical contacts are discussed. The relevant equations used in the elastohydrodynamic lubrication (EHL) of elliptical contacts are briefly described. Film thickness equations are developed for materials of high elastic modulus, such as metal, and for materials of low elastic modulus, such as rubber. In addition to the film thickness equations that are developed, plots of pressure and film thickness are presented. A theoretical study of the influence of lubricant starvation on film thickness and pressure in hard and soft elliptical elastohydrodynamic contacts is presented. From the results for both hard and soft EHL contacts a simple and important dimensionless inlet boundary distance is specified. It is also found that the film thickness for a starved condition can be written in dimensionless terms as a function of the inlet distance parameter and the film thickness for a fully flooded condition. contour plots of pressure and film thickness in and around the contact are shown for fully flooded and starved conditions. The theoretical findings are compared directly with results obtained experimentally.
Hamrock, B. J.↗