The damping effects of viscoelastic materials. II - Transverse vibrations of plates with viscoelastic coatings
Elastic metal thin plates transverse resonant free vibrations, analyzing viscoelastic coatings damping effects
Baumgarten, J. R.↗
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The damping effects of viscoelastic materials. I - Transverse vibrations of beams with viscoelastic coatings
Elastic metal thin beams transverse resonant free vibrations, analyzing viscoelastic coatings damping effects
Baumgarten, J. R.↗
Theoretical study of stress concentrations at circular holes and inclusions in strain hardening materials.
Nonlinear boundary value problems of an infinite elastic-plastic plate with a circular hole subjected to pure tension and pure shear at infinity are solved by a method involving Fourier series and finite difference. On the basis of these solutions, the validity of Neuber's relationship between the stress and strain concentration factors for the plane stress problems is examined and a generalized Stowell formula for the stress concentration factor is proposed for problems in which the applied loading may be pure shear as well as pure tension and, furthermore, other stress states. By the same method of solution, the stress distributions around a rigid circular cylindrical inclusion embedded in an infinite rigid-plastic matrix subjected to uniform transverse pure shear and tension are obtained.
Huang, W. C.↗
Three-dimensional CTOA and constraint effects during stable tearing in a thin-sheet material
A small strain theory, three-dimensional elastic-plastic finite element analysis was used to simulate fracture in thin sheet 2024-T3 aluminum alloy in the T-L orientation. Both straight and tunneled cracks were modeled. The tunneled crack front shapes as a function of applied stress were obtained from the fracture surface of tested specimens. The stable crack growth behavior was measured at the specimen surface as a function of applied stress. The fracture simulation modeled the crack tunneling and extension as a function of applied stress. The results indicated that the global constraint factor, alpha(sub g), initially dropped during stable crack growth. After peak applied stress was achieved, alpha(sub g) began to increase slightly. The effect of crack front shape on alpha(sub g) was small, but the crack front shape did greatly influence the local constraint and through-thickness crack-tip opening angle (CTOA) behavior. The surface values of CTOA for the tunneled crack front model agreed well with experimental measurements, showing the same initial decrease from high values during the initial 3mm of crack growth at the specimen's surface. At the same time, the interior CTOA values increased from low angles. After the initial stable tearing region, the CTOA was constant through the thickness. The three-dimensional analysis appears to confirm the potential of CTOA as a two-dimensional fracture criterion.
Dawicke, D. S.↗
Effects of irradiation damage on the elastic properties and hardness of complex transition metal diborides
Multi-principal component transition metal (TM) diborides represent a class of high-entropy ceramics (HECs) that have received considerable interest in recent years owing to their promising properties for extreme environment applications that include thermal/ environmental barriers, hypersonic vehicles, turbine engines, and next-generation nuclear reactors. While the addition of chemical disorder through the random distribution of TM elements on the cation sublattice has offered opportunities to tailor elastic stiffness and hardness, the effects of irradiationinduced structural damage on the physical properties of these complex materials have remained largely unexplored. To this end, changes in the hardness and elastic moduli of a high-entropy TM diboride (Hf0.2Nb0.2Ta0.2Ti0.2Zr0.2)B2 and three of its quaternary subsets following irradiation with 10 MeV gold (Au) ions to fluences of up to 6 × 10^15 Au cm-2 are investigated at the micrometer and sub-micrometer length-scales via the dispersion of laser-generated surface acoustic waves (SAW) and nanoindentation, respectively. The nanoindentation measurements show that the TM diborides exhibit an initial increase in hardness following irradiation with energetic Au ions, with a subsequent decrease in hardness following further irradiation. One quaternary composition, (Hf1/3Ta1/3Ti1/3)B2, exhibits a notable exception to the trend and continues to exhibit an increase in hardness with ion irradiation fluence. Although differences in the absolute values of the effective elastic moduli obtained from the measured SAW dispersion and nanoindentation are observed (and attributed to microstructural variations at the measurement length-scale), both techniques yield similar trends in the form of an initial reduction and subsequent saturation in the elastic modulus with increasing ion irradiation fluence. The quaternary TM diboride (Hf1/3Ta1/3Ti1/3)B2 again exhibits a departure from this trend. The high-entropy TM diboride (Hf0.2Nb0.2Ta0.2Ti0.2Zr0.2)B2 exhibits the greatest recovery in hardness and modulus when irradiated to high ion fluences following initial changes at low fluence, indicating superior resistance to radiation-induced damage over its quaternary counterparts. Opportunities for designing HECs with superior hardness and modulus for enhanced radiation resistance (compared to their single constituent counterparts) by tailoring chemical disorder and bond character in the lattice are discussed.
36 - MATERIALS SCIENCE↗
Material Modeling of Space Shuttle Leading Edge and External Tank Materials For Use in the Columbia Accident Investigation
Upon the commencement of the analytical effort to characterize the impact dynamics and damage of the Space Shuttle Columbia leading edge due to External Tank insulating foam, the necessity of creating analytical descriptions of these materials became evident. To that end, material models were developed of the leading edge thermal protection system, Reinforced Carbon Carbon (RCC), and a low density polyurethane foam, BX-250. Challenges in modeling the RCC include its extreme brittleness, the differing behavior in compression and tension, and the anisotropic fabric layup. These effects were successfully included in LS-DYNA Material Model 58, *MAT_LAMINATED_ COMPOSITE_ FABRIC. The differing compression and tension behavior was modeled using the available damage parameters. Each fabric layer was given an integration point in the shell element, and was allowed to fail independently. Comparisons were made to static test data and coupon ballistic impact tests before being utilized in the full scale analysis. The foam's properties were typical of elastic automotive foams; and LS-DYNA Material Model 83, *MAT_FU_CHANG_FOAM, was successfully used to model its behavior. Material parameters defined included strain rate dependent stress-strain curves for both loading and un-loading, and for both compression and tension. This model was formulated with static test data and strain rate dependent test data, and was compared to ballistic impact tests on load-cell instrumented aluminum plates. These models were subsequently utilized in analysis of the Shuttle leading edge full scale ballistic impact tests, and are currently being used in the Return to Flight Space Shuttle re-certification effort.
Carney, Kelly↗
An Improved Fracture Mechanics-Informed Multiscale Thermomechanical Damage Model for Ceramic Matrix Composites
This paper extends recent work done by the authors in modeling length scale-dependent damage behavior of ceramic matrix composites (CMCs) to include effects of local anisotropy introduced by matrix cracking. This model captures scale-dependent damage initiation and propagation behavior of the brittle matrix by employing internal state variable (ISV) theory within a multiscale modeling framework to obtain damaged matrix stress/strain constitutive relationships at each length scale. The damage ISV captures the effects of matrix cracking and growth by using fracture mechanics and the self-consistent scheme to determine the reduced stiffness of the cracked matrix. Matrix cracks, which activate when stress intensity factors near manufacturing induced cavities exceed the fracture toughness of the material, are assumed to be transversely isotropic in the plane of the crack, and matrix anisotropy occurs when the damaged stiffness tensor is rotated from the crack plane to the global axes. The crack progression and temporal evolution of the damage ISV are governed by fracture mechanics and crack growth kinetics. The model effectively captures first matrix cracking, which is the first significant deviation from linear elasticity. The nonlinear predictive capabilities of the material model are demonstrated for monolithic silicon carbide (SiC) and a 2D woven five-harness satin (5HS) carbon fiber SiC matrix (C/SiC) CMC.
Skinner, Travis↗
Large-scale reactive thermoset printing: Complex interactions between temperature evolution, viscosity, and cure shrinkage
Thermoset composites are strong candidates for large-scale material extrusion additive manufacturing (AM). However, uncured thermoset composites become unstable as print height increases. Here, chemical initiation of vinyl ester immediately before deposition was used to suppress collapse and enable large-scale thermoset printing. Structural stability was assessed by printing thin walls at various layer times and monitoring thermal gradients with an infrared camera. Stable printing was observed at a layer time of 4.50 min, approximately half the gel time of the material (8 min). Self-weight collapse occurred at short layer time (0.68 min), whereas warpage occurred at long layer time (6.50 min). Here, a new behavior was discovered at intermediate layer time (2.25 min) where the heat generated by the reaction causes new, un-gelled layers to flow. Forced convection eliminates this behavior, stabilizing the 2.25-min layer time print. These findings motivated development of a less exothermic material system, which was used to print a large-scale mold and demonstrate the value of this understanding. By presenting these challenges of large-scale reactive thermoset AM for the first time, this work motivates focused studies of the complex interplay between rheological, thermal, and chemical behaviors to improve the feasibility of large-scale thermoset AM. Tensile properties of the printed material were also measured. Longitudinal and transverse elastic moduli are 3.79 and 2.95 GPa, respectively, and corresponding tensile strengths are 36.11 and 18.83 MPa. The glass transition temperature is 93.13 °C.
36 MATERIALS SCIENCE↗
Bio-inspired non self-similar hierarchical elastic metamaterials
Hierarchy provides unique opportunities for the design of advanced materials with superior properties that arise from architecture, rather than from constitutive material response. Contrary to the quasi-static regime, where the potential of hierarchy has been largely explored, its role in vibration mitigation and wave manipulation remains elusive. So far, the majority of the studies concerning hierarchical elastic metamaterials have proposed a self-similar repetition of a specific unit cell at multiple scale levels, leading to the activation of the same bandgap mechanism at different frequencies. On the contrary, here, we show that by designing non self-similar hierarchical geometries allows us to create periodic structures supporting multiple, highly attenuative and broadband bandgaps involving (independently or simultaneously) different scattering mechanisms, namely, Bragg scattering, local resonance and/or inertial amplification, at different frequencies. The type of band gap mechanism is identified and discussed by examining the vibrational mode shapes and the imaginary component of the wavenumber in the dispersion diagram of the unit cell. Finally, we also experimentally confirm this by performing measurements in the lowest frequency regime on a 3D printed structure. Hierarchical design strategies may find application in vibration mitigation for civil, aerospace and mechanical engineering.
36 MATERIALS SCIENCE↗
On the elastic properties of fiber composite laminates with statistically dispersed ply orientations
Structural application of advanced composite filamentary materials requires lamination of the basic orthotropic plies into angle-ply laminates. The resulting elastic and strength properties depend on the pattern of orientation and are influenced by inevitable errors and inaccuracy in placement of the angle plies. Reviewed is the effect on elastic properties of orientation dispersion. The conventional constitutive relations are recast in a homologous form to account for orientation dispersion by addition of a single parameter. Graphical results are presented to show the behavior of the most important advanced composite materials. The results are directly useful for estimating effects of manufacturing inaccuracy and for design of partially oriented reinforced structures.
Robinson, E. Y.↗
Computing Viscoplastic Behavior Of A Material
Finite-element implementation developed for Robinson's unified model of viscoplasticity. Implemented via MARC general-purpose finite-element computer program by incorporating all of nonlinearity of material into initial load vector and treating vector as pseudo body force in finite-element equilibrium equations. In technique, each finite increment split into several equal subincrements, constitutive equations integrated by explicit Euler forward-difference method. HYPELA subroutine in MARC includes adaptive integration scheme selecting optimal sizes of subincrements. Spline function smooths discontinuous boundaries in Robinson's model to facilitate finite-element numerical calculations. Method used to calculate elastic, plastic, and creep deformations in solid materials at various temperatures; also used to study thermomechanical behavior of such things as hot pressure vessels and highly stressed components in engines.
Arya, V. K.↗
A Review of the Mechanical Properties of Materials Used in Nb 3 Sn Magnets for Particle Accelerators
Superconducting magnets experience significant thermo-mechanical loads throughout their life cycle. These are introduced by the electro-magnetic forces during powering, but also by the prestress applied in many magnet designs. Further to this, the large thermal excursion that components of different materials experience can generate significant internal forces. The loads are also experienced by the superconducting coils, whose critical current can decrease as a consequence of the applied strain. It is then crucial to predict the overall mechanical behavior and conservatively design a magnet, avoiding failure of the mechanical components and of the superconducting coils. Finite Element Analysis (FEA) is generally used to perform these tasks, but its results rely heavily on the material properties and models used. This is in particular true for the coil composite, which is simplified to allow reasonable model sizes in full magnet models. Here we present the state-of-art knowledge of the mechanical properties of the materials mostly used in superconducting magnet construction. We review elastic and plastic properties at room and cryogenic temperature, thermal contraction, and summarize the state-of-art failure criteria for these materials. Finally, the paper summarizes the present understanding of the mechanical behavior and limits of Nb3Sn coils. For the first time, an orthotropic failure criteria is proposed.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Residual thermal stresses in a solid sphere cast from a thermosetting material
Expressions are developed for the residual thermal stresses in a solid sphere cast from a chemically hardening thermosetting material in a rigid spherical mold. The description of the heat generation rate and temperature variation is derived from a first-order chemical reaction. Solidification is described by the continuous transformation of the material from an inviscid liquidlike state into an elastic solid, with intermediate properties determined by the degree of chemical reaction. Residual stress components are obtained as functions of the parameters of the hardening process and the properties of the hardening material. Variation of the residual stresses with a nondimensionalized reaction rate parameter and the relative compressibility of the hardened material is discussed in detail.
Levitsky, M.↗
High-temperature structure, elasticity, and thermal expansion of ε-ZrH 1.8
Zirconium hydride is a promising candidate material for nuclear microreactor applications as a solid-state moderator component, owing to its favorable neutronics properties and good thermal stability over other metal hydrides. Here, in the present work, the crystal structure, thermal expansion, and elastic properties of the hydrogen-rich ε phase hydride were measured at elevated temperatures in the range 300–900 K. Samples were prepared by direct hydriding Zircaloy-4 metal – a nuclear-grade zirconium alloy. Room-temperature lattice parameters agree well with those reported from literature for unalloyed zirconium hydride and fall within an observed quadratic H-content dependence. The coefficients of thermal expansion, determined from lattice expansion and dilatometry, agree well within our work but were about 30 % lower than those reported by others for unalloyed hydrides. Density functional theory-based molecular dynamics simulations were used to compare with thermal expansion and elasticity measurements. Results showed lattice parameter temperature dependence and slope of thermal expansion align with those from measurements. Based on diffraction scans at select temperatures, ε phase remained stable in air up to at least 770 K. Likewise, dilatometry showed smooth thermal expansion up to the thermal decomposition temperature around 950 K. The precise decomposition temperature was not determined via diffraction due to sparse scanning. The complete elastic property measurements were gathered for ε-phase Ziracloy-4 hydride for the first time. Young's modulus was lower compared to the metal and δ hydride phases. High-temperature elasticity measurements were limited to <350 K due to acoustic dissipation effects.
36 MATERIALS SCIENCE↗
Method and models for R-curve instability calculations
This paper presents a simple method for performing elastic R-curve instability calculations. For a single material-structure combination, the calculations can be done on some pocket calculators. On microcomputers and larger, it permits the development of a comprehensive program having libraries of driving force equations for different configurations and R-curve model equations for different materials. The paper also presents several model equations for fitting to experimental R-curve data, both linear elastic and elastoplastic. The models are fit to data from the literature to demonstrate their viability.
Orange, Thomas W.↗
Method and models for R-curve instability calculations
This paper presents a simple method for performing elastic R-curve instability calculations. For a single material-structure combination, the calculations can be done on some pocket calculators. On microcomputers and larger, it permits the development of a comprehensive program having libraries of driving force equations for different configurations and R-curve model equations for different materials. The paper also presents several model equations for fitting to experimental R-curve data, both linear elastic and elastoplastic. The models are fit to data from the literature to demonstrate their viability.
Orange, Thomas W.↗
A machine learning approach to determine the elastic properties of printed fiber-reinforced polymers
This work focuses on the simultaneous determination of the elastic constants and the fiber orientation state for a short fiber-reinforced polymer composite by performing a minimum of experimental tests. Here we introduce a methodology that enables the inverse determination of fiber orientation state and the in-situ polymer properties by performing tensile tests at the composite coupon level. We demonstrate the approach for the extrusion deposition additive manufacturing (EDAM) process to illustrate one application of the methodology, but the development is such that it can be applied to short fiber-reinforced polymer (SFRP) systems processed via other methods. Currently, developing composites additive manufacturing digital twins require extensive material characterization. In particular, the mechanical characterization of the orthotropic elastic properties of a composite involves extensive sample preparation and testing, therefore the elasticity tensor is generally populated using a micromechanics model. This, however, requires measuring the fiber orientation state in addition to knowing the constituent material properties. Experimentally measuring the fiber orientation state can be tedious and time consuming. Further, optical methods are limited to resolving the orientation of cylindrical fibers or cluster of non-cylindrical fibers, and computed tomography (CT) methods scan regions of volume that are much smaller than a full printed bead. Therefore, we propose a methodology, accelerated by machine learning, to identify the anisotropic mechanical properties and fiber orientation state at the same time. Early results show that inference of the fiber orientation and composite properties is possible with as few as three tensile tests. Our results show that a combination of the choice of the micromechanics model and reliable set of experiments can yield the nine elastic constants, as well as, the fiber orientation state.
36 MATERIALS SCIENCE↗
Bulk Metallic Glasses and Composites for Optical and Compliant Mechanisms
Mechanisms are used widely in engineering applications due to their ability to translate force and movement. They are found in kinematic pairs, gears, cams, linkages, and in flexure mechanisms (also known as compliant mechanisms). Mechanisms and flexures are used widely in spacecraft design, especially in the area of optics, where precise positioning of telescope mirrors requires elastic flexing of elements. A compliant mechanism is generally defined as a flexible mechanism that uses an elastic body deformation to cause a displacement (such as positing a mirror). The mechanisms are usually constructed as a single monolithic piece of material, and contain thin struts to allow for large elastic bending with low input force. This creates the largest problem with developing precise mechanisms; they must be fabricated from a single piece of metal, but are required to have strict accuracy on their dimensions. They are generally required to have high strength, elasticity, and low coefficient of thermal expansion.
Hofmann, Douglas C.↗