Thin Metastructures with Engineered Thermal Expansion

Lithia-alumina-silica (LAS) with metallic dispersions offers a new approach toward near-zero, isotropic, thermal expansion composites. The metallic phase contributes a positive coefficient of thermal expansion (CTE) to the negative CTE of the glass/ceramic matrix. In addition, the metal will increase the electrical and thermal conductivities over those of the matrix alone. The LAS system offers tailorable negative CTEs and light weight compared to other negative CTE ceramics. The most negative CTE phase is crystalline β-eucryptite, whose proportion in an initially glassy matrix can be controlled by heat treatment. Dispersed metal powders were both hot-pressed and cold-pressed and sintered together with LAS matrices prepared by sol gel methods. Super Invar powder was studied for its minimal CTE mismatch, while titanium powders offered a compromise between light weight and low CTE. An ultralow-expansion (ULE) glass- and linear variable differential transducer (LVDT)-based differential dilatometer was developed for rapid screening of compositions, while a double-laser Michelson interferometer was used for precise near-zero CTE measurements. The reinforced β-eucryptite glass/ceramic matrix exhibited both a U-shaped ΔL/L curve with temperature and some thermal hysteresis, depending on the fabrication and heat treatment sequences. The temperature of the zero-CTE portion of this curve was found to change with increasing titanium powder content. Results are also given for mixtures of Super Invar powders in ULE glass and β-eucryptite matrices. Negative CTEs in a LAS matrix above ambient temperatures were more difficult to obtain than below, although the use of petalite (high-silica LAS) appears promising.

The corrugated layer structure bismuth has been successfully tailored into negative thermal expansion along c axis by size effect. Pair distribution function and extended X-ray absorption fine structure are combined to reveal the local structural distortion for nanosized bismuth. The comprehensive method to identify the local structure of nanomaterials can benefit the regulating and controlling of thermal expansion in nanodivices.

In this thesis, the role of location-specific microstructural features in the fatigue performance of the safety-critical aerospace components made of Nickel (Ni)-base superalloys and linear friction welded (LFW) Titanium (Ti) alloys has been studied using crystal plasticity finite element (CPFE) simulations, energy dispersive X-ray diffraction (EDD), backscatter electron (BSE) images and digital image correlation (DIC).<br>In order to develop a microstructure-sensitive fatigue life prediction framework, first, it is essential to build trust in the quantitative prediction from CPFE analysis by quantifying uncertainties in the mechanical response from CPFE simulations. Second, it is necessary to construct a unified fatigue life prediction metric, applicable to multiple material systems; and a calibration strategy of the unified fatigue life model parameter accounting for uncertainties originating from CPFE simulations and inherent in the experimental calibration dataset. To achieve the first task, a genetic algorithm framework is used to obtain the statistical distributions of the crystal plasticity (CP) parameters. Subsequently, these distributions are used in a first-order, second-moment method to compute the mean and the standard deviation for the stress along the loading direction (σ_load), plastic strain accumulation (PSA), and stored plastic strain energy density (SPSED). The results suggest that an ~10% variability in σ_load and 20%-25% variability in the PSA and SPSED values may exist due to the uncertainty in the CP parameter estimation. Further, the contribution of a specific CP parameter to the overall uncertainty is path-dependent and varies based on the load step under consideration. To accomplish the second goal, in this thesis, it is postulated that a critical value of the SPSED is associated with fatigue failure in metals and independent of the applied load. Unlike the classical approach of estimating the (homogenized) SPSED as the cumulative area enclosed within the macroscopic stress-strain hysteresis loops, CPFE simulations are used to compute the (local) SPSED at each material point within polycrystalline aggregates of 718Plus, an additively manufactured Ni-base superalloy. A Bayesian inference method is utilized to calibrate the critical SPSED, which is subsequently used to predict fatigue lives at nine different strain ranges, including strain ratios of 0.05 and -1, using nine statistically equivalent microstructures. For each strain range, the predicted lives from all simulated microstructures follow a log-normal distribution; for a given strain ratio, the predicted scatter is seen to be increasing with decreasing strain amplitude and are indicative of the scatter observed in the fatigue experiments. Further, the log-normal mean lives at each strain range are in good agreement with the experimental evidence. Since the critical SPSED captures the experimental data with reasonable accuracy across various loading regimes, it is hypothesized to be a material property and sufficient to predict the fatigue life.<br>Inclusions are unavoidable in Ni-base superalloys, which lead to two competing failure modes, namely inclusion- and matrix-driven failures. Each factor related to the inclusion, which may contribute to crack initiation, is isolated and systematically investigated within RR1000, a powder metallurgy produced Ni-base superalloy, using CPFE simulations. Specifically, the role of the inclusion stiffness, loading regime, loading direction, a debonded region in the inclusion-matrix interface, microstructural variability around the inclusion, inclusion size, dissimilar coefficient of thermal expansion (CTE), temperature, residual stress, and distance of the inclusion from the free surface are studied in the emergence of two failure modes. The CPFE analysis indicates that the emergence of a failure mode is an outcome of the complex interaction between the aforementioned factors. However, the possibility of a higher probability of failure due to inclusions is observed with increasing temperature, if the CTE of the inclusion is higher than the matrix, and vice versa. Any overall correlation between the inclusion size and its propensity for damage is not found, based on inclusion that is of the order of the mean grain size. Further, the CPFE simulations indicate that the surface inclusions are more damaging than the interior inclusions for similar surrounding microstructures. These observations are utilized to instantiate twenty realistic statistically equivalent microstructures of RR1000 – ten containing inclusions and remaining ten without inclusions. Using CPFE simulations with these microstructures at four different temperatures and three strain ranges for each temperature, the critical SPSED is calibrated as a function of temperature for RR1000. The results suggest that critical SPSED decreases almost linearly with increasing temperature and is appropriate to predict the realistic emergence of the competing failure modes as a function of applied strain range and temperature.<br>LFW process leads to the development of significant residual stress in the components, and the role of residual stress in the fatigue performance of materials cannot be overstated. Hence, to ensure fatigue performance of the LFW Ti alloys, residual strains in LFW of similar (Ti-6Al-4V welded to Ti-6Al-4V or Ti64-Ti64) and dissimilar (Ti-6Al-4V welded to Ti-5Al-5V-5Mo-3Cr or Ti64-Ti5553) Ti alloys have been characterized using EDD. For each type of LFW, one sample is chosen in the as-welded (AW) condition and another sample is selected after a post-weld heat treatment (HT). Residual strains have been separately studied in the alpha and beta phases of the material, and five components (three axial and two shear) have been reported in each case. In-plane axial components of the residual strains show a smooth and symmetric behavior about the weld center for the Ti64-Ti64 LFW samples in the AW condition, whereas these components in the Ti64-Ti5553 LFW sample show a symmetric trend with jump discontinuities. Such jump discontinuities, observed in both the AW and HT conditions of the Ti64-Ti5553 samples, suggest different strain-free lattice parameters in the weld region and the parent material. In contrast, the results from the Ti64-Ti64 LFW samples in both AW and HT conditions suggest nearly uniform strain-free lattice parameters throughout the weld region. The observed trends in the in-plane axial residual strain components have been rationalized by the corresponding microstructural changes and variations across the weld region via BSE images. <br>In the literature, fatigue crack initiation in the LFW Ti-6Al-4V specimens does not usually take place in the seemingly weakest location, i.e., the weld region. From the BSE images, Ti-6Al-4V microstructure, at a distance from the weld-center, which is typically associated with crack initiation in the literature, are identified in both AW and HT samples and found to be identical, specifically, equiaxed alpha grains with beta phases present at the alpha grain boundaries and triple points. Hence, subsequent fatigue performance in LFW Ti-6Al-4V is analyzed considering the equiaxed alpha microstructure.<br>The LFW components made of Ti-6Al-4V are often designed for high cycle fatigue performance under high mean stress or high R ratios. In engineering practice, mean stress corrections are employed to assess the fatigue performance of a material or structure; albeit this is problematic for Ti-6Al-4V, which experiences anomalous behavior at high R ratios. To address this problem, high cycle fatigue analyses are performed on two Ti-6Al-4V specimens with equiaxed alpha microstructures at a high R ratio. In one specimen, two micro-textured regions (MTRs) having their c-axes near-parallel and perpendicular to the loading direction are identified. High-resolution DIC is performed in the MTRs to study grain-level strain localization. In the other specimen, DIC is performed on a larger area, and crack initiation is observed in a random-textured region. To accompany the experiments, CPFE simulations are performed to investigate the mechanistic aspects of crack initiation, and the relative activity of different families of slip systems as a function of R ratio. A critical soft-hard-soft grain combination is associated with crack initiation indicating possible dwell effect at high R ratios, which could be attributed to the high-applied mean stress and high creep sensitivity of Ti-6Al-4V at room temperature. Further, simulations indicated more heterogeneous deformation, specifically the activation of multiple families of slip systems with fewer grains being plasticized, at higher R ratios. Such behavior is exacerbated within MTRs, especially the MTR composed of grains with their c-axes near parallel to the loading direction. These features of micro-plasticity make the high R ratio regime more vulnerable to fatigue damage accumulation and justify the anomalous mean stress behavior experienced by Ti-6Al-4V at high R ratios.<br>

Inorganic/polymer composite films with adjustable small thermal expansion were prepared by incorporating sub-m sized particles of zirconium tungstate (ZrW2O8) into aromatic polyimide (PI). ZrW2O8 particles exhibit negative coefficients of thermal expansion (CTE) between 4.8 to 8.7 ppm/K. The cross-sectional SEM images of ZrW2O8/PI composite films indicate that filler particles are homogeneously dispersed in PI matrix without aggregation. The CTEs of these films are linearly decreased with increasing the volume fraction of ZrW2O8. The CTE of a composite film containing 60 vol% of filler is as low as that of metallic copper (17 ppm/K). Assuming that the thermal expansion behavior is three-dimensionally isotropic, PI composite films containing more than 50 vol% of ZrW2O8 could achieve coefficients of volumetric thermal expansion smaller than 50 ppm/K. Keyword: Polyimide / thin film / zirconium tungstate / thermal expansion / Organic-inorganic composite

Synthesis, processing, and characterization of negative thermal expansion zirconium tungstate nanoparticles with different morphologies

In this study, the effects of Nb and O contents on the negative thermal expansion behaviors including the coefficient of negative thermal expansion and matensite (α) stability of cold rolled (CR) Ti-34Nb alloys was investigated by optical microscopy, X-ray diffraction and Thermomechanical analysis. Results show that texture strength of CR-Ti-xNb-xO alloys is related to β stability, the addition of Nb and O (β stabilizers) enhances the texture strength. XRD results indicate that Nb and O inhibit the formation of α. The coefficient of negative thermal expansion of CR-Ti-xNb-xO alloys decrease with the increase of Nb and O contents. Moreover, cyclic thermal expansion results reveal that Nb and O promote the decomposition of α.

Nonlinearity of the coefficient of thermal expansion in brain tissue

In this paper, we discuss a newly characterized compound, ZrW2Og, that has been introduced into the composite materials with an adjustable and low thermal expansion for electronic applications. Offering a negative coefficient of thermal expansion (CTE) of approximate ‐9xlO–6/°C in a large temperature range, ZrW2Og was used as a particle filler in polymer‐matrix composites. The paper presents two kinds of composites, that is, polyester and epoxy with various volume fractions of ZrW20g. The CTEs of the polyester/ZrW2Og and epoxy/ZrW2Og composites have been proven adjustable in the ranges of 94 to 56x10–6 /°C and 54 to 18х 10–6 /°C, respectively, with ZrW2Og filler from 0 to 30 vol%. In addition, the analysis about the interfaces between the matrices and filler indicated that the interfaces may be beneficial to reduce the overall thermal expansion of the composites. The methods to further decrease composite CTEs are also discussed.

High‐gain, low‐weight, wide bandwidth, and miniaturized lens antennas with stable properties against temperature are intensely required in extreme environments such as aerospace field. However, high‐performance microwave dielectric ceramics with near‐zero thermal expansion and frequency shift with temperature are very rare; moreover, the requirement of 3D printing processes also restricts their developments. Ba0.4Sr0.6Zn2Si2O7 with negative coefficient of thermal expansion (CTE), which originates from the stretched [ZnO4] tetrahedral chain to the twisted one along b‐axis with temperature, and CaTiO3 with positive temperature coefficient of resonant frequency (τf) can effectively adjust both CTE and τf of Zn1.8SiO3.8 to near‐zero value in 0.95(0.9Zn1.8SiO3.8–0.1Ba0.4Sr0.6Zn2Si2O7)–0.05CaTiO3 ceramic. Then, a Ku‐band Luneburg lens integrative antenna fabricated by stereolithography 3D printing technology exhibits an average gain of 8.06 dBi at 10.45–11.39 GHz and 10.3 dBi at 12.27–13.45 GHz, which has potential applications in temperature‐stable satellite communication.

Multifunctional lattice metamaterial with high stiffness and a wide range of tailorable coefficient of thermal expansion (CTE) is desirable in many engineering structural application subjected to large fluctuation in temperature. Dual-constituent triangular lattice metamaterial composed of completely bi-layer curved rib elements (called the Lehman-Lakes lattice) has unbounded thermal expansion; however, its stiffness has a substantial decrease due to the initial curvature of rib element. In this study, a new double-curve rib element is proposed, in which the two curve parts are asymmetric and the layer one is partially covered by layer two in every curve part. Then, the dual-constituent triangular chiral lattice metamaterial (DTCLM) composed of the newly designed rib elements is presented in order to improve its stiffness. When the used materials are considered to be invar and steel, compared with the Lehman-Lakes lattice, the new proposed DTCLM with zero CTE has about 2.9 times improvement in stiffness; when achieving the same large positive or negative CTE, the stiffness has also obvious improvement. Besides, the thermomechanical analysis of the new proposed DTCLM is given by the closed-form analytical solution. The effectiveness of the analytical models and the optimized results are verified by the detailed numerical simulation.

Identification of low coefficient of thermal expansion in Al23Ce4Ni6 via combinatorial sputtering of Al-Ce-Ni-Mn thin films and upscaling to bulk materials

Structural phase transitions and negative thermal expansion in Sc2(MoO4)3

NZP family ceramics – NaZr2(PO4)3 (NZP), KZr2(PO4)3, RbZr2(PO4)3, Cs Zr2(PO4)3, CaZr4(PO4)6, SrZr4(PO4)6 (SrZP), and BaZr4(PO4)6 – were synthesized by a solid-state reaction, and their thermal expansion properties were investigated by X-ray diffraction measurement in a temperature range of -150 to 250 °C. The increases in the average thermal expansion coefficients of all the NZP family ceramics in this low temperature range (-150 to 250 °C) were smaller than those in a high temperature range (room temperature to 1000 °C). The thermal expansion coefficient of the SrZP ceramic was 0.2×10-6/°C between -150 to 250 °C, which is very small. This proved that SrZP has a near-zero thermal expansion coefficient in a low-temperature range.

The nonequilibrium Green's function method is applied to investigate the coefficient of thermal expansion (CTE) in single-walled carbon nanotubes (SWCNT) and graphene. It is found that atoms deviate about 1% from equilibrium positions at T=0 K, resulting from the interplay between quantum zero-point motion and nonlinear interaction. The CTE in SWCNT of different sizes is studied and analyzed in terms of the competition between various vibration modes. As a result of this competition, the axial CTE is positive in the whole temperature range, while the radial CTE is negative at low temperatures. In graphene, the CTE is very sensitive to the substrate. Without substrate, CTE has large negative region at low temperature and very small value at high temperature limit, and the value of CTE at T=300 K is $-6\times 10^{-6}$ K$^{-1}$ which is very close to recent experimental result, $-7\times 10^{-6}$ K$^{-1}$ (Nat. Nanotechnol. \textbf{10}, 1038 (2009)). A very weak substrate interaction (about 0.06% of the in-plane interaction) can largely reduce the negative CTE region and greatly enhance the value of CTE. If the substrate interaction is strong enough, the CTE will be positive in whole temperature range and the saturate value at high temperature reaches $2.0\times 10^{-5}$ K$^{-1}$.

Structurally efficient isogrid booms, manufactured from rigidizable composite materials, are becoming an enabling technology for spacecraft structures because of their high packing efficiency. Selection of the materials used in the construction of rigidizable space structures is commonly driven by mechanical performance properties at elevated temperatures. Mechanical properties testing was performed on composite tow samples and on an isogrid boom at various temperatures. To characterize elevated temperature behavior, the isogrid booms, and its subelement composite tows were manufactured from ILC’s TP283E shape memory polymer (SMP) matrix resin and a carbon reinforcement. Both the flexural modulus and the tensile modulus of the composite tow samples were determined as a function of temperature. These values were compared to the calculated values for the composite based on rule of mixtures analysis. The predicted rule of mixtures composite modulus is used in ILC’s isogrid analytical code to predict the structural properties of the isogrid boom. A number of composite tow samples were fabricated by ILC and mechanically characterized by the Aerospace Corporation to gather independent performance data. An isogrid boom was fabricated by ILC and mechanically characterized at elevated temperatures by James Madison University (JMU). JMU tested this boom in tension, compression, and also performed preliminary creep testing at various temperatures. A similar isogrid boom was fabricated by ILC and tested by The Aerospace Corporation for composite CTE performance. This paper discusses the results of both the composite tow testing and the isogrid boom testing in preand post-packing conditions. A discussion of the correlation between the predicted values and the actual test values is also presented. Introduction NASA and DoD space missions in the near future will require much larger satellites, the sizes of which will be beyond the capabilities of current technologies. The types of Gossamer spacecraft that will be needed include antennas, solar arrays, sunshields, solar sails, and telescopes (Figs. 1-2). Some systems being considered are hundreds of meters in size to accomplish mission goals. Due to the increase in payload size required, innovative support structures, which can be packed into the faring of available launch vehicles, must be developed. In recent years, research and development work has been performed in this area. Of the available options, one of the most promising technological advancements is the rigidizable inflatable structure. A rigidizable inflatable structure is one that is fabricated on Earth, packed into the launch container, and inflated for deployment once on orbit. After deployment, the material is rigidized, or hardened, to form a stiff composite structure that no longer needs the inflation gas for support. This class of structures has unique benefits such as low packing volume, reduced mass, and in most cases, very high deployed structural efficiency. Several types of construction can be used in a rigidizable inflatable including monocoque, isogrid, IsoTruss, and truss-frame booms. Each composite structure can be fabricated into a varying geometric shapes utilizing any number of resin and fiber types. The fibrous reinforcement can be in tow or woven fabric form. In order to optimize the structure, the sizes of the tows and the weave styles of the fabrics can be varied. It is also possible to manufacture near-zero coefficient of thermal expansion (CTE) booms through the fiber and resin selection and by optimizing the volume fractions of each. However, key to all mechanical performance properties is the ability to fold and tightly pack the material. Member AIAA † Associate Fellow AIAA Undergraduate Research Assistant, Dept. of Int. Science and Tech. Associate Professor, Dept. of Int. Science and Tech. Senior Scientist, Materials Sciences Dept. Distinguished Scientist, Space Materials Lab Figure 2. ILC 3.2m Diameter TSU Hexapod Testbed Figure 1. 1⁄2 Scale Next Generation Space Telescope Sunshield