Range Of Coefficient Of Thermal Expansion Research Articles

Multimaterial Additively Manufactured Metamaterials Functionalized with Customizable Thermal Expansion in Multiple Directions.

Metamaterials functionalized with customizable multidirectional coefficient of thermal expansion (CTE) are urgently needed for advanced shape control or dimensional stability under temperature variations. The currently reported metamaterials still lack the development of diverse base material systems and exploration of the multimaterial fabrication process. Especially, the reported range of customizable CTEs for metamaterials in multiple directions is limited within [-68.1, 56.4] ppm/°C. Here, this work explicitly proposes a strategy for closely linking base materials, additive manufacturing (AM) process, architecture, and CTE tunability, in order to provide a general guideline for the design or customization of such metamaterials. In detail, first, we systematically identify the key process parameters and related performance for additive manufacturing of polymers and propose various multimaterial systems such as polypropylene-polycarbonate (PP-PC). Then, six types of metamaterials have been fabricated with high quality by the established multimaterial additive manufacturing. By measuring the effective CTEs in multiple directions, the CTE tunability of metamaterials, including large positive values (+523.36 ppm/°C) and large negative values (-230.61 ppm/°C), far beyond the literature-reported CTE range, has been experimentally verified. Further, we have developed a bidirectional requirement-solution strategy here that acts as a bridge between design and fabrication. This work opens advanced avenues for metamaterials with multidirectionally customizable and extensive CTE tunability for a variety of engineering applications such as actuators, thermal stress relief, and improved structural stability.

Computational Design of High-Entropy Rare Earth Disilicates as Next-Generation Thermal/Environmental Barrier Coatings

Development of advanced thermal/environmental barrier coating (T/EBC) materials possessing balanced thermal-mechanical properties is crucial to protect SiC-based ceramic composites from chemical and thermal attack for better performance of components in the hot section of gas turbine engines. In this work we utilize density functional theory (DFT) together with combinatorial chemistry methodology to design high-performance high-entropy rare earth disilicates (β-RE2Si2O7 (RE=Yb, Y, Er, Lu, La, Ce,)) for enhanced phase stability, desired coefficient of thermal expansion (CTE), low lattice thermal conductivity and good mechanical properties. The CTE are determined by phonon calculations at different volumes within the quasi-harmonic approximation. The lattice thermal conductivities are evaluated by the Debye-Callaway model considering three phonon processes. We show that the solid solution of YYbSi2O7 exhibits lowered lattice thermal conductivity than pure cases and a good range of CTE. We also present good EBC candidate materials of Er1/4Lu1/4Y3/4Yb3/4Si2O7 and Er1/2Lu1/2Y1/2Yb1/2Si2O7 with very low lattice thermal conductivity < 0.23 W/m/K at 1500 K and a good match of average CTE (5.1 - 5.2×10−6 K−1) with SiC without compromising mechanical properties. These new EBC with outstanding multi-functional properties are believed to enable significant increases in the performance of protective components in gas turbines. This work also illustrates an efficient and reliable computational framework in accelerating the design of next-generation T/EBC.

Modelling and verification of a novel bi-material mechanical metamaterial cellular structure with tunable coefficient of thermal expansion

The tunable thermal expansion characteristic of metamaterials is beneficial to solve the problems caused by drastic temperature changes. Here, we propose a novel bi-material mechanical metamaterial cellular structure (NBMCS) that can adjust the coefficient of thermal expansion (CTE). Under some parameters restrictions, the structure can realize the regulation of its CTE in a wide range from -115 ppm/℃ to 83.6 ppm/℃ with Al alloy/Low carbon steel combination. A general thermoelasticity equation that builds the relationship among the temperature, the external force, and the displacement is derived, which is then assembled into a theoretical model of NBMCS. Through theoretical analysis and numerical simulations, the underlying mechanism among the CTE of NBMCS, geometric parameters, elastic modulus ratio, and CTE ratio is revealed. Experiments are carried out based on industrial camera and DIC method, which verify the theoretical modelling. Finally, the tunable range of CTE and elastic modulus for three different material combinations are compared. • A novel metamaterial structure with tunable coefficient of thermal expansion. • A general thermoelasticity equation for the structure is established. • Simulation and experiments are carried out to verify the theoretical modeling.

Study on the anomalous thermal expansion behavior of cold-rolled Ti-34 Nb alloy and its novel tailoring strategy

In this study, we have investigated the anisotropic in-plane thermal expansion behavior of cold-rolled (CR) Ti-34 Nb alloy and its relationship with temperature by means of continuous heating and cyclic heating-cooling thermal expansion measurement methods. A new microscopic model including the morphology of β and martensite (α″) phases, cold rolled textures and α″ content is proposed, which successfully explains the mechanism of anomalous positive thermal expansion of transverse direction (TD) and negative thermal expansion of rolling direction (RD). It is found that the coefficient of thermal expansion (CTE) of CR-Ti-34 Nb alloy is controlled by α″ content. The instantaneous CTEs of TD and RD (absolute value) both increase first and then decrease (nonlinearity) within the temperature range of anomalous thermal expansion, which is attributed to the increase of α″→β transformation rate (temperature increases by 1 °C) with increasing temperature and the significant decomposition of α″ phase above 260 °C. Moreover, we have excluded the influence of the anisotropy of α″ and internal stress on CTE. According to the abovementioned findings, α″ content is adjusted by pre-aging treatment for the first time, and a wide range of CTEs (−33.0 × 10−6 k−1 ~ 0.4 × 10−6 k−1) are obtained in CR-Ti-34 Nb alloy, including a variety of low (−6.3 × 10−6 k−1, −3.3 × 10−6 k−1) and zero (−1.5 × 10−6 k−1, −0.9 × 10−6 k−1, 0.4 × 10−6 k−1) CTEs with a wide temperature window of 275 °C (25 °C ~ 300 °C).

Designing Mechanical Metamaterials with Kirigami-Inspired, Hierarchical Constructions for Giant Positive and Negative Thermal Expansion.

Advanced mechanical metamaterials with unusual thermal expansion properties represent an area of growing interest, due to their promising potential for use in a broad range of areas. In spite of previous work on metamaterials with large or ultralow coefficient of thermal expansion (CTE), achieving a broad range of CTE values with access to large thermally induced dimensional changes in structures with high filling ratios remains a key challenge. Here, design concepts and fabrication strategies for a kirigami-inspired class of 2D hierarchical metamaterials that can effectively convert the thermal mismatch between two closely packed constituent materials into giant levels of biaxial/uniaxial thermal expansion/shrinkage are presented. At large filling ratios (>50%), these systems offer not only unprecedented negative and positive biaxial CTE (i.e., -5950 and 10 710ppm K-1 ), but also large biaxial thermal expansion properties (e.g., >21% for 20 K temperature increase). Theoretical modeling of thermal deformations provides a clear understanding of the microstructure-property relationships and serves as a basis for design choices for desired CTE values. An Ashby plot of the CTE versus density serves as a quantitative comparison of the hierarchical metamaterials presented here to previously reported systems, indicating the capability for substantially enlarging the accessible range of CTE.

Additively manufactured bi-material metamaterial to program a wide range of thermal expansion

The current research on bi-material diamond metamaterials, which can be used to program the coefficient of thermal expansion (CTE) over a wide range, mainly focuses on the theoretical design, while the corresponding experimental range of the CTEs is far narrower. In this study, a bi-material diamond metamaterial was additively manufactured using two polymers: nylon and polyvinyl alcohol (PVA). Without any need for extra processes such as bonding, welding, and mechanical fitting, the additively manufactured metamaterial integrated the nylon and PVA, providing an integrated fabrication process to ensure the expected programmable CTE. The experimentally measured CTEs agreed well with the theoretical predictions. When the material layout was selected as MAT-1 = PVA and MAT-2 = nylon, programmable CTEs ranging from 217.72 to 694.00 ppm/°C were obtained, which were larger than the CTEs of the nylon and PVA. When the material layout was MAT-1 = nylon and MAT-2 = PVA, even though both the nylon and the PVA had positive CTEs, a wide range of negative CTEs (varying from −25.02 to −369.01 ppm/°C) was obtained. The foregoing wide ranges of programmable CTEs are remarkably larger than the literature results, indicating the enhanced programmability of the bi-material metamaterial and stabilizing the foundation for the further design of multilevel and hierarchical metamaterials.

Thermal Expansion of Polyether Ether Ketone Bearing Components

Carbon fiber–reinforced polyether ether ketone (PEEK) is a strong candidate for aerospace bearing cages due to its low density and good mechanical properties. However, there are still concerns regarding its performance at the elevated temperatures seen in aerospace applications. In particular, an accurate measurement of PEEK's coefficient of thermal expansion (CTE) is critical to proper bearing design. In this paper, the CTE of as-manufactured PEEK cages was measured to determine the range of CTE that can be expected for production parts. A range of cage sizes and designs were considered in this study. Components that were manufactured from stock shapes through subtractive methods were studied in addition to components made via injection molding. The CTE of machined PEEK was found to be significantly higher than that of injection-molded PEEK and also varied significantly from part to part. In contrast, the CTE of molded PEEK cages was found to be fairly consistent between parts. Finally, the CTE of PEEK was found to increase above the glass transition temperature of 143 °C, but it was demonstrated that this increase is relatively small for injection-molded parts.

Drastic tailorable thermal expansion chiral planar and cylindrical shell structures explored with finite element simulation

Design of materials and structures with quite low coefficient of thermal expansion (CTE), even zero or negative CTE is important for industrial application where drastic temperature changes are encountered. In this paper, making use of the bending of bi-material beam and the unique deformation mechanism of chiral lattice structures, five sets of chiral lattice composite structures with tailorable CTEs are proposed, where synergic effects of rigid node rotation and bi-material ligament bending deformation are responsible for giant range of structural deformation due to temperature change, from positive CTE to negative CTE through adjusting the geometrical parameters of composite bi-material chiral unit cell, and the relationship between unit cell geometric parameters and CTEs of the structure are studied systematically through finite element analysis. Finally, design of bi-material cylindrical shells consisting of anti-tetra chiral unit cells are proposed, and its axial CTEs with different number of the unit cells along the circumferential are studied systematically, demonstrating the robust range of CTEs can be generated through adjusting the geometrical parameters of chiral bi-material unit cells. The proposed chiral structures demonstrated promising application potentials in industrial fields, such as: aerospace and microelectronics, where extremely high structural accuracy is required during harsh working temperature environment.

Design and analysis of lattice cylindrical shells with tailorable axial and radial thermal expansion

Current periodical lattice structures with tailorable coefficient of thermal expansion (CTE) can be hardly used as engineering structures since these configurations are neither planar nor regular three dimensional geometries. Here, lattice cylindrical shells, which are widely in aerospace engineering, are originally devised and analyzed to exclusively achieve a wide range of tailorable CTEs in both axial and radial directions. The thermal expansion behaviors are systematically calculated by finite element analysis, and the expressions of CTEs for the devised lattice cylindrical shells are well established. Warp effects are found in lattice cylindrical shells winded from planar triangle and planar square due to the sparse arrangement mode, and with few circumferential triangles, the radial CTE is significantly larger than those of the corresponding planar lattices. Tailorable thermal expansion characteristics including zero, large positive and negative values are confirmed. Moreover, in case study with aluminum alloy, stainless steel and invar, a wide range of thermal expansion ranged from −64.6 to 88.0 ppm∕∘C, which are remarkably larger than those of constituents, can be easily achieved through the devised lattice cylindrical shells. The wide range of CTEs obtained here can promote these lattice cylindrical shells to be used as structures under temperature variation service environment for purpose of obtaining dimensional stability and thermal expansion compensation.

Lightweight composite lattice cylindrical shells with novel character of tailorable thermal expansion

Composite lattice cylindrical shells widely utilized in aerospace engineering are susceptible to experience large temperature excursions, and generate undesirable thermal deformation. Here, we devise novel composite lattice cylindrical shells which can exclusively present a wide range of negative, positive and especially zero coefficient of thermal expansion (CTE) through structural design and rational arrangement of commonly available positive CTE composites. Theoretical analysis figures out the thermal deformation mechanism, and clearly establishes the important relationship that with adequate circumferential triangle units, the CTEs of the lattice cylindrical shells closely approach to the CTEs of the corresponding triangle and planar lattice composites. Finite element analysis firmly confirms the tailorable thermal expansion characteristics. Furthermore, in practical design of lattice cylindrical shells with commonly available composites, a wide range of tailorable thermal expansion up to −2200 to 2200 ppm/∘C, which is substantially larger than those of available engineering materials, can be easily achieved. Such wide range of CTEs and lightweight feature enable these composite lattice cylindrical shells to be potentially used in aerospace engineering.

Multilevel hierarchy in bi-material lattices with high specific stiffness and unbounded thermal expansion

Dual-material concepts that expand or contract as desired upon changes in temperature exist but have their limitations. One upon which we focus here is the trade-off caused by the inherent thermo-elastic coupling that they feature, a condition that makes desired changes in thermal expansion penalize elastic stiffness, and vice versa. In this paper, we present hierarchical bi-material lattices that are stiff and can be designed to attain a theoretically unbounded range of thermal expansion without (i) impact onto elastic moduli and (ii) severe penalty in specific stiffness. Through a combination of theory, numerical simulations and experiments, we demonstrate the thermomechanical performance of eight hierarchical lattices, including two fractal-like hierarchical lattices with self-repeating units that are built from dual-material diamond shapes with low and high coefficients of thermal expansion (CTE). Results show that the achievable range of CTE can be enlarged by 66% through the addition of one order of hierarchy only, and that for a given CTE range the specific stiffness can be at least 1.4 times larger than that of existing stretch-dominated concepts. The concepts here introduced can open up new avenues towards multifunctional devices and structurally efficient materials with simultaneously customized thermal expansion and mechanical properties.

Relationships between elastic anisotropy and thermal expansion in A2Mo3O12 materials.

We report calculated elastic tensors, axial Grüneisen parameters, and thermal stress distributions in Al2Mo3O12, ZrMgMo3O12, Sc2Mo3O12, and Y2Mo3O12, a series of isomorphic materials for which the coefficients of thermal expansion range from low-positive to negative. Thermal stress in polycrystalline materials arises from interactions between thermal expansion and mechanical properties, and both can be highly anisotropic. Thermal expansion anisotropy was found to be correlated with elastic anisotropy: axes with negative thermal expansion were less compliant. Calculations of axial Grüneisen parameters revealed that the thermal expansion anisotropy in these materials is in part due to the Poisson effect. Models of thermal stress due to thermal expansion anisotropy in polycrystals following cooling showed thermal stresses of sufficient magnitude to cause microcracking in all cases. The thermal expansion anisotropy was found to couple to elastic anisotropy, decreasing the bulk coefficient of thermal expansion and leading to lognormal extremes of the thermal stress distributions.

Coefficient of Thermal Expansion of Polymer Concrete with Different Polymeric Binders

The coefficient of thermal expansion (CTE) is one of the material factors affecting the behavior of concrete structures. This study reports the typical range of CTE for polymer concrete with different types of polymeric binder based on extensive literature surveys. The results revealed the CTE of polymer concrete generally fell between 12.5 and 28.6 x 10-6/°C, which is about twice or three times higher than that of ordinary cement concrete, because the CTE of polymeric binder is much larger than that of cementitious binders. The findings of this study will provide useful information for the design and analysis of polymer concrete members and repair components.

Physical Properties of Ternary NaPO3-KHSO4-MX (M=Na, K and X=Cl, Br) Glasses

This contribution focusses on some thermal, optical and mechanical properties of sulfophosphate glasses containing MX (M=Na, K and X=Cl, Br) synthesized in the NaPO3- KHSO4- MX systems. The synthesized samples of 1cm in thickness present large vitreous areas. These glasses are stable at room atmosphere and soluble in water. Characteristic temperatures of glass transition and onset of crystallization were measured. The temperature of glass transition and the coefficient of thermal expansion range between 180 and 254°C and between 217.10-7 k-1 and 270.10-7k-1, respectively. Refractive index of all the samples is found is close to 1.48 in the 633-1555nm wavelength range. The micro hardness and the elastic moduli of the samples were also measured.

Galliosilicate glasses for viscous sealants in solid oxide fuel cell stacks: Part III: Behavior in air and humidified hydrogen

Optimized boro-galliosilicate glasses were selected to evaluate their viscous sealing performance in both air and humidified hydrogen atmospheres. Selected low-alkali and alkali-free glasses show excellent performance, with viscous behavior maintained for more than 1000 h in wet hydrogen. Candidate sealants were thermally treated at 850 and 750 °C for up to 1000 h in contact with alumina coated 441 stainless steel (Al-SS) and 8 mol% yttria-stabilized zirconia (8YSZ). Each sealant crystallizes appreciably by 1000 h, and their coefficients of thermal expansion range from 10.2 to 11.7 × 10−6 K−1, 100–400 °C. The remnant amorphous phases in most of the partially crystallized sealants show softening points near or below the target operating temperatures, thus enabling viscous sealing. Humidified hydrogen in general increases the rate of crystallization but does not change the crystalline phases formed or interactions with 8YSZ. For the low-alkali GaBA series, wet H2 enhances the interfacial interaction between potassium in the glass phase and the protective alumina coating on the stainless steel.

Characteristics of the Sintered Phlogopite Mica/SiO2-B2O3-Al2O3-BaO-La2O3 Glass Blends

The thermal and crystalline properties of the sintered Phlogopite mica/SiO2-B2O3-Al2O3-BaO-La2O3 glass blends with the weight fraction of mica from 0 to 100% have been investigated in this paper. A small amount of Phlogopite mica addition raises the coefficient of thermal expansion (CTE) of the sintered phlogopite mica/SiO2-B2O3-Al2O3-BaO-La2O3 glass blends. However, the CTE of the blends decreases as the mica contents higher than 10 wt%. Besides, the CTE of the blends can be modified by adjusting the weight fraction of mica. In this study, the range of CTE varies from 9.7 to 18.1×10−6 ºC−1. The crystalline phases of BaSiO3 and BaAl2Si2O8 are found in the sintered Phlogopite mica/SiO2-B2O3-Al2O3-BaO-La2O3 glass blends. The amount of BaSiO3 phase in the sintered blends is observed at a maximum while the mica contents at 10 wt%. Additionally, the amount of BaAl2Si2O8 phase increases as the mica contents increases.

Coefficients of thermal expansion of (Ni0·5Al0·5)(1–x)Hfx alloys (x=0...0·2)

The coefficients of thermal expansion (CTEs) of Ni–Al–Hf alloys have been investigated due to their potential as corrosion resistant coatings in aggressive environments at high temperature. The CTEs of (Ni0·5Al0·5)(1–x)Hfx alloys (x=0...0·2) were measured between 473 and 1073 K (200–800°C) and range between 8 and 15×10–6 K–1 depending on temperature and alloy composition. The temperature dependence of the CTE was found to be properly described by a simple expression: (19·982–0·24016XHf)[0·15182+1·8287×10–3(T/K)–2·12378×10–6(T/K)2+8·87011×10–10(T/K)3]. It was shown that the CTE of (Ni0·5Al0·5)(1–x)Hfx alloys varies linearly with the amount of Hf in the alloy which allows the control of the CTE. Within the (Ni0·5Al0·5)(1–x)Hfx alloy composition range (x=0...0·2) it covers the CTE range of most of the austenitic and ferritic steels and the CTE of the coatings can be adjusted to those of the substrate to be protected without inducing additional strains at the coatings/substrate interface.

Refractory glass–ceramics based on alkaline earth aluminosilicates

Glass–ceramics that can be used at temperatures of 1200–1500 °C are found in the alkaline earth aluminosilicate field, and are generally nucleated internally with titania. These glass–ceramics have good strength (>100 MPa, abraded), can be tailored to produce high fracture toughness (2–5 MPa m 1/2), and have good dielectric properties. Coefficients of thermal expansion (CTEs) are low to moderate ((25–45) × 10 −7 °C −1, from 25 to 1000 °C). The major crystalline phase in the glass–ceramics exhibiting the lowest CTEs is hexagonal cordierite (indialite), while important toughening accessory phases are enstatite and acicular magnesium dititanate. The most refractory glass–ceramics that are easily melted at 1650 °C, yet when crystallized do not deform at 1450 °C, are based on strontium and barium monoclinic feldspars of the celsian type. CTEs range from 35 to 45 × 10 −7 °C −1. Acicular mullite is an important accessory phase aiding fracture toughness in these materials. Mullite glass–ceramics which contain considerable siliceous residual glass are probably the most refractory of these glass–ceramics, but they require melting above 1700 °C. Nevertheless, they can be used at temperatures near 1600 °C. Potential applications for refractory glass–ceramics include improved radomes, engine components, substrates for semiconductors and precision metallurgical molds.

Coefficient of Thermal Expansion of Concrete Materials

The new Mechanistic-Empirical Pavement Design Guide (MEPDG) requires the coefficient of thermal expansion (CTE) of concrete materials as a direct input to determine critical pavement distresses. The CTE can be determined using AASHTO TP 60. For this study, a CTE measuring device in compliance with AASHTO TP 60 was acquired. Three replicate specimens were prepared for each of 24 concrete and cement paste mixtures and tested at 7 and 28 days. The range of CTE determined in this study was in agreement with the range of values reported by other studies, and the variability of test results was favorably comparable. Analysis of variance and sensitivity analyses were performed to evaluate the influence of mixture properties on the CTE and the effect on pavement performance predictions of using Level 1- and 3-CTE inputs. It was concluded that the type of coarse aggregate used in portland cement concrete (PCC) mixtures significantly influenced the CTE and pavement performance predictions. The proportion of coarse aggregates in the PCC mixture could significantly affect the CTE depending on the types of aggregates used in the mixture. In addition, recommendations for Level-3 CTE input can be used for PCC mixtures with limestones and sandstones. However, CTE recommendations for PCC mixtures with gravels were not available for comparisons. It is recommended that a future CTE testing program for supporting implementation of the MEPDG include primary local aggregate types and that CTE recommendations for Level-3 CTE input in the design software be updated to include more aggregate types, especially gravels.

Measurement and Significance of the Coefficient of Thermal Expansion of Concrete in Rigid Pavement Design

The coefficient of thermal expansion (CTE) is a fundamental property of concrete. It has long been known to have an effect on joint opening and closing in jointed plain concrete pavement, crack formation and opening and closing in continuously reinforced concrete pavement, and curling stresses and thermal deformations in both types of pavements. However, it has not been included as a variable either in materials specifications or in the structural design of concrete pavements. Hundreds of cores were taken from Long-Term Pavement Performance sections throughout the United States and were tested by FHWA's Turner–Fairbank Highway Research Center laboratory, using the AASHTO TP 60 test procedure. The CTE values were then assimilated into groups on the basis of aggregate types, and the mean and range of CTE were calculated. These results were then used in the new mechanistic–empirical pavement design guide to determine the significance of the measured range of CTE on concrete pavement performance. The CTE of the concrete was found to vary widely, depending on the predominant aggregate type used in the concrete. Sensitivity analysis showed CTE to have a significant effect on slab cracking and, to a lesser degree, on joint faulting. Its overall effect on smoothness was also significant. Given that CTE has not been used before in routine pavement structural design, the conclusion is that this design input is too sensitive to be ignored and must be fully considered in specifications and in the design process to reduce the risk of excessive cracking, faulting, and loss of smoothness.