Tailorable Coefficient Of Thermal Expansion Research Articles

Impact resistance analysis of a dual-constituent negative Poisson’s ratio lattice metamaterial with tailorable coefficient of thermal expansion

The combination of parameters such as negative Poisson’s ratio (NPR) and negative coefficient of thermal expansion (NCTE) can result in novel materials with specialized functions to meet the requirements of multifunctional and multipurpose devices. However, the additional structural design to meet NCTE requires a re-examination of its impact resistance. In this paper, the deformation modes and impact resistance of dual-constituent re-entrant hexagonal lattice metamaterial (DRHLM) with both NPR and NCTE are investigated under different impact velocities, and the nominal stress–strain curves and energy absorption characteristics of DRHLM structures with different arch heights, chord lengths, and angles of the bottom edge ribs and the diagonal ribs are discussed. The results show that the bi-material bending ribs affect the energy absorption of the structure, and in most cases the DRHLM structure has a better energy absorption capacity than the traditional concave hexagonal structure, but too much or too little curvature of the bi-material portion reduces the energy absorption characteristics of the DRHLM structure. In addition, the increase in the pinch angle of the ribs leads to the weakening of the negative Poisson’s ratio effect, which is also detrimental to the energy absorption of the structure. The work done can provide guidance for finding the dimensional parameters of DRHLM structures with optimal energy absorption performance.

Latest research progress of SiCp/Al composite for electronic packaging

Abstract With the rapid development, microelectronic technology has put forward strict requirements for electronic packaging materials (EPMs). SiCp/Al composites with high volume fraction of SiC has become an ideal candidate for EPMs due to their superior properties including high thermal conductivity, tailorable coefficient of thermal expansion as well as low density in many fields. This study reviewed the manufacturing process of SiCp/Al composites in recent years. In addition, the interface between particle and matrix, the application, and the development trend of SiCp/Al composites has also been summarized.

Dual-constituent anti-tetra-chiral lattice metamaterial with tailorable coefficient of thermal expansion and excellent bandgap

Dual-constituent anti-tetra-chiral lattice metamaterial with tailorable coefficient of thermal expansion and excellent bandgap

Interface engineering toward high thermal conductivity in diamond composites

Diamond particle reinforced metal matrix (metal/diamond) composites with high thermal conductivity and tailorable coefficient of thermal expansion are an ideal thermal management material for electronic packaging applications. Interface engineering is the key to designing metal/diamond composites due to large difference between metal and diamond in both chemical and physical nature. In this paper, we briefly summarize recent progress in the interface engineering of metal/diamond composites and give some perspectives on future development in this field.

A Novel Re-Entrant-Type Metamaterial with Tunable Negative Poisson’s Ratios and Coefficients of Thermal Expansion

Introducing bi-material double-triangular elements into a standard re-entrant structure, a novel metamaterial is proposed in this work. The effect of geometrical parameters on negative Poisson’s ratio (NPR) and coefficient of thermal expansion (CTE) is studied theoretically and verified by finite element (FE) method. Results show that the proposed structure provides tunable Poisson’s ratios in wide ranges (from negative to positive) by adopting base materials with different elastic moduli. The horizontal Poisson’s ratio of the structure increases with the increment of the re-entrant angle, and decreases with the decrement of the elastic modulus ratio (i.e., the ratio of the elastic modulus of MAT-1 and MAT-2); while the vertical Poisson’s ratio decreases with the increment of the re-entrant angle, but is independent on the elastic modulus ratio. Moreover, comparing with various reported re-entrant structures, the proposed design enhances elastic modulus significantly owing to the introduced bi-material triangles. The structure also exhibits tailorable CTEs. The CTE of the structure decreases with the increment of the CTE ratios and the re-entrant angle.

Three-dimensional assembled dual-material lattice with tailorable thermal expansion: Design method, modeling, and testing

The lightweight dual-material metal lattice structure with the tailorable coefficient of thermal expansion (CTE) has attracted increasing attention for aerospace applications. However, previous work on these metal structures was mainly directed to theoretical design with the limited experimental demonstration in planar geometries because it is challenging to fabricate three-dimensional (3D) metal lattices with highly complex geometric connections. In this article, we propose a node assembly dual-material lattice design method enabling the experimentally demonstrated 3D designs with the tailorable CTE. A theoretical model of the thermal expansion and mechanical properties is provided to link the thermo-mechanical properties to the configuration and base materials. Based on the proposed design method and the theoretical model, we present three geometrical layouts with experimentally demonstrated CTEs of 34.77ppm/°C, -16.21ppm/°C, and 0.05ppm/°C, respectively. Notably, the achieved CTE of 0.05ppm/°C has never been reported in previous studies. In addition, the proposed assembled lattice can be extended periodically. Based on the demonstrations, we expect that the proposed method is promising for structurally efficient lattices design with high dimensional stability in aerospace engineering.

Planar bi-metallic lattice with tailorable coefficient of thermal expansion

Planar bi-metallic lattice with tailorable coefficient of thermal expansion

Mechanical performances and coupling design for the mechanical metamaterials with tailorable thermal expansion

Mechanical performances are of significance for the mechanical metamaterials with the tailorable coefficient of thermal expansion (CTE), when they are in service of mechanical loading. Hence, this work presents the analysis of the mechanical performances for a series of lightweight metamaterials with a wide range of tailorable CTEs. The closed-form expressions of the stiffness, yield/buckling strengths, failure modes and criteria are analytically established. It is revealed that the enhanced mechanical performances including high stiffness and strength can be obtained through reasonably modulating the cell geometries and base materials. In particular, the metamaterials in the Category A present the excellent geometrically independent yield and buckling strengths. The failure modes and corresponding criteria are originally identified especially considering the complicated loadings, geometries and base materials. These failure criteria provide references to the allowable loads to avoid the potential failure. More importantly, the coupling design of the tailorable CTE, relative density, stiffness and strength performances further reveals that the metamaterials are suitable for fulfilling various customized requirements in engineering applications. Particularly, the metamaterial BH satisfies the usage situation that requires low CTE, low density, high stiffness and strength. The analysis of the mechanical performances enhances the engineering applications of these metamaterials when both the function of tailorable CTE and mechanical capacities are in urgent need.

Thermal tuning of band gap properties in planar stretch-dominated lattices with tailorable coefficient of thermal expansion

The development of the current technology has increased the requirement for the versatility of acoustic metamaterials. In this study, the band gap (BG) tuning of the stretch-dominated thermal expansion lattice metamaterials with different configurations composed of triangular units is studied using the finite element method, and a design method for metamaterials tuned by external temperature changes in multiple frequency ranges is proposed. The results indicate that the stretch-dominated thermal expansion material can maintain the original customized thermal expansion performance while possessing the characteristics of the BG in addition to realizing different degrees of BG tunability when the temperature changes. The results provide a theoretical basis for attaining the thermal expansion/tunable BG dual-objectives design. The objective is to achieve the dual goals of tailorable coefficient of thermal expansion and tunable BG design through reasonable material selection and shape optimization.

Architected material analogs for shape memory alloys

Architected material analogs for shape memory alloys

Microstructural topology optimization for patch-based sandwich panel with desired in-plane thermal expansion and structural stiffness

Apart from the lightweight and excellent mechanical properties, sandwich panels can be endowed with tailorable in-plane coefficient of thermal expansion (CTE) through an elaborate design of periodic face-sheets. However, albeit that the microstructural topology of their periodic face-sheets promises unique thermal expansion behaviors, it may also bring significant influences to the structural stiffness of sandwich panels. In this study, we apply the topology optimization method to design face-sheet microstructures to enable the sandwich panels to possess desired in-plane CTEs, lightweight and benign mechanical properties, simultaneously. By introducing the patch-based cell as initial configuration, the existing thermally bending adjustment mechanism for thermal deformation control is integrated to the process of topology optimization. The entire topology optimization process including the equivalent mechanical properties prediction and the sensitivity computation is performed within an in-house program coupled with commercial finite element analysis software. To this end, a matching numerical sensitivity analysis method to extract sensitivities straightforwardly from software’s output is also developed on the basis of asymptotic homogenization method. Three types of specific optimization problems in terms of different objective functions and constraint conditions are proposed, solved, and studied, namely, in-plane zero thermal expansion combining with maximum stiffness, the other for in-plane zero thermal expansion optimal specific stiffness, and minimizing in-plane isotropic thermal expansion. Some specific resulting topologies, microstructural features, and design details are subsequently obtained. In particular, the current strategy of integrating effective mechanism and topological technology can be extended to design more microstructures for simultaneously tailorable CTE and high mechanical performance by replacing present thermal deformation control mechanism with others.

Simultaneously program thermal expansion and Poisson’s ratio in three dimensional mechanical metamaterial

The engineering materials and structures, which usually suffer both temperature variation and mechanical loading, motivate the urgent need of the multifunctional metamaterials with simultaneously programmable coefficient of thermal expansion (CTE) and Poisson’s ratio (PR). Whereas, the current 3D metamaterials can not continuously program the CTE and PR. Herein, a class of 3D metamaterial is originally devised by an exclusive geometrical methodology. The explicit expressions of the CTE and PR are theoretically established and are also verified by the numerical modeling. The analysis confirms that the CTE can be widely tailored by varying the geometrical parameters and selection of the constituents. Besides, the controllable PR can be also easily obtained by adjusting the geometrical parameters. Moreover, the devised 3D metamaterial gives paired tailorable CTE and controllable PR, including especially negative CTE + negative PR. An arrangement rule is developed to construct a series of hierarchical cells which can program CTE and PR in multi principle axes and can be periodically arrayed for obtaining the 3D cellular metamaterials. The devised 3D metamaterials are capable of realizing the widely coupled programmability of both CTE and PR and provide a strategy of shape morphing stimulated both by temperature variation and mechanical loading.

A novel 3D structure with tunable Poisson’s ratio and tailorable coefficient of thermal expansion based on a tri-material triangle unit

Auxetic materials and negative thermal expansion materials show great application potential in many important fields. In this paper, a novel three-dimensional truss structure with a tunable Poisson's ratio and tailorable coefficient of thermal expansion was developed. Since the deformation of each rod was dominated by axial tension or compression, the structure showed high stiffness. Equations regarding equivalent elasticity parameters and coefficients of thermal expansion of the structure were obtained by displacement and unit force methods. A numerical simulation verification was performed by ANSYS 16.0 software. The verification results indicated that the formulas have high precision and wide application scope. Through parametric analysis, we obtained the conditions for achieving a negative Poisson's ratio and negative thermal expansion coefficient. We also concluded that this material could realize a three-dimensional negative Poisson's ratio and bidirectional negative thermal expansion simultaneously by choosing reasonable geometric parameters and material combinations.

Robust Interferometry for Testing Thermal Expansion of Dual-Material Lattices

Dual-material lattices with tailorable coefficients of thermal expansion have been applied to a wide range of modern engineering systems. As supporting techniques for fabricating dual-material lattices with given coefficients of thermal expansion, the current existing methods for measuring the coefficient of thermal expansion have limited anti-interference ability. They ignore the measuring error caused by micro-displacement between the measurement sensor and the test sample. In this paper, we report a robust interferometric test method which can eliminate the measurement error caused by micro-displacement between the measurement sensor and the test sample. In the presented method, two parallel plane lenses are utilized to avoid the measurement error caused by translation, and the right lens is utilized as an angle detector to eliminate the measurement error caused by rotation. A robust interferometric testing setup was established using a distance measuring set and two plane lenses. The experiment results indicated that the method can avoid the measurement error induced by translation and has the potential to eliminate the measurement error induced by rotation using the rotational angle. This method can improve the anti-interference ability and accuracy by eliminating the measurement error. It is especially useful for high-precision thermal expansion measurement of dual-material lattices.

Bi-Material Re-Entrant Triangle Cellular Structures Incorporating Tailorable Thermal Expansion and Tunable Poisson's Ratio1

Abstract Based on the bi-material triangle lattice cell, a new cellular structure, bi-material re-entrant triangle (BRT) cellular structure, is devised to incorporate tailorable coefficient of thermal expansion (CTE) and tunable Poisson's ratio (PR) properties by replacing the straight base of a triangle with two hypotenuse members. A general thermoelasticity equation to systematically build the relationship among the external force, the temperature load, and the deformation for planar lattice structures with bounded joints is derived and then embedded into a theoretical model for the devised BRT structure. Using assembled thermoelasticity equation, effective PR, Young's modulus, as well as CTE are computed. In order to guide designers to construct initial concepts, the design domain for coupling negative CTE and negative PR properties is plotted. The material-property-combination region that can be achieved by this cellular structure is determined within an Ashby material selection chart of CTE versus PR. Nine available combinations of CTE and PR properties are extracted and demonstrated with abaqus simulation.

Design and Demonstration of Glass Panel Embedding for 3D System Packages for Heterogeneous Integration Applications

Abstract This article demonstrates a next-generation high-performance 3D packaging technology with smaller form factor, excellent electrical performance, and reliability for heterogeneous integration. High-density logic-memory integration, today, is built predominantly using interposers which are fundamentally limited in assembly pitch and interconnect lengths, and they also are expensive as the package sizes increase. On the other hand, high-frequency applications continue to use laminates which are also limited by package size and ability to integrate many components. Wafer-level fan-out (WLFO) packaging promises better performance and form factor at lower costs, but current WLFO packages are mold-based and hence are limited to small packages. This article presents a 3D packaging technology using glass panel embedding (GPE) for high-performance with potential for large body size heterogeneous integration applications. The tailorable coefficient of thermal expansion of glass allows a reliable direct board attach of large GPE packages that not only benefits the form factor and signal speed but also provides radical benefits to power delivery. Unlike interposers and silicon bridges, GPE packages are not bump-limited and can support I/O densities comparable with backend-of-line with silicon-like redistribution wiring at much lower costs. The fundamental limitations such as die shift and poor dimensional stability of current organic WLFO packages are addressed by parametric process improvements to reduce die shift to <2 μm while also improving the RDL surface planarity for high-yielding fine-line structures and integrating through glass via (TGV) in the fan-out region for 3D packaging. This article describes the fabrication process for 3D GPE, leading to demonstration of a technology using embedding of chips with all-Cu interconnections at 40-μm I/O pitch with TGVs at 300-μm pitch, thus enabling double-side RDL and assembly of chips to achieve three levels of device integration.

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.

A new design for enhanced stiffness of dual-constituent triangular lattice metamaterial with unbounded thermal expansion

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.

A cellular metastructure incorporating coupled negative thermal expansion and negative Poisson's ratio

Current reported cellular metastructures can either achieve only tailorable thermal expansion or obtain only tunable Poisson's ratio. By contrast, here, we develop a kind of lightweight cellular metastructure which incorporates coupled tailorable thermal expansion and tunable Poisson's ratio. That is a wide range of positive, zero and especially negative values of both thermal expansion and Poisson's ratio can be simultaneously obtained. The ranges and constraints of the geometrical parameters are revealed, and the relative densities are only about 2%, indicating excellent lightweight character. Besides, analytical expressions for coefficient of thermal expansion (CTE) and Poisson's ratio (PR) are theoretically established and numerically simulated. Parameter analysis confirms that the range of tailorable CTE can be enhanced through rationally selecting large values of CTE ratio, first geometrical angle and height ratio. By adjusting the second and third geometrical angles, Poisson's ratio also can be tuned to be large negative, near zero and positive values. Particularly, the metastructure can give paired negative CTE and negative PR. Different combinations of paired characteristics including positive CTE + negative PR, positive CTE + positive PR and negative CTE + positive PR are also flexibly available. Moreover, CTE and PR are found to be highly coupled. To simultaneously obtain specific CTE and PR, design parameters should be selected with consideration of the coupling effect. The results here are expected to contribute feasibility to structures with both temperature and mechanical sensitivities.

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.