Document Type


Date of Degree

Fall 2016

Degree Name

PhD (Doctor of Philosophy)

Degree In

Mechanical Engineering

First Advisor

Zhupanska, Olesya I

First Committee Member

Xiao, Shaoping

Second Committee Member

Ratner, Albert

Third Committee Member

Lu, Jia

Fourth Committee Member

Rahmatalla, Salam


Airframes operating in the hypersonic regime are subjected to complex structural and thermal loads. Structural loads are a result of aggressive high G maneuvers, rapid vehicle acceleration and deceleration, and dynamic pressure, while thermal loads are a result of aerodynamic heating. For such airframes, structural members are typically constructed from steel, titanium and nickel alloys. However, with most materials, rapid elevations in temperature lead to undesirable changes in material properties. In particular, reductions in strength and stiffness are observed, along with an increase in thermal conductivity, specific heat and thermal expansion. Thus, hypersonic airframes are typically designed with external insulation, active cooling or a thermal protection system (TPS) added to the structure to protect the underling material from the effects of temperature. Such thermal protection may consist of adhesively bonded, pinned, and bolted thermal protection layers over exterior panels. These types of attachments create abrupt changes in thermal expansion and stiffness that make the structure susceptible to cracking and debonding as well as adding mass to the airframe.

One of the promising materials concepts for extreme environments that was introduced in the past is the so-called Spatially Tailored Advanced Thermal Structures (STATS). The concept of STATS is rooted in functionally graded materials (FGMs), in which a directional variation of material properties exists. These materials are essentially composites and consist of two or more phases of distinct materials in which the volume fractions of each phase continuously change in space. Here, the graded material will serve a dual-purpose role as both the structural/skin member and thermal management with the goal of reducing the weight of the structure while maintaining structural soundness. This is achieved through the ability to tailor material properties to create a desired or enhanced thermomechanical response through spatial variation (e.g. grading).

The objective of this study is to present a computational framework for modeling and evaluating the thermomechanical response of STATS and FGMs for highly maneuverable hypersonic (Mach > 5) airframes. To meet the objective of this study, four key steps have been defined to study the thermomechanical response of such materials in extreme environments. They involve: (1) modeling of graded microstructures; (2) validation of analytical and numerical modeling techniques for graded microstructures; (3) determination of effective properties of variable composition composites; (4) parametric studies to evaluate the performance of FGMs for use in the hypersonic operating environment; (5) optimization of the material spatial grading in hypersonic panels aiming to improve the thermomechanical performance.

Modeling of graded microstructures, representing particulate reinforced FGMs, has been accomplished using power law distribution functions to specify the spatial variation of the constituents. Artificial microstructures consisting of disks and spheres have been generated using developed algorithms. These algorithms allow for the creation of dense packing fractions up to 0.61 and 0.91 for 2D and 3D geometry, respectively.

Effective properties of FGMs are obtained using micromechanics models and finite element analysis of representative volume elements (RVEs). Two approaches have been adopted and compared to determine the proper RVE for materials with graded microstructures. In the first approach, RVEs are generated by considering regions that have a uniform to slow variation in material composition (i.e., constant volume fraction), resulting in statistically homogenous piecewise RVEs of the graded microstructure neglecting interactions from neighboring cells. In the second approach, continuous RVEs are generated by considering the entire FGM. Here it is presumed that modeling of the complete variation in a microstructure may influence the surrounding layers due to the interactions of varying material composition, particularly when there is a steep variation in material composition along the grading direction. To determine these effects of interlayer interactions, FGM microstructures were generated using three different types of material grading functions, linear, quadratic and square root, providing uniform, gradual and steep variations, respectively. Two- and three-dimensional finite element analysis was performed to determine the effective temperature-dependent material properties of the composite over a wide temperature range. The outcome of the computational analysis show that the similar effective properties are obtained by each of the modeling approaches. Furthermore, the obtained computational results for effective elastic, thermal, and thermal expansion properties are consistent with the known analytical bounds.

Resulting effective temperature-dependent material properties were used to evaluate the time-dependent thermostructural response and effectiveness of FGM structural panels. Structural panels are subjected to time- and spatial-dependent thermal and mechanical loads resulting from hypersonic flight over a representative trajectory. Mechanical loads are the by-product of aggressive maneuvering at high air speeds and angles of attack. Thermal loads as a result of aerodynamic heating are applied to the material systems as laminar, turbulent and transitional heat flux on the outer surface. Laminar and turbulent uniform heat fluxes are used to evaluate the effectiveness of FGM panels graded in the through-thickness direction only. Transitional heat fluxes are used to evaluate the effectiveness of FGMs graded in two principal directions, e.g., through-thickness and the surface parallel to flow. The computational results indicate that when subjected to uniform surface heat flux, the graded material system can eliminate through-thickness temperature gradients that are otherwise present in traditional thermal protection systems. Furthermore, two-dimensional graded material systems can also eliminate through-thickness temperature gradients and significantly reduce in-plane surface temperature gradients when subjected to non-uniform surface aerodynamic heating.

Public Abstract

Aircraft operating in the hypersonic regime are subjected to complex thermal and structural loads. Airframes operating in this environment are typically constructed from structural materials protected from the effects of temperature by a thermal protection system (TPS) that is chemically or mechanically bonded over structural panels which can make structures susceptible to cracking and debonding. Thus the design of next-generation agile hypersonic airframes demands advanced materials capable of operating in extreme environments.

One promising material concept for extreme environments that was recently introduced is the idea of spatially tailored advanced thermal structures (STATS). The notion of STATS finds its roots in functionally graded materials (FGMs), in which spatial dependence of material properties exists. Particularly, metal-ceramic graded structures find novel applications as multifunctional thermostructural members through tailoring material properties to create desirable or enhanced thermostructural responses.

In the present thesis, a computational framework for modeling and evaluating the thermomechanical response of STATS for highly maneuverable hypersonic airframes is presented. The framework is formulated around the coupling of effective property estimation, thermostructural analysis and optimization. Numerical models based on micromechanical methods are used to confidently predict effective temperature- and spatial-dependent material properties. Using representative hypersonic loads, the thermostructural response is determined using finite element analysis (FEA) over a characteristic trajectory. Lastly, using surrogate modeling techniques, optimal material distribution is determined using optimization techniques to produce a minimum mass system capable of withstanding the extreme operating requirements.


FEM, FGMs, Hypersonics, Particulate Composites


xvii, 159 pages


Includes bibliographical references (pages 153-159).


Copyright © 2016 Phillip Eugene Deierling