Application of Functionally Graded Materials in Aircraft Structures

189 Pages·2005·1.38 MB·English

APPLICATION OF FUNCTIONALLY GRADED MATERIALS IN AIRCRACT
STRUCTURES

THESIS

William G. Cooley, Captain, USAF

AFIT/GAE/ENY/05-M04

DEPARTMENT OF THE AIR FORCE
AIR UNIVERSITY
AIR FORCE INSTITUTE OF TECHNOLOGY
Wright-Patterson Air Force Base, Ohio

APPROVED FOR PUBLIC RELEASE; DISTRIBUTION UNLIMITED
The views expressed in this thesis are those of the author and do not reflect the official
policy or position of the United States Air Force, Department of Defense, or the U.S.
Government.
AFIT/GAE/ENY/05-M04

APPLICATION OF FUNCTIONALLY GRADED MATERIALS IN AIRCRACT
STRUCTURES

THESIS

Presented to the Faculty
Department of Aeronautics and Astronautics
Graduate School of Engineering and Management
Air Force Institute of Technology
Air University
Air Education and Training Command
In Partial Fulfillment of the Requirements for the
Degree of Master of Science in Aeronautical Engineering

William G. Cooley, BS
Captain, USAF

March 2005

APPROVED FOR PUBLIC RELEASE; DISTRIBUTION UNLIMITED
AFIT/GAE/ENY/05-M04

APPLICATION OF FUNCTIONALLY GRADED MATERIALS IN AIRCRACT
STRUCTURES

William G. Cooley, BS
Captain, USAF

Approved:

____________//signed//_____________ ________
Dr. Anthony Palazotto (Chairman) Date

____________//signed//_____________ ________
Dr. Robert Canfield (Member) Date

____________//signed//_____________ ________
Dr. Richard Cobb (Member) Date
AFIT/GAE/ENY/05-M04
Abstract
Functionally Graded Materials (FGM) have continuous variation of material
properties from one surface to another unlike a composite which has stepped (or
discontinuous) material properties. The gradation of properties in an FGM reduces the
thermal stresses, residual stresses, and stress concentrations found in traditional
composites.
An FGM’s gradation in material properties allows the designer to tailor material
response to meet design criteria. For example, the Space Shuttle utilizes ceramic tiles as
thermal protection from heat generated during re-entry into the Earth’s atmosphere.
However, these tiles are prone to cracking at the tile / superstructure interface due to
differences in thermal expansion coefficients. An FGM made of ceramic and metal can
provide the thermal protection and load carrying capability in one material thus
eliminating the problem of cracked tiles found on the Space Shuttle.
This thesis will explore analysis of FGM flat plates and shell panels, and their
applications to real-world structural problems. FGMs are first characterized as flat plates
under pressure and thermal loading in order to understand the effect variation of material
properties has on structural response. Next, FGM shell panels under thermal loading are
analyzed. In addition, results are compared to published results in order to show the
accuracy of modeling FGMs using ABAQUS software. Conclusions drawn from FGM
characterization are used to develop a patch to retrofit a cracked aircraft exhaust wash
structure and reduce thermally induced cracking.
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Acknowledgments

I would like to express my sincere appreciation to my faculty advisor, Dr. Anthony
Palazotto, for his guidance and support throughout the course of this thesis effort. The
insight and experience was certainly appreciated. I would, also, like to thank my sponsor,
Dr. Ravinder Chona, from the Air Force Research Laboratory for both the support and
latitude provided to me in this endeavor.

William G. Cooley

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Table of Contents
Page
Abstract..............................................................................................................................iv
Acknowledgments................................................................................................................v
Table of Contents...............................................................................................................vi
List of Figures....................................................................................................................ix
List of Tables..................................................................................................................xvii
I. Introduction.....................................................................................................................1
Background...................................................................................................................1
Research Focus.............................................................................................................3
Research Outline..........................................................................................................4
II. Methodology..................................................................................................................6
Chapter Overview.........................................................................................................6
Research Focus and Development................................................................................6
Theoretical Formulation of FGM.................................................................................8
Physical Creation of FGMs........................................................................................12
Finite Element Modeling Technique..........................................................................13
Finite Element: Heat Transfer Methodology and Element Discussion......................15
Finite Element: Structural Analysis Methodology and Shell Element Discussion....25
Non-Linearity Background and Analysis...................................................................27
Finite Element Software, Pre-Processor, and Post-Processor....................................31
Flat Plate Coordinate Systems and Boundary Conditions..........................................33
Curved Panel Coordinate Systems and Boundary Conditions...................................35
Exhaust Wash Structure Coordinate Systems and Boundary Conditions..................35
Summary.....................................................................................................................36
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Page
III. Analysis and Results...................................................................................................37
Chapter Overview.......................................................................................................37
Flat Plate under Thermal Loading..............................................................................37
Flat Plate under Distributed Pressure Loading...........................................................46
Curved Panel under Concentrated Force Loading......................................................53
Curved Panel under Thermal Loading.......................................................................55
Exhaust Wash Structure under Thermal Loading (Structure Only)...........................59
Exhaust Wash Structure under Thermal Loading (Structure and Patch)...................66
Exhaust Wash Panel made of Zi-Ti FGM................................................................111
Summary...................................................................................................................113
IV. Conclusions and Recommendations.........................................................................116
Chapter Overview.....................................................................................................116
Conclusions of FGM Plate and Shell Research........................................................116
Conclusions of Exhaust Wash Panel Research........................................................117
Conclusions of Exhaust Wash Panel with FGM Patch Research.............................117
Recommendations for Action...................................................................................118
Recommendations for Future Research....................................................................119
Summary...................................................................................................................121
Appendix A. Flow Chart of Matlab & ABAQUS Coupling...........................................122
Appendix B. Sample ABAQUS Input File (Thermal Analysis).....................................123
Appendix C. Sample ABAQUS Input File (Structural Analysis)...................................126
Appendix D. Summarized Exhaust Wash Model Data (Stress and Deflection)..............130
Appendix E. Non-Linear Solution Example....................................................................166
Bibliography....................................................................................................................169
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Page
Vita...................................................................................................................................170
viii
List of Figures

Page
Figure 1. Thermal Protection...............................................................................................2
Figure 2. Variation of Volume Fraction..............................................................................9
Figure 3. Graphical Representation of n=0.2.....................................................................10
Figure 4. Graphical Representation of n=0.5.....................................................................11
Figure 5. Graphical Representation of n=1.0.....................................................................11
Figure 6. Graphical Representation of n=2.0.....................................................................12
Figure 7. Diagram Depicting FGM Gradation..................................................................13
Figure 8. SEM Picture of a YSZ / NiCoCrAlY FGM.......................................................13
Figure 9. Origin of Z-Axis.................................................................................................14
Figure 10. Conductive Heat Transfer Diagram..................................................................16
Figure 11. ABAQUS Shell Section Orientation (Photo Courtesy of ABAQUS [6])........19
Figure 12. Diagram of Thermal Stress-Displacement Analysis........................................20
Figure 13. Heat Transfer Element (DS4)...........................................................................21
Figure 14. Convective Heat Transfer Diagram..................................................................22
Figure 15. Structural Element S4.......................................................................................25
Figure 16. Plate Deflection Diagram.................................................................................27
Figure 17. SS1 Plate Boundary Condition.........................................................................34
Figure 18. SS2 Plate Boundary Condition.........................................................................34
Figure 19. SS3 Plate Boundary Condition.........................................................................34
Figure 20. SS4 Plate Boundary Condition.........................................................................34
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