A FINITE ELEMENT FRAMEWORK FOR

MULTISCALE/MULTIPHYSICS ANALYSIS OF STRUCTURES

WITH COMPLEX MICROSTRUCTURES

A Dissertation

by

JULIAN VARGHESE

Submitted to the Office of Graduate Studies of Texas A&M University in partial fulfillment of the requirements for the degree of

DOCTOR OF PHILOSOPHY

August 2009

Major Subject: Aerospace Engineering

A FINITE ELEMENT FRAMEWORK FOR

MULTISCALE/MULTIPHYSICS ANALYSIS OF STRUCTURES

WITH COMPLEX MICROSTRUCTURES

A Dissertation

by

JULIAN VARGHESE

Submitted to the Office of Graduate Studies of Texas A&M University in partial fulfillment of the requirements for the degree of

DOCTOR OF PHILOSOPHY

Approved by:

Chair of Committee, John D. Whitcomb Committee Members, Dimitris Lagoudas Zoubeida Ounaies Xin-Lin Gao Head of Department, Dimitris Lagoudas

August 2009

Major Subject: Aerospace Engineering

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ABSTRACT

A Finite Element Framework for Multiscale/Multiphysics Analysis of Structures with

Complex Microstructures. (August 2009)

Julian Varghese, B.Tech., University of Kerala, India;

M.S., Texas A&M University

Chair of Advisory Committee: Dr. John D. Whitcomb

This research work has contributed in various ways to help develop a better understanding of textile composites and materials with complex microstructures in general. An instrumental part of this work was the development of an object-oriented framework that made it convenient to perform multiscale/multiphysics analyses of advanced materials with complex microstructures such as textile composites. In addition to the studies conducted in this work, this framework lays the groundwork for continued research of these materials.

This framework enabled a detailed multiscale stress analysis of a woven DCB specimen that revealed the effect of the complex microstructure on the stress and strain energy release rate distribution along the crack front. In addition to implementing an oxidation model, the framework was also used to implement strategies that expedited the simulation of oxidation in textile composites so that it would take only a few hours. The simulation showed that the tow architecture played a significant role in the oxidation behavior in textile composites. Finally, a coupled diffusion/oxidation and damage progression analysis was implemented that was used to study the mechanical behavior of textile composites under mechanical loading as well as oxidation. A parametric study was performed to determine the effect of material properties and the number of plies in the laminate on its mechanical behavior. The analyses indicated a significant effect of the tow architecture and other parameters on the damage progression in the laminates.

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DEDICATION

To my parents

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ACKNOWLEDGEMENTS

I would like to express my deep sense of gratitude to my advisor, Dr. John D. Whitcomb, for supporting me financially, morally and academically. Without his patience and constant guidance, this work would have never been complete. The care and genuine regard for the well being of his students is something that can be found in very few people. I also wish to thank him and his lovely family for all the wonderful get- togethers we‘ve had over the years.

I would like to express my gratitude to Dr. Dimitris Lagoudas, Dr. Zoubeida Ounaies and Dr. Xin-Lin Gao for serving on my advisory committee and for providing the valuable time from their busy schedules. I also want to thank Dr. Thomas Strganac for readily offering to take Dr. Ounaies‘ place during my dissertation defense.

My sincere thanks also go to Aerospace Engineering Department staff, especially Ms. Karen Knabe, Pam McConal and Miriam Aldrete, who are among the sweetest people I have met in my life, for their kind help during my graduate studies here at Texas A&M.

A whole bunch of thanks goes to my teammates, both present and previous – Xiaodong, Jae, Deepak, Jong-il, Bhavya, Brian, Ross, Kevin and others. It was great being part of such a lively and friendly group of people. I am also thankful to all of my friends, especially Sandeep, Loka, Brandis, Aditya, Pratheesh, Kirti and many others for their support. I am thankful to all the people who have directly or indirectly helped me accomplish whatever I have.

Finally, I wish to express my sincere appreciation to my father, mother and sister for their never-ending support, love, prayers and sacrifices. Without them, I would not have been able to pursue graduate studies here at Texas A&M University.

This work is based on research supported by the Texas Institute for Intelligent Bio-Nano Materials and Structures for Aerospace Vehicles, funded by NASA Cooperative Agreement No. NCC-1-02038, and the US Air Force Office of Scientific Research (AFOSR), funded by Contract Ref No. FA9550-07-1-0207. Any opinions, findings and conclusions or recommendations expressed in this material do not necessarily reflect the

vi

views of the National Aeronautics and Space Administration or the AFOSR. I also wish to acknowledge the helpful discussions with Dr. K. Pochiraju, Dr. G. Tandon and Dr. G. Schoeppner.

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TABLE OF CONTENTS

Page

ABSTRACT ...... iii

DEDICATION ...... iv

ACKNOWLEDGEMENTS ...... v

TABLE OF CONTENTS ...... vii

LIST OF FIGURES ...... x

LIST OF TABLES ...... xvii

1.INTRODUCTION ...... 1

1.1 Introduction to Textile Composites ...... 2 1.2 Definition of Geometric Parameters in Plain Weave Composites ...... 4 1.3 Statement of Objectives...... 8

2.REVIEW OF STATE OF KNOWLEDGE ...... 10

2.1 Introduction ...... 10 2.2 Multiscale Analysis of Textile Composites ...... 22 2.3 Global / Local Analyses ...... 30 2.4 Progressive Failure Analyses ...... 33 2.5 Damage Due to Environmental Conditions ...... 35 2.6 Scope of Research ...... 40 2.7 Summary ...... 47

3. THEORY AND EQUATIONS ...... 48

3.1 Introduction ...... 48 3.2 Common Analysis Procedure ...... 48 3.3 Solid Mechanics ...... 51 3.4 Diffusion ...... 66 3.5 Oxidation ...... 78 3.6. Coupled Mechanical-Oxidation Analysis ...... 95 3.7 Summary ...... 100

4.DESIGN OF FINITE ELEMENT FRAMEWORK ...... 101

4.1 Introduction ...... 101 4.2 Why Object-Oriented Design? ...... 101

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Page

4.3 Framework Design ...... 103 4.4 Other Applications ...... 112 4.5 Summary ...... 113

5.MULTISCALE ANALYSIS OF WOVEN COMPOSITE DCB ...... 114

5.1 Introduction ...... 114 5.2 Hierarchical Analysis Strategy ...... 114 5.3 Configuration...... 119 5.4 Analysis of DCB Specimen ...... 121 5.5 Calculation of Strain Energy Release Rate ...... 124 5.6 Results and Discussion ...... 127 5.7 Summary ...... 137

6.IMPLEMENTATION AND VALIDATION OF OXIDATION MODEL ...... 138

6.1 Introduction ...... 138 6.2 Implementation of Oxidation Model ...... 138 6.3 Optimization and Validation ...... 144 6.4 Summary ...... 153

7.VALIDATION OF HOMOGENIZED OXIDATION PROPERTIES ...... 155

7.1 Introduction ...... 155 7.2 Material Properties and Configurations ...... 155 7.3 Results and Discussion ...... 160 7.4 Summary ...... 174

8.OXIDATION ANALYSIS OF TEXTILE COMPOSITES ...... 175

8.1 Introduction ...... 175 8.2 Hybrid Model ...... 175 8.3 Validation of Hybrid Model ...... 177 8.4 Oxidation Analysis of Plain Weave Laminate ...... 186 8.5 Storage of Oxidation Behavior Data from Hybrid Model ...... 189 8.6 Summary ...... 194

9.PREDICTION OF DAMAGE IN TEXTILE COMPOSITES IN OXIDIZING ENVIRONMENTS ...... 196

9.1 Introduction ...... 196 9.2 Damage Mechanisms in Textile Composites ...... 196 9.3 Configuration...... 201

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Page

9.4 Results and Discussion ...... 212 9.5 Summary ...... 233

10.CONCLUSIONS AND FUTURE WORK ...... 236

10.1 Development of Multiscale/Multiphysics Finite Element Framework ..... 236 10.2 Multiscale Analysis of Woven DCB S