Continuum Damage Mechanics Models and Their Applications to Composite Components of Aero-Engines A thesis for the degree of Doctor of Philosophy Tian-Hong Yu 2016 Composites Research Group, Faculty of Engineering, The University of Nottingham, Nottingham NG7 2RD, UK Acknowledgements First of all, I would like to thank my supervisor, Prof. Shuguang Li, who shared valuable expertise and provided important guidance to me throughout the course of this research project, which enabled me to achieve significant progress in the last three years. His attention to detail, patience and academic professionalism not only ensured the delivery of high quality supervision to my research project, but also inspired me to tackle technical problems with persistence and confidence, from which I will benefit for the rest of my life. I would also like to express my gratitude to my co-supervisors. My gratitude goes to Dr. Elena Sitnikova, for her helpful feedbacks on my research work and her comprehensive advice on my thesis writing, and to Dr. Richard Brooks, for his effort to help sourcing the materials for the experimental work. The generous support from AVIC Commercial Aircraft Engine Co. Ltd. (ACAE), both financially and technically, which made this research project possible, is gratefully acknowledged. My gratitude also goes to my fellow research team members from ACAE, for their support and the quality time we spent together working for a joint research program. Moreover, I am forever in debt to my parents for the understanding, encouragement and support they provided to me in the last few years, which allowed me to focus on my PhD study. i Abstract Built on top of a consistent continuum damage mechanics (CDM) damage representation formulation, a novel damage evolution law based on the concept of damage driving force is proposed for modelling the evolution of matrix damage in UD composites. This damage evolution law has the advantage of allowing different damage evolution constants to be associated with different loading modes (corresponding to the fracture modes in Fracture Mechanics) when dealing with mixed-mode loading conditions, which avoids the unrealistic assumption in many existing theories that different loading modes make the same contribution to damage evolution. A new CDM model for UD composites is developed incorporating this damage evolution law. Thanks to the laminate test cases designed and conducted in this project, it is found that the damage initiation and propagation related material constants can be determined using these tests. These damage-related material constants served as inputs to the UD composite CDM model. Apart from the tests on laminates, detailed experimental investigation was carried out regarding damage in two types of layer-to-layer interlock 3D woven composites which are reinforced by IM7 carbon fibre (CF) and E-glass fibre (GF), respectively. The experimental data obtained and the damage processes recorded for these 3D woven composites can serve as a good reference for future interest in this area, since currently only limited studies are available in the literature regarding damage in this type of 3D woven composites. The new UD composite CDM model is applied to predict intra-laminar damage in laminates and intra-tow damage in the 3D woven composites. Compared to the ii experimental results, it is found that the model produced satisfactory predictions but lacking the capability to predict a severe stress-strain nonlinearity caused by shear. A new pragmatic continuum damage model is developed to capture the damage effect of inter-tow cracks in the 3D woven composites caused by warp direction tensile loading. This model works in conjunction with the intra-tow damage predicted by the aforementioned UD composite CDM model. With the successful development of these damage models, a novel damage modelling methodology for textile composites is made possible and implemented in conjunction with the UnitCells© composite characterisation tool [1] and the artificial neural network tool developed in [1]. Through the artificial neural network for data interpolation, the constitutive behaviour of textile composite incorporating the effect of damage can be interpolated for any load combination, which is then readily available for engineering applications. iii Table of Contents Acknowledgements .................................................................................................. i Abstract ................................................................................................................... ii Table of Contents ................................................................................................... iv List of Figures ....................................................................................................... vii List of Tables ......................................................................................................... xv Abbreviations ..................................................................................................... xviii Notations .............................................................................................................. xix 1. Introduction ...................................................................................................... 1 1.1 Background ............................................................................................... 1 1.2 Aims & Objectives ................................................................................... 5 1.3 Structure of Thesis .................................................................................... 7 2. Literature Review ............................................................................................. 9 2.1 Composite Materials for Aerospace Applications .................................... 9 2.1.1 Benefits and History ........................................................................ 10 2.1.2 Issues Associated with Laminates ................................................... 14 2.1.3 3D Textile Composites .................................................................... 16 2.2 Failure in UD Composites under Static Loadings .................................. 21 2.2.1 Failure Mechanisms ........................................................................ 22 2.2.2 Failure Theories ............................................................................... 23 2.3 Damage in Laminates under Static Loading ........................................... 31 2.3.1 Damage Mechanisms ...................................................................... 31 2.3.2 Damage Modelling .......................................................................... 33 2.4 Damage in 3D Textile Composites under Static Loading ...................... 49 2.4.1 Damage Mechanisms ...................................................................... 49 2.4.2 Damage Modelling .......................................................................... 52 2.5 Summary ................................................................................................. 54 3. A Novel Formulation for Damage Evolution of UD Composites based on the Concept of Damage Driving Force ....................................................................... 58 3.1 Introduction ............................................................................................. 58 3.2 Derivation of Damage Driving Force ..................................................... 58 3.3 Critical Damage Driving Force .............................................................. 69 3.4 Unloading and Reloading Scenarios ....................................................... 70 iv 3.5 Damage Evolution Law and Incremental Material Constitutive Relationship ....................................................................................................... 71 3.6 Summary ................................................................................................. 76 4. Experimental Investigation of Damage in Composites by Quasi-static Tests 78 4.1 Introduction ............................................................................................. 78 4.2 Experimental Method ............................................................................. 79 4.2.1 Material Types and Specimens ........................................................ 79 4.2.2 Loading Device and Test Environment ........................................... 80 4.2.3 Strain Measurement ......................................................................... 80 4.2.4 Acoustic Emission ........................................................................... 81 4.3 Quasi-static Test on Laminates of IM7 Carbon Fibre ............................ 83 4.3.1 Specimen Manufacture and Dimensions ......................................... 83 4.3.2 Material Properties of the UD Lamina ............................................ 85 4.3.3 Result and Discussion ..................................................................... 85 4.4 Quasi-static Test on 3D Woven Composites .......................................... 98 4.4.1 Specimen Manufacture and Dimensions ......................................... 98 4.4.2 3D Woven Composite Reinforced by IM7 Carbon Fibre ............... 99 4.4.3 3D Woven Composite Reinforced by E-glass Fibre ..................... 125 4.5 Summary ............................................................................................... 143 5. Implementation and Verification of Proposed Damage