Residual Strength and Fatigue Lifetime of ... - Solid Mechanics
Residual Strength and Fatigue Lifetime of ... - Solid Mechanics Residual Strength and Fatigue Lifetime of ... - Solid Mechanics
1.2 Overview of the Thesis In this thesis a step-by-step analysis approach has been adopted for the analysis of debonded sandwich structures exposed to static and cyclic loading. The thesis is divided into two main parts. The first part addresses debonded sandwich structures exposed to quasi-static loading. The analysis initially considers debonded sandwich columns and then further develops to geometries like debonded panels. The second part of this thesis addresses the failure of debond damaged sandwich structures exposed to fatigue loading. The thesis consists of six chapters as follows: 1. Introduction 2. Face/Core Debond Propagation in Sandwich Columns 3. Failure of Uniformly Compressed Debond Damaged Sandwich Panels 4. Fatigue Crack Growth Simulation in a Bimaterial Interface 5. Face/core Interface Fatigue Crack Propagation in Sandwich Structures 6. Conclusion and Future Work The first and the last chapters are introduction and final remarks and comments on future work. In Chapters 2 and 3 failure of debonded sandwich composites exposed to static loading is investigated. Chapter 2 contains an analysis of buckling driven crack propagation in foam cored sandwich columns with face/core debonds. LEFM and the finite element method are applied in order to analyse the behaviour of debonded sandwich columns with various PVC core materials and glass/epoxy face sheets. Associated compression tests are carried out to validate the numerical results. In Chapter 3 the numerical analysis method developed in Chapter 2 is extended further from column to panel level, and buckling driven debond propagation in sandwich panels with a circular debond is studied. Furthermore, the simulation results are validated against compression tests on debonded sandwich panels with various PVC and PMI core materials and debond diameters. In Chapters 4 and 5 the numerical tools which have been developed earlier to determine fracture parameters like the energy release rate and mode-mixity are utilised to simulate fatigue debond growth in sandwich composites. In Chapter 4 a numerical method is developed to overcome the obstacle of computational limitations. The method accelerates the simulation of fatigue crack growth by eliminating the need for simulation of all individual cycles. The acceleration method is verified by reference simulations of all individual cycles, at the end of the chapter. The developed numerical scheme is utilised to simulate 2D fatigue face/core debond growth in sandwich X-joints in Chapter 5. Additionally, the simulations are validated against fatigue tests conducted on the Sandwich Tear Test (STT) specimen representing an idealised sandwich X-joint. Finally, the developed numerical scheme is further extended from beam to panel level to simulate 3D fatigue debond growth in sandwich panels. Sandwich panels with circular debonds are tested under cyclic loading and the debond growth is monitored utilising a Digital Image Correlation (DIC) system. Consequently, the crack growth rate measured in the experiments is used to validate the developed numerical scheme. 4
These numerical and experimental studies provide a better understanding of the behaviour of debond damaged sandwich composites under static or fatigue loading. Moreover, they develop reliable analysis tools for assessing the damage tolerance and fatigue lifetime of debonded sandwich composites. Since Linear Elastic Fracture Mechanics (LEFM) for the interfaces is the main theoretical foundation of this thesis, it will be presented in the next section of the Introduction. Finally, a brief history of fatigue analysis in sandwich composites will be presented in the last section of the Introduction. 1.3 Linear Elastic Fracture Mechanics Griffith in 1920 established the foundations of fracture mechanics. He applied a stress analysis of an elliptical hole from Inglis (1913) to the unstable crack propagation problem. Based on the principle of energy conservation of thermodynamics, Griffith proposed the energy balance concept for fracture. According to Griffith’s theory, a crack may be formed or propagate if the potential energy change provided by strain energy and external forces, resulting from crack growth, is enough to overcome the surface energy and generate new surfaces. In 1948 Irwin extended Griffith’s concept to metals by including plastic energy dissipation at the crack tip. In 1956 Irwin proposed the Griffith energy or energy release rate G as a measure of available energy for crack growth as where is the potential energy and dA is the crack area increment. According to Equation (1.1) the critical energy release rate Gc or fracture toughness can be defined as where Ws is the required energy for creation of new surfaces. Generally, a crack may experience three types of loading, see Figure 1.3. Mode I loading where the applied load tends to open the crack, mode II loading where the in-plane shear loading tends to slide one crack face against the other and mode III corresponding to the out-of-plane shear and sliding of the crack flanks. A crack may be loaded in any of these three modes or in a mixedmode combination of them. In 2D modelling of a crack problem, only the first two modes are typically used. 5 (1.1) (1.2)
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1.2 Overview <strong>of</strong> the Thesis<br />
In this thesis a step-by-step analysis approach has been adopted for the analysis <strong>of</strong> debonded<br />
s<strong>and</strong>wich structures exposed to static <strong>and</strong> cyclic loading. The thesis is divided into two main<br />
parts. The first part addresses debonded s<strong>and</strong>wich structures exposed to quasi-static loading. The<br />
analysis initially considers debonded s<strong>and</strong>wich columns <strong>and</strong> then further develops to geometries<br />
like debonded panels. The second part <strong>of</strong> this thesis addresses the failure <strong>of</strong> debond damaged<br />
s<strong>and</strong>wich structures exposed to fatigue loading. The thesis consists <strong>of</strong> six chapters as follows:<br />
1. Introduction<br />
2. Face/Core Debond Propagation in S<strong>and</strong>wich Columns<br />
3. Failure <strong>of</strong> Uniformly Compressed Debond Damaged S<strong>and</strong>wich Panels<br />
4. <strong>Fatigue</strong> Crack Growth Simulation in a Bimaterial Interface<br />
5. Face/core Interface <strong>Fatigue</strong> Crack Propagation in S<strong>and</strong>wich Structures<br />
6. Conclusion <strong>and</strong> Future Work<br />
The first <strong>and</strong> the last chapters are introduction <strong>and</strong> final remarks <strong>and</strong> comments on future work.<br />
In Chapters 2 <strong>and</strong> 3 failure <strong>of</strong> debonded s<strong>and</strong>wich composites exposed to static loading is<br />
investigated. Chapter 2 contains an analysis <strong>of</strong> buckling driven crack propagation in foam cored<br />
s<strong>and</strong>wich columns with face/core debonds. LEFM <strong>and</strong> the finite element method are applied in<br />
order to analyse the behaviour <strong>of</strong> debonded s<strong>and</strong>wich columns with various PVC core materials<br />
<strong>and</strong> glass/epoxy face sheets. Associated compression tests are carried out to validate the<br />
numerical results. In Chapter 3 the numerical analysis method developed in Chapter 2 is<br />
extended further from column to panel level, <strong>and</strong> buckling driven debond propagation in<br />
s<strong>and</strong>wich panels with a circular debond is studied. Furthermore, the simulation results are<br />
validated against compression tests on debonded s<strong>and</strong>wich panels with various PVC <strong>and</strong> PMI<br />
core materials <strong>and</strong> debond diameters. In Chapters 4 <strong>and</strong> 5 the numerical tools which have been<br />
developed earlier to determine fracture parameters like the energy release rate <strong>and</strong> mode-mixity<br />
are utilised to simulate fatigue debond growth in s<strong>and</strong>wich composites. In Chapter 4 a numerical<br />
method is developed to overcome the obstacle <strong>of</strong> computational limitations. The method<br />
accelerates the simulation <strong>of</strong> fatigue crack growth by eliminating the need for simulation <strong>of</strong> all<br />
individual cycles. The acceleration method is verified by reference simulations <strong>of</strong> all individual<br />
cycles, at the end <strong>of</strong> the chapter. The developed numerical scheme is utilised to simulate 2D<br />
fatigue face/core debond growth in s<strong>and</strong>wich X-joints in Chapter 5. Additionally, the simulations<br />
are validated against fatigue tests conducted on the S<strong>and</strong>wich Tear Test (STT) specimen<br />
representing an idealised s<strong>and</strong>wich X-joint. Finally, the developed numerical scheme is further<br />
extended from beam to panel level to simulate 3D fatigue debond growth in s<strong>and</strong>wich panels.<br />
S<strong>and</strong>wich panels with circular debonds are tested under cyclic loading <strong>and</strong> the debond growth is<br />
monitored utilising a Digital Image Correlation (DIC) system. Consequently, the crack growth<br />
rate measured in the experiments is used to validate the developed numerical scheme.<br />
4
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