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2023 | Book

Fracture Analysis of Layered Beams With an Elastically Coupled Behavior and Hygrothermal Stresses

Application to Metal-to-Composite Adhesive Joints


About this book

This book presents an analytical framework for calculating the fracture toughness of generally layered beam structures with an elastically coupled response and hygrothermal stresses. The beam under study features several peculiarities: it consists of multiple layers of dissimilar materials, features bending-extension coupling, and contains residual hygrothermal stresses. Here, a generic analytical model is proposed to compute the energy release rate and the mode mixity. Mechanics of composite materials, crack closure integral, and energetic methods are among the theoretical tools employed for developing the model.

A wealth of new closed-form expressions is presented, together with their validation through finite element analyses, which enables investigating various material systems and testing configurations. Experimentalists will find directions for the design and interpretation of delamination tests on laminated composites with uncommon stacking sequences. At the same time, theoreticians can exploit the analytical solution as a benchmark test for more refined analytical and numerical models.

Furthermore, the book gives novel insights into the fracture behavior of a titanium-to-CFRP adhesive joint, which is intended for application in the hybrid laminar flow control of a future aircraft. It reports on experiments and theoretical analyses that help understand the behavior of this novel joint. All in all, this book offers extensive updates on methods for fracture analysis of materials with an elastically coupled behavior and residual stresses. It addresses students, researchers, and engineers alike.

Table of Contents

Chapter 1. Introduction
The present chapter is the opening chapter of the book and introduces the reader to its content, structure, and contributions to knowledge. In Sect. 1.1, the general background of the current work and its motivations are presented. Next, in Sect. 1.2, the general aim and specific objectives of the thesis are set out. Then, in Sect. 1.3, the organization of the book is explained, and an overview of the content of each chapter is given before Sect. 1.4 specifies the contribution of the thesis to scientific knowledge. Lastly, Sect. 1.5 provides some definitions for basic concepts and terms that we will encounter often in the remainder of the book.
Panayiotis Tsokanas
Chapter 2. The Effect of Residual Hygrothermal Stresses on the Energy Release Rate and Mode Mixity of Interfacial Cracks in Beams with Bending–Extension Coupling
The present chapter proposes an analytical framework for calculating the mode I and mode II components of the ERR of an interfacial crack between two generally layered sublaminates while considering the effects of BEC and RHTS. In this model, both sublaminates are modeled as Timoshenko beams, the crack tip is assumed to be semi-rigid (rotationally flexible), and mode partitioning is performed according to the so-called global partitioning method. ERR and MM are obtained for a generally loaded cracked beam specimen and are then reduced for some typical interfacial fracture test configurations. Next, an asymmetrically disbonded FML is analyzed using the DCB and ENF configurations. Notably, the inherent contact problem in the case of the ENF configuration is also approached analytically. It is demonstrated that the effect of RTS on the ERR and MM of the FML, which has largely been ignored in the relevant literature, is non-negligible and might even be significant. The analytical results are validated through a comparison against numerical ones via the finite element method. Lastly, the proposed analytical solution is well-suited for future experimental data reduction purposes since it is provided as closed-form expressions and does not require complicated calculations.
Panayiotis Tsokanas
Chapter 3. Fracture Toughness of Metal-to-Composite Adhesive Joints with Bending–Extension Coupling and Residual Thermal Stresses
The current chapter presents results of the analysis of the mode I and mode II interfacial fracture behaviors of a metal-to-composite adhesive joint between thin titanium and CFRP adherents, which is destined for application in the leading edge of the wing of the future aircraft. An engineering approach is followed for the design of fracture toughness tests for this joint. The vacuum-assisted resin transfer molding (VARTM) technique is employed to manufacture specimens subsequently tested using the DCB and the ENF configurations. Because these specimens are too thin, we stiffen them on both the titanium and composite sides with two aluminum backing beams to ensure the titanium does not yield during the subsequent DCB and ENF tests. The analytical model proposed in Chap. 2 is used to determine the fracture toughness from the experimental data. Recall that this model can consider the BEC induced by the aluminum beams and the RTS caused by manufacturing. The analytical fracture toughness calculations are validated using 2D FEA. In addition, crack propagation analyses based on the VCCT and the CZM are performed to capture the observed behavior and to extract the fracture toughness properties of the joint. Lastly, a comparison of various DRSs in the literature reveals the level of error if factors such as the BEC or the RTS are ignored. This error is often significant.
Panayiotis Tsokanas
Chapter 4. Interfacial Fracture Toughness of a Titanium-to-CFRP Adhesive Joint
In the present chapter, the interfacial fracture behavior of a titanium-to-CFRP adhesive joint is investigated experimentally using the DCB and ENF test configurations. A potential application of this joint is in the wings of future large passenger aircraft. Four distinctive, industry-relevant manufacturing approaches are proposed: co-bonding with and without adhesive; and secondary bonding, using thermoset and thermoplastic CFRP. The VARTM technique is used for all of them. After manufacturing, the panels are cut into test specimens. Because these specimens are too thin (approximately 2.4 mm thick), we stiffen them on both titanium and composite sides with two aluminum backing beams to ensure the titanium will not yield during the subsequent DCB and ENF tests. The DRS proposed in Chap. 2 is used to determine the fracture toughness of the joint. As highlighted in the previous two chapters, this considers effects such as BEC and RTS induced by manufacturing. The load-versus-displacement responses, fracture behaviors during testing, and fracture toughness performances of the four MOs under consideration are presented and compared.
Panayiotis Tsokanas
Chapter 5. Energy Release Rate and Mode Partitioning of Moment-Loaded Fracture Tests on Layered Beams with Bending–Extension Coupling and Hygrothermal Stresses
In the present chapter, the analytical framework proposed in Chap. 2 is enriched, and the study of the fracture toughness of the titanium-to-CFRP joint presented in Chaps. 3 and 4 is extended. New closed-form expressions are derived for the ERR and MM of interfacial fracture tests on layered beams with BEC and RHTS, loaded with uneven bending moments. The analytical model uses Timoshenko beam kinematics, a semi-rigid interface model, and the crack closure integral for mode partitioning. The proposed expressions are validated via the finite element method in two typical examples of metal-to-composite joints. In addition, experiments employing the DCB-UBM test setup are performed in a titanium-to-CFRP adhesive joint, and the new analytical expressions are used to achieve data reduction. We demonstrate that the effect of RTS on the ERR and MM of the metal/composite interfaces can be non-negligible and, thus, should be considered in the design and analysis of such structures. The proposed formulae serve as a DRS to determine fracture toughness and MM of moment-loaded tests on arbitrarily layered beams with BEC and hygrothermal stresses.
Panayiotis Tsokanas
Chapter 6. Closed-Form Solution for Interfacially Cracked Layered Beams with Bending–Extension Coupling and Hygrothermal Stresses
This chapter further investigates the problem of the mechanical behavior of an interfacially cracked layered beam with possible BEC and RHTS, as well as shear deformations and crack-root rotations, which was introduced in Chap. 2. The chapter presents a mechanical model of a beam that results by assembling two sublaminates by a semi-rigid interface. The beam is clamped at its one end and interfacially cracked and generally loaded at the other. First, the mathematical problem is formulated and analytically solved in terms of the internal forces, strains, displacements, and interfacial stresses. Novel closed-form expressions are derived regarding these quantities and thoroughly reported in tables. Compared to the extant literature, the proposed expressions stand out for their generality; they apply to beams with arbitrary layers of random thicknesses and materials and consider general loading, BEC, and RHTS. Next, we highlight some specific cases by appropriately reducing the general expressions. As an example, we investigate the mechanical responses of composite laminates with possible BEC and RHTS using the DCB configuration. Lastly, the chapter discusses new ways to deepen our knowledge of additional aspects of the fracture response of interfacially cracked beams with BEC and RHTS.
Panayiotis Tsokanas
Chapter 7. Conclusion
This is the last chapter of the present book, and it provides the reader with the main conclusions of the entire work and recommendations for future research. First, in Sect. 7.1, the major findings of the thesis are summarized. Subsequently, in Sect. 7.2, the strengths of the proposed analytical model and solution are outlined. Lastly, some key aspects of the ongoing research work by our group are presented in Sect. 7.3, along with suggestions for future research steps.
Panayiotis Tsokanas
Fracture Analysis of Layered Beams With an Elastically Coupled Behavior and Hygrothermal Stresses
Panayiotis Tsokanas
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