INTERFACIAL FRACTURE TOUGHNESS OF UNCONVENTIONAL SPECIMENS: SOME KEY ISSUES

Laboratory specimens used to assess the interfacial fracture toughness of layered materials can be classified as either conventional or unconventional. We call conventional a specimen cut from a unidirectional composite laminate or an adhesive joint between two identical adherents. Assessing fracture toughness using conventional specimens is a common practice guided by international test standards. In contrast, we term unconventional a specimen resulting from, for instance, bimaterial joints, fiber metal laminates, or laminates with an elastically coupled behavior or residual stresses. This paper deals with unconventional specimens and highlights the key issues in determining their interfacial fracture toughness(es) based on fracture tests. Firstly, the mode decoupling and mode partitioning approaches are briefly discussed as tools to extract the pure-mode fracture toughnesses of an unconventional specimen that experiences mixed-mode fracture during testing. Next, we elaborate on the effects of bending-extension coupling and residual thermal stresses often appearing in unconventional specimens by reviewing major mechanical models that consider those effects. Lastly, the paper reviews two of our previous analytical models that surpass the state-of-the-art in that they consider the effects of bending-extension coupling and residual thermal stresses while they also offer mode partitioning

Interfacial fracture analysis of layered beams with elastic couplings and hygrothermal stresses using an elastic-interface model

This work presents our progress in studying the problem of an interfacial crack in a layered beam with bending-extension coupling (BEC) and residual hygrothermal stresses (RHTS). These effects have occupied us in our recent work [1–3]. Here, we consider a beam element that is an assemblage of two sublaminates connected by a linearly elastic (until fracture) interface of negligible thickness. Both sublaminates may have arbitrary stacking sequences (which introduces BEC) and are modeled as shear-deformable laminated beams. In addition, we assume that the beam element is affected by RHTS. The mathematical problem is formulated and then reduced to two differential equations in the interfacial stresses. To formulate and solve this mathematical problem, we rely heavily on our recent work in [3], which, in turn, extended the so-called enhanced beam theory model proposed in [4]. In simpler words, the present work updates the model of [3] to account for RHTS, while it also discusses some issues not mentioned there (e.g., on the boundary conditions). The aim of the work is twofold. First, we intend to explore the mechanical behavior of the beam element. Thus, we derive explicit analytical expressions for various mechanical quantities: internal forces and moments, strain measures, and generalized displacements in both sublaminates. The effect of the RHTS on these expressions is highlighted through comparison with the respective solutions in [3] that ignore this effect. The second aim of the work is to determine the energy release rate (ERR) and its mode I and mode II contributions. For this purpose, we adopt the J-integral method, also using the so-called interface potential energy. For the beam element under consideration that is affected by residual stresses, J-integral ceases to be path independent [5]. We address this issue using a recently proposed approach [5], which, in a nutshell, splits the loading into two steps. Thus, we compose a valid J-integral solution that allows computing the ERR. Mode partitioning is achieved by assuming, as in [3], that the compressive normal stresses at the crack tip do not promote the crack opening. Ongoing work on validating the proposed analytical solutions using finite element analysis will be presented in a subsequent publication. Lastly, future extensions for the calculations of other essential mechanical quantities (e.g., compliance) are possible

Fracture Toughness Analysis of Non-Conventional Specimens: Some Key Issues

The specimens used to characterize the interfacial fracture toughness may be grouped as conventional and non-conventional. We call conventional a specimen cut from, for example, a symmetric composite or a similar adhesive joint. Analyzing the fracture toughness using conventional specimens is a common practice guided by existing standards. In contrast, we call non-conventional a specimen resulting from, for instance, bi-material joints, thin laminates that need to be stiffened before testing, or laminates with an elastically coupled behavior or residual stresses. Here, we collect such cases of peculiar specimens and highlight issues related to the following three steps of the process of fracture toughness analysis: specimen design, testing, and data reduction. Our particular focus is on making suggestions for a proper evaluation of the fracture toughness

Mode II fracture toughness of asymmetric metal-composite adhesive joints

The paper presents an experimental investigation of the mode II fracture toughness behavior of dissimilar metal-composite adhesive joints using the end-notched flexure (ENF) test. The adhesive joint under study consists of a thin titanium sheet joined with a thin CFRP laminate and is envisioned to be applied in the hybrid laminar flow control system of future aircraft. Four different industrial technologies for the manufacturing of the joint are evaluated; co-bonding with and without adhesive and secondary bonding using either a thermoset or a thermoplastic composite. The vacuum-assisted resin transfer molding (VARTM) technique is employed for the manufacturing of the titanium-CFRP joint. After manufacturing, the joint is stiffened from its both sides with two aluminum backing beams to prevent large deformations during the subsequent ENF tests. Towards the fracture toughness determination from the experimental data, an analytical model recently reported by the authors is applied; that model considers the bending-extension coupling of each sub-laminate of the joint as well as the effect of the manufacturing-induced residual thermal stresses. The load-displacement behaviors, failure patterns, and fracture toughness performances for each of the four manufacturing options (MO) investigated are presented and compared

On the conditions for pure-mode fracture

In a symmetrically cracked planar body, fracture modes I and II are respectively associated to systems of symmetric and antisymmetric forces w.r.t. the crack plane. These forces respectively produce only normal stresses and relative transverse displacements or only shear stresses and relative tangential displacements on the crack plane. The same pure-mode conditions do not apply in general for asymmetrically cracked bodies. Williams proposed the following pure-mode conditions for an asymmetrically cracked isotropic beam: (i) pure mode I, if the moments of the two sub-beams at the crack-tip cross-section are equal and opposite; (ii) pure-mode II, if the curvatures of the two sub-beams at the crack-tip cross-section are equal. Although questioned, Williams' conditions have been used by several authors. Valvo proved that the standard virtual crack closure technique (VCCT) may be inappropriate for analysing problems with highly asymmetric cracks since negative values for either mode I or mode II contribution to the energy release rate (ERR) may be calculated. To remedy this shortcoming, he suggested the following pure-mode conditions: (i) pure mode I, if the tangential crack-tip force is zero; (ii) pure mode II, if the crack-tip opening displacement is zero. Later, Valvo proposed the following conditions instead: (i) pure mode I, if the crack-tip sliding displacement is zero; (ii) pure mode II, if the normal crack-tip force is zero. In both the above proposals, the two pure modes are associated to energetically orthogonal systems of forces, so always non-negative modal contributions to the ERR are obtained. This revised VCCT was then adapted to generally layered beams. Wang and Harvey independently proposed the same energetically orthogonal pure-mode conditions. This presentation will discuss the various pure-mode conditions proposed, also with reference to experimental tests existing in the literature or to be specifically designed, aiming to clarify which theoretical proposals for pure modes (or mode partitioning) are to be preferred

Mode decoupling versus mode partitioning to determine pure-mode fractures in unconventional specimens

There is a growing research and industrial interest in determining the interfacial fracture toughness of non-traditional material systems such as dissimilar adhesive joints, asymmetrically stacked composite laminates (possibly with an elastically coupled behavior), fiber metal laminates, and thin laminates with adhesively bonded backing beams. To determine the interfacial toughness of such material systems, laboratory coupons are extracted that inherently feature a material asymmetry w.r.t. the crack plane. Because of this asymmetry, which introduces mode mixity even if the specimen is loaded in pure mode, we here call those specimens unconventional. To characterize the pure-mode fracture toughnesses of unconventional specimens, researchers attempt to decouple fracture modes I and II (and III, if present) through an appropriate design of the specimens. Emphasis has been given to the case of a bi-material adhesive joint under pure-mode I loading, where two decoupling conditions have been proposed in the literature: (a) mode decoupling is achieved when the differential equation of the mode I (mode II) fracture is only governed by the interfacial normal (shear) stress and relative transverse (axial) displacement [1]; (b) mode decoupling is achieved when the bending rigidities of the two adherents are equal [2]. Those two conditions are translated into the design formulae E1h12 = E2h22 and E1h13 = E2h23, respectively, where Ei and hi are the Young’s modulus and thickness of adherent i, i ∈ {1,2}, respectively. Our presentation will review the existing decoupling conditions and discuss their correctness. Mode decoupling is impossible for a coupon with pre-defined material properties and thicknesses that cannot be tailored using the above design formulae. In addition, in the presence of residual thermal stresses, common for layered material systems, decoupling conditions are not available in the literature. An appropriate mode partitioning scheme can be selected in such cases to determine the modal contributions to the energy release rate. During the last three decades, several mode partitioning methods have been proposed, which could be classified into four families [3]: methods based on a rigid interface and the beam theory; methods based on linear elastic fracture mechanics; elastic-interface methods; and miscellaneous methods. In our presentation, we will review those methods and emphasize two models we have proposed [4,5] that can consider the effects of bending–extension coupling and residual hygrothermal stresses

Mode decoupling in interlaminar fracture toughness tests on bimaterial specimens

The present work has a two-fold objective: (i) to critically review the methods for fracture mode decoupling in unconventional laboratory specimens, such as the asymmetric double cantilever beam (ADCB) specimen; and (ii) to propose mode decoupling conditions and associated specimen design formulae to obtain pure fracture modes when bimaterial specimens are tested in ADCB and asymmetric end-notched flexure (AENF) configurations. In the first part of the paper, the literature on fracture mode decoupling is reviewed to shed light on some controversial points. We start with discussing various pure-mode conditions suggested by different authors and continue with the simplest case of the bimaterial joint. Our review also considers complex cases, such as the presence of bending–extension coupling or residual (hygrothermal) stresses. In the second part of the paper, bimaterial specimens loaded in ADCB and AENF test configurations are investigated. Employing energetically orthogonal mode decomposition, Engesser–Castigliano’s theorem, and the laminated beam theory, we illustrate specimen design criteria enabling to obtain pure fracture modes. The obtained specimen design formulae are validated through finite element analyses

On the decoupling of fracture modes in interlaminar fracture tests on bimaterial specimens

We start by reviewing methods for fracture mode decoupling in unconventional laboratory specimens. Then, we propose energetically orthogonal mode decoupling conditions and associated specimen design criteria to obtain pure fracture modes when bimaterial specimens are tested in asymmetric double cantilever beam and asymmetric end-notched flexure test configurations. This work hopefully sheds light on some controversial points in the relevant literature

Sustainable Development Approaches through Wooden Adhesive Joints Design

Over recent decades, the need to comply with environmental standards has become a concern in many industrial sectors. As a result, manufacturers have increased their use of eco-friendly, recycled, recyclable, and, overall, more sustainable materials and industrial techniques. One technique highly dependent on petroleum-based products, and at the edge of a paradigm change, is adhesive bonding. Adhesive bonding is often used to join composite materials and depends upon an adhesive to achieve the connection. However, the matrices of the composite materials and the adhesives used, as well as, in some cases, the composite fibres, are manufactured from petrochemical products. Efforts to use natural composites and adhesives are therefore ongoing. One composite that has proven to be promising is wood due to its high strength and stiffness (particularly when it is densified), formability, and durability. However, wood must be very carefully characterised since its properties can be variable, depending on the slope of the grains, irregularities (such as knots, shakes, or splits), and on the location and climate of each individual tree. Therefore, in addition to neat wood, wood composites may also be a promising option to increase sustainability, with more predictable properties. To bond wood or wooden composite substrates, bio-adhesives can be considered. These adhesives are now formulated with increasingly enhanced mechanical properties and are becoming promising alternatives at the structural application level. In this paper, wooden adhesive joints are surveyed considering bio-adhesives and wood-based substrates, taking into consideration the recent approaches to improve these base materials, accurately characterise them, and implement them in adhesive joints