1. Introduction
In many industries, including those operating in the automotive, aerospace, and aviation sectors, adhesive bonding technology has increasingly become a viable substitute for traditional mechanical joining methods. Adhesively bonded joints offer several significant advantages over other common joining techniques such as bolting and riveting, a more uniform stress distribution along the bonded area which avoids stress concentrations and improves load transmission and fatigue resistance. Other important benefits include this technology’s capacity to easily bond dissimilar materials together and the increased flexibility it provides to the joint design [
1]. As a result of these advantages, structural weight and cost reductions can be obtained with the use of well-designed bonded joints.
The growth in the use of adhesives, especially those of the structural nature, has led to a need for fast and effective adhesive mechanical characterisation techniques that can provide the data needed to help structural designers in the adhesive selection process and grant precise optimisation of bonded connection performance. Characterising the mechanical properties and knowing the limitations of each adhesive provides crucial insights for ensuring quality control, enhancing bond performance and facilitating the usually challenging adhesive selection process [
1]. Currently, multiple different tests must be performed to obtain a set of the most relevant mechanical properties for joint design, such as tensile tests and shear tests, for strength and stiffness, and fracture tests in both mode I and mode II, to determine the toughness of the adhesive.
Tensile properties are commonly determined through bulk tensile tests and butt joints [
2]. The ASTM D 897 and ASTM D 2095 standards describe directives related to the practical aspects and methodology of preparing and testing to perform this type of test. The first one uses short circular specimens made of metal or wood, and the second is more general and includes round and square geometries [
2].
For shear properties, the thick adherend shear test (TAST) appears as a common choice, since it relies on an easily produced specimen and a simple testing setup [
2]. It also emerges as a valid substitute for the conventional single lap shear (SLS) joint, which although simple to execute is beset with complex stress states and, therefore, is not suitable for characterisation of the strength properties of adhesives. TAST tests can be performed using two different standards, ASTM D3983 and ISO 11003-2, where the main difference is in the size of the specimen. However, difficulties concerning the stress concentrations generated due to edge effects have been reported, directly influencing the acquisition of reliable data. In order to acquire accurate experimental results, a modified TAST fixture was created by Cognard et al. [
3], although it is still not standardised. It provides a stiffer apparatus combined with a more compact specimen, resulting in a more uniform adhesive stress condition in the joint and severe restriction of edge effects [
2].
The most popular test specimens for determining the critical energy release rate in mode I (the tensile opening mode), i.e.,
, are the double cantilever beam (DCB),
Figure 1, and the tapered double cantilever beam (TDCB) adhesive joint test specimens. In contrast to the more complex and expensive specimens used in TDCB testing, the DCB test uses simpler, less expensive specimens. Although the TDCB has the advantage of showing a linear change in compliance with crack length [
4], this only makes them effective in situations where it is not practical or desirable to measure crack lengths while carrying out the test. However, even though Blackman et al. [
5] showed that the values of
obtained through these tests were independent of the test’s geometry, it is often better to use simpler specimens, and, as a result, DCB tests are commonly preferred. Furthermore, multiple crack independent data reduction schemes have been developed for DCB tests, which further simplifies the use of this configuration [
6], by removing the need to directly monitor crack propagation. Both these tests have been studied since the 1960s and the work of different authors has led to the publication of an ASTM D3433 standard in 1973. Being revised by Blackman et al. [
5] through an inter-laboratory round-robin test programme, this resulted in the publication of BS 7991 in 2001. More recently, due to the increased popularity of fiber-reinforced polymer matrix composites, a new international standard has been published, named ISO 25217 [
2].
On the other hand, only the testing of composites is currently standardised for pure mode II (the in-plane shearing mode) fracture toughness (
) characterisation by means of the end-notched flexure (ENF) test, although this process has been successfully modified for adhesive joint testing. The end-loaded split (ELS) is also proposed and widely used for the determination of mode II fracture toughness [
7,
8],
Figure 2. The most common mode II tests do, however, still have certain limitations.
Under shear loads, especially for ductile adhesives, bonded joints have been reported to have a large fracture process zone (FPZ) compared to mode I or mixed-mode fracture tests and compared to other specimen dimensions, owing to the adhesive layer’s plasticity. The large FPZ involved, along with the lack of crack opening, makes visual evaluation of the crack length difficult. To address this, approaches based on J-integral [
9] or an effective crack length (
) that are non-crack dependent have been developed [
6,
10,
11,
12,
13,
14,
15]. Furthermore, the commonly used end-notched flexure (ENF) test presents instability problems associated with the crack propagating in the direction of the highest flexural moment, so other tests have been developed to avoid this effect, including the tapered ENF (TENF) test, the stabilised ENF (SENF) test, the over-notched flexure (ONF), the four-point ENF (4ENF), or the inverse ELS (I-ELS) [
16] test, among others, to achieve stable propagation. However, other issues arise from these tests, such as challenges with the production of the specimens (TENF), the complexity of the test setup (SENF), or friction-related issues (4ENF and ONF). The end-loaded split tests, in addition to having simpler manufactured specimens, based on DCB specimens, have shown encouraging results in recent studies, such as the advantage of having stable crack propagation under displacement control when the ratio between the initial crack and the span length is higher than 0.55, in composite joints [
12,
17,
18,
19,
20].
Recent research has shown that certain criteria must be met in order to obtain stable crack propagation during an ELS test. First, it is necessary ensure formation of the entire FPZ by reaching steady-state crack propagation and, as a result, the R-curve plateau; second, to ensure the test’s stability under displacement control; third, to avoid significant deflections; and fourth, to avoid adherend failure during testing. The span length (
), initial crack length (
), and, if necessary, height (
) of the ELS specimen geometry must be changed in order to satisfy these requirements [
21,
22].
Contrarily to the strength tests, fracture tests rely heavily on procedures of data reduction to extract from the P- curves the material’s energy release rate, . There are two main types of formulations that can be devised, based either on Linear Elastic Fracture Mechanics (LEFM), i.e., the Compliance-based Beam Method (CBBM), or Non-linear Fracture Mechanics (NLFM), i.e., the J-integral.
Some of the classical LEFM data reduction schemes used to obtain fracture energies [
6,
23], based on the Irwin–Kies equation, are the Compliance Calibration Method (CCM), the Direct Beam Theory (DBT), and the Corrected Beam Theory (CBT), with this last one having the correction factor
, proposed in 1992 by Wang and Williams [
24,
25], to account for the crack tip rotation and deflection.All of these approaches require measuring the crack length, which can be difficult, especially in Mode II and when the crack propagates suddenly. When extensive damage occurs, such as microcracking or fiber bridging, this also becomes a problem [
26]. More recently, the CBBM [
6,
11] approach, based on an equivalent crack length concept, was used to characterise the fracture of bonded joints by developing a data reduction scheme method that took into account the Timoshenko beam theory and the specimen’s compliance. This proposed methodology eliminates the need to measure the crack length during propagation and accounts for FPZ effects, which are especially important in ductile adhesives and mode II loading. Furthermore, this data reduction method can be applied to Mode I [
6], Mode II [
11] and Mixed Mode [
27,
28].
As for the NLFM approaches, the J-integral, whose formulation was developed for elastic materials in the late 60’s by Cherepanov [
29] and Rice [
30], is the most well known and is based on the application of a contour integral. Rice also demonstrated that, as long as the deformation theory of plasticity is used, the J-integral is independent of the contour for any elastic or elasto-plastic material [
31]. As a result, several researchers [
32,
33,
34] were able to use this approach when studying ductile materials. Therefore, the J-integral is only valid in materials with a non-linear stress–strain relation if there is no unloading in any point of the material, implying that the stress–strain relation is non-linear elastic [
35]. Furthermore, the J-integral can be used in all loading modes, including Mode I [
34,
35,
36], Mode II [
33,
37,
38], and Mixed Mode [
39,
40,
41].
Sun and Blackman [
36] employed several methods to obtain the fracture toughness of three distinct adhesives and assessed their applicability in each situation in a Mode I study in which
,
, and the cohesive laws were all simultaneously determined. The authors discovered that for the brittle adhesive and toughened epoxy, all of the
values obtained using the LEFM method agreed with the
values, proving their validity. The
values for a ductile polyurethane adhesive, on the other hand, were 15% higher than the
, values, indicating that the same methods are not valid. Furthermore, the same authors used Digital Image Correlation (DIC) to automate the measurement of crack length and fracture toughness in Mode I with structural adhesives. They discovered that for all three adhesives, the CBBM and the CBT with a crack length extended to the compression zone produced G values very similar to J. More specifically, they found nearly identical values for all CBT cases and one adhesive in CBBM, while the remaining two showed a 6% increase in comparison to the J values.
Although there are several specimens developed to characterise the mechanical behaviour of adhesives to be studied, so far there are no tests that combine more than one loading condition simultaneously. Ultimately, to fully mechanically characterise an adhesive the following is necessary: four specimens, four testing procedures and four data reductions schemes. In addition to having to perform the four tests separately with their specific apparatuses, it is also mandatory to have the knowledge on how to properly manufacture, test and treat the obtained data, making adhesive characterisation a complex, time-consuming and costly procedure for non-specialised personnel.As such, from an industrial point of view, companies could increase their competitiveness by not having to hire third parties for this purpose by performing all tests in house.
With this in mind a novel experimental tool [
42], that sequentially loads a unified specimen in the four previously mentioned loading scenarios in a single test, is being developed at INEGI (Porto, Portugal). This is performed by combining a butt joint for tensile strength, the modified TAST concept for shear strength, the DCB for mode I fracture toughness, and the ELS—for mode II fracture toughness. Other than the novel specimen and apparatus, the goal of this project is to simplify the adhesive characterisation procedure as much as possible in all aspects, manufacturing, testing and data reduction.
Thus, the present work focuses on part of the bigger picture, the development of an intermediate concept, in which both fracture tests required to characterise the adhesive in mode I and mode II can be performed with a single test.
In this manuscript, the fracture component of the unified specimen was numerically tested, combining the DCB test for mode I, and the ELS test for mode II, resulting in the specimen presented in
Figure 3. Due to the combined character of the novel concept, a new mode I test is defined, as a modified DCB (mDCB) test, where the usually solid double cantilever beams are replaced by a solid beam on the bottom and the full-fledged ELS specimen on top, as seen in
Figure 3.
As a result of the significant discrepancy between the cross-head displacements required to have mode I or mode II propagation, and being tested with a specially designed apparatus, mode I and mode II cracks propagate independently and in that order. This enables each test to be analysed separately, considering the whole specimen for mode I, and only the ELS for mode II, since at this stage the mDCB’s bottom bar has completely debonded from the composed specimen.
This work was performed using two structural epoxy adhesives of distinct nature, one being brittle and the other tough, to validate the applicability range of the specimen. Additionally, the study was divided into two steps, starting with the ELS test since it influences the mode I component, and then the mDCB test was analysed as a whole. This was done to isolate each fracture mode and understand their isolated particularities. As such, the ELS specimen geometry was firstly analysed by computing behaviour changes as a function of the specimen’s dimensions and assessing the limitations of this test associated to the existence of a clamp tool. Finally, the study concludes with an analysis of the geometry of the novel modified DCB test, focusing mainly on the influence of the stiffness discontinuity present in the top composed beam (ELS specimen) on the mode I characterisation process, comparing it with the standard DCB test, as a benchmark reference.
As an outcome, several guidelines for the design of this unified specimen for combined mode I and mode II fracture characterisation are proposed, and a custom mode I data reduction method for the mDCB specimens was successfully employed.