On different 3D printing methods and fracture performance in DCB composite specimens including structured interfaces

Theoretical and Applied Fracture Mechanics 122 (2022) 103552 Available online 8 September 2022 0167-8442/© 2022 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/bync-nd/4.0/). Contents lists available at ScienceDirect Theoretical and Applied Fracture Mechanics journal homepage: www.elsevier.com/locate/tafmec On different 3D printing methods and fracture performance in DCB composite specimens including structured interfaces M.T. Aranda∗, J. Reinoso, I.G. García Departamento de Mecánica de Medios Continuos y Teoría de Estructuras, Escuela Técnica Superior de Ingeniería, Universidad de Sevilla, Camino de los Descubrimienos s/n, 41092 Sevilla, Spain ARTICLE INFO Keywords: Biomimetic interfaces Structured interfaces 3D printing Fracture toughness Composite materials ABSTRACT This work experimentally analyzes the influence of the printing direction on the fracture resistance capabilities of composite specimens incorporating structured interfaces in their geometrical definition. In particular, we compare horizontal and vertical direction fiber deposition using 3D printing capabilities in order to identify the best scenarios that maximize the corresponding fracture performances. For this purpose, DCB specimens including improved structured interfaces designed with fiber in the profile region of the specimen are produced. These designs were created using 3D printing in long fiber composites. Experimental evidences reveal a remarkable increase in fracture toughness in structured interface profiles printed in the vertical direction compared to structured interface profiles printed in the horizontal direction, specifically 217% for the best configuration and 118% for the most unfavorable configuration. Present results show the potential benefits for the generation of novel design concepts with improvements in fracture resistance capabilities, fostering new perspectives in the definition of composite structures. 1. Introduction Natural resources such as bone, wood, and shells aided the technological development of humanity in its early stages. As history advanced, these materials were gradually replaced with synthetic compounds with improved mechanical performances. Nowadays, scientists are inspired by the distinctive qualities of the complex designs of natural structures, which can be lightweight and offer combinations of mechanical properties that often overcome those of their components. Hence, natural organisms provide a rich source of inspiration for novel ideas. They allow us to benefit from the vast number and diversity of solutions that have been perfected over millions of years of evolution. Specifically, they arrest crack propagation and prevent catastrophic failure [1–4]. Although mimicking the properties of natural material is a complex process, the first steps in characterization, modeling, and manufacturing have been taken. Such progress is encouraging the growing conviction that highly damage-tolerant bioinspired structures can be designed and manufactured [5]. For instance, biological structural materials often combine stiff and soft components in hierarchical structures (Fig. 1(a)). In particular, in this search for optimization of the response of different engineering components, the study of the material of nacre can be highlighted [6,7], where interfaces with complex geometries provide a preferred path for ∗Corresponding author. E-mail address: [email protected] (M.T. Aranda). crack deflection, thus contributing to the increase in fracture resistance (Fig. 1(b)). In this respect, a prospective route for further research would comprise the exploitation of so-called structured interfaces. In particular, this concept is referred to the idea of non-planar interfaces with structural patterns (structured interfaces) in contrast to standard flat interfaces. This idea generally stems from nature observation, so they are also known as biomimetic interfaces [8,9]. Additive manufacturing is a promising new technology to meet this challenge since provides a fast, accurate, and repeatable way to fabricate the biomimetic designs, (Fig. 1(c)). As an example of the high impact and applicability of these concepts, in the recent literature, find bio-inspired designs with 3D printing: interlocking suture materials including the friction and contact [15], bone-shaped 3D structures with a ‘‘brick and structure mortar’’ that creates high fracture toughness [16,17], mechanics of suture-shaped joints that connect more rigid components (containing triangular, rectangular, trapezoidal, etc.), hierarchical and fractal interfaces, the influence of the geometry of the shape of wave and its length parameters (such as amplitude and wavelength, among others) [12,18,19]. In this context, the works of Zavattieri using interface designs are remarkable. Sinusoidal in adhesive joints [18] by using cohesive elements to predict the fracture mechanism or the development of fracture processes in helical or https://doi.org/10.1016/j.tafmec.2022.103552 Received 23 May 2022; Received in revised form 28 July 2022; Accepted 22 August 2022 Theoretical and Applied Fracture Mechanics 122 (2022) 103552 2 M.T. Aranda et al. Fig. 1. (a) Transmission electron microscope cross-section image of the woodpecker’s beak at different length scales (Adapted from [10]), (b) Internal structure of the nacre and numerical analysis (Adapted from [7]) and (c) A jig-saw-like interface laser engraved glass specimen (Adapted from [11]), sinusoidal DCB interface in a metal specimen (Adapted from [12]) and 3D printed samples with interlocking suture (Adapted from [13]). (d) Illustration of an undesirable response attributed to the printing process. Crack growth migrates to the adjacent region of the specimens. Schematic of material used into the profile, showing the incapability of employing fibers into the structured profile [14]. Bouligand structures. Lastly, as this proposal is more geared towards technology transfer, it is mentionable that many of these investigations have given rise to numerous patents that are capable of being industrially implemented and commercialized [20]. However, the vast majority of these works have been fundamentally oriented towards the analysis of metallic alloys [12,21] or polymeric materials such as nylon fibers [22] and ABS materials [23–25]. Within the context of composite materials, only a very limited number of investigations have focused on the production of composite components, including specimens with biomimetic interfaces. Specifically, as has been amply reported in the related literature, composites exhibit excellent capacities in terms of specific stiffness and resistance. This has promoted that their incorporation in different engineering applications has experimented an extraordinary increase in the last decades. Composite materials have been used extensively in strategic and highly technological sectors such as aeronautical, space, automotive, and energy (with particular prevalence in the development of renewable energies). Motivated by this technological impact, continuous research efforts have been performed for the development of increasingly efficient structures, minimizing the required structural weights and consequently reducing the corresponding ecological impact in terms of fuel consumption or optimizing the structural response to the appearance of damage phenomena. In fact, the interfaces are mainly designed for shear load transfer and have been analyzed by different authors, see e.g. [26–29]. However, the interface could transfer tensile load in certain joint configurations, such as the run-out in the aeronautical sector. In these regions of stringer-skin joints, the interface is mainly subjected to tensile load, thus the design has to focus on avoiding peeling and debonding risks for these aircraft components, see e.g. [30–35]. From a manufacturing perspective, current processes for the production of composite structures of long fibers are mainly limited in their dimensions and in their global automation for the use of the autoclave in its curing process. Although there have been advances aimed at eliminating the autoclave as a necessary element through various techniques [36,37], currently its use is widespread. In light of the previous arguments, the principal idea behind the use of structured interfaces introduced in this section might foster a new paradigm in the conception of the structural joints in engineering composite structures. Furthermore, these developments might lead to the proper exploitation of the load bearing capabilities mentioned above, with significant economic, environmental and societal impact. Research activities on this matter have been originally carried out at the Group of Elasticity and Strength of Materials (GERM) of the Universidad de Sevilla (US) in the use of manufacturing procedures based on 3D printing techniques. A first action in this direction was performed by Justo et al. [38], where an exhaustive characterization analysis of the different mechanical properties in terms of stiffness and resistance of various specimens manufactured by such procedures was Theoretical and Applied Fracture Mechanics 122 (2022) 103552 3 M.T. Aranda et al. Fig. 2. Comparison of printing direction for specimens including structured interfaces which could provide a preferred crack path. (a) Schematic of the specimen manufactured in horizontal direction defined in [14]. (b) Schematic of the specimen under study designed in vertical direction. Improved design with fiber around the structured profile. Fig. 3. (a) Double cantilever beam (DCB) with a flat interface of length 𝐿, thickness ℎ, width 𝑊and pre-crack length 𝑎0. (b) DCB with trapezoidal interface of parameters 𝐴, amplitude, and 𝑙, wavelength. Distance between the left end of the beam and the applied displacement point is represented by b. (c) Magnified view of trapezoidal interface. The actual crack length measured from the initial point (0;0) is 𝑎𝑠. The projection of the crack length 𝑎𝑠along the 𝑥-axis is 𝑎𝑥and the angle of the leaning section is 𝛼= tan−1 4𝐴 𝛼. (d) Zoom view of material used. carried out. Justo et al. [38] showed that in the current state of the art, specimens obtained by 3D printing are not competitive, in relation to their mechanical properties with those produced in an autoclave, thus inviting significant improvements in current technical capabilities. Subsequently, a detailed research from experimental, analytical and numerical points of view in relation to the mechanical behavior of composite specimens manufactured with 3D printing including structured interfaces with trapezoidal patterns (see Fig. 1(d)) was performed by García-Guzmán et al. [14]. Promising perspectives emanate from this study, where every structured configuration increased the fracture energy with respect to the reference straight interface in the debonding process, see Fig. 1(d). Special attention was given to various aspects that emerged of crucial importance, such as: (i) the definition of a reliable fabrication procedure for the fabrication of DCB specimens of composite materials for subsequent testing, including structured interfaces. (ii) the identification of the geometric definition of such interfaces, which corresponds to the most advantageous scenario in terms of fracture resistance, using the 𝐴∕𝜆(amplitude/wavelength of the structured pattern), see Fig. 3. However, relying on the main conclusions drawn by García-Guzmán et al. [14], Additive Layer Manufacturing (ALM) production capabilities showed notable manufacturing drawbacks. The most important aspect was related to the impossibility of using fibers into the structured profile region of the specimen due to the printing direction parameter, see Fig. 1(d). This limitation could induce less fracture toughness in such regions and on some occasions cause undesirable results, e.g. crack growth could migrate from the interface to the bulk, not being confined to adjacent regions of the specimens. Motivated by these real scenarios, this study aims to improve the current design proposed by García-Guzmán et al. [14]. It is particularly relevant for the ALM technique to evaluate the influence of the printing direction parameter on the fracture resistance capabilities. The comparison between these two configurations (see Fig. 2) will allow to identify the best 3D printing scenarios. Currently, how the processing parameters, such as printing directions, influence the quality of the printed products has received very scarce attention [17,39]. In order to explore the influence of these processing parameters, an experimental campaign based on digital image correlation (DIC) is carried out, evaluating the capability of structured interfaces to address the crack path. In the sequel, the organization of the article is as follows. In Section 2, the specimens design and fabrication procedure are described. The experimental campaign will be presented in Section 3, including a description of the experimental setup, a detailed analysis of the results and their corresponding interpretation. The experimental comparison of fracture capabilities in structured interface printing in vertical direction respect to horizontal direction will be addressed in Section 4. Finally, the main conclusions are summarized in Section 5. 2. Specimen design and fabrication The main goal of this study concerns the exploration of alternative designs for specimens including interfaces with structural profiles (Fig. 2). For that purpose, this section discusses the design considerations regarding the definition of specimens in the vertical direction, which will then be compared to specimens manufactured in the horizontal direction as established by García-Guzmán et al. [14]. Theoretical and Applied Fracture Mechanics 122 (2022) 103552 4 M.T. Aranda et al. Fig. 4. 3D view of types of specimen design studied with the different interface configurations: (a) flat interface, (b) structured interface, 𝑡1(𝜆=8 mm, A =2 mm), (c) structured interface, 𝑡2(𝜆=6 mm, A =2 mm) and structure interface 𝑡3(𝜆=4 mm, A=2 mm). According to the specifications [40,41], a schematic definition of the bonded double cantilever beam (DCB) specimen employed in this study is represented in Fig. 3(a) for flat interfaces and Fig. 3(b) for structured interfaces. Both specimen types consisted of two laminates bonded by an intermediate very thin adhesive layer with identical overall dimensions: length, 𝐿= 169 mm, width, 𝑊=25 mm, thickness, 𝑡=4.8 mm, and the same initial crack tip position, which is located at a distance, 𝑎0=40 mm, from the left side of the beams where the load is applied. Note that the beam thickness, 𝑡, used in the experiments are limited to the minimum thickness for which it is possible to print fibers around the contour of the structured interfaces. Fig. 2(b) shows the direction under study, which was set with the material deposition along the width direction of the specimen (referred to as printing in vertical direction), which located the longitudinal axis (L) and the thickness axis (t) of the specimen on the printing bed. The main advantage of setting the vertical direction as the printing direction is that the structured profile could be manufactured using fiberglass, i.e. the reinforced fiber may reach the contour of the structured interface (Fig. 2(b)). This led to an innovative design of structured interfaces of in DCB-type composite specimens in comparison to those described in [14] where reinforcing fibers could not reach the region of the structured profile (Fig. 2(a)). These limitations stemmed from the specifications of the 3D printing system, requiring a minimum area equal to 6.45 cm2to use fiber-reinforced material within a layer during the manufacturing process. The layers of the trapezoidal interface consisted of small rectangles whose areas were smaller than this threshold value. Details of the structured interface are shown in Fig. 3(c). Among the differing patterning options, García-Guzmán et al. [14] showed that trapezoidal profiles can provide an excellent compromise between fracture resistance and geometric tolerance using the production capabilities aforementioned. Consequently, the geometric considerations of the patterned interfaces were designed following the guidelines of the best scenarios discussed by García-Guzmán et al. [14] setting: three different wavelengths (𝜆=4,6,8 mm) and an amplitude of the pattern (A =2 mm) were determined. This leads to the structured configurations: i) t1(𝜆=8 mm, A =2 mm), t2(𝜆=6 mm, A =2 mm) and t3(𝜆=4 mm, A =2 mm). A sketch of the different designs used is presented in Fig. 4. The identical overall dimensions were employed with flat interface specimens, in order to guarantee a similar bending stiffness with respect to the patterned specimens. Another improvement of the new design was the generation of the initial crack. The precrack in [14] was previously produced as a notch during the printing, resulting in artificially higher values of peak load. In order to avoid some of these defects and to guarantee an initial crack length (a0) in line with standard DCB specimens, a non-adhesive film was inserted along the first 40 mm of each beam during the joining process, generating a non-adhesion zone (Fig. 16). This film was 20 μm Table 1 Measurements of Width, length and thickness for the produced DCB specimens with trapezoidal interface profiles employed in the experimental campaign. Name W1W2W3t1t2t3L p125.17 25.1 25.1 10.2 10.1 10.17 169.6 p225.05 25.05 25.01 9.55 9.45 9.71 169.52 p325 25.1 25.1 9.9 9.9 9.9 169.6 p425.12 25.19 25.02 10.15 10.07 10.2 169.5 p525.15 25 24.98 10.07 9.91 9.75 169.3 t1−1 25 25.1 25.1 9.92 10.1 10.1 169.5 t1−2 25.02 25.1 24.94 10 9.99 10 169 t1−3 25.2 25.3 25.4 10.1 10.4 10.6 169.6 t1−4 24.97 24.96 24.99 10.1 10.05 10.2 169.57 t1−5 25.1 25.1 25.1 10.2 10.3 10.44 169.4 t1−6 25.1 25.08 25 10.3 10.2 10.3 169.3 t2−1 25 25 25.1 10.15 10.7 10.77 169.7 t2−2 25.1 25.06 25 10.18 10.3 10.3 169.5 t2−3 24.94 25.17 25.1 9.61 10 10.1 169.5 t2−4 25 25 25.1 10.1 10.2 10.44 169.5 t2−5 25.09 25.1 25 10.8 10.44 10.29 169.4 t3−1 25.17 25.12 25.2 10.23 10.49 10.43 169.9 t3−2 25.15 25.24 25.1 9.9 10 10.2 169.4 t3−3 25.1 25.1 25.1 10.1 10 10 169.3 t3−4 25.1 25.1 25.1 10.1 10.1 10.1 169.4 t3−5 25.2 25.08 25.1 9.72 10.17 9.94 169.39 in thickness approximately, preventing this zone from being adhered to the epoxy and thus generating a crack once the epoxy was cured. As a result, some defects found in [14] were avoided. The specimens with flat and wavy interface were manufactured via additive manufacturing (AM) using the 3D printing equipment (MarkTwo®3D-printer) which includes the CAD software Eiger®for the definition of the solid model. The composite printer employs Filament Fusion Fabrication (FFF) technology through two printing media: (i) Composite Base filament onyx (composed of micro carbon fiber filled nylon) and (ii) Continuous Fiber Reinforcement (CFR). Particularly, the production of hybrid onyx–fiberglass specimens were considered. The nozzle temperature used for onyx and fiberglass was 265 ◦C and 255 ◦C, respectively. The objectives regarding the use of fiberglass for the current prototypes were twofold: (i) taking advantage of the superior strength and stiffness properties of fiberglass over onyx from a mechanical point of view, (ii) the idealization of a robust design and printing process that allowed the production of DCB coupons incorporating structured interfaces to be carried out within acceptable geometrical tolerances. The mechanical properties of onyx material herein employed are: Elastic modulus 𝐸=2.4 GPa and Poisson’s ratio 𝜈=0.34 and for the fiberglass reinforced material are: 𝐸11 =25.84 GPa; 𝐸22 =1.13 GPa; 𝜈12 =0.37; 𝐺12 =0.88 GPa (obtained experimentally by Justo et al. [38] and Mudarra Acebedo [42] for a laminated direction of 0◦.). Each of the beams that composed the DCB system consisted of 250 layers with 0.1 mm in thickness. The production of hybrid onyx– fiberglass is considered in every layer in the positions illustrated in Fig. 2. The first and last layers of the vertical print were totally produced using onyx to ensure a good surface finish of the external surface of the samples. After machining the specimens, the dimensions and standard deviation values were checked. In this way, the thickness and width of each specimen were carefully measured. Thickness and width were the mean values obtained from three points selected to be representative of the specimen, according to the tolerances recommended in [41], (see Table 1). In addition, measurements using the TR100 surface roughness tester revealed an initial arithmetic mean roughness of R𝑎around 6-8 μm across all the specimens. The two sides of the DCB coupons for each configuration (flat or structured) were manufactured and cleaned in order to eliminate any additional debris and contaminants. Subsequently, the final system Theoretical and Applied Fracture Mechanics 122 (2022) 103552 5 M.T. Aranda et al. Fig. 5. Example of observations through a microscope to measure the adhesive thickness of the specimen. was assembled. For this purpose, the two beams of each DCB coupon were bonded with the adhesive at room temperature. The mechanical properties of the adhesive are: ultimate strength 𝜎u=31.5 MPa, rupture strain 𝜖f=1.76%, Elastic modulus 𝐸= 4.1 GPa. These properties were obtained when the adhesive was strained at 0.1 min−1 after being cured for 45 min at 75 ◦C[43]. The two beams were joined together using zip ties in the middle and on both sides of the specimen, via the induction of low pressure and the proper adhesive thickness. Finally, the samples were cured at room temperature (controlled) for a period of 6 days. The samples were also carefully examined with the aim of determining the adhesive thickness. This thickness ranges from 0.05 mm to 0.1 mm, the smallest thickness corresponding to the oblique region of the structured profile, whereas the largest values correspond to the horizontal sections. This was due to the structured profile of each beam does not fit each other completely. Future developments are planned to improve this aspect (see Fig. 5). According to AITM1-0053 [40] and ISO Central Secretary [41] five samples of each configuration were produced. In total, twenty specimens were manufactured with the structured profiles described above. 3. Experimental campaign 3.1. Experimental set-up In this section, the set-up of the experimental campaign and a detailed description of the tests are outlined. The experimental setup, as shown in Fig. 6, consisted of: (i) a mechanical system to apply tensile loading on the DCB specimen, and (ii) a DIC system to record the specimen during crack growth. Tests were performed using a universal testing machine INSTRON 4482, with a load cell of 5 kN under displacement-control conditions. The loading application was carried out by the adoption of a uniform applied displacement of 1 mm/min during the tests. The current experimental program was executed in an environmentally controlled room at 22 ◦C and 1 atm. Prior to the conduction of the test, auxiliary guiding lines for crack location were marked on both sides of the specimen for the initial and final crack lengths, a𝑖=50 mm and a𝑖+𝑛=110 mm, see Fig. 6. To avoid any influence of the incorporated non-adhesive film, the specimen was preloaded until the crack length exceeds approximately 10 mm from the initial length of the non-adhered region. The crack tip (a𝑖) was then equal to 50 mm from the beginning of the specimen. Then, the sample was completely unloaded. This corresponds to the first loading–unloading in Fig. 7. The position of the crack tip of the precrack on both edges of the specimen was marked and then the specimen was reloaded at a rate of 1 mm/min till the crack reaches the final length mark, a𝑖+𝑛=110 mm. Crack length was monitored during the whole test. After the reloading of specimens, the load decreases as the crack starts to propagate along the interface. The energy released in each configuration is represented by the enclosed area between the part of the curve corresponding to crack growing and the straight lines joining this curve with the origin, these straight lines representing the hypothetical unloading curves, see Fig. 7. The digital image correlation (DIC) technique was also employed during each test to track position of the crack tip. A random speckle pattern was sprayed over the specimen surface, and the corresponding images were acquired before and after the fracture event. Fig. 8 shows the map of the displacement at different stage of the structured (𝑡1−1) interfaces in comparison with the results for flat interfaces. The displacements (Y) were identical between the two configurations until the first stage, when the fracture reaches the first mark. During the second stage, the displacement of the structured interface is more than double of the flat interface. In contrast, as can be observed from the time parameter, the fracture grows more slowly in the structured interface scenario, at around half the rate of the flat interface specimen, due to the complex profile. Fig. 9 depicts the strain map at various stages for structured (t1− 1) and flat interfaces. Before the propagation it can be observed a continuity in strain field across the interfaces, which indicates perfect bonding. Once the crack starts to propagate, it is possible to observe where a discontinuity in the vertical strain field occurred, which allows detecting the crack tip positions in each moment. As can be seen, there is not a significant variation in strain across the specimen in the two configurations. 3.2. Experimental results This section describes the experimental results using the new design of interfaces and the comparison between 3D printed onyx–fiberglass reinforced DCB specimens with flat and trapezoidal interface profiles. The experimental load–displacement curves for four structured patterns with different aspect ratios, amplitude/wavelength =2/8, 2/6, 2/4, 0 (flat) are displayed in Fig. 10. For each interface geometry, five specimens were tested. The curves for structured specimens exhibit similar characteristics to those observed for flat DCBs. It was noticed that the initial slopes for each design were quite close to each other, indicating that such arrangements had similar bending stiffness. It was also observed that the load–displacement curves for structured geometric show periodic ‘‘serrations’’ which are less noticeable for A/𝜆 =1/4. Fig. 11 shows some representative load–displacement curves with the aim to compare the general trend of each configuration. We note that the bending stiffness in the flat specimen curves results higher than that of the structured specimens. For the different cases of structured geometries, the bending stiffness result identical. It also distinguished that critic load value, Pc, increases with increasing A/𝜆. To provide a more performed insight of the crack propagation phases during the tests, Fig. 12 depicts one representative load– displacement curve and the DIC images at different phases for a structured interface 𝜆=8 mm. This evolution curve is distinguished by periodic crests with positive and negative slope regions. A similar behavior is observed for sinusoidal interfaces metallic alloys in [12]. The sketch of the pattern in Fig. 12 shows schematic of the structured interfaces with the periods of slow (red) and fast (blue) crack propagation. In fact, the positive slope regions during the evolution correspond to the stable crack growth along the positive inclined sections (red) and followed by an unstable crack growth (blue) featuring to a drop in the load value of the curve. This means that when the crack reaches the crest, this begins to grow at a much higher rate with respect to the applied displacement, decreasing the load. The crack propagation then slows down, which corresponds to the next crest, and the load begins to increase again following again the cycle. Theoretical and Applied Fracture Mechanics 122 (2022) 103552 6 M.T. Aranda et al. Fig. 6. Close-up photograph of the experimental setup under study. Trapezoidal interface specimen (A/𝜆=2/8 mm) with load blocks. Black marks in the specimen indicate the projection of the actual crack length along the 𝑥-axis in the position 𝑎𝑥1=50 mm and 𝑎𝑥2=110 mm. Specimens were prepared using the DIC procedure, which included spotting with black and white sprays. Due to the thickness of the specimen, the speckle patterns were very small and are not visible in the photo. Fig. 7. Load–displacement curve for structured interface t1(A= 2 mm;𝜆= 8 mm). The filled area represents the energy released during the DCB tests between effective crack lengths of a𝑥1=10 mm and a𝑋2=70 mm. A comparable crack propagation behavior is observed in the other types of configurations, A/𝜆=2/6 and 2/4, as depicted in Figs. 13 and 14, respectively. The structured DCBs induce intermittent crack extension that resemble specific portions of the structured interfaces with stable-unstable behavior. However, it is observed in these types of configurations that the evolution of stable crack growth advances a larger profile distance with increasing A𝜆. The quantification of bonded joint fracture toughness energy for each specimen was carried out by processing the data from the load– displacement curve. In this case, we assumed that this evaluation could be obtained using standard methods that have been widely used on flat DCBs [40,41]. It should be noted that AITM1-0053 [40] was used instead of ISO Central Secretary [41]. The ISO standard bases its calculations on stiffness (analyzing the specimen as a beam), whereas AITM bases its estimates on the area under the curve to calculate the fracture toughness in mode I. The load–displacement curve of a structured interface is characterized by the corresponding peaks (i.e., the crack propagates quickly and it is followed by crack arrests that correspond to small drops in the load value). For this reason, AITM1-0053 [40] is preferable as it would be able to take into account the area under those peaks. In addition, the ISO standard makes some hypotheses to calculate the stiffness, as uniform beam section, which could be not applicable to specimens with structured interfaces. Thus, the AITM standard will be used here and the fracture toughness in Mode I is Theoretical and Applied Fracture Mechanics 122 (2022) 103552 7 M.T. Aranda et al. Fig. 8. DIC representing vertical displacement during crack propagation for structured (t1−1) and flat (p5) interfaces. Theoretical and Applied Fracture Mechanics 122 (2022) 103552 8 M.T. Aranda et al. Fig. 9. DIC representing vertical strain during crack propagation for structured (t1−1) and flat (p5) interfaces. Theoretical and Applied Fracture Mechanics 122 (2022) 103552 9 M.T. Aranda et al. Fig. 10. Experimental load–displacement curves for patterns configurations with different aspect ratios, amplitude/wavelength 0-flat (black), 2/8 (red), 2/6 (green), 2/4 (blue). calculated using the following expression: 𝐺Ic =𝐴 𝑎𝑊 (1) where: •𝐺Ic is the fracture toughness energy in J∕m2, •𝐴is the energy to achieve the total propagated crack length in 𝐽, •𝑎is the propagated crack length (𝑎=𝑎𝑖+𝑛−𝑎𝑖) in mm (final crack length minus initial crack length) and, •𝑊is the width of the specimen in mm. However, DCB specimens with structured interfaces are prone to develop mixed mode fracture conditions at the interface. Accordingly, complying with the premise that energy is exclusively dissipated at the interface and for elastic deformation of the DCB beams, it is necessary to differentiate between two probable essential energy release rate values [12,14]: (i) Considering the energy dissipated during the crack propagation when the crack is extended along the 𝑥-direction, defined by a𝑥in Fig. 3, obtaining the effective or apparent critical energy release rate, 𝐺𝑥 Ic, as follows: 𝐺x Ic = − 𝜕𝛱f(𝑎x) 𝜕(𝑊 𝑎x)(2) where 𝛱𝑓(a𝑥) is the energy dissipated during the crack propagation when the crack grows an area dA𝑓=Wda𝑥. (ii) Alternatively, considering the energy dissipated during the crack propagation when the crack is extended along the S-direction, designed by a𝑠in Fig. 3, obtaining the actual critical energy release rate, 𝐺𝑠 Ic, as follows: 𝐺𝑠 Ic = − 𝜕𝛱𝑓(𝑎𝑠) 𝜕(𝑊 𝑎𝑆)(3) where 𝛱𝑓(a𝑠) is the energy dissipated during the crack propagation when the crack grows an area dA𝑓=Wda𝑠and s-direction is defined as the curvilinear pattern following the crack surface. Particularly, the actual area formed by the crack growth (𝑊× 𝑎𝑠) and its projection on the horizontal plane (𝑊×𝑎𝑥), between two different effective crack lengths (a𝑥1and a𝑥2), were employed to quantify such properties. Thus, for flat interfaces, this distance can be obtained by directly measuring the test specimen 𝑎𝑥=𝑎𝑠. In contrast, for specimens with trapezoidal interfaces, the crack advance (a𝑠) may be defined as a function of interface geometrical parameters and the distance along the horizontal axis (x-axis): 𝑎𝑠=𝑎𝑠(𝑎𝑥,A, 𝜆). The energy released in each configuration is represented by the enclosed area between the experimental curve and the straight lines from the origin to each marker, see Fig. 7. Table 2 represents the effective and actual critical energy release rates, 𝐺𝑥 Ic and 𝐺𝑠 Ic, for the DCBs with trapezoidal and flat interfaces studied. It is observed that for higher A∕𝜆ratios, higher improvements in fracture resistance are obtained with respect to flat interfaces, in