Double Cantilever Beam Specimens Research Articles

Propagation rate transients in J-controlled fatigue characterization of adhesives

Fatigue analyses of adhesively bonded composite laminates were conducted to investigate discrepancies in experimentally measured rates of crack propagation in double cantilever beam specimens subjected to increasing or decreasing load histories. A cohesive fatigue damage model that accounts for the quasi-static traction-separation response and bridging was used in a finite element model of the test to identify transient effects caused by the evolution of the process zone in the adhesive, as well as the long-range, low-intensity bridging induced by the knit supporting carrier inside the adhesive. In addition to the quasi-static cohesive properties, the fatigue model requires two parameters that were obtained by fitting the rates of propagation at two experimental data points. The results indicate that the analyses accurately reproduce transient and steady-state rates of propagation observed in the experimental results, as well as the threshold of propagation. Transient rates of propagation consistently exceed those in steady state, which underscores the need to understand transients and account for them in fatigue characterization. The results also highlight that a Paris curve for steady-state propagation can be obtained most quickly using a decreasing load function, but that this curve is an unconservative bound to the rates of propagation. A lateral shift in the Paris curve is proposed for a conservative characterization that removes the effect of bridging and other R-curve effects.

Effect of laser treatment on strength of moisture-degraded epoxy adhesive joints and microscopic observation of treated surface

ABSTRACT We examined the effect of laser processing surface treatment on the mechanical strength of adhesion. In addition to laser processing, double cantilever beam (DCB) and lap joint (LJ) specimens were prepared using an epoxy adhesive on aluminum plates that underwent acid etching, sandblasting, and acetone wiping. The open face method was employed to accelerate moisture degradation, and the tensile-shear strength and energy release rate of the specimens were measured. Laser processing resulted in remarkably high values of the measured energy release rate, even when the adhesive deteriorated. To examine the reason for the high strength, we performed a detailed fracture surface analysis and electron microscopic observation of the adhesive interface. When the interface of the fractured surface was observed, the laser treated surface was densely formed with fine filamentous protrusions that held the adhesive well. These filaments exhibited high oxidation resistance and achieved strong adhesion even when the adhesive and adherend deteriorated because of moisture. The laser treated adherend surface exhibited two strong anchoring effects owing to a significant increase in the surface area and the microfilamentous structure on the surface. However, the type of surface treatment did not have a significant effect on the LJ adhesion strength.

Environmental fatigue crack growth of PV glass/EVA laminates in the melting range

AbstractThe delamination of encapsulants in photovoltaic (PV) modules is a common issue that leads to power loss due to optical losses. Encapsulant debonding is usually examined under monotonic loading conditions subsequent to environmental exposure such as damp heat. Service‐relevant, superimposed environmental‐mechanical fatigue loads are not considered adequately. Hence, the environmental fatigue delamination resistance of thermally toughened double glass laminates with an ethylene vinyl acetate copolymer (EVA) adhesive layer was investigated in this study. Focus was given to the melting range of EVA, in which the non‐crosslinked crystalline phase fraction is already in the partly molten state. Double cantilever beam specimens were tested on an electrodynamic test machine at temperatures of 60, 70, 80, and 90°C and relative humidity (rh) levels of 2%, 30%, 50%, and 80%. The fractured surfaces were characterized by digital microscopy, Fourier transform infrared spectroscopy (FTIR), X‐ray photoelectron spectroscopy (XPS), and differential scanning calorimetry (DSC). The cyclic fatigue tests revealed a decay in delamination resistance at elevated temperature and humidity levels. At 70°C, the delamination resistance was low, regardless of the relative humidity. Most of the laminates failed by debonding. XPS analysis showed a reduction of the C=O and C–O content, along with an increase in Si–O content with increasing relative humidity. For laminates tested at 60 and 70°C, an EVA recrystallization peak was observed in DSC experiments. This peak was shifted to significantly higher temperatures at 80% rh. XPS and DSC indicated local hydrolysis within the porous fracture process zone ahead of the crack tip. Consequently, acetic acid formation led to a decrease in delamination resistance, resulting in lower fatigue threshold values. The investigations confirmed the significant impact of environmental conditions on the fatigue delamination resistance within glass/encapsulant laminates. Notably, acetic acid formation and a significant reduction in delamination properties were observed after around 100 h of environmental fatigue exposure.

Fracture toughness of aged oil paints

The fracture toughness in opening mode GIc for selected oil paints from Mecklenburg's Paint Reference Collection after approximately 30 years of natural ageing was determined using the procedure adopted from the ASTM D5528–13 standard in which double cantilever beam specimens are split in tensile tests. The careful reglueing procedure allowed multiple fracturing tests to be carried out that not only improved statistics of the measurements but also provided insight into the variation of the fracture toughness across the paint film observed for some paints. The latter was due to pigment sedimentation or chemical change of the oil binder as a result of the easier access of oxygen from the side open to the air. For the lead white paint, used over centuries both in paint films and oil grounds, the GIc values more than doubled from 18 to 39 J/m2 for three consecutive cracks formed at an increasing distance from one side of the paint film. The study demonstrated that fracture toughness corresponding to the first crack formation in aged oil paints ranged between 10 and 40 J/m2, relatively low values compared to the animal glue-based ground in paintings. In consequence, oil paints are more vulnerable to crack initiation and growth induced by tensile stress than the ground layer. The measurements filled the gap in the knowledge required for the analysis of fracturing or delamination processes in paintings.

Three-Dimensional Probabilistic Semi-Explicit Cracking Model for Concrete Structures

This paper introduces a three-dimensional (3D) semi-explicit probabilistic numerical model for simulating crack propagation within the framework of the finite element method. The model specifically addresses macrocrack propagation using linear volume elements. The criteria governing the macrocrack propagation is based on the softening behavior observed in concrete under uniaxial tension. This softening behavior corresponds to a dissipated cracking energy that is equal to the mode I critical fracture energy (GIC) used in the Linear Elastic Fracture Mechanics theory (LEFM). The probabilistic nature of this model revolves around the random distribution of two mechanical properties: tensile strength (ft) and fracture energy, which varies based on the volume of finite elements. The scattering of the fracture energy increases as the volume of finite elements decreases in order to consider the strong heterogeneity of the material. This work primarily aims to estimate the relationship between the standard deviation of GIC and the volume of finite elements through the development of the numerical model. For this purpose, an inverse analysis is conducted based on a fracture mechanical test simulation. This test involves macrocrack propagation in a large Double Cantilever Beam (DCB) specimen with a crack length exceeding two meters. The proposed inverse analysis procedure yields highly significant results, indicating that the numerical model effectively evaluates both crack length and crack opening during propagation.

Crack propagation in adhesive bonded 3D printed polyamide: Surface versus bulk patterning of the adherends

The confined build space of 3D printers often necessitates breaking down larger objects into sub-components for efficient printing. Addressing this challenge, related existing research emphasizes the growing adoption of structural adhesives as a key method for joining 3D printed components. In this context, the present study combines finite element modeling, design exploration, and additive manufacturing, to ascertain the role of the adherends’ architecture on the mechanics of crack growth in adhesive bonded 3D printed materials. Finite element simulations and experiments are carried out using Double Cantilever Beam (DCB) specimens comprising epoxy-bonded selective laser sintered polyamide (PA). In particular, the study includes adherends that feature either sub-surface hollow channels of various shapes (bulk patterns) or sinusoidal interfaces with different aspect ratios (surface patterns). The objective is to demonstrate how the proposed patterning strategies not only promote crack shielding and delayed growth but also unlock energy-absorbing processes, such as interfacial void growth and buckling, that are absent in the control joint (i.e., no patterns). Therefore, customizing the architecture of the adjoined layers ultimately results in toughening and enhanced damage tolerance in adhesive joints that comprise 3D printed materials.

Dynamic fracture response of adhesive joints subjected to mode-I impact wedge loading

ABSTRACT This paper aims to examine the behavior of cracked adhesive joints experimentally and numerically when they are subjected to quasi-static and dynamic loads using the tensile and falling-wedge impact tests, respectively. Double cantilever beam (DCB) specimens were manufactured and tested under impact loading with varying impact energies to analyze the adhesive joint mode-I dynamic fracture response. To determine quasi-static and dynamic mode-I fracture energies, the compliance-based beam method (CBBM) was utilized accounting for the axial force exerted by the wedge. It was found that by changing the loading condition from quasi-static to impact, the maximum force and fracture energy of adhesively bonded joints were considerably increased by 275% and 452%, respectively. However, within the impact test conditions, increases of 10% and 22% were obtained in maximum force and fracture energy when the impact energy was tripled. The adhesive joints tested under static loading experienced a mixed interfacial/cohesive failure pattern, whereas by shifting the loading condition to impact, the failure pattern turned fully cohesive. The quasi-static and dynamic fracture responses of adhesive joints were modeled using the cohesive zone model employing a triangular traction-separation law. The numerical and experimental results exhibited reasonable correlation.

Effects of carbon/glass nonwoven interleaving veils and their areal density on opening and shearing mode interlaminar fracture toughness of glass epoxy composites

The study explores the impact of Carbon and Glass nonwoven interleaving veils with varying areal density on delamination resistance in unidirectional (UD) Glass epoxy composites under Opening (Mode-I) and Shearing (Mode-II) mode loadings. Commercially available non-woven Carbon and Glass interleaves with areal densities of 15, 20, 25, and 30 g/m2 were used to manufacture the interleaved Glass epoxy laminates. Double Cantilever Beam (DCB) and End Notch Flexural (ENF) specimens were used to determine the mode-I and mode-II fracture energies. The results reveal that, during mode-I initiation, interleaved laminates exhibit a lower interlaminar fracture toughness (IFT) except for the Carbon fiber interleaved laminates of areal density 30 g/m2. However, during propagation, all veils interleaved laminates presented significant improvement in IFT ranging from 5 to 25 % accompanied by substantial fiber bridging. In case of mode-II test, the laminates with Carbon and Glass veils exhibit enhanced IFT (60–182 %) with increasing areal density compared with the non-interleaved Glass laminates. Optical and scanning electron micrographs (SEM) provide evidence of fracture mechanisms involved in the interleaved and non-interleaved composite laminates.

The effect of abrading treatment method on the bonding surface characteristics and fracture behavior of glass fiber-epoxy composite adhesive joints

The effect of the mechanical abrading method on the bonding surface characteristics and fracture response of glass fiber-reinforced polymer (GFRP) composite adhesively bonded joints was investigated. Double cantilever beam specimens were manufactured by bonding GFRP substrates with an epoxy adhesive to evaluate the mode-I adhesive joint fracture response. The bonding surfaces were treated with degreasing and abrading methods utilizing sandpapers with various grit sizes ranging from P60 to P800. The results showed that the sandpaper grit size can considerably change the bonding surface properties comprising the surface energy, roughness, morphology, and water drop contact angle and consequently, it can affect the joint fracture behavior. Reducing the sandpaper grit size continuously increased the surface roughness but there were optimum values for the surface energy and water drop contact angle. The fracture resistance of adhesive joints followed the trend of bonding surface energy as the higher the bonding surface energy, the higher the joint fracture resistance. The fracture energy and load-bearing capacity of adhesive joints were improved by 62 and 34%, respectively, when the joint bonding surfaces were abraded with P240. However, further reducing the sandpaper grit size to P60 caused a decrease in the fracture energy and load-bearing capacity of adhesive joints by 18 and 44%, respectively, compared to the joint with degreased and non-abraded bonding surfaces. Moreover, the abrading method considerably changed the microscopic and macroscopic failure modes of adhesive joints.

Cohesive Properties of Bimaterial Interfaces in Semiconductors: Experimental Study and Numerical Simulation Using an Inverse Cohesive Contact Approach.

Examining crack propagation at the interface of bimaterial components under various conditions is essential for improving the reliability of semiconductor designs. However, the fracture behavior of bimaterial interfaces has been relatively underexplored in the literature, particularly in terms of numerical predictions. Numerical simulations offer vital insights into the evolution of interfacial damage and stress distribution in wafers, showcasing their dependence on material properties. The lack of knowledge about specific interfaces poses a significant obstacle to the development of new products and necessitates active remediation for further progress. The objective of this paper is twofold: firstly, to experimentally investigate the behavior of bimaterial interfaces commonly found in semiconductors under quasi-static loading conditions, and secondly, to determine their respective interfacial cohesive properties using an inverse cohesive zone modeling approach. For this purpose, double cantilever beam specimens were manufactured that allow Mode I static fracture analysis of the interfaces. A compliance-based method was used to obtain the crack size during the tests and the Mode I energy release rate (GIc). Experimental results were utilized to simulate the behavior of different interfaces under specific test conditions in Abaqus. The simulation aimed to extract the interfacial cohesive contact properties of the studied bimaterial interfaces. These properties enable designers to predict the strength of the interfaces, particularly under Mode I loading conditions. To this extent, the cohesive zone modeling (CZM) assisted in defining the behavior of the damage propagation through the bimaterial interfaces. As a result, for the silicon-epoxy molding compound (EMC) interface, the results for maximum strength and GIc are, respectively, 26 MPa and 0.05 N/mm. The second interface tested consisted of polyimide and silicon oxide between the silicon and EMC layers, and the results obtained are 21.5 MPa for the maximum tensile strength and 0.02 N/mm for GIc. This study's findings aid in predicting and mitigating failure modes in the studied chip packaging. The insights offer directions for future research, focusing on enhancing material properties and exploring the impact of manufacturing parameters and temperature conditions on delamination in multilayer semiconductors.

Determination of the Probabilistic Properties of the Critical Fracture Energy of Concrete Integrating Scale Effect Aspects

This paper presents an extension of the validation domain of a previously validated three-dimensional probabilistic semi-explicit cracking numerical model, which was initially validated for a specific concrete mix design. This model is implemented in a finite element code. The primary objective of this study is to propose a function that enables the estimation of the critical fracture energy parameter utilized in the model and validate its effectiveness for various concrete mix designs. The model focuses on macrocrack propagation and introduces significant aspects such as employing volume elements for simulating macrocrack propagation and incorporating two key factors in governing its behavior. Firstly, macrocrack initiation is linked to the uniaxial tensile strength (ft). Secondly, macrocrack propagation is influenced by a post-cracking dissipation energy in tension. This energy is taken equal to the mode I critical fracture energy (GIC) based on the linear elastic fracture mechanics theory. Importantly, both ft and GIC are probabilistic properties influenced by the volume of concrete under consideration. Consequently, in the numerical model, they are dependent on the volume of the finite elements employed. To achieve this objective, numerical simulations of fracture mechanical tests are conducted on a large double cantilever beam specimen. Through these simulations, we validate the proposed function, which is a crucial step towards expanding the model’s applicability to all concrete mix designs.

INFLUENCE OF PLY ORIENTATION ON INTERLAMINAR FRACTURE TOUGHNESS OF CARBON/EPOXY COMPOSITES

Delamination is a concern for the structural integrity of fiber-reinforced polymer composite structures. The decisive material parameter for delamination is fracture toughness (G<sub>Ic</sub>). The main objective of this study was to investigate the in-plane, quasi-static fracture toughness (both initiation and propagation) of two laminate composites. Both composites contain carbon fibers in an epoxy matrix. The tests were performed using double cantilever beam specimens with different ply orientations according to ASTM standards. The effect of ply orientation was evaluated using data reduction methods to obtain fracture toughness. The experiments revealed that the ply sequence changed the crack propagation mechanism, increasing the initiation and propagation fracture toughness values for 90/90 layup during mode I interlaminar tests, by 80% and 69%, respectively. In addition, the mode I fracture toughness increased by 40% after 50 mm crack extension.

Mode I fracture behavior of glass fiber composite-steel bonded interface – Experiments and CZM

Debonding is characterized as the governing failure mode in the innovative wrapped composite joints made with glass fiber composite material wrapped around steel hollow sections without welding. The prerequisite for predicting debonding failure of wrapped composite joints is to obtain fracture behavior of the composite-steel bonded interface. The mode I fracture behavior of the bonded interface was experimentally investigated using glass fiber composite-steel double cantilever beam (DCB) specimens. The crack length a and the crack tip opening displacement (CTOD) during the test were accurately measured by analyzing the digital image correlation (DIC) data while the strain energy release rate (SERR) was calculated through the extended global method (EGM). The cohesive zone modeling (CZM) was utilized in the finite element model with the proposal of a four-linear traction-separation law to simulate the mode I fracture process. An approach is introduced to determine the critical stages of the proposed four-linear cohesive law by combining accurate measurements of crack length a and CTOD, along with SERR values. The validity of the four-linear cohesive law and the introduced approach to determine the critical stages were confirmed by good agreement in both global and local behavior between the testing and the FEA results.

Cohesive Zone Modeling of the Interface Fracture in Full-Thermoplastic Hybrid Composites for Lightweight Application.

With the increasing demand for lightweight and high-performance materials in the automotive and aerospace industries, full-thermoplastic hybrid composites have emerged as a pivotal solution, offering enhanced mechanical properties and design flexibility. This work aims to numerically model the fracture strength in full-thermoplastic hybrid composites made by forming and overmolding organosheets. The mode I fracture was investigated by modeling the behavior of T-joint specimens under a tensile test following the cohesive zone modeling (CZM) approach. The sample was designed to replicate the connection between the laminate and the overmolded part. Double cantilever beam (DCB) specimens were manufactured with organosheets and tested to mode I opening to determine the interlaminar fracture toughness. The fracture toughness out of the mode I test with DCB specimens was used to define the CZM parameters that describe the traction-separation law. Later, due to the particular geometry of the T-join specimens that under tensile load work close to pure mode I, the cohesive parameters were determined by inverse analysis, i.e., calibrating the theoretical models to match experimental results. The fracture resistance T-joint specimens appeared dependent on the fiber-bridging phenomenon during the delamination. In particular, the presence of fiber-bridging visible from the experimental results has been replicated by virtual analyses, and it is observed that it leads to a higher energy value before the interface's complete breakage. Moreover, a correspondence between the mode I fracture toughness of the DCB specimen and T-joint specimens was observed.

Resistance-welded thermoset composites: A Bayesian approach to process optimisation for improved fracture toughness

Joining thermoset composites via resistance welding offers a novel highly efficient assembly method for next-generation aerospace structures. Resistance-welded joints combine the benefits of bonding with the capacity for high-volume manufacturing rates and eliminate the need for complex surface preparation. The influence of key welding parameters on the joint performance is investigated by assessing the Mode I fracture toughness. Double Cantilever Beam specimens with different welding parameter combinations are manufactured, tested and compared with each other. Thermoset laminates are made weldable by co-curing a chemically compatible thermoplastic film with an uncured thermoset laminate. A Bayesian approach is used to study the correlation between processing parameters and to select parameters yielding high performance by training a Gaussian process emulator. Observed Mode I fracture toughness values are comparable to high-performance thermoplastic composites. This is equivalent to an improvement of approximately 290% in Mode I fracture toughness when compared to a co-cured thermoset joint.

Fracture prediction of solder joints using two-parameter fracture mechanics

Two-parameter fracture mechanics theory is a novel approach to investigate the fracture behavior of solder joints. The present study showed that the single-parameter fracture mechanics was not valid for evaluating the fracture behavior of these joints. Therefore, the ability of the two-parameter (J-Q) fracture mechanics method was assessed. J (critical strain energy release rate) and Q (The constraint parameter) parameters were calculated for the double cantilever beam (DCB) specimens. The two-parameter fracture mechanics theory was observed to be valid for the DCB specimens examined in this research. The J-Q loci extracted from two distinct experimental data sets (adherend thickness and loading arm variation) were coincident. The overlap of two J-Q locus curves indicates the uniqueness of the J-Q locus and capability to predict fracture load.

Numerical modelling of the mode I fracture behavior in composite laminates with significant R-curve effect

Significant R-curve effect is very common in the mode I fracture of composite laminates. Accurate simulation of fracture with R-curve effect is important for damage tolerance design of composite structures. However, traditional numerical methods usually do not consider the R-curve effect. In this work, four methods, including three phenomenological methods and cohesive zone model with multi-linear constitutive relation are presented. The three phenomenological methods are based on bilinear cohesive zone model, virtual crack closure technique and extended finite element method respectively with the consideration of R-curve. It is interesting to know which method is more suitable for modelling delamination growth with significant R-curve effect. To achieve this goal, double cantilever beam specimen is modeled and delamination growth is simulated using above four methods. Comparisons between the numerical results and the experimental results of laminates with different material types and stack sequences are made for these methods. Finally, the accuracy, computational efficiency and parameter acquisition of these methods are discussed with the goal of finding a suitable method for delamination modelling in laminated composites. It is shown that the cohesive zone model with multi-linear constitutive relation shows good accuracy in all studied cases.

On the Cover: A Composite Rigid Double Cantilever Beam Specimen for Assessing the Traction–Separation Response of Mode I Delamination in Composite Laminates

On the Cover: A Composite Rigid Double Cantilever Beam Specimen for Assessing the Traction–Separation Response of Mode I Delamination in Composite Laminates

Experimental and numerical investigation on the mode I and mode II interlaminar fracture toughness of nitrogen-doped reduced graphene oxide reinforced composites

An experimentaland computational study is carried out to investigate the toughening effect of nitrogen-doped reduced graphene-oxide particles (ND-RGOP) in mode I and mode II delamination of carbon fiber/epoxy laminates. For mode I, both delamination initiation and propagation toughness are enhanced by 126.3% and 119.3% with 0.8 ND-RGOP addition. In addition to mode I toughness enhancement, ND-RGOP reinforcement also increases mode II toughness. The highest mode II delamination toughness value was obtained in 0.4ND-RGOP laminates with an increase of 45.6% compared to neat laminates. However, as seen in the bending tests, the maximum force of the end notch bending (ENF) specimens with 0.8 ND-RGOP added is not lower than that of neat laminates. The interlaminar fracture toughness is high due to the rough path of delamination with ND-RGOP addition, which is also observed by FESEM images of the delamination surfaces. In addition to the experiments, a cohesive zone model with parametric traction stress value was prepared in ABAQUS/CAE to obtain the critical traction stresses in the delamination of laminates. The critical normal traction stress of double cantilever beam (DCB) specimens is increased by over 20% with the addition of ND-RGOP. Besides, the critical interlaminar shear stress in mode II delamination for ENF samples is significantly improved.

On adhesively bonded joints with a mixed failure mode—An experimental and numerical study

Cohesive zone model (CZM) has been extensively used to study interfacial failure behaviors such as fracture of adhesively bonded joints (ABJs). Accurate and efficient identification of traction–separation law (TSL) in CZM signifies an important issue for design and analysis of adhesive structures. In this study, a modified Arcan fixture was developed and employed to investigate the mixed mode failure behaviors of ABJs for carbon fiber reinforced plastic (CFRP) substrates under a tensile-shear coupling load, in which the double cantilever beam (DCB) test was carried out to characterize fracture toughness for benchmark data. With the help of digital image correlation (DIC) technique, the interfacial displacement field was obtained. The virtual crack closure technique (VCCT) was adopted to decouple the mode mixture at different tension-shear angles of the Arcan specimens. Based on the traction–separation law for each mixed ratio of failure mode, a refined CZM was established. In this study, the Arcan and DCB specimens bonded with a flexible adhesive of 3M DP190 were prepared and tested. The experiments were carried out for the ABJs with two adhesive layer thicknesses of 0.3 mm and 1 mm, respectively, to investigate the influence of bonding thickness. Based on the extracted CZM parameters, a finite element (FE) analysis model was developed and validated with the experimental results. Unlike the traditional predetermined damage evolution law, a new CZM was established without a priori cohesive damage evolution; and the effectiveness of the proposed model for the TSL extraction was verified. By using this method, the mechanical response of the bonding interface under complex stress state was well predicted and the FE modeling of ABJ’s fracture was accurately achieved. The study is anticipated to gain new understanding and fundamental data on mixed failure mode, thereby enabling better design of ABJs for engineering applications.