Tapered Double Cantilever Beam Research Articles

Analysis of creep crack growth in bonded joints based on a Paris' law-like approach

Creep crack growth is one of the factors that could affect the durability of a bonded joint and compromise the safety of structures over long periods of time. However, numerical tools and test methods relating to creep crack growth in bonded joints are not widely available yet. In this work, a Creep Crack Growth Model (CCGM) is proposed for adhesively bonded joints. The model describes the relation between the crack growth rate and the energy release rate. The CCGM is fitted with results from Roller Wedge Driven creep crack growth (RWDC) tests and validated against the results obtained from tapered double cantilever beam (TDCB) tests with a constant load applied. Additionally, it is demonstrated that the proposed model can be introduced in a fatigue tool commercially available from the finite element method (FEM) code Abaqus to predict creep crack growth. The FEM results show that the phenomenological expression fitted from experimental tests results, which is used as input for the FEM tool, is reproduced with accuracy. Moreover, it is shown that the CCGM is capable of predicting creep crack growth rates when a different specimen geometry is used, thus demonstrating that the model correctly captures the physics of the problem.

Energy transfer and release during the fracture of UD fiber-reinforced thermoplastic composites

This study delves into the complex dynamics of energy transfer and release during the fracture of unidirectional (UD) fiber-reinforced thermoplastic composites. Conducted through meticulous experimental observations and rigorous energy analysis, the research presents groundbreaking conclusions on the fracture toughness and energy conversion efficiency of UD carbon fiber composites under various loading conditions. A prominent focus is on how these mechanical properties are intricately linked to the sample’s fiber orientation angles and the external conditions applied during testing.The work employed tapered double cantilever beam (TDCB) as the far-field boundary to investigate the energy changes, transfer, and conversion processes during the crack propagation of unidirectional fiber reinforced thermoplastics (UDFRTPs) structures. It was found that throughout the entire propagation process, blunt extension occurs first followed by inertial extension. This is because in the initial stage of crack propagation, the stored elastic energy in the structure is relatively small, making the crack tip prone to blunting. This continuous blunting impedes the release of internal strain energy in the structure, with blunt extension accounting for a very small proportion of the entire fracture process. When the internal strain energy in the structure continues to increase to a certain extent, the blunting of the crack tip cannot prevent the release of a large amount of elastic energy inside the structure. At the same time, the excess released strain energy converts into kinetic energy and continually impacts the blunted region at the crack tip. At this point, the propagation transitions into the inertial extension stage, which occupies a significant portion of the entire fracture process.

Protonated benzimidazole segment induced interfacial limited linear grafting in aramid fiber/epoxy resin interface towards strong and tough composites

To induce both high strength and high toughness advantages while ensuring high interfacial grafting density is the intrinsic conflict in fiber reinforced polymer composite structure design. In this article, utilizing the alkalinity of benzimidazole contained aramid fiber (PBIA), we prepared protonated fiber surface via simple Lewis acid solution soaking to adjust polymerization process of epoxy resin matrix, and accomplished linear interfacial polymerization/grafting limited in composite interface as Atomic Force Microscopy (AFM) confirmed, thus strong and tough interface with high grafting density was obtained. As 1H NMR spectrum confirmed, protonated benzimidazole unit on fiber surface could convert interfacial molecular configuration of composite from crosslinking to linearity, where the linearity configuration dominated interfacial grafting density was also promoted due to their improved surface electron density as Differential Scanning Calorimetry (DSC) and Density Functional Theory (DFT) calculated results revealed. Therefore, ex-situ experiments like Tapered Double-Cantilever Beam (TDCB) tearing test revealed that the protonated benzimidazole segment could highly enhance interfacial tearing toughness (KⅠC) by 33.80%, where the practical interfacial shear strength (IFSS) and interfacial shear toughness (GⅠC) in the composite also respectively increased by 60.16% and 66.56% at maximum, which leaded to the optimization in mechanical strength and toughness of the composite short beam.

Effect of Temperature on the Functionalization Process of Structural Self-Healing Epoxy Resin

This work deals with developing a self-healing resin designed for aeronautical and aerospace applications. The bifunctional epoxy precursor was suitably functionalized to enhance its toughness to realize good compatibilization with a rubber phase dispersed in the hosting epoxy resin. Subsequently, the resulting mixture was loaded with healing molecules. The effect of the temperature on the epoxy precursor’s functionalization process was deeply studied. Fourier trans-former infrared (FT-IR) spectroscopy and dynamic mechanical analyses (DMA) evidenced that the highest temperature (160 °C) allows for obtaining a bigger amount of rubber phase bonded to the matrix. Elastomeric domains of dimensions lower than 500–600 nanometers were found well distributed in the matrix. Self-healing efficiency evaluated with the tapered double cantilever beam (TDCB) method evidenced a healing efficiency for the system functionalized at 160 °C higher than 69% for all the explored fillers. The highest value was detected for the sample with DBA, for which 88% was found. The healing efficiency of the same sample functionalized at 120 °C was found to decrease to the value of 52%. These results evidence the relevant role of the amount and distribution of rubber domains into the resin for improving the resin’s dynamic properties. The adopted strategy allows for optimizing the self-healing performance.

Micromechanical transverse tensile crack propagation of unidirectional fiber reinforced epoxy SMC slice imbedded in a TDCB specimen

A mode-I type of crack propagation and branching on account of fracture energy failure mechanisms methodology is investigated in unidirectional (UD) fiber reinforced epoxy sheet molding compounds (SMC). In order to eliminate the influence of structural boundary conditions with various crack lengths on tip K (stress intensity factor) value to a greatest extent, a tapered double cantilever beam (TDCB) tensile sample is selected as the far-field boundary, the SMC slices with pre-cracks are embedded into TDCB samples, which are referred to as the embedded TDCB (E-TDCB) geometries. By applying the transvers tensile load to E-TDCB, embedded SMC is provided with far-field driving force for crack propagation, so as to obtained a great agreement between stable crack propagation and minor tip K oscillation. Both E-TDCB and dummy TDCB (d-TDCB) samples were selected for experimental test with comparation. The dynamic crack propagation parameters (work components of far-field driving force as well as crack length and Crack tip open displacement et al.) were measured and analyzed with progressive damage criterion. Although in disparate principle, the numerical prediction with proposed constitutive law correlates well with experimental results.

Measurement of the interfacial strain energy release rate of adhesively bonded structures with metallic substrates before and after water ageing

The aim of the presented work is to propagate cracks at interfaces between adhesive joints and metallic substrates and to measure the Strain Energy Release Rate (SERR). In order to propagate at a specific interface and not cohesively, a specific specimen was developed, based on a modification of the Tapered Double Cantilever Beam (TDCB) specimen. In particular, the dimensions of one substrate were reduced to create an asymmetry in the specimen and drive the propagation path towards one interface. The authors present experimental results showing repetitive interfacial failures and a procedure to evaluate the SERR. The non-linear behaviour responsible of non-linear deformation in the substrate was taken into account in the calculations of the SERR. Through a numerical inverse method using Finite Element Analysis (FEA) and Cohezive Zone Modelling (CZM), the SERR was calculated for an epoxy based structural adhesive at the interface with a stainless-steel substrate. Then, the procedure was carried out to measure the interfacial SERR after different ageing times.

Microencapsulated healing agents for an elevated-temperature cured epoxy: Influence of viscosity on healing efficiency

Among many applications, elevated-temperature cured epoxy resins are widely used for high-performance applications especially for structural adhesive and as a matrix for structural composites. This is due to their superior chemical and mechanical properties. The thermosetting nature of epoxy produces a highly cross-linked polymer network during the curing process where the resulting material exhibited excellent properties. However, due to this cross-linked molecular structure, epoxies are also known to be brittle, and once a crack initiated in the material, it is difficult to arrest the crack propagation. Earlier research found that the inclusion of encapsulated healing agents is able to introduce self-healing ability to the room-temperature cured epoxies. The current study investigated the self-healing behaviour of an elevated-temperature cured epoxy, which incorporated the dual-capsule system loaded with diglycidyl-ether of bisphenol-A (DGEBA) resin and mercaptan. The microcapsules were prepared by the in-situ polymerisation method while the fracture toughness and the self-healing capability of the tapered-double-cantilever-beam (TDCB) epoxy specimens were measured under Mode-I fracture toughness testing. We investigated the effect of temperature on viscosity of the healing agents and how these values influence the formation of uniform healing on the fracture surfaces. It was found that incorporation of the dual-capsule self-healing system onto an elevated-temperature cured epoxy slightly changed the fracture toughness of the epoxy as indicated by the Mode-I testing. In the case of thermal healing at 70°C, the self-healing epoxy exhibited a recovery of up to 111% of its original fracture toughness, where a uniform spreading of the healant was observed. The excellent healing behaviour is attributed to the lower viscosity of the healant at higher temperature and the higher glass transition temperature ( Tg) of the produced healant film. The DSC analysis confirmed that the healing process was not contributed by the post-curing of the host epoxy.

Development of a highly efficient extrinsic and autonomous self-healing polymeric system at low and ultra-low temperatures for high-performance applications

There is a growing demand of self-healing materials to overcome the costs derived from repairing and substituting pieces and components due continuous damages. Among the pursued strategies, the development of self-healing systems capable of operate at real low temperatures remains unsolved. In this study, we report the development of an extrinsic self-healing system for composite materials that has demonstrated an efficiency above 100% at low/ultra-low temperatures. This mechanism is based on the Ring-Opening Metathesis Polymerization (ROMP) of a blend of 5-ethylidenenorbornene/dicyclopentadiene (ENB/DCPD) monomers in the presence of ruthenium-based 3rd generation Grubbs’ catalyst (G3). The blend was microencapsulated in formaldehyde-free polyurea vessels and dispersed into three different commercial epoxy resins. Tapered Double Cantilever Beam (TDCB) specimens of the modified resins were manufactured, tested and healed at low/ultra-low temperature conditions completely autonomously. All samples showed high self-healing efficiency, demonstrating the potential incorporation in real composite materials for high performance fields.

A study on the fracture characteristics of tapered double cantilever beams made of heterogeneous composites with adhesive interfaces

In this study, CFRP and aluminum properties were investigated by carrying the static experiment on the shape-dependent bonding structure, and designed tapered double cantilever beam (TDCB) made of heterogeneous composites with the angle of inclination as a variable. The results showed that the maximum reaction force generated was the greatest when the slope angle was 8°. When the specimen is designed using heterogeneous composite materials, the maximum reaction force of the specimen with an inclination angle of 10° is slightly lower than that of a specimen with inclination angle of 8°. However, these results show that it is possible to obtain a design advantage by supplementing the shape. The results of this study can be used as basic data for the safe design of mechanical structures using composite materials and heterogeneous composites.

In situ encapsulation technique for fabrication of self‐healing thermosetting polyurethane with tungsten (VI) chloride

Polymeric composites as materials with special engineering structure and favorable properties are widely used in different industries. The concept of self‐healing in polymers, inspired by biological systems, has been introduced in recent years. Growing applications of thermosetting polyurethanes have also resulted in their extensive use in engineering applications. There are various methods for self‐healing mechanisms, one of which involves microcapsules containing healing agents. Given that the most past research on encapsulation‐based methods carried out for self‐healing epoxy resins, the present work aims to develop the in situ technique and examine the healing efficiency for thermosetting polyurethanes due to their wide variety of applications. To do so, urea–formaldehyde microcapsules, 73 μm in average diameter containing dicylopentadiene as the healing agent, phenylacetylene as the coactivator, and nonylphenol as the dissolution agent were synthesized using in situ polymerization technique. Tungsten (VI) chloride catalyst was used for the implementation of ring‐opening metathesis polymerization. The sizes of microcapsules were measured using optical microscopes, and surface morphology and shell‐wall thickness of microcapsules were examined using FESEM. The healing efficiency was calculated using samples with tapered double‐cantilever beam (TDCB) geometry. Moreover, the impact of adding microcapsules as well as catalyst on mechanical properties of polyurethane resin was studied.

Investigation of the mode I fracture properties of adhesively bonded joints after water ageing

ABSTRACT To investigate the mode I fracture properties of adhesively bonded joints after water ageing, the authors reduced here the width of Tapered Double Cantilever Beam (TDCB) specimens to 5 mm (compared to typical values encountered in literature at 10 mm). This was decided in order to reach the desired water absorption levels within a reasonable time. However, this operation was found to increase the impact of the edge effects on the fracture results, which were illustrated by finite element simulations. Hence, to improve consistency and stability of crack propagation, special beaks were added on the surfaces of the substrates close to the adhesive layer, based on previous solutions implemented for Arcan specimens. The results showed that the fracture energy decreased very rapidly to about half of its initial (unaged) value, and remained almost constant for all water ageing times that were examined in this work (4, 8, and 12 months).

Crack growth mechanism on SGA adhesive joints

The fracture toughness and fracture process of second generation acrylic (SGA) adhesive joints were investigated in detail using tapered double cantilever beam (TDCB) tests. The distribution of granular elastomer with a size of ca. 150 nm in the bulk specimen by transmission electron microscopy (TEM) observation was similar to the distribution of cavitation determined by scanning electron microscopy (SEM) observation of the fracture surface. A mechanism was proposed for the role of the elastomer and acrylic phase in the cohesive failure process of SGA. A dimple, which is evidence of ductile fracture, was observed on the fracture surface. The relationships between the size of dimples, their number and energy release rate were clarified. An understanding of the proposed failure mechanisms is useful for constructing a numerical model for stress analysis and explaining the fracture phenomenon.

The use of tapered double cantilever beam (TDCB) in investigating fracture properties of particles modified epoxy

This study compares fracture energy of an epoxy polymer from the addition of different wt% of nanoparticles, for both experimental and FEA modelling studies. Silica and core–shell rubber (CSR) particles, and the hybrid of both (from 0.5 wt% to the maximum concentration of 25.4 wt%) are used. An increase in fracture energy was found in the CSR and hybrid specimens, but clustering of particles caused a reduction in the mechanical properties when the concentration of particles was high. As there was interfacial failure found with some tapered double cantilever beam (TDCB) specimens. Therefore, the fracture energies measured with TDCB specimens are also compared with simulation results using the finite element analysis software ‘Abaqus’. These results provided further information for the next stage of investigations in fracture properties of particles modified epoxy.

Linear elastic analysis of the loading rate dependency of the fracture properties of structural adhesives in the mixed mode I+II plane

In this paper, the fracture properties of a structural adhesive are investigated via the Tapered Double Cantilever Beam (TDCB) and the Mixed Mode Bending (MMB) tests. The experiments were performed at low to fairly low loading rates. The results were analyzed using Linear Elastic Fracture Mechanics (LEFM). It is shown that the testing speed has considerable impact on the fracture behaviour when close to mode II. Nonetheless, TDCB and MMB Load-Unload tests revealed significant non-linearities. Arcan tests demonstrated the important sensibility of the adhesive material properties to the strain rate. Therefore, the relevance of the LEFM approach is also discussed.

A Study on the Fatigue Fracture for Out-Plane Shear According to TDCB Slope Angle by Using UD CFRP

Weight lightening in transport machines satisfies both internal combustion engines’ performance and efficiency and emission reduction technologies. Weight lightening is a part of ongoing research to increase the range of electric power sources. Carbon fiber reinforced plastics (CFRP) is a lightweight material with the highest specific strength. However, CFRP is used as a metal and dissimilar material in the part because it is vulnerable to the manufacturing process due to by the cracks in internal fiber structures. In this study, the design dimensioning, mechanical strength characteristics, and durability characteristics of tapered double cantilever beam (TDCB) with mode III (Out-plane shear) load according to slope angle using UD CFRP were determined through the adhesive peeling static and fatigue test. Mode III (Out-plane Shear) adhesive peeling static and fatigue tests showed that TDCB specimen has excellent strength and durability of 8° as a result of the mode III adhesive peeling static and fatigue test. The standards and methods used in this study were conducted in accordance with the British industrial standards (BS 7991) and ISO international standards (ISO 11343).

Calibration of nasgro equation for mixed-mode loading using experimental and numerical data

A procedure to calibrate the NASGRO equation in a high yield-strength steel under mixed-mode loading (I + II) is presented. The calibration consists in obtaining the material parameters known as C, m, p and q. The procedure is based on experimental and numerical results. The experimental tests were used to characterize the material and obtain fatigue crack growth data. For the fatigue tests, tapered double cantilever beam (TDCB) specimens with different maximum load and load ratio values were used. Through the numerical analysis, the stress intensity factors, the crack growth direction and the crack path coordinates were calculated. The numerical analysis was performed using XFEM and the maximum energy release rate criterion. The calibrated model allows predicting the number of load cycles with an RMS value of less than 5%, compared with the experimental results.

Toughening effect of nanocomposite-wall microcapsules on the fracture behavior of epoxy

In this research the reinforcing effect of nanocomposite-wall microcapsules on the fracture toughness and fracture energy of epoxy under mode I was studied. The fracture specimens with the geometry of localized tapered double cantilever beam (TDCB) were used to take the advantage of crack length independent-measurement in determining the fracture properties. The crack length investigations were performed experimentally and numerically to extract the calibration parameters and also evaluate the optimal crack length of TDCB specimens. Three types of microcapsules including hollow microcapsule (CH), ethyl phenylacetate core microcapsule (CEPA) and NH2-CNT reinforced-wall microcapsule (CCNT) were synthesized and used as reinforcements. The scanning electron microscopy study of synthesized microcapsules proved the successful presence of CNTs in the shell and on the wall of CCNT microcapsules. The hollow capsule-loaded epoxy composite exhibited enhanced fracture properties as compared to the neat epoxy. Moreover, the SEM study of fracture surface of CH reinforced specimen revealed a characteristic crack tail toughening mechanism. The CEPA microcapsule decreased fracture properties of neat epoxy. The maximum improvement of fracture properties belonged to the specimen containing the CCNT microcapsules. It was observed that the composite-wall microcapsule was able to increase the fracture toughness and fracture energy of neat epoxy by 59% and 165%, respectively, due to the developments of considerable out-of-plane fracture and large plastic deformation.

Fracture envelope estimation of a structural adhesive by dedicated fracture tests

Cohesive zone modelling (CZM) is widespread for the strength analysis of bonded joints. The fracture toughness (GC) is required to use CZM. A scarcely studied mixed-mode test is the Asymmetric Tapered Double-Cantilever Beam (ATDCB), which merges a Tapered Double-Cantilever Beam (TDCB) adherend with a Double-Cantilever Beam (DCB) adherend. This work addresses the ATDCB test to estimate the fracture envelope of a structural adhesive. TDCB and End-Notched Flexure (ENF) tests were also performed to acquire the tensile (GIC) and shear fracture toughness (GIIC), respectively. Numerically, mixed-mode CZM laws were constructed based on the obtained data, and the results were compared with experiments, to validate the CZM laws and the mixed mode propagation criterion. As a result, the best damage propagation criterion for mixed mode was estimated and validated.

Comparative evaluation of different fracture tests for the tensile fracture toughness of a ductile adhesive

The tensile fracture toughness (GIC) and shear fracture toughness (GIIC) are of great importance for both CZM and conventional fracture mechanics. The main objective of this work is to compare the Double-Cantilever Beam (DCB) and Tapered Double-Cantilever Beam (TDCB) tests to obtain GIC of adhesive joints. For both tests, methods that do not need the measurement of the crack length (a) were tested. A CZM analysis was considered to reproduce the experimental load-displacement (P-δ) curves and obtain tensile CZM laws of each tested adhesive, to test the suitability of the data reduction methods and study the effect of the CZM parameters on the outcome of the simulations. It was shown that the data reduction methods for the TDCB test tend to underestimate GIC for ductile adhesives.

Microcapsules of multilayered shell structure synthesized via one-part strategy and their application in self-healing coatings

Abstract The microcapsules of multilayered shells structure loaded with dicyclopentadiene (DCPD) were prepared via one-part strategy in Pickering emulsions stabilized by hydrolyzed poly(glycidyl methacrylate) (PGMA) nanoparticle. The target microcapsules had polyurethane (PU) inner shell layer, phenol-formaldehyde (PF) outer shell layer, and PGMA outermost layer. Meanwhile, in order to compare with the target microcapsules, the microcapsules of double layered shells (Sample 1) were both acquired. Size distribution, morphology, chemical structure and reaction heat of the capsules were studied by particle size analysis, scanning electron microscopy (SEM), fourier transform infrared spectra (FTIR), nuclear magnetic resonance (NMR), and differential scanning calorimetry (DSC). It was found that the ingredients of PF, PU and PGMA were contained in the target microcapsules of multilayered shells, and the encapsulated core materials still kept high chemical reactivity. The resistant properties against thermal and solvent were evaluated by thermogravimetric analysis (TGA) and the solvent immersion test. When the IPDI content was suitable, the multilayered shells microcapsules (Sample 2, 3) possessed excellent thermal and solvent resistances comparing with Sample 1. In addition, the coatings embedded Sample 3 have displayed good self-healing performance by SEM, electrochemical impedance spectroscopy (EIS), salt immersion test and the tensile analysis of tapered double cantilever beam (TDCB) fracture specimens.