Tapered Double Cantilever Beam Research Articles

Modeling of Self‐Healing phenomena in a Polymer matrix within the Framework of the Theory of Porous Media

AbstractIn this work, a multiphase material model will be presented in order to simulate self‐healing effects in a polymer. The material model is developed using the Theory of Porous Media (TPM). In order to describe the damage behavior of the polymer, the well known (1 − D)‐approach is included, and for the description of the healing, a phase change between the liquid like healing agents and the solid healed material is considered. This phase change depends on the amount of catalysts inside the polymer matrix. The applicability of the developed model, in order to describe the time dependency of the healing mechanism, will be shown by a virtual experiment of a self‐healing tapered double cantilever beam (TDCB). (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Fatigue Analysis and Experimental Verification at Tapered Double Cantilever Beam(TDCB) Model of Aluminum Foam

Fatigue Analysis and Experimental Verification at Tapered Double Cantilever Beam(TDCB) Model of Aluminum Foam

Rate dependent behavior of crash-optimized adhesives – Experimental characterization, model development, and simulation

The mechanical properties of crash-optimized adhesive BETAMATE 1496V are characterized over a wide range of strain rates. The information gathered from the mechanical tests are used for developing a fully rate-dependent constitutive law for cohesive interface elements considering both, the strain rate dependency of the initiation stress and the strain rate dependency of the fracture toughness. The model is calibrated and verified against experimental data for tapered double cantilever beam (TDCB) and tapered end notched flexure (TENF) tests. Finally, the model is validated against quasi-static and dynamic experimental results on an adhesively bonded T-joint. The numerical predictions show good correlation with the experimental results.

A Study of Analysis on Fatigue Property at Adhesive Part of Tapered Double Cantilever Beam(TDCB) Model Composed of Aluminum Foam

A Study of Analysis on Fatigue Property at Adhesive Part of Tapered Double Cantilever Beam(TDCB) Model Composed of Aluminum Foam

Autonomous Self‐Healing of Epoxy Thermosets with Thiol‐Isocyanate Chemistry

Thiol‐isocyanate chemistry, combined with a dual capsule strategy, is used for the development of extrinsic self‐healing epoxy materials. It is shown that the amine groups present in the matrix both serve as a catalyst for the addition reaction between a thiol and an isocyanate and as a way to covalently link the healed network structure to the surrounding resin. The tapered double cantilever beam (TDCB) geometry is used for evaluating the recovery of the fracture toughness at room temperature after different healing times. Using manual injection of the healing agents into the crack, a healing efficiency up to 130% is obtained for the EPIKOTE 828/DETA epoxy material. On the other hand, when two types of microcapsules, one containing a tetrathiol reagent and the other a low toxic isocyanate reagent, are incorporated into this epoxy thermoset (20 wt%), a recovery of more than 50% is reached. The influence of parameters such as the amount and core content of the microcapsules on the healing efficiency is investigated. Furthermore, the thiol‐isocyanate chemistry is also tested for an industrial cold‐curing epoxy resin (RIM 135/RIMH 137).

On the experimental mixed-mode failure of adhesively bonded metallic joints

The use of adhesively bonded structures is widespread in various engineering fields, as they provide many advantages over other conventional types of mechanical joints. In this study, we use a crash optimized, single-component epoxy adhesive (SikaPower®-498 made of a rigid epoxy matrix containing soft, tough polymer inclusions that provide additional ductility to the adhesive layer) at a constant layer thickness of 0.5mm to bond metallic substrates. We investigate its fracture properties under mode I and mixed-mode I/II loadings, in order to obtain the full fracture envelope. Mode I loading has been performed using the ISO 25217 standard: the substrates were designed according to the TDCB (Tapered Double Cantilever Beam) geometry, and the fracture toughness GIC has been calculated by means of the ECM (Experimental Compliance Method). Mixed-mode I/II loading has been applied using the MMB (Mixed Mode Bending) experimental fixture described in the ASTM D6671 standard. The fracture toughness GC has been calculated via Finite Element Analysis and mode partitioning has been determined according to the methodology described in the standard. The mixed mode fracture behavior measured using the previous two methodologies shows that the adhesive seems to follow the Benzeggagh–Kenane failure criterion (expressed in 2D).

Fatigue Response of Solvent-Based Self-Healing Smart Materials

We investigated the healing of epoxy resins with embedded ethyl phenylacetate (EPA) solvent loaded capsules and shape memory alloy (SMA) wires under fatigue loading in tapered double cantilever beam (TDCB) mode. Under cyclic loading, the kinetics of solvent diffusion are in competition with the rate of damage propagation. We showed that the active mechanism of self-healing under continuous loading is different from that in quasi-static testing. Crack arrest was observed after some initial crack growth, resulting from the diffusion of EPA solvent into the crack tip, involving local plasticization of the epoxy. Finite element analysis confirmed that the lower modulus and higher elongation at break of the solvated epoxy reduced the stresses at the crack tip. This effect combined with the well-studied microcapsule toughening effect, tremendously increased the toughness of plain epoxy. For epoxy with embedded SMA wires, completely fractured samples, healed using SMA activation, showed similar fatigue resistance as virgin samples. Furthermore, SMA activation during a 10 min break also stabilized crack progression, compared to at least 2 h needed to reach the same effect without SMA wires.

High-strain-rate fracture of adhesively bonded composite joints in DCB and TDCB specimens

Double-cantilever beam (DCB) and tapered double-cantilever beam (TDCB) specimens are the test configurations most commonly used to measure the fracture toughness of composites and adhesive joints. Strain rates of 1 to 18.47 m/s were applied to the test specimens via high-speed hydraulic test equipment. Because the fracture occurs through the adhesively bonded joints and the cracks grow rapidly, the crack length and beam displacement were recorded by a high-speed camera. An energy range from 0 to 10 J was often observed in the high-strain-rate fracture experiments for nonlinear plastic behavior of the dynamically loaded adhesively bonded DCB and TDCB specimens. The range of energy release rates (fracture energy) for TDCB specimen was 2 to 3 times higher than that of a DCB specimen for all high strain rates. The fracture energy of automotive adhesive joints can be estimated using the experimental results in this study for the fracture toughness (GIC) under high rates of loading. The crack grows as the applied fracture energy exceeds the value of the critical energy release rate (GIC) at the crack tip. The energy release rate was calculated using the fracture mechanics formula. The key fracture mechanics parameter, the fracture energy GIC, was ascertained as a function of the test rate and can be used to assess and model the overall joint performance.

Effects of bond gap thickness on the fracture of nano-toughened epoxy adhesive joints

The current work is a combined experimental-numerical study of the fracture behaviour of a nano-toughened, structural epoxy adhesive. The mode I fracture toughness of the adhesive is measured using tapered double-cantilever beam (TDCB) tests with various bond gap thicknesses ranging from 0.25 mm to 2.5 mm. Circumferentially deep-notched tensile specimens are independently employed to measure the cohesive strength of the adhesive as a function of constraint. The experimental TDCB test results are predicted numerically for each bond gap thickness using the Finite Volume method and a Dugdale cohesive zone model. A unique relationship between the fracture energy and the constraint level is established. The effect of bond gap thickness on the fracture behaviour of TDCB joints is hence directly attributed to the variation of the intrinsic fracture energy with constraint and not to the variation of the ‘far field’ plastic zone size with bond gap thickness. Using the well known Rice and Tracey void growth model, a link is established between the voids observed in the fracture process zone, the constraint imposed by the thickness of the adhesive and the resulting fracture energy.

Development of optimized autonomous self-healing systems for epoxy materials based on maleimide chemistry

Maleimide chemistry involving amines and thiols is presented and evaluated for the design of autonomous self-healing epoxy materials. Model reactions show that amines react rapidly with maleimide compounds at room temperature via the Michael addition reaction. Moreover, thiols and maleimides react readily in the presence of tertiary amines that are present in the epoxy material. The maleimide conjugation reaction with residual amines in the epoxy material ensures chemical bonding of the newly formed network with the original materials during crack healing, while in the crack plane, multifunctional thiols react with difunctional maleimides to fill the crack area. Healing efficiencies are evaluated using the tapered double cantilever beam (TDCB) test method with manual injection of the healing agents, revealing a maximum healing efficiency up to 121% for EPON 828 epoxy material. Furthermore, the use of maleimide chemistry has also been evaluated for self-healing applications towards a cold-curing resin that is currently used for infusion of wind turbine blades (RIM resin). While the healing efficiency is strongly dependent on the type of epoxy material, the average maximum peak load for fracture after healing is roughly the same for all tested epoxy materials.

Improving solvent-based self-healing materials through shape memory alloys

Healing of epoxy resins can be accomplished using a combination of embedded ethyl phenylacetate (EPA) solvent loaded capsules and shape memory alloy (SMA) wires. Upon crack formation, the EPA solvent diffuses in the resin and induces swelling which tends to close the crack, while the SMA wires upon heating reduce the crack gap and foster residual epoxy cure. The kinetics of EPA diffusion in the epoxy matrix were measured so as to evaluate the swelling thickness versus time, and concentration at saturation. The largest healable crack gap was found to be 30 μm after 24 h. EPA solvent was shown to lower the curing reaction kinetics and the glass transition temperature ( T g ) of the epoxy, as well as its stiffness and strength. Healing efficiency was assessed using long-groove tapered double cantilever beam (TDCB) test samples, with embedded SMA wires across the crack plane. The healing efficiency greatly improved when the crack gap was reduced to 30 μm, from 24% for samples without SMA wires to 78% for samples with SMA wires activated according to an optimized scenario.

Self-healing thermoset using encapsulated epoxy-amine healing chemistry

Self-healing was achieved with a dual-microcapsule epoxy-amine chemistry in thermoset epoxy. One capsule contained a modified aliphatic polyamine (EPIKURE 3274) while the second capsule contained a diluted epoxy monomer (EPON 815C). Amine microcapsules were prepared by vacuum infiltration of EPIKURE 3274 into hollow polymeric microcapsules. Epoxy microcapsules were prepared by an in situ polymerization method. Both types of capsules were incorporated into an epoxy matrix (EPON 828:DETA) and recovery of mode-I fracture toughness was measured using tapered-double-cantilever-beam (TDCB) specimens. The optimal mass ratio of amine: epoxy capsules was 4: 6 and an average healing efficiency of 91% was achieved with 7 wt% amine capsules and 10.5 wt% epoxy capsules. Long-term stability of the healing system was demonstrated for six months at ambient conditions. Thermal stability was investigated by post curing samples at 121 °C and assessing healing performance.

Self‐Healing of an Epoxy Resin Using Scandium(III) Triflate as a Catalytic Curing Agent

AbstractA novel Lewis acid‐catalysed self‐healing system is investigated for implementation into epoxy‐based fibre reinforced polymer (FRP) composite materials. The catalyst, scandium(III) triflate, is selected using a qualitative approach and subsequently embedded with pre‐synthesised epoxy‐solvent loaded microcapsules, into an epoxy resin. Healing is initiated when microcapsules are ruptured at the onset of crack propagation. The epoxy monomer healing agent contained within actively undergoes ring‐opening polymerisation (ROP) on contact with the locally dispersed catalyst, forming a new polymer to bridge the two fractured crack planes. Self‐healing performance is quantified using a tapered double cantilever beam (TDCB) test specimen and the effects of microcapsule content and healing temperature and time are all independently considered. As an initial ‘proof of concept’ study, results show that a material recovery value of greater than 80% fracture strength is achieved for this novel Lewis acid‐catalysed self‐healing epoxy resin.

Characterisation of the Fracture Energy and Toughening Mechanisms of a Nano-Toughened Epoxy Adhesive

In this study the adhesive joint fracture behaviour of a nano-toughened epoxy adhesive was investigated. Two experimental test methods were used; (i) the standard tapered double cantilever beam (TDCB) test to measure the mode I adhesive joint fracture energy, GIC, as a function of bond gap thickness and (ii) a circumferentially deep notched tensile test to determine the cohesive strength of the adhesive for a range of constraint levels. It was found that the fracture energy of the adhesive followed the well-known bond gap thickness dependency [1]. SEM analysis of the TDCB fracture surfaces revealed significant plastic void growth. Finally, numerical modelling of the experimental tests suggested that most of the fracture energy was dissipated via highly localised plasticity in the fracture process zone ahead of the crack tip.

On experimental methods to investigate the effect of layer thickness on the fracture behavior of adhesively bonded joints

A number of different experimental methods are used at two independent laboratories to evaluate the influence of layer thickness on the fracture properties of one batch of a crash resistant epoxy adhesive. Both mode I and II are considered. Novel, as well as state of the art methods are used. In mode I, the Double Cantilever Beam (DCB) and two versions of the Tapered Double Cantilever Beam (TDCB) specimens are utilized; in mode II, two versions of the End Notch Flexure (ENF) and the End-Loaded Shear Joint (ELSJ) specimens are used. Good agreement between the test results is achieved for thin layers in both fracture modes. For thicker layers the variation is larger.

On the Mutual Effect of Viscoplasticity and Interfacial Damage Progression in Interfacial Fracture of Lead-Free Solder Joints

The main goal of this paper is to shed light on the effect of strain rate and viscoplastic deformation of bulk solder on the interfacial failure of lead-free solder joints. For this purpose, interfacial damage evolution and mode I fracture behavior of the joint were evaluated experimentally by performing stable fracture tests at different strain rates employing an optimized tapered double cantilever beam (TDCB) design. The viscoplastic behavior of the solder was characterized in shear, and the constitutive parameters related to the Anand model were determined. A rate-independent cohesive zone damage model was identified to best simulate the interfacial damage progression in the TDCB tests by developing a three-dimensional (3D) finite-element (FE) model and considering the viscoplastic response of the bulk solder. The influence of strain rate on the load capability and failure mode of the joint was clarified by analyzing the experimental and simulation results. It was shown how, at the lower strain rates, the normal stress generated at the interface is limited by the significant creep relaxation developed in the bulk solder and thus is not sufficiently high to initiate interfacial damage, whereas at higher rates, a large amount of the external energy is dissipated into interfacial damage development.

Use of the tapered double-cantilever beam geometry for fracture toughness measurements and its application to the quantification of self-healing

The successful invention of self-healing polymer composites a decade ago necessitated a methodology to quantify the ability of the material to heal and recover structural properties following damage. Healing efficiency was defined as the ratio of healed to virgin fracture toughness, η = KIChealed/ KICvirgin. Early work took advantage of the crack length independence offered by a tapered double-cantilever beam (TDCB) fracture geometry to simplify calculation of healing efficiency to the ratio of healed to virgin critical loads, η = PChealed/ PCvirgin. The current work investigates the application of the TDCB geometry and three common geometries utilized in the broader fracture literature (the compact tension (CT), single-edge notch bend (SENB), and single-edge notch tension (SENT) geometries) to the measurement of healing efficiency. While the TDCB geometry simplifies the calculation of healing efficiency because the crack lengths do not need to be accounted for, it is shown that if the virgin and healed crack lengths are not accurately accounted when using the CT, SENB, and SENT geometries, errors in calculated healing efficiency can be several hundred per cent. The TDCB geometry is reviewed at length, including the underlying theory and experimental calibration and validation of TDCB geometry.

Toughening Self-healing Epoxy Resin by Addition of Microcapsules

Microcapsules, filled with healing agent, not only has the ability to heal automatically the epoxy materials but also it can increase the virgin fracture toughness of epoxy. We investigated the effect of microcapsules on the fracture toughness of epoxy resins. The fracture toughness are measured using a tapered double-cantilever beam (TDCB) specimen. The fracture toughness depend strongly on the concentration of microcapsules added to the epoxy. Fracture of the neat epoxy is brittle, exhibiting a mirror fracture surface. Addition of 10 wt.% poly (urea-formaldehyde) (PUF) yields up to 58.2% increase in fracture toughness and induced a change in fracture plane morphology to hackle markings. Toughening mechanisms was study by observing the morphology of fracture plane by SEM.

Self-healing of a high temperature cured epoxy using poly(dimethylsiloxane) chemistry

A high temperature cured self-healing epoxy is demonstrated by incorporating microcapsules of poly(dimethylsiloxane) (PDMS) resin and separate microcapsules containing an organotin catalyst. Healing is triggered by crack propagation through the embedded microcapsules in the epoxy matrix, which releases the healing agents into the crack plane initiating crosslinking reactions. A series of tapered double-cantilever beam (TDCB) fracture tests were conducted to measure virgin and healed fracture toughness. Healing efficiencies, based on fracture toughness recovery, ranged from 11 to 51% depending on the molecular weight of PDMS resin, quantity of healing agent delivered, and use of adhesion promoters.

The fracture behaviour of structural adhesives under high rates of testing

Structural adhesive joints were subjected to high loading rates in mode I and their resulting fracture behaviour was studied in detail. Joints were formed between unidirectional carbon-fibre epoxy composites and between aluminium alloy substrates bonded with a tough, single-part automotive adhesive (XD4600) from Dow Automotive. Double cantilever beam (DCB) and tapered double cantilever beam (TDCB) tests were performed, from quasi-static loading rates up to 15 m/s, and a test rig was developed incorporating high-speed video acquisition for the high-speed tests. A detailed data reduction strategy was developed to account for (i) the types of different fracture behaviour regimes encountered, (ii) the dynamic effects in the test data, and (iii) the contribution of kinetic energy in the specimen arms to the energy balance. Using the above data reduction strategy, increasing the test rate over six decades (from 10 −5 to 10 1 m/s) was found to lead to a reduction in the value of the adhesive fracture energy, G Ic , by about 40% of its quasi-static value, i.e. from 3.5 to about 2.2 kJ/m 2. Further, at quasi-static loading rates, the measured adhesive fracture energies were independent of substrate material and test geometry (i.e. DCB or TDCB). However, at faster loading rates, the TDCB tests induced higher crack velocities for a given loading rate compared with the DCB test geometry, and neither the test rate nor the crack velocity were found to be the parameter controlling the variation in G Ic with increased test rate. Thus, an isothermal–adiabatic model was developed and it was demonstrated that such a model could unify the DCB and TDCB test results. Indeed, when the G Ic values were plotted as a function of 1/√time, where the time was defined to be from the onset of loading the material to that required for the initiation of crack growth, the results collapsed onto a single master curve, in agreement with the isothermal–adiabatic model.