Tapered Double Cantilever Beam Test Research Articles

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.

Mode I traction-separation measured using rigid double cantilever beam applied to structural adhesive

ABSTRACTAdhesive joining facilitates the development of multi-material vehicle structures; however, widespread adoption requires material properties to characterize adhesive joints for implementation in finite element (FE) models. Specifically, modeling adhesive joints using the cohesive zone method requires measuring the Mode I traction-separation response, which currently requires multiple tests. To address this need, a new method to determine the Mode I response was developed using the Rigid Double Cantilever Beam (RDCB) test, where the steel adherend geometry was designed to ensure high stiffness compared to structural epoxy adhesives. The samples were tested in tension with displacements measured from high-resolution imaging of the test. A new analysis method was developed with resulting Mode I traction-separation response within the expected range for this structural adhesive. The analysis was verified using a FE model of the test and compared to Tapered Double Cantilever Beam test data. Importantly, the predicted force-displacement response from the FE model, using the measured traction-separation curve, compared well to the measured force-displacement data. The proposed RDCB test demonstrated the ability to determine the Mode I response of a toughened structural adhesive using a single test, the results of which can then be readily implemented into FE simulations.

Numerical assessment of the Double-Cantilever Beam and Tapered Double-Cantilever Beam tests for the GIC determination of adhesive layers

ABSTRACTFracture mechanics-based techniques have become very popular in the failure prediction of adhesive joints. The most commonly used is cohesive zone modeling (CZM). For both conventional fracture mechanics and CZM, the most important parameters are the tensile and shear critical strain energy release rates (GIC and GIIC, respectively). The most common tests to estimate GIC are the Double-Cantilever Beam (DCB) and the Tapered Double-Cantilever Beam (TDCB) tests. The main objective of this work is to compare the DCB and TDCB tests to obtain the GIC of adhesive joints. Three adhesives with varying ductilities were used to verify their influence on the precision of the typical methods of data reduction. For both tests, methods that do not need the measurement of crack length (a) were tested. A CZM analysis was considered to reproduce the experimental load–displacement (P-δ) curves and obtain the tensile CZM laws of each tested adhesive, to test the suitability of the data reduction methods, and to study the effect of the CZM parameters on the outcome of the simulations. The CZM models accurately reproduced the experimental tests and confirmed that the data reduction methods for the TDCB test tend to underestimate GIC for ductile adhesives.

Acoustic emission study of the TDCB test of microcapsules filled self-healing polymer

The failure process of self-healing microcapsule filled epoxy composites was investigated with Acoustic Emission (AE) measurement during tapered double cantilever beam (TDCB) tests. Unfilled, epoxy microcapsule filled and self-healing microcapsule (dual-microcapsules consisting of epoxy capsules and trifluoromethanesulfonic acid (TfOH) capsules) filled epoxy matrix specimens were compared. It was found that, with acoustic emission measurements, reliable data can be retrieved about the nature and progress of crack propagation and failure. Comparing the unfilled and the microcapsule filled specimens, considerably more AE hits were detected in the latter case due to the cracking of capsules and capsule-matrix debonding, which was confirmed by scanning electron microscopy investigations. Also, key differences were observed in the shape of the sum of AE hits curves and amplitude ranges of detected AE hits. Uniform distribution of the healing agent was demonstrated by energy-dispersive X-ray spectroscopy.

Investigations on the energy balance in TDCB tests

The Tapered Double Cantilever Beam (TDCB) test is an established method to determine the critical strain energy release rate of adhesives in mode I. Provided that the adherends stay elastic, that the adhesive layer is not too flexible and that inertia effects can be neglected, the experiment allows to identify the work required by the adhesive layer per area of crack growth. The evaluation according to the standard does not permit to distinguish between different sources of dissipation in the adhesive layer or at the adhesive-adherend interfaces, though. This paper proposes two approaches to gain a more detailed understanding of the dissipation in mode I crack growth of adhesive layers.The first investigation method uses detailed finite element simulations of the TDCB test based on an elastic–plastic adhesive material model derived from tests on bulk specimens. The simulation is used to distinguish between the work required for the plastic deformation of the entire adhesive layer and the work consumed by the crack and the adhesive in its vicinity. The dependence of this distribution of work on the adhesive layer thickness is studied. The second approach adds a temperature measurement by an infrared camera to the TDCB test. This measurement allows observation of the thermo-elastic effect in the adhesive layer and of the heat generation at the crack. Finally, the results of the two approaches are employed to estimate the energy balance in the TDCB test. The application to a ductile epoxy adhesive shows the feasibility of the proposed methods.

Comparative evaluation of the Double-Cantilever Beam and Tapered Double-Cantilever Beam tests for estimation of the tensile fracture toughness of adhesive joints

The continuous development observed in bonded joints, along with the improvements of the adhesives’ properties, are resulting in an increase of the bonded joint applications, as well as the variety of applications. Regarding the strength prediction of adhesive joints, two highly relevant methods are Fracture Mechanics and Cohesive Zone Models (CZM). By Fracture Mechanics, this is usually carried out by an energetic analysis. CZM enable the simulation of damage initiation and propagation. The tensile critical strain energy release rate (GIc) of adhesives is one of the most important parameters for predicting the joint strength. Two of the most commonly used tests are the Double-Cantilever Beam (DCB) and the Tapered Double-Cantilever Beam (TDCB). This work aims to assess the capability of the DCB and TDCB test to estimate the value of GIc of adhesive joints. Three types of adhesives with different levels of ductility are used, to study the accuracy of the typical data reduction methods under conditions that are not always consistent with Linear Elastic Fracture Mechanics (LEFM) principles. For both test protocols, methods that do not require measurement of the crack length (a) during the test are evaluated. In the DCB test, these are the Compliance Calibration Method (CCM), Corrected Beam Theory (CBT) and Compliance-Based Beam Method (CBBM). The methods used in the TDCB test are the Simple Beam Theory (SBT), CCM and CBT. With few exceptions, the results were consistent between the different methods considered for each test. The discrepancy of results is higher when comparing the two types of tests, except for the brittle adhesive. It was concluded that the data reduction methods for the TDCB test are too conservative to measure GIc of ductile adhesives.

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.

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.

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.

Development of a simple mixed-mode fracture test and the resulting fracture energy envelope for an adhesive bond

Characterizing the fracture energy of bonded adhesive joints over a range of mode mixities often requires special fixtures or a variety of test configurations. By pairing a tapered and a constant thickness adherend, a hybrid double cantilever beam (DCB) specimen is proposed. This asymmetric tapered DCB configuration can be used to determine the fracture energy as a function of mode mixity. As the debond propagates, the relative stiffness of the adherends varies in a systematic manner, resulting in a range of mode mixities from 0° to approximately 20°. Strain energy release rates were obtained using corrected beam theory and a finite element fracture analysis. Single-leg bending tests were used to determine the fracture energy at mode mixity up to 56°. Constant thickness and tapered DCB tests were used to determine the mode I fracture energy. The resulting fracture envelope was constructed in order to show the dependence of the fracture energy on mode mixity for a two part acrylic adhesive.

The measurement of cohesive and interfacial toughness for bonded metal joints with epoxy adhesives

The types of crack growth in adhesive joints are reviewed and three are identified, namely central cohesive, asymmetric cohesive and interfacial. Test methods for measuring fracture toughness associated with these cracks are then outlined and include a Tapered Double Cantilever Beam (TDCB) test for a central cohesive crack and peel tests on flexible laminates for the other types of crack. In particular, fixed arm and mandrel peel tests are used. Two aerospace adhesives are used to prepare test specimens in order to conduct these tests. For one of these adhesives, all three types of crack growth were recorded and this provided an opportunity to make detailed comparisons of the three associated fracture toughness values. Of particular interest was the use of the mandrel peel method because it enabled a fracture transition (asymmetric cohesive to interfacial fracture) to be observed during the test. The fracture toughness value associated with a central cohesive crack was similar in magnitude to that for an asymmetric cohesive crack. However, the fracture toughness for interfacial fracture was much lower, but similar in magnitude to the expected value of half the fracture toughness from a TDCB test.

Measurement of Fracture Toughness of Plasma‐Sprayed Al2O3 Coatings Using a Tapered Double Cantilever Beam Method

The fracture toughness of plasma‐sprayed Al2O3 coatings in terms of the critical strain energy release rate GIc was measured using a tapered double cantilever beam (TDCB) approach. The fracture surfaces were examined using a scanning electron microscope (SEM). The measurement yielded the mean GIc values from 13 to 27 J/m2 for the sprayed Al2O3 coatings at different spray distances. These values agree well with those obtained by the conventional double cantilever beam approach. The dependence of the observed GIc on spray distance is consistent with that for the lamellar bonding ratio. These results suggest that the TDCB test is a reliable approach for measuring the GIc of thermal‐spray coatings without the crack‐length measurement.

Investigation on the Brittle Fracture Propagation-arrest Characteristics of Low C-Ni Steel Plates by Tapered Double Cantilever Beam Test

Investigation on the Brittle Fracture Propagation-arrest Characteristics of Low C-Ni Steel Plates by Tapered Double Cantilever Beam Test

テーパ形DCB試験によるNi添加鋼板の脆性破壊伝播停止特性について

テーパ形DCB試験によるNi添加鋼板の脆性破壊伝播停止特性について