Mode II fracture energy characterization of brittle adhesives using compliance calibration method

The end‐notched flexure (ENF) test is widely used for measuring the Mode II critical strain energy release rate of adhesively bonded joints (ABJs). Unstable crack growth in ENF joints with brittle adhesives is a common phenomenon. Classic data reduction methods like the direct beam theory (DBT) and the compliance‐based beam method (CBBM) usually result in unacceptable scatter when crack grows unstable. In this study, the application of a compliance calibration method (CCM) for ENF adhesive joints with a brittle adhesive is experimentally investigated. For this purpose, ENF specimens were manufactured and tested. Different data reduction methods were considered for treating the results. Afterwards, the obtained fracture energies were used as an input parameter in a finite element (FE) analysis with a cohesive zone model to evaluate the validity of the experimental data. It is shown that the fracture loads obtained by the CCM have the best agreement with the experimental ones comparing with the other data reduction approaches. To study the effect of geometry on the CCM results, ENF specimens with different adhesive thicknesses, substrate thicknesses and span lengths were also considered in this study, and some general conclusions are made about the geometrical parameters effect on the Mode II fracture energy.     

Analysis of mode II interlaminar fracture and damage behavior in end notched flexure testing of GFRP woven laminates at cryogenic temperatures

Summary Interlaminar fracture and damage behavior of glass fiber reinforced polymer (GFRP) woven laminates at cryogenic temperatures is investigated for end notched flexure (ENF) pure Mode II configuration. The corrected beam theory (CBT) and finite element analysis (FEA) are used to calculate the Mode II interlaminar fracture toughness of ENF specimen at room temperature (RT), liquid nitrogen temperature (77 K) and liquid helium temperature (4 K). A FEA coupled with damage is also employed to study the damage distributions within the specimen and to examine the effect of damage on the Mode II energy release rate. The numerical results show that damage occurs at the matrix and causes a decrease in the energy release rate. The technique presented can be efficiently used for the characterization of cryogenic Mode II interlaminar fracture and damage behavior of woven laminate ENF specimens.     

Experimental investigation on test methods for mode II interlaminar fracture testing of carbon fiber reinforced composites

In this paper, experimental investigation on the test methods for mode II interlaminar fracture testing of carbon fiber reinforced composites are carried out. Mode II interlaminar fracture testing of unidirectional composite of carbon fiber reinforced epoxy (T800/#3631) are conducted using four kinds of test methods, namely end notched flexure (ENF) test, end loaded split (ELS) test, four-point bend end notched flexure (4ENF) test, and over notched flexure (ONF) test. An analytical model based on a point-friction assumption and classical beam theory is proposed to evaluate the effect of friction between crack faces on the mode II interlaminar fracture toughness in the 4ENF and ONF tests. The analytical model is validated by the comparison of analytical results with previous ones obtained from finite element analysis. Experimental results show that the ENF test gives reliable initiation value of fracture toughness with a small scatter and that the average value of fracture toughness obtained from 4ENF test is about 2% higher than that obtained from the ENF test. The effect of friction in the 4ENF test is much lower than that in the ONF test in which the effect of friction increases with the crack growing. It is concluded that the 4ENF test method is an effective test method for the experimental evaluation of mode II propagation interlaminar fracture toughness of carbon fiber reinforced composites.     

Buckling strength of adhesively-bonded single and double-strap repairs on carbon-epoxy structures

This work reports on an experimental and finite element method (FEM) parametric study of adhesively-bonded single and double-strap repairs on carbon-epoxy structures under buckling unrestrained compression. The influence of the overlap length and patch thickness was evaluated. This loading gains a particular significance from the additional characteristic mechanisms of structures under compression, such as fibres microbuckling, for buckling restrained structures, or global buckling of the assembly, if no transverse restriction exists. The FEM analysis is based on the use of cohesive elements including mixed-mode criteria to simulate a cohesive fracture of the adhesive layer. Trapezoidal laws in pure modes I and II were used to account for the ductility of most structural adhesives. These laws were estimated for the adhesive used from double cantilever beam (DCB) and end-notched flexure (ENF) tests, respectively, using an inverse technique. The pure mode III cohesive law was equalled to the pure mode II one. Compression failure in the laminates was predicted using a stress-based criterion. The accurate FEM predictions open a good prospect for the reduction of the extensive experimentation in the design of carbon-epoxy repairs. Design principles were also established for these repairs under buckling.     

Delamination growth mechanisms in woven glass fiber reinforced polymer composites under Mode II fatigue loading at cryogenic temperatures

The purpose of this research is to characterize the cryogenic delamination growth behavior in woven glass fiber reinforced polymer (GFRP) composite laminates subjected to Mode II fatigue loading. Mode II fatigue delamination tests were performed at room temperature, liquid nitrogen temperature (77 K) and liquid helium temperature (4 K) using the four-point bend end-notched flexure (4ENF) test method, and the delamination growth rate data for the woven GFRP laminates were obtained. The energy release rate range was determined by the finite element method. Microscopic examinations of the specimen sections and fracture surfaces were also carried out. The present results are discussed to obtain an understanding of the fatigue delamination growth mechanisms in the woven GFRP laminates under Mode II loading at cryogenic temperatures.     

Overcoming the cohesive zone limit in composites delamination: modeling with slender structural elements and higher-order adaptive integration

Cohesive element (CE) is a well-established finite element for fracture, widely used for the modeling of delamination in composites. However, an extremely fine mesh is usually needed to resolve the cohesive zone, making CE-based delamination analysis computationally prohibitive for applications beyond the scale of lab coupons. In this work, a new CE-based method of modeling delamination in composites is proposed to overcome this cohesive zone limit on the mesh density. The proposed method makes use of slender structural elements for the plies, a compatible formulation with adaptive higher-order integration for the CEs, and the corotational formulation for geometrically nonlinear analysis. The proposed method is verified and validated on the classical benchmark problems of Mode I, II, mixed-mode delamination, a buckling-induced delamination problem and a double-delamination problem. The results show that elements much larger than the cohesive zone length can be used while retaining accuracy.     

Novel cohesive beam model for the End-Notched Flexure (ENF) specimen

This paper presents a new Cohesive Beam Model (CBM) for the mode II interlaminar fracture End-Notched Flexure (ENF) specimen. The ideal linear elastic solution agrees with a recent analysis and is similar to the well-known Corrected Beam Theory. However, the cohesive zone is known to be particularly important for modelling the large mode II fracture process zone. CBM with a bilinear cohesive law agreed very well with finite element analyses. Comparison with experimental results for two carbon/epoxy laminates indicated that the bilinear cohesive law provides a fairly good conservative approximation.     

Constitutive models for cohesive zones in mixed-mode fracture of plain concrete

Discrete mixed-mode fracture (modes I and II) of plain concrete is investigated using a coupled and an uncoupled cohesive zone constitutive model in a finite element context. Fracture surfaces are confined to inter-element boundaries that are not necessarily coincident with the actual fracture surfaces. For this reason, traction components on the cohesive zone do not correspond to actual values either. In this work is demonstrated that only the coupled model is able to cope with these spurious traction components, that must decrease with crack opening. It is shown also that, in this regard, the key variable is the plastic potential adopted in the integration of tractions. Three mixed-mode fracture examples were tested in this work: a three-point single-edge notched beam, double-edge notched plates under variable lateral and normal deformation and four-point double-edge notched beams. A good fitting with experiments was obtained only for the coupled model. Mode II parameters can change in a large range without noticeable change in results, at least in the tested examples.     

Effect of compressive transverse normal stress on mode II fracture toughness in polymeric composites

Effect of transverse normal stress on mode II fracture toughness of unidirectional fiber reinforced composites was studied experimentally in conjunction with finite element analyses. Mode II fracture tests were conducted on the S2/8552 glass/epoxy composite using off-axis specimens with a through thickness crack. The finite element method was employed to perform stress analyses from which mode II fracture toughness was extracted. In the analysis, crack surface contact friction effect was considered. It was found that the transverse normal compressive stress has significant effect on mode II fracture toughness of the composite. Moreover, the fracture toughness measured using the off-axis specimen was found to be quite different from that evaluated using the conventional end notched flexural (ENF) specimen in three-point bending. It was found that mode II fracture toughness cannot be characterized by the crack tip singular shear stress alone; nonsingular stresses ahead of the crack tip appear to have substantial influence on the apparent mode II fracture toughness of the composite.     

Experimental Determination of Fracture Toughness of CFRP in Mode II by Raman Spectroscopy

Fracture toughness of Mode II of carbon fiber reinforced plastic (CFRP) was investigated using end notched flexure (ENF) specimens and a Raman coating method. Distribution of shear strain near the crack tip of CFRP was measured by Raman spectroscopy. A thin film of PbO on the measured surface of the ENF specimen was deposited by physical vapor deposition (PVD) as pretreatment to measure the strain by Raman spectroscopy. Fracture toughness of CFRP in Mode II was determined using the Raman results. The results coincided closely with those measured by the compliance method and FEM analyses (finite element method).     

Numerical investigation on the loading-delamination-unloading behavior of adhesive joints

An elastic-plastic interface model at finite deformations is utilized to investigate the irreversible delamination behavior of adhesive joints subjected to loading-delamination-unloading. The interface model accounts for the irreversible delamination in the fracture process zone induced by the localized plastic deformation and damage. The interfacial parameters in the cohesive model are obtained by fitting the available experimental data. Results suggest that the cohesive model can capture the irreversible delamination failure behavior observed in adhesively bonded joints during a loading-unloading cycle. The overall nonlinear response is dominated by the cohesive strength and initial damage displacement jump. Further, we also investigate the effect of the ductile mechanisms for the bulk layer on the competition between the plastic deformation of the bulk layer and the delamination of the interface. It is observed that the degradation of unloading stiffness is attributed to the inelastic behavior of the interface.     

Finite element analysis of the end notched flexure specimen for measuring mode II fracture toughness

This paper presents a finite element analysis of the End Notched Flexure (ENF) test specimen for Mode II interlaminar fracture testing of composite materials. Virtual crack closure and compliance techniques employed to calculate strain energy release rates from linear elastic two-dimensional analysis indicate that the ENF specimen is a pure Mode II fracture test within the constraints of small deflection theory. Furthermore, the ENF fracture specimen is shown to be relatively insensitive to process induced cracks offset from the laminate midplane. Frictional effects are investigated by including the contact problem in the finite element model. A parametric study investigating the influence of delamination length, span, thickness and material properties is presented to assess the accuracy of beam theory expressions for compliance and strain energy release rate, G_II. Finite element results indicate that data reduction schemes based upon beam theory underestimate G_II by approximately 20–40% for typical unidirectional graphite fiber composite test specimen geometries. Consequently, an improved data reduction scheme which retains the simplicity of beam theory but also includes the accuracy of the finite element method is proposed.     

A bilinear cohesive zone model tailored for fracture of asphalt concrete considering viscoelastic bulk material

A bilinear cohesive zone model (CZM) is employed in conjunction with a viscoelastic bulk (background) material to investigate fracture behavior of asphalt concrete. An attractive feature of the bilinear CZM is a potential reduction of artificial compliance inherent in the intrinsic CZM. In this study, finite material strength and cohesive fracture energy, which are cohesive parameters, are obtained from laboratory experiments. Finite element implementation of the CZM is accomplished by means of a user-subroutine which is employed in a commercial finite element code (e.g., UEL in ABAQUS). The cohesive parameters are calibrated by simulation of mode I disk-shaped compact tension results. The ability to simulate mixed-mode fracture is demonstrated. The single-edge notched beam test is simulated where cohesive elements are inserted over an area to allow cracks to propagate in any general direction. The predicted mixed-mode crack trajectory is found to be in close agreement with experimental results. Furthermore, various aspects of CZMs and fracture behavior in asphalt concrete are discussed including: compliance, convergence, and energy balance.     

Reinvestigation of the effect of plasticity on delamination process of Si/Cu interface in a ductile nano-cantilever

Previous experimental investigations (Hirakata et al. Int J Fract 145:261–271, 2007) have demonstrated that Si/Cu/SiN/Pt/C nano-cantilever is delaminated along the interface between Cu and Si layers when subjected to monotonically bending load, and the measured load-displacement relationship shows a nonlinear behavior. Based on the continuum mechanics model, this study carries out numerical simulations on the crack nucleation and propagation along the Si/Cu interface in order to clarify the effect of plasticity on the fracture behavior of the ductile nano-component. Exponential type of cohesive zone model (CZM) combined with finite element method was adopted to characterize the constitutive relationship of the Si/Cu interface. Two sets of simulations are performed, i.e., Cu layer obeys either linear elastic or Ramberg–Osgood elasto-plastic constitutive relation. The characteristic parameters of interfacial adhesion are extracted through calibration via experimental results. The simulation results indicate that (i) cohesive strength and work of separation are the dominating CZM parameters, and the exponential CZM is suitable for describing the interfacial delamination between the Cu and Si film layers; (ii) the Cu film layer in this nano-cantilever more favorably obeys a linear elastic constitutive relation; (iii) comparing to bulk Cu, nano-scale Cu has a much higher yield stress and hardening rate, which leads to little plastic deformation of the nano-cantilever specimen during the entire delamination process. The numerical predictions are in good agreement with the experimental results, wherein brittle fracture occurred during the Si/Cu interfacial delamination. And the nonlinear load-displacement behavior observed by the tests may be due to the cohesive law of the Si/Cu interface, instead of the plastic deformation of the Cu film layer.     

Determination of cohesive laws of composite bonded joints under mode II loading

In this work, mode II cohesive laws of carbon–epoxy composite bonded joints were obtained using the direct method applied to the end notched flexure (ENF) test. The direct method is based on the differentiation of the relation between the evolution of the fracture energy (J_II) and the crack tip opening displacement in mode II (CTOD_II) during the test. A data reduction scheme based on equivalent crack length concept was used to obtain the evolution of the fracture energy during the test. The method allows overcoming problems related to identification of crack tip in mode II tests and the presence of a non-negligible fracture process zone (FPZ), which both difficult the right estimate of J_II. The digital image correlation technique (DIC) was used to monitor the CTOD_II, which was synchronized with the load–displacement data. A trapezoidal cohesive law was fitted to the experimental one in order to perform numerical simulations using finite element analysis. The main goal was to validate all the procedure used to get the cohesive laws. The good agreement obtained between the numerical and experimental load-CTOD_II curves and between the cohesive laws demonstrates the adequacy of the proposed procedure concerning the evaluation of the composite bonded joints cohesive laws under mode II loading.     

On the role of stress waves in dynamic rupture of cylindrical tubes

A systematic experimental/computational study was performed to investigate the role of stress waves in ductile fracture of cylindrical tubes. The stress waves were created by high‐speed moving load, which was produced by detonation of explosive cord inside two intact and two pre‐flawed steel tubes. Several distinct phenomena like cyclic crack growths in Modes I and III, crack flap bulging and crack curving/branching were observed and simulated by finite element (FE) method. The FE models were composed of 3D brick elements equipped with interface cohesive elements. The analysis results showed that the crack growths in Modes I and III were governed by the detonation‐induced stress waves. The crack speeds were obtained based on the increments of cyclic crack growth and the time period of the stress waves. The estimated crack speed range was 63–230 m s^?1 for the axial growth, whereas the average speed for growth in Mode III was 100 m s^?1.     

Cohesive fracture modeling of crack growth in thick-section composites

This paper presents a combined method for modeling the mode-I and II crack growth behavior in thick-section fiber reinforced polymeric composites having a nonlinear material response. The experimental part of this study includes crack growth tests of a thick composite material system manufactured using the pultrusion process. It consists of alternating layers of E-glass unidirectional roving and continuous filament mats in a polymeric matrix. Integrated micromechanical and cohesive finite element (FE) models are used to simulate the crack growth response in eccentrically loaded single-edge-notch, (tension), ESE(T) and notched butterfly specimens. Micromechanical constitutive models for the mat and the roving layers are used to generate the effective nonlinear material behavior from the in situ fiber and matrix responses. The validity of the numerical modeling approach before the onset of crack growth is investigated using an infrared thermal method. Cohesive FE models are calibrated and used to simulate the complete crack growth behavior for different crack configurations. The proposed integrated framework of multi-scale material models with cohesive fracture models is shown to be an effective method for predicting the structural and material responses including failure load and crack growth in thick-section fiber reinforced polymeric composites.     

Evaluation of initiation criteria used in interlaminar fracture tests

The objective of this work was to evaluate the non-linearity (NL) and 5% offset or maximum load (5%-Max) criteria that are commonly used to define initiation in interlaminar fracture tests. This study is in the sequence of a previous paper where the mode I DCB and mode II ENF specimens were analysed. Finite element (FE) simulations of delamination growth were here performed for the mode II end-loaded split (ELS) and 4-point end-notched flexure (4ENF) tests. The results indicated that the formation of large process zones could affect significantly NL criteria. The maximum load point gave the most accurate toughness values, especially for the 4ENF specimen. Finally, present and previous results were compared to experimental data available in the literature.     

Effect of Mode-Mixity on the Fracture Toughness of Ti-6Al-4V/FM-5 Adhesive Joints

Using several different fracture tests, the fracture toughness of a chromic acid anodized titanium (Ti-6A-4V)/polyimide (FM-5) adhesive system was evaluated. Mode I, mode II, and mixed mode (I and II) tests were conducted using double cantilever beam (DCB), end notch flexure (ENF), and mixed mode flexure (MMF) geometries. Interfacial type failures were observed in the ENF and MMF specimens as a result of the mode II loading inherent in these tests. Pure mode I loading, as is the case with symmetric DCB specimens, resulted in cohesive failures with a fracture energy around 2500 J/m² on as-received specimens. The asymmetric DCB specimens had fracture energy values around 2000 J/m², the MMF specimens close to 1970 J/m², and ENF specimens around 1300 J/m². All the above measurements were made on as-bonded (unaged) specimens. Titanium/FM-5 bonds supplied by the Boeing Company were then aged in one of three different environments for 2 and 6 months respectively. The environments included: 177^degC in air and 2 psia, and 204^degC in air. Following the aging, DCB, ENF, and MMF tests were conducted on the specimens. The results showed that aging in all three environments resulted in decreases in fracture energy for the above specimen testing configurations. The largest drop (20 percent) in fracture toughness was noted in specimens aged for 6 months in air at 204^degC. An unusual finding from this study, in contrast to what other researchers have seen on other systems, was that increasing mode II loading resulted in significant reductions in toughness. Crack path selection and interaction with the woven glass scrim within the bonded specimens may be responsible for the lower mode II fracture energies. From the tests conducted, failure envelopes were developed to predict failure energy and type for use in designing structural joints. This revised version was published online in July 2006 with corrections to the Cover Date.     

Monitoring of delamination onset and growth during Mode I and Mode II interlaminar fracture tests using guided waves

A delamination monitoring method was proposed to characterize Mode I and Mode II delamination onset in carbon fiber/epoxy (CF/EP) composite laminates through interrogation of guided waves activated and captured using piezoelectric actuators and sensors in a pitch–catch configuration. Mode I and Mode II interlaminar fracture tests were conducted using double cantilever beam (DCB) and end notch flexure (ENF) specimens to evaluate the proposed method. The changes in wave propagation velocity and wave magnitude (or attenuation), and the degree of waveform similarity between excitation and response signals, were calculated as delamination-sensitive wave parameters and plotted versus displacement recorded using a materials testing system. The kink points determined from wave parameter–displacement curves agreed well with the deviation from linearity (NL), visual observation (VIS) and maximum load (Max) points, which are often used in conventional methods for determining interlaminar fracture toughness. The propagation characteristics of the A₀ wave mode in a low frequency range were demonstrated to have high sensitivity to Mode I and in particular Mode II delamination onset in CF/EP composite laminates. It was concluded that the guided waves propagating in the DCB and ENF specimens were capable of determining Mode I and Mode II interlaminar fracture toughness, complementing current practices based on visual inspection or trivial interrogation using load–displacement curve alone.