Extraction of rate-dependent fracture properties of adhesive interface involving large-scale yielding

Interface debonding is one of the major failure modes for the adhesive joints of polymer–matrix composites. The interfacial fracture properties of adhesive interfaces involving large-scale yielding is difficult to determine. A hybrid method that combines modified data reduction and inverse analysis was used to determine the fracture energy of the composite propellant/insulation interface at different loading rates. The modified data reduction adopts effective crack length to account for the effect of the fracture progress zone and avoid monitoring the crack length. These estimated values of the fracture energy were then calibrated by inverse analysis based on the Hooke–Jeeves algorithm in which the interface layer is characterized by a cohesive zone model. The whole process of inverse analysis is conducted automatically without any intervention by procedures. Experimental and numerical results indicate that the proposed data reduction provided fracture energy sufficiently similar to those obtained by the inverse analysis. Moreover, the fracture energy of the propellant/insulation interface was found to rely heavily on the loading rate with a non-monotonic trend.     

Stress singularity in a rectangular bond specimen of a solid rocket motor: Effects and elimination

The propellant/liner interface is the weakest and most concerning part of the grain structure in a solid rocket motor. Rectangular bond specimen tests have gradually become one of the standard methods to measure the bonding abilities of propellant/liner/insulation joints. We performed a three-dimensional numerical study to give full knowledge of this new test, paying close attention to the stress singularity at the crack tip. The asymptotic stress field was presented to show the singularity at the crack tip on the steel/insulation interface. Subsequently the stress singularity was investigated numerically. Numerical results show that the stress singularity has a considerable effect on the stress distribution of the nearby propellant. Also we proposed some methods to eliminate these effects, such as inserting a cohesive zone model into the steel/insulation interface or increasing the thickness of insulation layer. Moreover, Mises stress and maximum principle stress have completely opposite distributions on the propellant/liner interface; thus the accurate failure criterion can be confirmed by the damage initialization observed in experiments.     

Modeling the temperature-dependent mode I fracture behavior of adhesively bonded joints

An ethylene propylene diene monomer (EPDM) rubber film has been used as an inhibitor and insulation in solid rocket motors (SRMs) due to its excellent heat-insulating property. EPDM is wrapped on the surface of the grain layer-by-layer via an adhesive; thus, the adhesive property between EPDM films is one of the key factors that influence the structural integrity of an SRM. The adhesive properties are largely temperature dependent, therefore, it is essential to study the effect of temperature on the properties of the bonding interface between EPDM films. In this article, double cantilever sandwich beam (DCSB) and uniaxial tensile experiments were performed to study the temperature-dependent mode I fracture of the bonding interface, in the service temperature range of the SRMs. A comparison of experimental and numerical results obtained using experimental parameters indicates that the fracture parameters determined by the simple beam theory (SBT) and the compliance-based beam method (CBBM) are not accurate. Next, we obtained accurate parameters using an inverse analysis method. Moreover, we made an initial attempt to establish a temperature-dependent cohesive zone model to predict the temperature-dependent fracture behavior of adhesively bonded joints. Good agreement between experimental and numerical results demonstrates that this temperature-dependent model is applicable.     

Analysis of the cohesive zone and crack length correction in the adhesively bonded double cantilever beam specimen

The double cantilever beam specimen has been increasingly employed to enable the development of cohesive zone models for adhesive joints. Evaluation of the traction–separation law (TSL) requires elaborate experimental techniques and usually relies on data measured until the crack initiation point. Nonetheless, current standards stipulate fracture energy measurements under steady-state crack propagation. This paper investigated the influence of the cohesive zone on the commonly used corrected beam theory data reduction scheme. Analytical solutions for the elastic–perfectly plastic, bilinear, and trapezoidal laws were developed using a beam model. The role of the elastic traction decay zone was found to be significant for high strength moderately tough adhesives. Nevertheless, the results showed that the sensitivity of the crack length correction to the cohesive zone can be exploited to obtain approximate TSLs.     

Effect of moisture on pure mode I and II fracture behaviour of composite bonded joints

The effect of moisture on the fracture properties of composite bonded joints under pure mode I and pure mode II was analysed in this work. The double cantilever beam and end notched flexure tests were used for mode I and mode II fracture characterisation, respectively. Three different moisture conditions (55% and 75% of relative humidity (RH) and immersion in distilled water (IW)) were tested to assess its influence on the fracture behaviour under both pure loading modes. It was verified that fracture energy is drastically affected for the immersion in water in both loading modes. A cohesive zone model was also used to estimate the influence of RH on the cohesive parameters defining the law that mimics accurately the fracture process for each case. It was concluded that alterations on the cohesive laws reflect an increase of material brittle behaviour with the increase of the moisture uptake.     

Cohesive Zone Model Characterization of the Adhesive Hysol EA-9394

Abstract

The cohesive zone model approach is attractive for the analysis of failure of adhesively bonded structures. While the numerical implementation of cohesive elements has been well established, there remains a lack of cohesive material data. The present paper contributes to efforts to fill this void. An investigation of crack growth in the widely used structural adhesive Hysol EA-9394 is presented, and the adhesive is characterized by a cohesive zone law. Crack growth experiments were performed on specimens consisting of aluminum adherends bonded by use of the adhesive. Measurements of the surface topography leading reconstruction of fracture processes indicate that plastic deformation is absent during fracture. Thus, the cohesive zone law can directly be determined from the energy release rate and the material separation measured at the initial crack tip. The cohesive zone law is then applied in finite element model to predict crack growth. The predicted strain fields during crack growth are well matched to those obtained by digital image correlation measurements. An independent set of crack growth experiments was performed, and finite element models based on the cohesive law were used to predict the outcome of these experiments. Again good agreement between simulation and experiment was obtained. The results give confidence that the cohesive zone model parameters are transferable to the analysis of structures bonded with the adhesive Hysol EA-9394 in general. A comparison of the cohesive zone law for Hysol EA-9394 demonstrates that this adhesive possesses high strength and moderate toughness. Limits to the transferability regime are discussed.     

The effect of the bond between the matrix and the aggregates on the cracking mechanism and fracture parameters of concrete

The aggregate–matrix interface plays a leading role in the fracture mechanisms and in the fracture response of concrete. In this work, the influence of the interface on the macroscopic fracture parameters of concrete is investigated. Eleven concrete batches were cast with the same matrix. Different—crushed or rounded—aggregates from the same quarry were used, and several surface treatments were applied to improve or degrade the bond between the matrix and the particles. Fracture tests (three-point bending tests and Brazilian splitting tests) were carried out to determine the fracture energy and other relevant fracture parameters of the concrete batches. The modulus of elasticity and the compressive strength were obtained from uniaxial compression tests. The macroscopic fracture behaviour was modeled by the cohesive crack model with a bilinear softening curve. The results show that concretes with the same matrix and aggregates, and similar behaviour under uniaxial compression, can give very different fracture responses. The work shows how fracture behaviour is governed by the interfacial properties that are also behind the cracking mechanism.     

Analysis of the fracture process zone and effective crack length in the adhesively bonded end-notched flexure specimen

The mode II fracture of adhesive joints is well-known to involve large fracture process zones. Their effect in fracture energy measurements can be taken into account by the effective crack length approach. Moreover, fracture process zones can be simulated by cohesive zone models, which are increasingly used for structural analysis of adhesive joints. This paper aimed at evaluating the influence of the traction-separation law on the fracture process zone and on the effective crack length in end-notched flexure tests. Novel analytical cohesive zone models were developed for the bilinear and trapezoidal traction-separation laws. The latter were shown to affect significantly the energy dissipation rate versus effective crack length curve prior to crack initiation. Therefore, this effect seems to provide a simple approach for evaluating approximate traction-separation laws. The models here developed are easy to apply and provide simple approximate expressions useful for specimen selection.     

Fatigue analysis of composite bonded repairs

Abstract

The present work intends to describe all procedures developed in order to predict the fatigue/fracture behaviour of single-strap repairs of carbon-epoxy composites. The main goal is to validate a mixed-mode I + II cohesive zone model for high-cycle fatigue based on the modified Paris law. A preliminary static fracture characterisation in mode I, mode II and mixed-mode I + II is necessary in order to achieve the static energetic criterion describing fracture of the bonded joint. Subsequently, the same tests were carried out under high-cycle fatigue loading in order to determine the evolution of the modified Paris law parameters as function of mode ratio. These fatigue/fracture characterisation tests were also used to validate the cohesive mixed-mode I + II zone model appropriate for high-cycle fatigue. The model was then used to predict fatigue life of the single-strap repairs and revealed good performance when compared with experimental results. Finally, the model was utilised to assess the influence of specimen geometry on the fatigue life of these structural repairs. It was concluded that such type of models can be considered appealing tools concerning the optimisation of repaired structures fatigue life.     

Cohesive and continuum mixed-mode damage models applied to the simulation of the mechanical behaviour of bonded joints

The objective of this work is to discuss the adequacy of cohesive and continuum damage models for the prediction of the mechanical behaviour of bonded joints. A cohesive mixed-mode damage model appropriate for ductile adhesives is presented. The double cantilever beam and the end-notched flexure tests are proposed in order to evaluate the cohesive properties of the adhesive as a thin layer under mode I and mode II, respectively. A new data reduction scheme based on the crack equivalent concept is also proposed to overcome crack-monitoring difficulties during propagation in these fracture characterization tests. An inverse method to determine the cohesive parameters of the trapezoidal softening law is discussed. A continuum mixed-mode damage model is developed in order to better simulate the cases where adhesive thickness plays an important role. The model is applied to evaluate the effect of adhesive thickness on fracture characterization of adhesive joints. Some important conclusions about the advantages and drawbacks of cohesive and continuum damage models are reported.     

The effects of curing temperature on fracture energy and cohesive parameters for the adhesive Araldite 2015

This paper attempts to investigate the effects of curing temperature on the fracture energy, the glass transition temperature (T_g) and cohesive parameters for the adhesive Araldite 2015. Relationship between curing temperature and the glass transition temperature was taken into account. Tensile tests were performed on the dogbone-shaped bulk specimens to evaluate the effect of curing temperature on the mechanical properties of the adhesive. DCB test results were used to obtain the cohesive laws of the adhesive Araldite 2015. The exponential and PPR cohesive zone models were used to obtain some of the fracture properties. Inverse analyses were also performed, if the experimental softening curves are incompatible with the numerical ones. It was seen that softening behavior of the adhesive can be easily controlled by the shape parameters available in the PPR cohesive zone model. It is seen from the DCB test results that curing the adhesive about the temperature at which the T_g∞ is obtained caused the adhesive to have more ductility, higher load-carrying capacity and higher fracture energy than curing it below or above the temperature at which T_g∞ is attained. Here, the T_g∞ is the T_g of the fully cured network. Experimental and numerical R curves were obtained to account for deviations between experiments and simulations. A good agreement between the numerical and experimental load-displacement curves was achieved showing the adequacy of the cohesive model used.     

Predicting environmental degradation of adhesive joints using a cohesive zone finite element model based on accelerated fracture tests

A framework was developed to predict the fracture toughness of degraded adhesive joints by incorporating a cohesive zone finite element (FE) model with fracture data of accelerated aging tests. The developed framework addresses two major issues in the fracture toughness prediction of degraded joints by significant reduction of exposure time using open-faced technique and by the ability to incorporate the spatial variation of degradation with the aid of a 3D FE model. A cohesive zone model with triangular traction-separation law was adapted to model the adhesive layer. The degraded cohesive parameters were determined using the relationship between the fracture toughness, from open-faced DCB (ODCB) specimens, and an exposure index (EI), the time integration of the water concentration. Degraded fracture toughness predictions were done by calculating the EI values and thereby the degraded cohesive parameters across the width of the closed joints. The framework was validated by comparing the FE predictions against the fracture experiment results of degraded closed DCB (CDCB) joints. Good agreement was observed between the FE predictions and the experimental fracture toughness values, when both ODCB and CDBC were aged in the same temperature and humidity conditions. It was also shown that at a given temperature, predictions can be made with reasonable accuracy by extending the knowledge of degradation behavior from one humidity level to another.     

Strength Prediction of Adhesively Bonded Single Lap Joints Under Salt Spray Environment Using a Cohesive Zone Model

The aim of this research was to develop an experimental–numerical approach to characterize the effect of salt spray environment on adhesively bonded joints and predict the degradation in joint strength. Experiments were conducted on bulk adhesive specimens and single lap joints (SLJs) under salt spray condition and the corresponding experimental results were reported. The environment degradation factor, Deg, was incorporated into a bilinear cohesive zone model (CZM) to simulate the degradation process of the joints. The degraded CZM parameters, determined from static tests on bulk adhesive, were imported into the CZM using an approximate moisture concentration gradient approach. The reduction in residual strength of SLJ under salt spray environment was successfully predicted through comparing the experimental and numerical results.     

Open hole compressive strength of composite laminates and sandwich panels: comparison between Budiansky–Fleck–Soutis model and experiments

Abstract

In this study, the compressive behaviour of carbon fibre reinforced plastic quasi-isotropic laminates and sandwich panels with carbon fibre reinforced plastic face sheets and syntactic foam core has been investigated. Experimentally determined open hole strengths have been compared with theoretical predictions obtained by applying a linear cohesive zone model. The unnotched compressive strength has been experimentally determined, and the in-plane fracture toughness has been analytically predicted as input parameters of the model. Buckling phenomena occurred on some specimens, and they have been taken into account. Evaluation of macroscopic failure modes in compression tests on unnotched specimens led to a better understanding on the advantages of the analytical model and on the possibility of applying the model to sandwich structures. The experimental results were in good agreement with the analytical prediction by the Budiansky–Soutis–Fleck cohesive zone model, and the difference between theoretical and experimental open hole strengths of Syncore sandwich panels was <9%.     

Interlaminar mechanical properties of carbon fiber reinforced plastic laminates modified with graphene oxide interleaf

By taking the advantage of the excellent mechanical properties and high specific surface area of graphene oxide (GO) sheets, we develop a simple and effective strategy to improve the interlaminar mechanical properties of carbon fiber reinforced plastic (CFRP) laminates. With the incorporation of graphene oxide reinforced epoxy interleaf into the interface of CFRP laminates, the Mode-I fracture toughness and resistance were greatly increased. The experimental results of double cantilever beam (DCB) tests demonstrated that, with 2 g/m² addition of GO, the Mode-I fracture toughness and resistance of the specimen increase by 170.8% and 108.0%, respectively, compared to those of the plain specimen. The improvement mechanisms were investigated by the observation of fracture surface with scanning electron microscopies. Moreover, finite element analyses were performed based on the cohesive zone model to verify the experimental fracture toughness and to predict the interfacial tensile strength of CFRP laminates.     

Predicting the strength of adhesively bonded joints of variable thickness using a cohesive element approach

One major characteristic of bonded structures is the highly localised nature of deformation near sharp corners, ply-terminations, and ends of joints where load transfer occurs. This paper presents an investigation of the use of a cohesive zone model in predicting the strong effects of stress concentration due to varying adherend thickness on the pull-off strength measured by the Pneumatic Adhesion Tensile Testing Instrument. A comparison is made with the point-strain-at-a-distance criterion, where the plastic deformation of the adhesive is analysed using a modified Drücker–Prager/cap plasticity material model. The fracture properties of the cohesive zone model were determined using double-cantilever and end-notch flexural specimens, and the cohesive strengths were measured using tensile and lap shear tests. Comparisons with experimental results reveal that the cohesive zone model with perfectly plastic (or non-strain-softening) cohesive law provides accurate predictions of joint strengths.     

Review of the Adhesively Bonded Interface in a Solid Rocket Motor

One of the most challenging requirements in a solid rocket motor (SRM) is the integrity of the charge structure which is a multilayer adhesive joint involving the propellant, liner, and insulation. The propellant/liner/insulation interface is considered to be the weakest part of the whole structure. This interface has some of the usual features of an adhesively bonded interface, as well as its own special characteristics: the co-cured process, ingredient migration between interfaces, and complicated damage mechanisms. We give a technical and critical review of the past 50 years of existing research on many aspects of the propellant/liner/insulation interface in terms of the adhesive properties and adhesive mechanisms, ingredients migration, damage determination, and fracture analysis. To present a comprehensive outline of this interface we also clarify some remaining problems which should be addressed in the future. With significant improvements in the theoretical and experimental studies of the propellant/liner/insulation interface, the problem of integrity failure of the charge structure in SRM will be well resolved.     

Modeling and experimental validation of interfacial fatigue damage in fiber‐reinforced rubber composites

This article presents an experimental and numerical study of short‐fiber‐reinforced rubber sealing composites (SFRC) at different stress amplitudes (1 MPa, 2 MPa, and 3 MPa). The curves of the maximum strain varying with the number of cycles were obtained by the fatigue test, and the damage modes of SFRC at different stress amplitudes were determined by scanning electron microscope. A finite element model (FEM) was established, where fibers distributed randomly and the stress‐based fatigue damage model integrating with a bilinear traction‐separation law of the cohesive zone model was embedded in the fiber/matrix interface. The effect of different stress amplitudes on the fatigue damage of SFRC was investigated by FEM where the interfacial debonding behavior was considered. The predictions at stress amplitudes of 1 MPa are generally consistent with experimental data. The predictions at high stress amplitudes (2 MPa and 3 MPa) are agreeable with experimental data at low number of cycles. POLYM. ENG. SCI., 58:920–927, 2018. © 2017 Society of Plastics Engineers     

Combined damaged elasticity and creep modeling of ceramics with wedge splitting tests

During the crack propagation in common refractory ceramics at high temperatures, creep may occur in the wake of a process zone and in front of a crack tip. To account for this phenomenon, an integrated material constitutive model was developed by combining the mechanical behavior following isotropic damaged elasticity concept and Norton-Bailey creep. The post peak fracture behavior followed the bilinear softening law and a simple criterion was defined to consider the creep asymmetricity in uniaxial tension and compression. The material constitutive model was applied to inversely identify mode I fracture parameters with wedge splitting tests of an alumina spinel material at 1200 °C. It showed that the mean ratio of the nominal notch tensile strength to the actual tensile strength was 1.93 and the mean pure fracture energy was 297.6 N/m. In addition, the creep contributed 12.9% on average into the total fracture energy.     

Cohesive fracture model for functionally graded fiber reinforced concrete

A simple, effective, and practical constitutive model for cohesive fracture of fiber reinforced concrete is proposed by differentiating the aggregate bridging zone and the fiber bridging zone. The aggregate bridging zone is related to the total fracture energy of plain concrete, while the fiber bridging zone is associated with the difference between the total fracture energy of fiber reinforced concrete and the total fracture energy of plain concrete. The cohesive fracture model is defined by experimental fracture parameters, which are obtained through three-point bending and split tensile tests. As expected, the model describes fracture behavior of plain concrete beams. In addition, it predicts the fracture behavior of either fiber reinforced concrete beams or a combination of plain and fiber reinforced concrete functionally layered in a single beam specimen. The validated model is also applied to investigate continuously, functionally graded fiber reinforced concrete composites.