The prediction of crack growth in bonded joints under cyclic-fatigue loading I. Experimental studies

The performance of adhesively-bonded joints under monotonic and cyclic-fatigue loading has been investigated using a fracture-mechanics approach. The joints consisted of an epoxy film adhesive which was employed to bond aluminium-alloy substrates. The effects of undertaking cyclic-fatigue tests in (a) a ‘dry’ environment of 55% relative humidity at 23°C, and (b) a ‘wet’ environment of immersion in distilled water at 28°C were investigated. In particular, the influence of employing different surface pretreatments for the aluminium-alloy substrates was examined. In addition, single-lap joints were tested under cyclic fatigue loading in the two test environments, and a back-face strain technique has been used which revealed that crack propagation, rather than crack initiation, occupied the dominant proportion of the fatigue lifetime of the single-lap joints. In Part II, the data obtained in the present Part I paper will be employed to predict theoretically the lifetime of the adhesively-bonded single-lap joint specimens.     

A numerical analysis of the elastic-plastic peel test

The adhesive fracture energy, G_c, is determined from two types of elastic-plastic peel tests (i.e. the single-arm 90° and T-peel methods) and a linear-elastic fracture-mechanics (LEFM) test method (i.e. the tapered double-cantilever beam, TDCB method). A rubber-toughened epoxy adhesive, with both aluminium-alloy and steel substrates, has been used in the present work to manufacture the bonded joints. The peel tests are then modelled using numerical methods. The overall approach to modelling the elastic-plastic peel tests is to employ a finite-element analysis (FEA) approach and to model the crack advance through the adhesive layer via a node-release technique, based upon attaining a critical plastic strain in the element immediately ahead of the crack tip. It is shown that this ‘critical plastic strain fracture model (CPSFM)’ results in predicted values of the steady-state peel loads which are in excellent agreement with the experimentally-measured values. Also, the resulting values of G_c, as determined using the FEA CPSFM approach, have been found to be in excellent agreement with values from previously-reported analytical and direct-measurement methods. Further, it has been found that the calculated values of G_c are independent of whether a standard LEFM test or an elastic-plastic peel test method is employed. Therefore, it has been demonstrated that the value of the adhesive fracture energy, G_c, is independent of the geometric parameters studied and the value of G_c is indeed a characteristic of the joint, in this case for cohesive fracture through the adhesive layer. Finally, it is noted that the FEA CPSFM approach promises considerable potential for the analysis of peel tests which involve very extensive plastic deformation of the peeling arm and for analysing, and predicting, the performance of more complex adhesively-bonded geometries which involve extensive plastic deformation of the substrates.     

The use of a cohesive zone model to study the fracture of fibre composites and adhesively-bonded joints

Analytical solutions for beam specimens used in fracture-mechanics testing of composites and adhesively-bonded joints typically use a beam on an elastic foundation model which assumes that a non-infinite, linear-elastic stiffness exists for the beam on the elastic foundation in the region ahead of the crack tip. Such an approach therefore assumes an elastic-stiffness model but without the need to assume a critical, limiting value of the stress, _max, for the crack tip region. Hence, they yield a single fracture parameter, namely the fracture energy, G _c. However, the corresponding value of _max that results can, of course, be calculated from knowledge of the value of G _c. On the other hand, fracture models and criteria have been developed which are based on the approach that two parameters exist to describe the fracture process: namely G _c and _max. Here _max is assumed to be a critical, limiting maximum value of the stress in the damage zone ahead of the crack and is often assumed to have some physical significance. A general representation of the two-parameter failure criteria approach is that of the cohesive zone model (CZM). In the present paper, the two-parameter CZM approach has been coupled mainly with finite-element analysis (FEA) methods. The main aims of the present work are to explore whether the value of _max has a unique value for a given problem and whether any physical significance can be ascribed to this parameter. In some instances, both FEA and analytical methods are used to provide a useful crosscheck of the two different approaches and the two different analysis methods.     

Comparison of Analytical, Numerical, and Experimental Methods in Deriving Fracture Toughness Properties of Adhesives Using Bonded Double Lap Joint Specimens

Stress and fracture analysis of bonded double lap joint (DLJ) specimens have been investigated in this paper. Numerical and analytical methods have been used to obtain shear- and peel-stress distributions in the DLJ. The generalized analytical solution for the peel stress was calculated for various forms of the DLJ geometry and, by using crack closure integral (CCI) and by means of the J-integral approach, the analytical strain energy-release rate, G, was calculated. Experimental fracture tests have also been conducted to validate the results. The specimens were made of steel substrates bonded by an adhesive and loaded under tension. Specimens with cracks on both sides and at either end of the DLJ interface were tested to compare the fracture behavior for the two crack positions where tensile and compressive peel stresses exist. Tests confirmed that the substrates essentially behave elastically. Therefore, a linear elastic solution for the bonded region of the DLJ was developed. The fracture energy parameter, G, calculated from the elastic experimental compliance for different crack lengths, was compared with numerical and analytical calculations using the experimental fracture loads. The stresses from analytical analysis were also compared with those from the finite element results. The strain energy-release rate for fracture, G_f, for the adhesive has been shown to have no R-curve resistance, was relatively independent of crack length, and compared well with those obtained from numerical and analytical solutions. However, it was found that fracture energy for the crack starter in the position where the peel stress was tensile was about 20% lower than where the crack was positioned at the side, where the peel stress was found to be compressive.     

COHESIVE ZONE MODELS AND THE PLASTICALLY DEFORMING PEEL TEST

The peel test is a popular test method for measuring the peeling energy between flexible laminates. However, when plastic deformation occurs in the peel arm(s) the determination of the true adhesive fracture energy, G c , from the measured peel load is far from straightforward. Two different methods of approaching this problem have been reported in recently published papers, namely: (a) a simple linear-elastic stiffness approach, and (b) a critical, limiting maximum stress, σmax , approach. In the present article, these approaches will be explored and contrasted. Our aims include trying to identify the physical meaning, if any, of the parameter σmax and deciding which is the better approach for defining fracture when suitable definitive experiments are undertaken.

Cohesive zone models Fracture mechanics Laminates Peel tests Plastic deformation     

Comparison of Analytical,Numerical, and Experimental Methods in Deriving Fracture Toughness Properties of Adhesives Using Bonded Double Lap Joint Specimens

Stress and fracture analysis of bonded double lap joint (DLJ) specimens have been investigated in this paper. Numerical and analytical methods have been used to obtain shear- and peel-stress distributions in the DLJ. The generalized analytical solution for the peel stress was calculated for various forms of the DLJ geometry and, by using crack closure integral (CCI) and by means of the J-integral approach, the analytical strain energy-release rate, G, was calculated. Experimental fracture tests have also been conducted to validate the results. The specimens were made of steel substrates bonded by an adhesive and loaded under tension. Specimens with cracks on both sides and at either end of the DLJ interface were tested to compare the fracture behavior for the two crack positions where tensile and compressive peel stresses exist. Tests confirmed that the substrates essentially behave elastically. Therefore, a linear elastic solution for the bonded region of the DLJ was developed. The fracture energy parameter, G, calculated from the elastic experimental compliance for different crack lengths, was compared with numerical and analytical calculations using the experimental fracture loads. The stresses from analytical analysis were also compared with those from the finite element results. The strain energy-release rate for fracture, G _f , for the adhesive has been shown to have no R-curve resistance, was relatively independent of crack length, and compared well with those obtained from numerical and analytical solutions. However, it was found that fracture energy for the crack starter in the position where the peel stress was tensile was about 20% lower than where the crack was positioned at the side, where the peel stress was found to be compressive.     

Cohesive zone models and the plastically deforming peel test

The peel test is a popular test method for measuring the peeling energy between flexible laminates. However, when plastic deformation occurs in the peel arm(s) the determination of the true adhesive fracture energy, G c , from the measured peel load is far from straightforward. Two different methods of approaching this problem have been reported in recently published papers, namely: (a) a simple linear-elastic stiffness approach, and (b) a critical, limiting maximum stress, σ max , approach. In the present article, these approaches will be explored and contrasted. Our aims include trying to identify the physical meaning, if any, of the parameter σ max and deciding which is the better approach for defining fracture when suitable definitive experiments are undertaken. Cohesive zone models Fracture mechanics Laminates Peel tests Plastic deformation     

Predicting the service-life of adhesively-bonded joints

A fracture-mechanics approach has been used to predict the cyclic-fatigue performance of the adhesively-bonded single-lap joint and a typical bonded component, represented by an adhesively-bonded `top-hat' box-beam joint. The joints were tested under cyclic-fatigue loading in either a `wet' or `dry' environment, respectively. Several steps were needed to predict the cyclic-fatigue lifetime of these joints. Firstly, fracture-mechanics tests were used to obtain the relationship between the rate of fatigue crack growth per cycle, da/dN, and the maximum strain-energy release-rate, G <sub>max</sub>, applied during the fatigue cycle for the adhesive/substrate system under investigation, in both a `dry' and a `wet' test environment. Secondly, analytical and finite-element theoretical models were developed to describe the variation of the strain-energy release-rate with crack length, as a function of the applied fatigue loads, for the single-lap joint and the `top-hat' box-beam joint. Thirdly, the experimental results from the short-term fracture-mechanics tests, obtained under similar test conditions and in the same environment as were used for the single-lap or bonded box-beam joints, were combined with the modelling results from the theoretical studies. This enabled the cyclic-fatigue performance of the single-lap or bonded box-beam joints to be predicted over relatively long time-periods. Finally, the agreement between the theoretical predictions and the experimentally-measured cyclic-fatigue behaviour for the joints was found to be very good.     

Rheological properties,cure characteristics,and morphology of acrylonitrile‐based nanorubber modified epoxy

This article investigates the effects of nano carboxylic acrylonitrile butadiene rubber (CNBR‐NP) and nano acrylonitrile butadiene rubber (NBR‐NP) on the rheological properties and cure characteristics of epoxy. Dynamic mechanical behavior of carbon fiber reinforced polymer composites (CFRP) with the nanorubber‐modified matrices was also studied. Rheological study showed that NBR‐NP blends attained lower viscosity in comparison to CNBR‐NP blends and both systems exhibited shear‐thinning behavior. Scanning electron microscopy (SEM) images revealed that CNBR‐NP could be dispersed evenly within the epoxy matrix using industrial mixing process whereas partial agglomeration was observed in NBR‐NP blends. The dynamic mechanical analysis (DMA) data showed that the addition of nanorubber has negligible effect on the glass transition temperature of the epoxy. The difference in the dispersion ability of these two nanorubbers in epoxy is related to the difference in van der Waals forces between single nanoparticles, the chemical formula and the polarity of the systems. © 2015 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2015 , 132, 41911.