H. Hadavinia

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,σmax, for the crack tip region. Hence, they yield asingle fracture parameter, namely the fracture energy,Gc. However, the corresponding value ofσmax that results can, of course, be calculated from knowledge of the value ofGc. On the other hand, fracture models and criteria have been developed which are based on the approach thattwo parameters exist to describe the fracture process: namelyGcandσmax. Hereσmax 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 ofσmax 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.

Analytical solutions for cohesive zone models

Solutions are given for a cantilever beam specimen using a beam on elastic foundation model to incorporate various cohesive zone traction laws. These included both positive and negative linear slopes and constant stresses. Negative slopes give rise to multiple solutions. However, all the solutions give very similar results for energy release rate and beam root rotation confirming insensitivity to the form of the traction law. The use of these solutions to analyse peeling is discussed.

The calculation of adhesive fracture energies in mode I: revisiting the tapered double cantilever beam (TDCB) test

Abstract Analytical corrections have been derived for a beam theory analysis for the adhesively bonded tapered double cantilever beam test specimen to account for the effects of beam root rotation and for the real, as opposed to idealised, profile of the beam as required experimentally. A number of adhesive–substrate combinations were tested according to a new test protocol and the new analysis method for data reduction is compared critically with the existing simple beam theory and experimental compliance approaches. Correcting the beam theory for root rotation effects is shown to be more important than correcting only for the effects of shear deformation of the substrates. Results from a finite element analysis, using a cohesive zone model, also showed close agreement with the proposed new corrected beam theory analysis method.

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

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

Abstract 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.

The prediction of crack growth in bonded joints under cyclic-fatigue loading II. Analytical and finite element studies

Abstract In Part I (Int. J. Adhesion Adhesives (2003) in press) the performance of adhesively bonded joints under monotonic and cyclic-fatigue loading was investigated. 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 studied. The basic fracture-mechanics data for these different joints in the two environments were measured, as well as the behaviour of single-lap joints. In the present paper, Part II, a method for predicting the lifetime of adhesively bonded joints and components has been investigated. This prediction method consists of three steps. Firstly, the fracture-mechanics data obtained under cyclic loading in the environment of interest have been modelled, resulting in an expression which relates the rate of crack growth per cycle, da/dN, to the maximum applied strain-energy release-rate, Gmax, in a fatigue cycle. Secondly, this relationship is then combined with an analytical or a computational description of the variation of Gmax with the crack length, a, and the maximum applied load per unit width, Tmax, per cycle in the joint, or component. Thirdly, these data are combined and the resulting equation is integrated to give a prediction for the cyclic-fatigue lifetime of the bonded joint or component. The theoretical predictions from the above method, using different approaches to describe the variation of Gmax with the crack length, a, and applied load, Tmax, in the single-lap joint, have been compared and contrasted with each other, and compared with the cyclic-fatigue behaviour of the lap joints as ascertained from direct experimental measurements.

Off-axis Crashworthiness Characteristic of Woven Glass/Epoxy Composite Box Structures

This study investigates the influence of off-axis loading on the fracture mechanism and specific energy absorption (SEA) of glass/epoxy twill/weave composite box structures. In this regard, the off-axis angles of 5°, 10°, 20°, and 30° of loading direction with respect to the composite box axis is studied experimentally under quasi-static crushing process. At the off-axis angle of 5°, the crushing process behavior is similar to that of the axial crushing and fracture mechanisms, such as bundle fracture and interlaminar crack propagation in Mode-II are observed. These are characteristic of brittle fracture crushing mode. For crushing at an off-axis angle of 10°, additional interwall crack propagation at one side of the box is also found. This increases the energy absorbing capability of glass/epoxy composite box at this angle. The sidewall crack is a mixed-mode crack. To characterize this crack, the mixed-mode interlaminar fracture toughness, G I/IIC, is measured using asymmetric double cantilever beam (ADCB) test method. For other angles, the non-symmetrical fracture mechanisms are found at four sides of the composite boxes. The arriving of sustained crushing stage is delayed by increasing the off-axis crushing angle. Owing to this fact, the energy absorbing capability is reduced by increasing the off-axis loading angle. An analytical solution is proposed to predict the mean force of axial crushing in brittle fracture crushing mode. The off-axis crushing process of composite boxes is also simulated by finite element software LS-DYNA and the results are verified with the relevant experimental results.

Delamination of impacted composite structures by cohesive zone interface elements and tiebreak contact

Maximising impact protection of fibre reinforced plastic (FRP) laminated composite structures and predicting and preventing the negative effects of impact on these structures are paramount design criteria for ground and space vehicles. In this paper the low velocity impact response of these structures will be investigated. The current work is based on the application of explicit finite element software for modelling the behaviour of laminated composite plates under low velocity impact loading and it explores the impact, post impact and failure of these structures. Three models, namely thick shell elements with cohesive interface, solid elements with cohesive interface, and thin shell elements with tiebreak contact, were all developed in the explicit nonlinear finite element code LS-DYNA. The FEA results in terms of force and energy are validated with experimental studies in the literature. The numerical results are utilized in providing guidelines for modelling and impact simulation of FRP laminated composites, and recommendations are provided in terms of modelling and simulation parameters such as element size, number of shell sub-laminates, and contact stiffness scale factors.

Toughening of epoxy adhesives by combined interaction of carbon nanotubes and silsesquioxanes

The extensive use of adhesives in many structural applications in the transport industry and particularly in the aeronautic field is due to numerous advantages of bonded joints. However, still many researchers are working to enhance the mechanical properties and rheological performance of adhesives by using nanoadditives. In this study the effect of the addition of Multi-Wall Carbon Nanotubes (MWCNTs) with Polyhedral Oligomeric Silsesquioxane (POSS) compounds, either Glycidyl Oligomeric Silsesquioxanes (GPOSS) or DodecaPhenyl Oligomeric Silsesquioxanes (DPHPOSS) to Tetraglycidyl Methylene Dianiline (TGMDA) epoxy formulation, was investigated. The formulations contain neither a tougher matrix such as elastomers nor other additives typically used to provide a closer match in the coefficient of thermal expansion in order to discriminate only the effect of the addition of the above-mentioned components. Bonded aluminium single lap joints were made using both untreated and Chromic Acid Anodisation (CAA)-treated aluminium alloy T2024 adherends. The effects of the different chemical functionalities of POSS compounds, as well as the synergistic effect between the MWCNT and POSS combination on adhesion strength, were evaluated by viscosity measurement, tensile tests, Dynamic Mechanical Analysis (DMA), single lap joint shear strength tests, and morphological investigation. The best performance in the Lap Shear Strength (LSS) of the manufactured joints has been found for treated adherends bonded with epoxy adhesive containing MWCNTs and GPOSS. Carbon nanotubes have been found to play a very effective bridging function across the fracture surface of the bonded joints.

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

ABSTRACT 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.