Mixed-mode fatigue crack growth under biaxial loading

Studies on crack growth in a panel with an inclined crack subjected to biaxial tensile fatigue loading are presented. The strain energy density factor approach is used to characterize the fatigue crack growth. The crack growth trajectory as a function of the initial crack angle and the biaxiality ratio is also predicted. The analysis is applied to 7075-T6 aluminium alloy to predict the dependence of crack growth rate on the crack angle. The effect of crack angle on the cyclic life of the component and on the cyclic life ratio is presented and discussed.     

Mixed-mode fracture of adhesively bonded metallic joints under quasi-static loading

Quasi-static tests have been carried out to characterise mixed-mode fracture using a Double Cantilever Beam (DCB) specimen. The DCB consists of equal thickness mild steel adherends bonded with FM-73M epoxy adhesive and is tested under pure mode I, pure mode II and a range of mode-mixity conditions, using a relatively simple loading fixture. The test method is analysed using closed-form and finite element methods, which agree well provided that the adhesive deformation is considered. The strain energy release rate components at fracture are presented in a conventional G_I (mode I)-G_II (mode II) failure plot using closed-form Linear Elastic Fracture Mechanics (LEFM) methods reported previously in the literature. The results showed that the strain energy release rate is enhanced in the situation of the mode II (in-plane shearing) dominated mixed mode condition as compared to the mode I (opening mode) dominated mixed mode.     

Fatigue crack growth simulation in adhesively bonded composite joints

A numerical model has been developed for simulating fatigue crack growth (debonding) in adhesively bonded composite joints subjected to mode‐I, mode‐II, and mixed‐mode I + II loading conditions. The model employs a cohesive zone model described by a modified bilinear traction‐separation law. Fatigue damage in the composite adherends is not considered in the model. To account for crack divergence and reduce sensitivity of numerical results on mesh density, a crack front detection algorithm based on the effective element's length was employed. The model is implemented as a user‐defined subroutine (UMAT) in the commercial FE code LS‐DYNA. The model's input parameters, in the form of a modified Paris law, and the validation data were obtained from experimental tests conducted by the authors. It was found that the model is able to successfully simulate crack growth in the regime of the experimental data.     

Damage mechanisms in composite bonded joints under fatigue loading

In the present paper, the fatigue damage mechanisms in composite bonded joints are analysed and discussed, with particular emphasis on the influence of layer orientation at the adhesive–adherend interface, corner geometry at the end of the overlap area and the stacking sequence. Results indicate that the corner geometry at the end of the bonded area as well as the length of the overlap have a significant influence on the fatigue strength of the joints, while the layer orientation at the adhesive/adherend interface was seen to have a lesser influence on the fatigue performance. The evolution of fatigue damage, consisting in its essential features of crack initiation followed by propagation up to a critical length, is investigated by means of optical and scanning electron microscopy and by monitoring the stiffness of the tested joints. As a result, it is seen that a 45° oriented layer at the adhesive-interface makes crack paths much more complicated with respect to 0° oriented interface joints, with an increase in the crack propagation resistance. Moreover, measurements of the evolution of axial stiffness are promising in order to develop a simplified technique to assess the crack propagation during fatigue life.     

Plasticity induced crack closure in adhesively bonded joints under fatigue loading

The mean load of a cyclic loading has a large effect on fatigue crack growth rates in metallic materials and bonded joints. In metallic structures, this effect has been attributed to plasticity-induced crack closure, but little is known about the mechanism responsible for this mean load effect on fatigue crack growth in adhesively bonded joints. This paper presents a computational investigation of the plasticity-induced crack closure mechanism affecting disbond growth in adhesively bonded joints under fatigue loading. The results show that the ratios of crack-opening and crack-closure are approximately independent of the level of plastic constraint, indicated by the ratio between the plastic zone size and the adhesive thickness. An effective strain-energy release rate parameter, which accounts for the crack closure behaviour, has been developed as a new correlating parameter for disbond growth. Comparisons with the experimental results pertinent to four different adhesive bonded joints reveal that this new correlating parameter is capable of unifying the fatigue growth rates by eliminating the effect of mean loads.     

Mixed-mode crack growth in ductile thin-sheet materials under combined in-plane and out-of-plane loading

Ductile thin-sheet structures, such as fuselage skin or automobile panels, are widely used in engineering applications. These structures often-times are subjected to mixed mode (I/II/III) loading, with stable crack growth observed prior to final fracture. To characterize specific specimen deformations during stable tearing, a series of mixed-mode I/III stable tearing experiments with highly ductile thin-sheet aluminum alloy and steel specimens have been measured by using three-dimensional digital image correlation (3D-DIC). Measurements include (a) specimen’s deformed shape and 3D full-field surface displacement fields, (b) load-crack extension response and (c) crack path during stable tearing, (d) angular and radial distributions of strains and (e) the mixed mode crack-opening displacement (COD, measured at 1-mm from crack tip along crack surface) variation as a function of crack extension. Results indicate that for both aluminum alloy and steel at all mixed-mode I/III loading conditions (Φ = 30°, 60° and 90°), the crack tip fields have almost identical angular and radial polar strain distributions. The mixed mode I/III fields were different from those observed for the nominal Mode I loading case (Φ = 0°). The effect of the Mode III loading component is that it lowers the magnitude of the dominant strain component ε _θθ ahead of the growing crack tip and increases the singularity of the strain as compared with that in the mode I case. In addition, measurements indicate that the average mixed mode I/III stable COD for AL6061-T6 (GM6208 steel) is 4×(3×) greater than the average Mode I stable COD.     

Interlaminar crack onset in co‐cured and co‐bonded composite joints under mode I cyclic loading

Composite joints exhibit different behavior in regard to delamination resistance when dealing with fatigue phenomenon. This research work focuses on an investigation to understand the failure mechanisms on the interfacial strength domain for delamination onset in cocured and cobonded joints. The analysis was based on strain energy release rate versus number of cycles plots that were obtained from fatigue tests in mode I with a stress ratio R = 0.1. The analysis encompassed from the microscopic to mesoscopic level obtained from scanning electron microscopic, and the images processed to extract the most relevant fracture patterns. The main difference between the two technologies was the stress concentration at the crack tip in which the cobonded joint presents a fabric carrier that blunts the adhesive layer, then delaying the delamination. This paper provides important information and guidelines to aid designers in the selection of the best composite joint for high‐performance structural applications.     

Mixed-mode fracture analysis of composite bonded joints considering adhesives of different ductility

We propose a method for simulating linear elastic crack growth through an isogeometric boundary element method directly from a CAD model and without any mesh generation. To capture the stress singularity around the crack tip, two methods are compared: (1) a graded knot insertion near crack tip; (2) partition of unity enrichment. A well-established CAD algorithm is adopted to generate smooth crack surfaces as the crack grows. The M integral and \(J_k\) integral methods are used for the extraction of stress intensity factors (SIFs). The obtained SIFs and crack paths are compared with other numerical methods.     

Mixed-mode dynamic crack propagation in graded materials under thermo-mechanical loading

Mixed-mode dynamic crack growth behavior in functionally graded materials (FGMs) under thermo-mechanical loading is studied. Asymptotic analysis in conjunction with displacement potentials has been used to develop thermo-mechanical stress fields for a mixed mode propagating crack in a FGM. The shear modulus, mass density, thermal conductivity and coefficient of thermal expansion of the FGM are assumed to vary exponentially along the gradation direction. First, asymptotic temperature fields are derived for an exponential variation of thermal conductivity and later these temperature fields are used in deriving stress fields. Using asymptotic thermo-mechanical stress fields the variation of maximum shear stress, circumferential stress and strain-energy density as a function of temperature around the crack tip are generated. Finally, utilizing the minimum strain-energy density criterion and the maximum circumferential stress criterion, the crack growth direction for various crack-tip speeds, non-homogeneity coefficients and temperature fields are determined.     

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.     

Adhesively bonded joints under cyclic loading spectra

Abstract Current designs which involve the use of composite materials in primary aircraft structures are often conservative. This, in turn, significantly lowers the weight advantage that composites have over established metallic airframe materials. Strain restrictions are often applied because the failure mechanism(s) in (fibre) composite joints and stiffener runouts where the stress state is often complex, are not fully understood. Nevertheless, from the airworthiness perspective it is essential that both the static strength and the fatigue behaviour of the components subjected to complex multiaxial stress conditions are both understood and predicted. This topic is extremely complex, and numerous criteria ranging from the purely empirical to the theoretical have been proposed. In both cases, it is necessary to know the localised stress–strain history. One common design methodology is to keep the stresses so low that fatigue will not be an issue. However, this can lead to an overly conservative design. On the other hand, while a detailed (nonlinear) finite element analysis can be performed it is often both resource‐intensive and time‐consuming. The present paper shows that Glinka's hypothesis can be used in order to calculate the localised stresses and strains for a bonded joint subjected to cyclic loading. This is a new result and has not previously been noted. It has the potential to extend the Hart‐Smith design methodology to the adhesively bonded joints in order to encompass durability considerations. This formulation also raises the possibility of enabling the degree of conservatism inherent in traditional joint design to be relaxed provided that failure occurs in the adhesive. This paper also addresses the problem of variable adhesive thickness. We show that while variable adhesive thickness can change the stress and the energy fields, the peak in the strain energy density is relatively insensitive to the stress–strain relationship for the adhesive and that Glinka's hypothesis still appears to be true. This means that, for the present class of problems, even if there is variability in the thickness of the adhesive bond the energy field and, hence, the strength of the joint can be estimated from a purely linear elastic analysis of the joint, provided that failure occurs in the adhesive.     

Fatigue crack growth in adhesively bonded composite-metal double-lap joints

This paper presents experimental and numerical investigations of the fatigue crack initiation and growth mechanism in metal-to-composite bonded double-lap joints. Fatigue tests were conducted under tension dominated loading, with crack lengths being measured optically. Examination of the fracture surface using scanning electron microscope revealed that fatigue cracks were near the interface between the co-cured adhesive and the first ply of the composite adherend. The finite element method has been used to determine the strain-energy release rate of a fatigue crack growing along the first ply of the composite. The effects of spew fillet size and crack initiation modes have also been studied by the finite element method. Comparison of the present experimental crack growth results with those measured using double-overlap joints, where the fatigue cracks were driven by pure mode II loading, indicate that the tensile mode loading has a overwhelming effect on the fatigue crack growth rates. The present results suggest that fatigue failure of metal-composite double-lap joints is mainly driven by tensile mode loading due to the peel stress.     

Mixed-mode crack growth predictions

The problem of slow stable growth of an inclined crack in a plate subjected to uniaxial tension is studied by the strain energy density criterion. The stable crack growth process is simulated by predicting a series of crack growth steps corresponding to a piecewise loading increase when material elements along the direction of crack extension absorb a critical amount of elastic strain energy density. Crack instability takes place when the last ligament of crack extension takes a critical value which is a material constant. The critical stress at the onset of crack initiation and unstable crack extension is determined for various crack inclination angles. Three different loading step increments corresponding to three different loading rates are considered and their effect on stable crack growth is analysed. Furthermore, the influence of loading history on the crack growth process for three different loading types is studied. The complete crack growth patterns for all types of load are determined and analysed. It is obtained that the amount of slow crack growth can be increased by lowering the rate of loading. The effect of the loading history on the failure load and the crack paths is established.     

Analysis of bolted–bonded composite single-lap joints under combined in-plane and transverse loading

A semi-analytical solution method is developed for stress analysis of single-lap hybrid (bolted/bonded) joints of composite laminates under in-plane as well as lateral loading. The laminate and bolt displacements are based on the Mindlin and Timoshenko beam theories, respectively. For the adhesive, the displacement field is expressed in terms of those of laminates by using the shear-lag model. The derivation of the governing equations of equilibrium of the joint is based on the virtual work principle, where the kinematics of each laminate are approximated by local and global functions and the bolt kinematics is assumed in terms of cubic Hermitian polynomials. The capability of the present approach is justified by validation and demonstration problems, including the analysis of bolted and bonded joints and hybrid joints with and without considering a disbond between the adhesive and laminates.     

Creep crack growth under history-dependent loading

We discuss the influence of loading history on creep crack growth. Our attention is mainly focused on the following three aspects of this problem: (i) principal laws of history-dependent creep strain of materials; (ii) creep behavior of cracks, including the choice of suitable fracture parameters that may help to predict cracking; (iii) the importance of taking the history-dependent response of the material into account. We performed numerical calculations based on the use of an appropriate constitutive model and fracture theory for (1) and (2), respectively, to analyze results of tests for (3).Battelle, Columbus, Ohio. UES Incorporated, Dayton, Ohio. Published in Fiziko-Khimicheskaya Mekhanika Materialov, Vol. 30, No. 4, pp. 37–45, July – Augus, 1994.     

Mixed-mode fracture of adhesively-bonded pultruded composite lap joints

The fracture behavior of adhesively-bonded double- and stepped-lap joints composed of pultruded glass fiber-reinforced polymer composite laminates and subjected to axial tension was experimentally investigated and numerically modeled. Two methods were used for the calculation of the strain energy release rate: the experimental compliance method and the virtual crack closure technique. Their results showed good agreement for stepped-lap joints, while significant deviations were observed for double-lap joints due to small stiffness changes. The experimental compliance method results were sensitive to these small changes and the virtual crack closure technique accuracy was affected by the inability of the finite element analysis to accurately model the behavior before visual crack initiation. The dominant fracture mode changed from Mode I to Mode II in the case of stepped-lap joints, while an almost constant mode ratio was retained for double-lap joints in the applied loading range. A non-convex mixed-mode fracture criterion was established for crack initiation and propagation based on the virtual crack closure technique results. Both the experimental compliance method and the virtual crack closure technique proved applicable for the interpretation of the fracture mechanics data of the structural joints examined, provided that stiffness degradation can be accurately described.     

Mixed-mode fatigue crack growth behaviour in aluminium alloy

Fatigue crack propagation tests in compact mixed-mode specimens were carried out for several stress intensity ratios of mode I and mode II, K_I/K_II, in AlMgSi1-T6 aluminium alloy with 3 mm thickness. The tests were performed in a standard servo-hydraulic machine. A linkage system was developed in order to permit the variation of the K_I/K_II ratio by changing the loading angle. Crack closure loads were obtained through the compliance technique. A finite element analysis was also done in order to obtain the K_I and K_II values for the different loading angles. Crack closure increases under mixed-mode loading conditions in comparison to mode-I loading due the friction between the crack tip surfaces. Moreover, the crack closure level increases with the K_I/K_II ratio decrease. Correlations of the equivalent values of the effective stress intensity factor with the crack growth rates are also performed. Finally, an elastic–plastic finite element analysis was performed to obtain the plastic zones sizes and shapes and model the effect of mixed-mode loading on crack closure.     

Mixed-mode crack growth from an unusual source

Out-of-plane crack growths were observed in compact tension specimens under static and quasi-static loading conditions at 650 °C in a nickel based alloy U720Li. The apparent mixed-mode crack growth behaviour may be explained based on a stability argument. The actual occurrence of the unstable crack growth may depend also on other factors such as the crack growth mechanism, grain size and loading mode.