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.     

The determination of the mode II adhesive fracture resistance, GIIC, of structural adhesive joints: an effective crack length approach

This paper reports results from the mode II testing of adhesively-bonded carbon-fibre-reinforced composite substrates using the end-loaded split (ELS) method. Two toughened, structural epoxy adhesives were employed (a general purpose grade epoxy-paste adhesive, and an aerospace grade epoxy-film adhesive). Linear Elastic Fracture Mechanics was employed to determine values of the mode II adhesive fracture energy, G_IIC for the joints via various forms of corrected beam theory. The concept of an effective crack length is invoked and this is then used to calculate values of G_IIC. The corrected beam theory analyses worked consistently for the joints bonded with the epoxy-paste adhesive, but discrepancies were encountered when analysing the results of joints bonded with the epoxy-film adhesive. During these experiments, a microcracked region ahead of the main crack was observed, which led to difficulties in defining the true crack length. The effective crack length approach provides an insight into the likely errors encountered when attempting to measure mode II crack growth experimentally.     

Effect of mixed mode I/II on fracture behaviour of laminated metal matrix composites

Abstract

The effects of mixed mode loading (I/II) on the fracture toughness and fracture behaviour of both 6090/SiC/20_p-6013 diffusion bonded laminates and 2080/SiC/20_p-2080 adhesive bonded laminates tested in the crack arrester orientation were investigated. The effects of layer thickness and volume fraction ratio on the fracture behaviour under the mixed mode were also studied. The fracture behaviour under mode I/II of available similar discontinuously reinforced aluminium (DRA) materials was additionally compared to that of the laminates. The fracture behaviour of laminates under mode I/II was dependent on the volume fraction ratio and generally different from that of the monolithic and DRA. The increase in the fracture toughness of DRA by lamination with ductile layers under mode I changes somewhat under increasing load mixity, for 75/25 and 50/50 diffusion bonded laminate and 60/40 adhesive bonded laminate ABL. This results from extensive interfacial separation and delamination between the layers.     

A multiscale parametric study of mode I fracture in metal-to-metal low-toughness adhesive joints

The failure of adhesively-bonded joints, consisting of metallic adherends and epoxy-based structural adhesive with a relatively low toughness ~200 J/m², has been studied. The failure was via quasi-static mode I, steady-state crack propagation and has been modelled numerically. The model implements a ‘top-down approach’ to fracture using a dedicated steady-state, finite-element formulation. The damage mechanisms responsible for fracture are condensed onto a row of cohesive zone elements with zero thickness, and the responses of the bulk adhesive and of the adherends are represented by continuum elements spanning the full geometry of the joint. The material parameters employed in the model are first quantitatively identified for the particular epoxy adhesive of interest, and their validity is verified by comparison with experimental results. The model is then used to conduct a detailed study on the effects of (a) large variations in the geometrical configuration of the different types of specimens and (b) the adherend stiffness on the predicted value of the adhesive fracture energy, G _a . These numerical modelling results reveal that the adhesive fracture energy is a strong nonlinear function of the thickness of the adhesive layer, the other variables being of secondary importance in influencing the value of G _a providing the adhesive does not contribute significantly to the bending stiffness of the joint. These results which fully agree with experimental observations are explained in detail by identifying, and quantifying, the different sources of energy dissipation in the bulk adhesive contributing to the value of G _a . These sources are the locked-in elastic energy, crack tip plasticity, reverse plastic loading and plastic shear deformation at the adhesive/adherend interface. Further, the magnitudes of these sources of energy dissipation are correlated to the degree of constraint at the crack tip, which is quantified by considering the opening angle of the cohesive zone at the crack tip.     

Mode I fracture toughness of an adhesively bonded composite–composite joint in a cryogenic environment

To determine the effect of cryogenic temperature on the adhesive fracture toughness of an adhesively bonded joint with composite adherends, monotonic mode I adhesive fracture toughness tests were performed at liquid nitrogen temperature (−196 °C) and at room temperature (27 °C). From these experimental tests, the critical strain energy release rate for both test temperatures was evaluated for the selected bonded joint system constructed of carbon-BMI adherends bonded with AF-191M film adhesive. Experimental results exhibit reduced adhesive fracture toughness at the cryogenic temperature and a profound difference in fracture mode.     

An integrated approach based on acoustic emission and mechanical information to evaluate the delamination fracture toughness at mode I in composite laminate

This paper addresses a new method based on the combination of mechanical behavior and acoustic emission (AE) information of composite materials during mode I delamination. The method is based on a special purpose function, called sentry function, which is defined as the logarithm of the ratio between mechanical energy and acoustic energy (f = Ln(E_s/E_a)). The sentry function is used to study the delamination process and to evaluate the delamination fracture toughness in mode I. The relationship between cumulative fracture toughness energy release rate (G_I) and the integral of the sentry function during crack propagation showed a transition point with two sensitive regions below and above it. This behavior can be followed to obtain the critical strain energy release rate value (G_Ic). Results obtained by means of the sentry function are compared with results obtained by a methodology proposed by other authors.     

Effects of mixed-mode ratio and step-shaped micro pattern surface on crack-propagation resistance of carbon-fiber-reinforced plastic/adhesive interface

This study investigated the effects of the mixed-mode ratio of applied loads (G_II/G) and aspect ratio A of step-shaped micro patterns on the crack-propagation resistance of a carbon-fiber-reinforced plastic (CFRP)/adhesive interface fabricated by in-mold surface modification. Experiments showed that the fracture behaviors change and that the apparent mixed mode fracture toughness G_C increases with G_II/G and A. We used the Benzeggagh–Kenane (B–K) failure criterion for the mixed-mode fracture toughness considering the transition of the failure mode of the step-shaped micro patterns. The B–K criterion agreed well with the improvement of G_C due to an increase in G_II/G for various fixed values of A. We clarified the relationship between the aspect ratio A and the parameter η, which is required to describe the B–K criterion, and therefore, η can be estimated from A. Consequently, it was verified that G_C of the CFRP/adhesive interface with step-shaped micro patterns can be predicted for arbitrary G_II/G and A values by substituting the η–A relationship in the B–K criterion.     

Comparison of failure mechanisms between rubber-modified and unmodified epoxy adhesives under mode II loading condition

The effect of rubber modification on fracture toughness of adhesive joints under mode II loading condition was investigated in comparison with that under mode I loading, wherein the two adhesives rubber-modified and unmodified were used. To evaluate the fracture toughness on the basis of R-curve characteristics under mode II loading condition, four-point bend tests had been conducted for the adhesively bonded end-notched flexure (ENF) specimens. Thus obtained R-curves revealed the following trend: its behavior did not appear for the unmodified adhesive, whereas the rubber-modified adhesive exhibited a typical behavior. In the initial stage of crack propagation, G _IIC of the rubber-modified adhesive is lower than that of the unmodified adhesive, but becomes greater in the range of Δa > 25 mm. Nevertheless, the significant improvement of the fracture toughness with the rubber modification under mode I loading condition was not observed under mode II loading. Moreover, FEM analysis was made to elucidate the relation between the above fracture behavior and stress distributions near the crack tip. The results gave the reasonable relationship between evolution of plastic zone and the area with high void-fraction as well as the R-curves behavior. In addition, macroscopic and SEM observations for the fracture surfaces were also conducted.     

Mixed-mode cohesive fracture of adhesive joints: Experimental and numerical studies

A broad experimental and analytical effort using fracture mechanics as the prime tool was conducted to investigate and improve the understanding of the mixed-mode cohesive fracture behavior of bonded joints. As a part of experimental efforts, mixed-mode fracture tests were performed using modified Arcan specimens consisting of several combinations of adhesive, composite and metallic adherends with a special loading fixture, in which by varying the loading angle, from 0° to 90°, mode-I, mixed-mode and mode-II fracture data were obtained. Finite element analyses were also carried out on specimens with different adherends. The main objective of this study was to determine the fracture toughness K_IC and K_IIC for a range of substrates under mixed-mode loading conditions. Another goal was to study the relationship between the stress intensity factors and the fracture toughness. Based on those analyses, mixed mode fracture criterion for the adhesively bonded systems under consideration determined. Fracture surfaces obtained at different mixed-mode loading conditions for various adherends were finally discussed.     

Orientation and loading condition dependence of fracture toughness in cortical bone

The fracture toughness at crack initiation were determined for bovine cortical bone under tension (mode I), shear (mode II), and tear (mode III). A total of 140 compact tension specimens, compact shear specimens and triple pantleg (TP) specimens were used to measure fracture toughness under tension, shear, and tear, respectively. Multiple-sample compliance method was utilized to measure the critical strain energy release rate (G_c) at the a/W=0.55 (crack length, a, to specimen width, W, ratio). The critical stress intensity factor (K_c) was also calculates from the critical loading (P_c) of the specimens at the a/W=0.55. The effect of the anisotropy of bone on its resistance to crack initiation under shear and tear loading was investigated as well. Fracture toughness of bone with precrack orientations parallel (designed as longitudinal fracture) and vertical (designed as transverse fracture) to the longitudinal axis of bone were compared. In longitudinal fracture, the critical strain energy release rate (G_c) of cortical bone under tension, shear, and tear was 644±102, 2430±836, and 1723±486 N/m, respectively. In transverse fracture, the critical strain energy release rate (G_c) of cortical bone under tension, shear, and tear was 1374±183, 4710±1284, and 4016±948 N/m, respectively. An unpaired t-test analysis demonstrated that the crack initiation fracture toughness of bone under shear and tear loading were significantly greater than that under tensile loading in both longitudinal and transverse fracture (P<0.0001 for all). Our results also suggest that cortical bone has been “designed” to prevent crack initiation in transverse fracture under tension, shear, and tear.     

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.     

Interactions between propagating cracks and bioinspired self-healing vascules embedded in glass fibre reinforced composites

This study considers the embedment of a bioinspired vasculature within a composite structure that is capable of delivering functional agents from an external reservoir to regions of internal damage. Breach of the vascules, by propagating cracks, is a crucial pre-requisite for such a self-healing system to be activated. Two segregated vascule fabrication techniques are demonstrated, and their interactions with propagating Mode I and II cracks determined. The vascule fabrication route adopted played a significant role on the resulting laminate morphology which in-turn dictated the crack-vascule interactions. Embedment of the vascules did not lower the Mode I or II fracture toughness of the host laminate, with vascules orientated transverse to the crack propagation direction leading to significant increases in G_I and G_II through crack arrest. Large resin pockets were found to redirect the crack around the vascules under Mode II conditions, therefore, it is recommended to avoid this configuration for self-healing applications.     

Finite element analysis of axial splits in composite Iosipescu specimens

In this paper, a finite element analysis of skew-symmetric splits along the fiber direction in unidirectional composite Iosipescu specimens is performed. The energy release rates G _I, G _II, and G _total associated with axial splits in cracked Iosipescu specimens under external biaxial loading conditions are computed by four different numerical schemes: displacement correlation, displacement extrapolation, J-integral, and the modified crack closure integral. Using beam theory analysis, an analytical solution for the energy release rates is also proposed. Axial splits in Iosipescu specimen propagate under mixed mode conditions, with G _I and G _II varying with the crack length a. For short and medium crack lengths G _I>G _II, while for long cracks, G _II is dominant. The energy release rates G _I, G _II, and G _total are strongly dependent on the biaxial type of loading. The G-estimates obtained by the modified crack closure integral schemes are found to be the most accurate among all the numerical schemes chosen in this study. In the analyses of axial splits in composite Iosipescu specimens, the displacement correlation and extrapolation techniques yielded poor results. For long crack lengths, the analytical results from the beam theory analysis are in fair agreement with those from the modified crack closure integral schemes; however, for short and medium crack lengths, there is a significant difference between the analytical and numerical results. In composite Iosipescu specimens, stable crack propagation (mode I dominant) can be achieved by increasing the tension/shear ratio in the external loading boundary conditions.     

Mixed-mode fracture characterization of adhesive joints

A novel load jig is presented which allows mixed-mode fracture testing of adhesive joints and composite laminates over the entire range from mode I to mode II, by using a single equal adherend double-cantilever-beam specimen. Experiments performed with the load jig showed that G_IIC was approximately three times higher than G_IC for the tested adhesive system consisting of FPL-etched 7075-T6 aluminium adherends bonded with Cybond 4523GB (American Cyanamid) epoxy adhesive. Experimental data showed that G_C was independent of crack length and that there was no dependence of G_IC on adherend thickness. Comparison of G_IIC values obtained by using the load jig to test conventional end notch flexure (ENF) specimens indicated that there are relatively small friction effects between crack faces in mode II testing of ENF specimens. The experimental data were also used to evaluate three different analytical techniques for the mode partitioning of unequal adherend specimens.     

Damage zone around crack tip and fracture toughness of rubber-modified epoxy resin under mixed-mode conditions

Damage zones that form around crack tips before the onset of fracture provide significant data for evaluating the fracture behavior of polymeric materials. The size of the damage zone correlates closely with the fracture toughness of the resin. In this study, we investigate the relationship between the fracture toughness and damage zone size around crack tips of a rubber-modified epoxy resin under mixed-mode conditions. The fracture toughness, G_C, based on the energy release rate, is measured using an end-notched circle type (ENC) specimen. The deformation of rubber particles in the damage zones is also observed using an optical microscope. The results show that the fracture toughness, G_C, of the rubber-modified epoxy resin is closely related to the area of the damage zone. In the specimen with a loading angle of 30°, the rubber particles were deformed ellipsoidally due to the difference between the first and second principal stresses.     

Fracture toughness analysis of inclined crack in cylindrical shell repaired with bonded composite patch

Adhesively bonded composite patch repair has been widely used to restore or extend the service life of cracked structural components due to its efficiency and cost-effectiveness compared to mechanical repair technique. Current available knowledge on patch repair mainly focus on flat damaged structures and the corresponding analysis methods and empirical databases are computationally efficient. In contrast, only limited work has contributed to studying patch repair to curved damaged structures. Authors have developed an adhesive element in conjunction with a shell element to investigate the effect of curvature on the adhesive stresses and mode I fracture toughness of the cracked host shell in the curved repairs. In this paper, this technology is again employed to model an adhesively bonded composite patch repair to a cylindrical shell embedded with an inclined through-thickness crack. The total strain energy release rate (SERR), calculated by the modified virtual crack closure technique (VCCT), is used to evaluate the mix-mode fracture toughness of the damaged structure and further to estimate the efficiency of patch repair. An automatic mesh generation scheme is proposed to conduct a quick parametric analysis, which can also be used to structural optimization design of composite patch repair. The numerical results are presented to show the effect of curvature and inclined angle of the through-thickness crack on fracture toughness of the repaired structure subject to different loads.     

Fatigue de-bond growth in adhesively bonded single lap joints

The fatigue de-bond growth studies have been conducted on adhesively bonded lap joint specimens between aluminium and aluminium with Redux-319A adhesive with a pre-defined crack of 3 mm at the bond end. The correlations between fracture parameters and the de-bond growth data are established using both numerical and experimental techniques. In the numerical method, geometrically non-linear finite element analyses were carried out on adhesively bonded joint specimen for various de-bond lengths measured from the lap end along the mid-bond line of the adhesive. The finite element results were post processed to estimate the SERR components G _I and G _II using the Modified Virtual Crack Closure Integral (MVCCI) procedure. In experimental work, specimens were fabricated and fatigue de-bond growth tests were conducted at a stress ratio R = − 1. The results obtained from both numerical analyses and testing have been used to generate de-bond growth curve and establish de-bond growth law in the Paris regime for such joints. The de-bond growth rate is primarily function of mode-I SERR component G _I since the rate of growth in shear mode is relatively small. The value of Paris exponent m is found to be 6.55. The high value of de-bond growth exponent in Paris regime is expected, since the adhesive is less ductile than conventional metallic materials. This study is important for estimating the life of adhesively bonded joints under both constant and variable amplitude fatigue loads.     

Comparison of Interlaminar Fracture Toughness in Unidirectional and Woven Roving Marine Composites

This paper investigates the effect of fibre lay-up and matrix toughness on mode I and mode II interlaminar fracture toughness (G_Ic and G_IIc) of marine composites. Unidirectional and woven roving fibres were used as reinforcements. Two vinyl ester resins with different toughness were used as matrices. Results from both modes showed toughness variation that is consistent with matrix toughness. Values of G_Ic were not significantly influenced by fibre lay-up except at peak load points in the woven roving/brittle-matrix composite. Each peak load point, caused by interlocked bridging fibres, signified the onset of unstable crack growth. For unidirectional specimens, crack growth was stable and G_Ic statistically more reliable than woven roving specimens, which gave fewer G_Ic values due to frequent unstable crack growth. Mode II tests revealed that, except for crack initiation, G_IIc was higher in woven roving composites. This was due to fibre bridging, perpendicular to the crack growth direction, which encouraged stable crack growth and increased energy absorption. Mode II R-curves were obtained for the woven roving specimens. These R-curves provide additional information useful for characterising delamination resistance. The paper concludes that composites with woven roving fibres show similar mode I delamination characteristics to the unidirectional composites; but their mode II delamination characteristics, after crack initiation, are quite different.     

Interlaminar fracture analysis in the GI–GIII plane using prestressed transparent composite beams

In this paper the mixed-mode I/III prestressed split-cantilever beam fracture specimen is developed, which combines the mode-III modified split-cantilever beam and the well-known double-cantilever beam specimens using a special rig. The most important feature of the novel beam-like specimen is that it is able to provide any combination of the mode-I and mode-III energy release rates. First, the mode-I part of the energy release rate is fixed by inserting a steel roller between the specimen arms inducing a fixed crack opening displacement. Second, the mode-III part of the energy release rate is provided by the external load using a special rig. A simple closed-form solution is developed using beam theory as a data reduction scheme and for the calculation of the energy release rates of the new configuration. The applicability and the limitations of the novel fracture mechanical test are demonstrated using unidirectional glass/polyester composite specimens. If only crack propagation onset is involved then the mixed-mode I/III prestressed split-cantilever beam specimen can be used to obtain the fracture criterion of transparent composite materials in the G_I–G_III plane in a relatively simple way.     

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.