Characterizing delamination of fibre composites by mixed mode cohesive laws

A novel method is used for the determination of mixed mode cohesive laws and bridging laws for the characterisation of crack bridging in composites. The approach is based on an application of the J integral. The obtained cohesive laws were found to possess high peak stress values. Mixed mode cohesive stresses were found to depend on both the normal and tangential crack opening displacements. The bridging laws, which are to be used together with a mode mixity dependent crack tip fracture energy, were found to possess relative low bridging stresses; the peak normal bridging stress was approximately 2 MPa during pure Mode I and the maximum shear stress during pure Mode II was about 10 MPa.     

Experimental and numerical investigations of mixed mode crack growth resistance of a ductile adhesive joint

Polymeric adhesive joints are extensively employed in various industrial and technological applications. It has been observed that in ductile adhesive joints, interface fracture is a common mode of failure which may involve stable crack propagation followed by catastrophic growth. The objectives of this paper are to investigate the effects of bondline thickness and mode mixity on the steady state energy release rate J_ss of such a joint. To this end, a combined experimental and numerical investigation of interfacial crack growth is carried out using a modified compact tension shear specimen involving two aluminium plates bonded by a thin ductile adhesive layer. A cohesive zone model along with a simple traction versus separation law is employed in the finite element simulations of crack growth. It is observed that J_ss increases strongly as mode II loading is approached. Also, it enhances with bondline thickness in the above limit. These trends are rationalized by examining the plastic zones obtained from the numerical simulations. The numerically generated J_ss values are found to agree well with the corresponding experimental results.     

Mode II fracture characterization of a hybrid cork/carbon-epoxy laminate

Fracture characterization under mode II loading of a hybrid laminate composed by a unidirectional carbon fiber-epoxy composite and cork was performed using the End Notched Flexure test. A data reduction scheme based on equivalent crack length concept, specimen compliance and Timoshenko beam theory was applied to evaluate fracture toughness under mode II loading of a composed beam (cork and carbon-epoxy composite). The adopted procedure depends exclusively on the data issuing from load–displacement (P–δ) curve and does not require crack length monitoring during the test which is a difficult task to be accomplished with the necessary accuracy in the ENF test. A numerical analysis using cohesive zone modeling and an inverse procedure was performed to assess the mode II cohesive law that simulates the material fracture under shear loading. It was concluded that hybridization is advantageous relative to monolithic carbon-epoxy laminate in which concerns the observed failure mode, which altered from typically brittle to very ductile thus contributing to avoid sudden shear failures in real applications.     

Determination of cohesive laws by the J integral approach

The determination of cohesive laws for describing large scale failure process zones is discussed. Firstly, a general approach for determination of cohesive laws, by the measurement of the J integral and end-opening of the cohesive zone of double cantilever beam specimens loaded with pure bending moments, is described. Next, two case stories are reviewed: failure of adhesive joints and splitting of a unidirectional carbon fibre/epoxy composite. For the adhesive joints, measured failure strengths of bonded panels having a central notch were found to in very good agreement with predictions from cohesive law parameters determined on test specimens. For the problem of splitting of unidirectional composites, micromechanisms were observed in situ during cracking. A cohesive law shape, predicted by a micromechanics model, was found to agree well with macroscopic cohesive law determined by the J integral approach. The cohesive law was used for predicting effect of specimen shape on strength; predictions were confirmed by experiments. Finally, some ideas regarding determination of mixed mode cohesive laws are discussed.     

Fatigue crack growth acceleration due to intermittent overstressing in adhesively bonded CFRP joints

Double cantilever beam joints were used to investigate cohesive and interlaminar crack growth in bonded composite joints under constant and variable amplitude (VA) loading. Numerical crack growth integration was used to predict the VA fatigue life using constant amplitude data. This underestimated the fatigue crack growth rate for interlaminar cracks, indicating crack growth acceleration due to load interactions. This was also the case for cohesive cracks subjected to a moderate initial strain energy release rate (G_max). An unstable crack growth regime was also identified for the case of high initial G_max cohesive crack propagation. This behaviour is attributed to the development of a damage zone ahead of the crack tip.     

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.     

A data reduction method based on the J-integral to obtain the interlaminar fracture toughness in a mode II end-loaded split (ELS) test

Various difficulties arise in the data reduction of the end-loaded split (ELS) test. On one hand, a small Fracture Process Zone (FPZ) at the crack front is assumed in the existing mode II end-loaded split test methodologies based on Linear Elastic Fracture Mechanics (LEFM). However, mode II fracture has been reported to involve large FPZ and a fuzzy crack tip. Furthermore, the ELS test, is usually affected by geometrical non-linearities.This work proposes a closed-form solution based on the J-integral to determine the interlaminar fracture toughness in an ELS test. This solution avoids the need to measure the crack length, and is applicable when a large FPZ is present, as occurs in adhesive bonded joints between CFRP. In addition, because the ELS test involves large vertical deflections, a correction of the formulation for large displacements has been implemented.This new methodology has been compared to other methods available in the literature based on LEFM by means of an experimental campaign of delamination tests using unidirectional CFRP specimens in order to make a first validation of the method.     

Comparison of mode I and mode II elastic-plastic fracture toughness for two low alloyed high strength steels

In the present work, mode I and mode II tests were carried out on two low alloyed high strength steels. An asymmetrical four point bend specimen and J _II-integral vs. crack growth resistance curve technique were used for determining the mode II elastic-plastic fracture toughness, J _IIc · J _II-integral expression of the specimen was calibrated by finite element method. The results indicate that the present procedure for determining the J _IIc values is easy to use. Moreover, the mode I fracture toughness J _Ic is very sensitive to the rolling direction of the test steels, but the mode II fracture toughness J _IIc is completely insensitive to the rolling direction of the steels, and the J _IIc /J _Ic ratio is not a constant for the two steels, including the same steel with different orientations. Finally, the difference of the fracture toughness between the mode I and mode II is discussed with consideration of the different fracture mechanisms.     

Fracture characterization of sandwich structures interfaces under mode I loading

The accurate prediction of failure of sandwich structures using cohesive mixed-mode damage models depends on the accurate characterization of the cohesive laws under pure mode loading. In this work, a numerical and experimental study on the asymmetric double cantilever beam (DCB) sandwich specimen is presented with the objective to characterize the debonding fracture between the face sheet and the core under pure mode I. A data reduction method based on beam theory was formulated in such a way to incorporate the complex damaging phenomena of the debonding due to the material and geometric asymmetry of the specimen, via the consideration of an equivalent crack length (a_e). Experimental DCB tests were performed and the proposed methodology was followed to obtain the debonding fracture energy (G_Ic). The experimental tests were numerically simulated and a cohesive damage model was employed to reproduce crack propagation. An inverse method was followed to obtain the local cohesive strength (σ_u,I) based on the fitting of the numerical and experimental load–displacement curves. With the value of fracture energy and cohesive strength defined, the cohesive law for interface mode I fracture is characterized. Good agreement between the numerical and the experimental R-curves validates the accuracy of the proposed data reduction procedure.     

A numerical investigation on the geometry dependence of the crack growth resistance in CT specimens

The influence of the specimen thickness B and the ligament length b on the J _R -curves is numerically investigated for CT specimens. The thickness effect is taken into account with 2-D analyses by dividing a plain sided specimen into a plane stress part and a plane strain part. The fracture process is controlled by experimentally determined critical values of the crack tip opening displacement for crack growth initiation (CTOD_i) and the crack tip opening angle for stable crack growth (CTOA_C). It is shown that for the global behaviour of a plain sided specimen, the B/b ratio is essential. The difference between the geometry dependence of the initiation value of the J-integral and the geometry dependence of the slope of the J _R -curves is also shown.     

Fracture criterion for kinking cracks in a tri-material adhesively bonded joint under mixed mode loading

The fracture behavior of a composite/adhesive/steel bonded joint was investigated by using double cantilever beam specimens. A starter crack is embedded at the steel/adhesive interface by inserting Teflon tape. The composite adherend is a random carbon fiber reinforced vinyl ester resin composite while the other adherend is cold rolled steel. The adhesive is a one-part epoxy that is heat cured. The Fernlund-Spelt mixed mode loading fixture was employed to generate five different mode mixities. Due to the dissimilar adherends, crack turning into the adhesive (or crack kinking) associated with joint failure, was observed. The bulk fracture toughness of the adhesive was measured separately by using standard compact tension specimens. The strain energy release rates for kinking cracks at the critical loads were calculated by a commercial finite element analysis software ABAQUS in conjunction with the virtual crack closure technique. Two fracture criteria related to strain energy release rates were examined. These are (1) maximum energy release rate criterion (G_max) and, (2) mode I facture criterion (G_II = 0). They are shown to be equivalent in this study. That is, crack kinking takes place at the angle close to maximum G or G_I (also minimum G_II, with a value that is approximately zero). The average value of G_IC obtained from bulk adhesive tests using compact tension specimens is shown to be an accurate indicator of the mode I fracture toughness of the kinking cracks within the adhesive layer. It is concluded that the crack in tri-material adhesively bonded joint tends to initiate into the adhesive along a path that promotes failure in pure mode I, locally.     

The cohesive zone model in a problem of delayed hydride cracking of zirconium alloys

The crack tip model with the cohesive zone ahead of a finite crack tip has been presented. The estimation of the length of the cohesive zone and the crack tip opening displacement is based on the comparison of the local stress concentration, according to Westergaard's theory, with the cohesive stress. To calculate the cohesive stress, von Mises yield condition at the boundary of the cohesive zone is employed for plane strain and plane stress. The model of the stress distribution with the maximum stress within the cohesive zone is discussed. Local criterion of brittle fracture and modelling of the fracture process zone by cohesive zone were used to describe fracture initiation at the hydride platelet in the process zone ahead of the crack tip. It was shown that the theoretical K _IH-estimation applied to the case of mixed plane condition within the process zone is qualitatively consistent with experimental data for unirradiated Zr-2.5Nb alloy. In the framework of the proposed model, the theoretical value of K ^H _IC for a single hydride platelet at the crack tip has been also estimated.     

Critical assessment of the application of the J-integral and CTOD concepts to circumferentially cracked copper bars

The aim of this work is to explore experimentally the validity of the concepts of J-integral and crack tip opening displacement for characterizing the stress and strain state at the tip of an axisymmetrical crack in a bar undergoing large plastic strain before crack extension. The tests are made on extruded copper round bars presenting a very high ductility. Three different analytical formulations of the J-integral proposed in the literature for circumferentially cracked bars are compared at initiation of cracking. The limit between shallow crack and deep crack geometries is experimentally demonstrated. It is found that, in neither of these geometries, J and _CTOD are dominant. However, the ratio J_c/_c is constant for deep cracks, which suggests an alternative fracture criterion consisting in postulating the dissipation of an average critical energy per unit volume until crack extension.     

Interlaminar fracture analysis in the GII-GIII plane using prestressed transparent composite beams

This work presents the mixed-mode II/III prestressed split-cantilever beam specimen for the fracture testing of composite materials. In accordance with the concept of prestressed composite beams one of the two fracture modes is provided by the prestressed state of the specimen, and the other one is increased up to fracture initiation by using a testing machine. The novel beam-like specimen is able to provide any combinations of the mode-II and mode-III ERRs. Data reduction is made by using the virtual crack-closure technique. 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 beam specimen can be used to obtain the fracture criterion of transparent composite materials in the G_II-G_III plane in a relatively simple way.     

Fracture toughness of ISO 3183 X80M (API 5L X80) steel friction stir welds

Friction stir welding (FSW) is a solid-state joining process with numerous advantages such as good dimensional stability and repeatability, which is widely used Al alloys and with a great potential for critical joining applications involving high melting temperature alloys. Twelve millimeter thick plates of ISO 3183 X80M (API 5L X80) steel was friction stir welded using two passes on both sides of the plate using ceramic tools. Different heat inputs were obtained using a fix travel (welding) speed in combination with several spindle speeds. The fracture toughness of the two-pass joints was evaluated at 25 °C using the critical crack tip opening displacement (CTOD_m), revealing that joints produced with lower spindle speeds presented higher toughness at the heat-affected zone (HAZ) and stir zone (SZ), which are comparable with the base metal (BM) toughness. On the other hand, joints produced using higher spindle speeds presented low fracture toughness at the SZ and elevated CTOD_m toughness at the HAZ. The joints produced with low spindle speeds showed CTOD_m-values above the offshore standard (DNV-OS-F101) requirements.     

Modeling dynamic crack propagation in fiber reinforced composites including frictional effects

Dynamic crack propagation in a unidirectional carbon/epoxy composite is studied through finite element analyses of asymmetric impact (shear loading) of a rod against a rectangular plate. A finite deformation anisotropic visco-plastic model is used to describe the constitutive response of the composite. Crack propagation is simulated by embedding zero thickness interface element along the crack path. An irreversible mixed-mode cohesive law is used to describe the evolution of interface tractions as a function of displacement jumps. Contact and friction behind the crack tip are accounted for in the simulations. The failure of the first interface element at the pre-notch tip models onset of crack extension. Crack propagation is modeled through consecutive failure of interface elements. The dynamic crack propagation phenomenon is studied in terms of crack initiation time, crack speed, mode I and mode II displacement jumps and tractions associated with the failure of interface elements, effective plastic strain at the crack tip and path independent integral J^′. Analyses are carried out at impact velocities of 5, 10, 20, 30 and 40 m/s, assuming the crack wake is frictionless. Moreover, analyses at impact velocities of 30 and 40 m/s are also carried out with a friction coefficient of 0.5, 1, 5 and 10 along the crack surfaces. The analyses show that steady-state intersonic crack propagation in fiber reinforced composite materials occurs when the impact velocity exceeds a given threshold. A steady-state crack speed of 3.9 times the shear wave speed and 83% of the longitudinal wave speed is predicted in the cases in which the impact velocity is above 10 m/s. Detailed discussion is given on the features of sub-sonic and intersonic crack propagation. It is shown that friction effects, behind the crack tip, do not have a significant effect on maximum crack speed; however, they do on characteristics of the shock wave trailing the crack tip. The analyses also show that the contour integral J^′, computed at contours near the crack tip, is indeed path independent and can serve as a parameter for characterizing intersonic crack propagation.     

An Investigation of the Effects of Crack Front Curvature on the Crack-Tip Opening Displacement of A707 Steel

This paper examines the effects of crack front curvature on the fracture toughness (crack-tip opening displacement) of A707 steel. Fracture mechanics specimens, in which the radii of curvature of the crack fronts are controlled in an effort to simulate potential variations in crack front profiles in fracture experiments, were produced by machining and fatigue pre-cracking. Three-point bend crack-tip opening displacements (CTOD_c) were measured in accordance with the ASTM E-1290 code. The results show that the critical CTOD_c increases with increasing crack front curvatures between 0.05 and 0.17 mm^–1. In all cases, stable crack growth and final catastrophic failure of the specimens are found to occur by transgranular ductile dimpled fracture, in which the ductile dimples are nucleated around MnS or Al₂(Mg)O₃ inclusions. The implications of the results are discussed for the measurement of critical CTOD_c in specimens with varying levels of crack front curvature.     

Influence of the crack plane asymmetry over GII results in carbon epoxy ENF specimens

In this paper unidirectional carbon epoxy End Notch Flexure samples (ENF) with different crack plane positions have been analyzed in order to study the influence of the degree of asymmetry over the load state at the crack tip. This study has been performed from different points of view: experimental, numerical approaches (Finite Element Models) and fractographic observations.From these studies it has been concluded that the deviation of the crack plane from the specimen midplane has no influence or little influence over the corresponding critical value of the energy release rate in mode II (G_II).In other words, the asymmetry of the crack plane does not induce mode I load state at the crack tip while the energy release rate related to the mode II load remains almost constant as the crack plane moves from the midplane.Fractographic observations have shown “hackle markings” structures typical from mode II fracture.Finally, a good agreement was found between experimental and numerical procedures as errors were always lower than 7%.     

Fracture mechanics analysis of anisotropic plates by the boundary element method

This paper presents an analysis of mixed mode fracture mechanics problems arising in anisotropic composite laminates. The boundary element method (BEM) and the J _k integral are presented as accurate techniques to compute the stress intensity factors K _I and K _II of two dimensional anisotropic bodies. Using function of a complex variable a decoupling procedure is derived to obtain the stress intensity factors. The procedure is based on the computation of the J ₁-integral and of the ratio of relative displacements at the crack faces, near the crack tip. Applications are presented for unidirectional and symmetric laminates of glass, boron and graphite-epoxy materials. Numerical examples of problems of pure mode I and mixed mode deformations are given, in order to demonstrate the accuracy of the method.     

An FEM study on crack tip blunting in ductile fracture initiation

Ductile fracture is initiated by void nucleation at a characteristic distance (I_c) from the crack tip and propagated by void growth followed by coalescence with the tip. The earlier concepts expressed I_c in terms of grain size or inter-particle distance because grain and particle boundaries form potential sites for void nucleation. However, Srinivas et al. (1994) observed nucleation of such voids even inside the crack tip grains in a nominally particle free Armco iron. In an attempt to achieve a unified understanding of these observations, typical crack-tip blunting prior to ductile fracture in a standard C(T) specimen (Mode I) was studied using a finite element method (FEM) supporting large elasto-plastic deformation and material rotation. Using a set of experimental data on Armco iron specimens of different grain sizes, it is shown that none of the locations of the maxima of the parameters stress, strain and strain energy density correspond to I_c. Nevertheless, the size of the zone of intense plastic deformation, as calculated from the strain energy density distribution ahead of the crack tip in the crack plane, compares well with the experimentally measured I_c. The integral of the strain energy density variation from the crack tip to the location of void nucleation is found to be linearly proportional to J_IC. Using this result, an expression is arrived at relating I_c to J_IC and further extended to CTOD_c.