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.     

Mixed-mode I/II wood fracture characterization using the mixed-mode bending test

In this work fracture characterization of wood under mixed-mode I/II loading is addressed. The mixed-mode bending test is used owing to its aptitude for easier alteration of mode ratio. Experimental tests were performed covering a wide range of mode ratios in order to obtain a mixed-mode fracture criterion for the maritime pine (Pinus pinaster Ait.) in the RL crack propagation system. A data reduction scheme based on beam theory and crack equivalent concept was used to overcome some difficulties inherent to the test. The method does not require crack length monitoring during propagation and provide an entire resistance curve allowing easier identification of the fracture energy. A numerical analysis using cohesive elements was also performed to validate the method. The linear energetic fracture criterion was proved to be the most adequate to describe the failure envelop of this wood species.     

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.     

Experimental investigation of mixed-mode fracture behaviour of woven laminated composite

In this paper, the mixed-mode interlaminar fracture behaviour of woven carbon-epoxy composite was investigated based on experimental and numerical analyses. A modified version of Arcan specimen was employed to conduct a mixed mode fracture test using a special loading device. A full range of mixed-mode loading conditions including pure mode-I and pure mode-II loading were created and tested. This test method has a simple procedure, clamping/unclamping the specimens are easy to achieve and only one type of specimen is required to generate all loading conditions. Also, finite element analysis was carried out for different loading conditions in order to determine correction factors needed for fracture toughness calculations. Interlaminar fracture toughness was determined experimentally with the modified version of the Arcan specimen under different mixed-mode loading conditions. Results indicated that the interlaminar cracked specimen is tougher in shear loading condition and weaker in tensile loading condition. Response of woven carbon-epoxy composite was also investigated through several criteria and the best criterion was selected. The interlaminar fracture surfaces of the carbon-epoxy composite under different mixed-mode loading conditions are examined by scanning electron microscopy (SEM).     

Composite toughness enhancement with interlaminar reinforcement

An experimental investigation of a newly proposed through-thickness reinforcement approach aimed to increase interlaminar toughness of laminated composites is presented. The approach alters conventional methods of creating three-dimensional fiber-reinforced polymer composites in that the reinforcing element is embedded into the host laminate after it has been cured. The resulting composite is shown to possess the benefits of a uniform surface quality and consolidation of the original unreinforced laminate. This technique was found to be highly effective in suppressing the damage propagation in delamination double-cantilever beam (DCB) test samples under mode I loading conditions. Pullout testing of a single reinforcing element was carried out to understand the bridging mechanics responsible for the improved interlaminar strength of reinforced laminate and stabilization and/or arrest of delamination crack propagation. The mode I interlaminar fracture of reinforced DCB samples was modeled using two-dimensional cohesive finite-element scheme to support interpretation of the experiments.     

Buckling strength of adhesively-bonded single and double-strap repairs on carbon-epoxy structures

This work reports on an experimental and finite element method (FEM) parametric study of adhesively-bonded single and double-strap repairs on carbon-epoxy structures under buckling unrestrained compression. The influence of the overlap length and patch thickness was evaluated. This loading gains a particular significance from the additional characteristic mechanisms of structures under compression, such as fibres microbuckling, for buckling restrained structures, or global buckling of the assembly, if no transverse restriction exists. The FEM analysis is based on the use of cohesive elements including mixed-mode criteria to simulate a cohesive fracture of the adhesive layer. Trapezoidal laws in pure modes I and II were used to account for the ductility of most structural adhesives. These laws were estimated for the adhesive used from double cantilever beam (DCB) and end-notched flexure (ENF) tests, respectively, using an inverse technique. The pure mode III cohesive law was equalled to the pure mode II one. Compression failure in the laminates was predicted using a stress-based criterion. The accurate FEM predictions open a good prospect for the reduction of the extensive experimentation in the design of carbon-epoxy repairs. Design principles were also established for these repairs under buckling.     

Interlaminar fracture characterization for plain weave fabric composites

For the analysis of laminated composite plates under transverse loading and drilling of composites, all the elastic, strength and fracture properties of the composite plates are essential. Interlaminar critical strain energy release rate properties in mode I, mode II, mixed mode I/II and mode III have been evaluated for two types of plain weave fabric E-glass/epoxy laminates. The double cantilever beam test and the end notch flexure test have been used for mode I and mode II loading. The mixed mode bending test and split cantilever beam test have been used for mixed mode I/II and mode III loading. It is observed that the plain weave fabric composite with lesser strand width has higher interlaminar fracture properties compared to the plain weave fabric composite with more strand width. Further, crack length versus crack growth resistance plots have been presented for mode III loading. In general, it is observed that total fracture resistance is significantly higher than the critical strain energy release rate.     

Bone fracture characterization using the end notched flexure test

A miniaturized version of the end notch flexure test was used in the context of pure mode II fracture characterization of bovine cortical bone. To overcome the difficulties intrinsic to crack length monitoring during its propagation an equivalent crack method was employed as data reduction scheme. The proposed method was validated numerically by means of a finite element analysis including a cohesive zone modeling and subsequently applied to experimental results to determine the fracture energy of bone under pure mode II loading. Finally, a cohesive law representative of fracture behavior of each specimen was determined employing an inverse method, considering a trapezoidal shape for the softening law. The consistency of the obtained results leads to the conclusion that the trapezoidal law is adequate to simulate fracture behavior of bone under mode II loading. The proposed testing setup and the employed data reduction scheme constitute powerful tools in which concerns fracture characterization of bone under pure mode II loading and can be viewed as the main outcomes of this work.     

Fracture surface evolution and apparent delamination toughness in split composite beam specimens subjected to mixed mode I–III loading

The influence of specimen twisting during global anti-plane shear loading in composite split beam specimens is studied. Tests were conducted on specimens with different thicknesses and delamination lengths to produce different amounts of specimen twisting prior to fracture. It is shown that specimen twisting causes mode I stresses to develop, thereby producing mixed mode I–III conditions along the delamination front. This causes near-tip transverse cracks to initiate, prior to delamination advance, at an orientation related to the mode mix. Unlike in homogeneous materials, transverse crack extension is accompanied by planar delamination advance, and transverse crack rotation during extension is restricted by the laminate’s fibers. The overall fracture surface evolution is therefore strongly controlled by specimen geometry. The influence of these findings on the apparent delamination toughness as obtained from composite split beam and other types of mode III tests is discussed.     

A New Procedure for Mode I Fracture Characterization of Cement‐Based Materials

Fracture characterization under mode I loading of a cement‐based material using the single‐edge‐notched beam loaded in tree‐point‐bending was performed. A new method based on beam theory and crack equivalent concept is proposed to evaluate the Resistance‐curve, which is essential to determine fracture toughness with accuracy. The method considers the existence of a stress relief region in the vicinity of the crack, dispensing crack length monitoring during experiments. A numerical validation was performed by finite element analysis considering a bilinear cohesive damage model. Experimental tests were performed in order to validate the numerical procedure. Digital image correlation technique was used to measure the specimen displacement with accuracy and without interference. Excellent agreement between numerical and experimental load–displacement curves was obtained, which validates the procedure.     

Fracture behavior and toughening mechanism in Zanchor reinforced composites under mode II loading

The mode II interlaminar fracture behavior and the toughening mechanism of Zanchor reinforced composite laminates were investigated by using the End Notched Flexure (ENF) and Interlaminar Shear (ILS) specimens. The ENF test results demonstrated that the Zanchor process was highly effective to improve the mode II fracture toughness of composite laminates, where the fracture toughness increased almost linearly with the Zanchor density. The R-curves of Zanchor composites were roughly divided into the transition and stable regions, where the width of the transition region became larger as the Zanchor density increased. The macroscopic fracture behavior of the Zanchor composites was still brittle under mode II loading like that of the base composite, where the crack tip process zone was estimated to be rather small regardless of the Zanchor density. The ILS test results demonstrated that the square of the normalized shear strength increased linearly with the Zanchor density and agreed quantitatively with the normalized fracture toughness. The wedge effect was supposed to be the dominant toughening mechanism against the mode II fracture, where the entangled fiber bundles partly sustained the shear stress in the vicinity of the crack tip. The entangled fiber bundles played an important role to form the mode II fracture surface, where the microscopic fracture pattern of the entangled fiber bundles was mainly the breakage of the fiber bundles rather than the pull-out or debonding of the fiber bundles.     

Analysis of mode I delamination of z-pinned composites using a non-dimensional analytical model

We present a non-dimensional analytical model for crack propagation in a z-pinned double cantilever beam specimen (DCB) under mode I loading. Effect of various design parameters on the crack bridging length and apparent fracture toughness are investigated using this model. The efficacy of the analytical model is evaluated by comparing the results with 3D finite element (FE) simulations of the DCB. In the FE model the z-pins are modeled as discrete nonlinear elements. Bi-linear cohesive elements are used ahead of the crack tip to account for the interlaminar fracture toughness of the composite material. The results for load–deflection and crack length obtained from the analytical model and the FE model are compared and found to be in good agreement. The proposed non-dimensional analytical model will be useful in the design and analysis of translaminar reinforcements for composite structures.     

Interlaminar and intralaminar fracture characterization of composites under mode I loading

The interlaminar and intralaminar fracture of laminated composites under mode I loading was studied using the double cantilever beam test. The effect of bridging on the measured fracture energy was assessed by cutting fibres during crack propagation. The fracture energy was evaluated considering a previously developed data reduction scheme based on the beam theory and crack equivalent concept. The model only requires the applied load–displacement data and provides a complete R-curve allowing the definition of the critical energy from the plateau value. A cohesive damage model was used to validate the procedure. It was verified experimentally that bridging phenomenon is pronounced, being more important in intralaminar tests. However, a detailed observation of the intralaminar R-curves showed that the intrinsic toughness, without fibre bridging effects, is similar to the interlaminar one.     

Numerical and experimental investigation on lap shear fracture of Al/CFRP laminates

This paper presents a new approach to numerically investigate the lap shear fracture of a hybrid laminate made of Carbon Fibre Reinforced Plastic (CFRP) and metal foil plies (e.g. aluminium), validated by corresponding experiments. The numerical Finite Element (FE) model of the hybrid laminate, subjected to lap shear fracture, is composed of five laminas with alternating metal/CFRP layers with cohesive elements lying within Al/CFRP interface. In the FE model, individual CFRP laminas are assumed as an orthotropic homogenized continuum under plane stress, and aluminium facesheets are modelled as an elastic–plastic continuum. The Al/CFRP interface is represented via quadratic cohesive elements, the constitutive law of which is an exponentially decaying law representing the degrading behaviour of the interface (implemented as user element in ABAQUS). The numerical model captures the experimentally obtained results with minimal error, and predicts the failure modes successfully. The influence of specimen geometry (e.g. overlap length, total length, and total width) on lap shear fracture response is analyzed in detail in this study, too, in order to confirm the specimen design for the test, as there is still no corresponding test standard for hybrid laminates.     

Intersonic delamination in curved thick composite laminates under quasi-static loading

Dynamic delamination in curved composite laminates is investigated experimentally and numerically. The laminate is 12-ply graphite/epoxy woven fabric L-shaped laminate subject to quasi-static loading perpendicular to one arm. Delamination initiation and propagation are observed using high speed camera and load–displacement data is recorded. The quasi-static shear loading initiates delamination at the curved region which propagates faster than the shear wave speed of the material, leading to intersonic delamination in the arms. In the numerical part, the experiments are simulated with finite element analysis and a bilinear cohesive zone model. Cohesive interface elements are used between all plies with the interface properties obtained from tests. The simulations predict a single delamination initiating at the corner under pure mode-I stress field propagating to the arms under pure mode-II stress field. The crack tip speeds transition from sub-Rayleigh to intersonic in conjunction with mode change. In addition to intersonic mode-II delamination, shear Mach waves emanating from the crack tips in the arms are observed. The simulations and experiments are found to be in good agreement at the macro-scale, in terms of load-displacement behavior and failure load, and at the meso-scale, in terms of delamination initiation location and crack propagation speeds. Finally, a mode dependent crack tip definition is proposed and observation of vibrations during delamination is presented. This paper presents the first conclusive evidence of intersonic delamination in composite laminates triggered under quasi-static loading.     

Modeling of the dynamic delamination of L-shaped unidirectional laminated composites

One of the widely used geometrically complex parts in advanced commercial aircraft is the L-shaped composite. Due to the sharp curved geometry, interlaminar opening stresses are induced and delamination occurs under considerable mode-mixities in L-shaped beams. Dynamic phenomena during delamination initiation and propagation of L-shaped beams are investigated using dynamic (explicit) finite element analysis in conjunction with cohesive zone methods. The 2-D model consists of 24 plies of unidirectional CFRP laminate with an initial 1 mm crack at the center of the laminate at the bend. Loading is applied parallel to one of the arms quasi-statically. The loading type yields different traction fields and mode-mixities in the two sides of the crack in which delamination occurs under shear stress dominated loading on one crack tip and opening stress dominated loading on the other. The speed of the delamination under shear dominated loading at one side is 800 m/s and under normal stress dominated loading is 50 m/s. In addition radial compressive waves at the interface are observed. Finally, as the thickness is changed, a different failure mode is observed in which a secondary crack nucleates at the arm and propagates towards the center crack.     

Numerical analysis of the ENF and ELS tests applied to mode II fracture characterization of cortical bone tissue

The objective of this work is to verify numerically the adequacy of the ENF and the ELS tests to determine the fracture toughness under mode II loading of cortical bovine bone tissue. A data‐reduction scheme based on the specimen compliance and the equivalent crack concept is proposed to overcome the difficulties inherent to crack monitoring during its growth. A cohesive damage model was used to simulate damage initiation and growth, thus assessing the efficacy of the proposed data‐reduction scheme. The influences of the initial crack length, local strength and toughness on the measured fracture energy were analysed, taking into account the specimen length restriction. Some limitations related to spurious influence on the fracture process zone of the central loading in the ENF test, and clamping conditions in the ELS test were identified. However, it was verified that a judicious selection of the geometry allows, in both cases, a rigorous estimation of bone toughness in mode II.     

Interlaminar and intralaminar fracture modes in 0/90 cross-ply glass/epoxy laminate

Delamination of a cross-ply 0/90 glass fibre-reinforced composite laminate with an epoxy-phenol matrix was studied using a double cantilever beam test. Fracture toughness was determined by measurement of bend angle of the cantilever beams. Results obtained with this method were in agreement with those from conventional compliance and area methods. Two different fracture modes were observed: interlaminar and intralaminar. In the interlaminar fracture mode, crack jumps in the space between two neighbouring 0° and 90° plies were observed. With the interlaminar fracture mode, during crack initiation G_Ic decreased with crack length. Intralaminar fracture mode consisted of the gradual growth of a crack through a 0° ply. Fibres bridging the opposite sides of the crack were observed in this case, and fracture toughness G_Ic did not change with crack length. G_Ic (420 J m⁻²) at intralaminar fracture mode was approximately twice that at interlaminar fracture mode (220 J m⁻²). The difference in fracture toughness was explained by the dissipation of energy by fibres bridging the opposite sides of the crack at intralaminar fracture mode.     

Interlaminar shear stresses in laminated composite plates under thermal and mechanical loading

The combined effects of thermal and mechanical loadings on the distribution of interlaminar shear stresses in composite laminated thin and moderately thick composite plates are investigated numerically using the commercially available software package MSC NASTRAN/PATRAN. The validity of the present finite element analysis is demonstrated by comparing the interlaminar shear stresses evaluated using the experimental measurement. Various parametric studies are also performed to investigate the effect of stacking sequences, length to thickness ratio, and boundary conditions on the interlaminar shear stresses with identical mechanical and thermal loadings. It is observed that the effect of thermal environment on the interlaminar shear stresses in carbon-epoxy fiber-reinforced composite laminated plates are much higher in asymmetric cross-ply laminate and anti-symmetric laminate compared to symmetric cross-ply laminate and unidirectional laminate under identical loadings and boundary conditions.     

Influence of shear parameters on mixed–mode fracture of concrete

The influence of the mode II fracture parameters on the mixed mode fracture experimental tests of quasibrittle materials is studied. The study is based on experimental results and numerical analyses. For the numerical study, a procedure for mixed mode fracture of quasibrittle materials is presented. The numerical procedure is based on the cohesive crack approach, and extends it to mixed mode fracture. Four experimental sets of mixed mode fracture were modelled, one from Arrea and Ingraffea and another from a nonproportional loading by the authors, both with bending concrete beams. Two other sets of experimental fracture were modelled, based on double-edge notched testing; in these tests an important mode II is beforehand expected. The numerical results agree quite well with experimental records. The influence of the main parameters for mode II fracture on the mixed mode fracture is studied for the four experimental set of tests and compared with these results. In all them, large changes in the mode II fracture energy hardly modify the numerical results. The tangential and normal stresses along the crack path during the loading proccess are obtained, also with different values of the mode II fracture energy. For the studied experimental tests it is concluded that the crack is initiated under mixed mode but propagated under predominant mode I. This allows a development of mixed mode fracture models, mainly based on standard properties of the material measured by standard methods, avoiding the problems associated with the measurement of mode II fracture parameters, such as mode II fracture energy and cohesion.