Mixed-mode Bending Test Research Articles

Crack tip identification with long FBG sensors in mixed-mode delamination

The uncertainty of the crack tip position inside composite coupons during a delamination test under variable fracture mode conditions reduces the accuracy of the experimental results. In this work a method is presented where the crack tip position is located using long embedded Fibre Bragg Grating (FBG) sensors together with the Optical Low Coherence Reflectometry (OLCR) technique. With this technique the local Bragg wavelength is measured which then enables to calculate the axial strain profile within the grating. Carbon/epoxy samples are tested under different mode ratios through the standard Mixed-Mode Bending (MMB) test. Embedded long FBG sensors are used to measure the axial strain profile along the whole grating at different stages of the test. The crack tip can be precisely identified with the long embedded FBGs and then checked by means of a visual inspection after complete delamination of the sample. The data indicate that the long FBG sensor detects the crack tip inside the sample at least as precisely as the traditionally performed visual inspections carried out during the test by means of the lateral markings. Numerical simulations using cohesive elements are in good agreement with the experimental data.

Mixed-Mode Bending Test for Fracture Toughness of Composite Bonding Adhesive Layer

This paper describes the mixed-mode bending test fracture toughness of composite adhesive J116-b. The test theory and experimental requirements are introduced. The fracture toughness of mode I, mode II, and different mode mixture of 0.4, 0.6, and 0.8 are obtained. It is found that the total fracture toughness is increasing with the increasing of mode mixture. It is also obtained that the technique of calculating fracture toughness by considering the influence of the weight of lever and attach apparatus is more accurate.

Study on Mixed-Mode Interlaminar Fracture of Laminated Composites

The superposition-finite element method is developed to analyze the mixed-mode delamination in laminated composites. Both a coarse global mesh and an overlaying fine local mesh are integrated into the finite element analysis model. The whole design domain is discretized by a uniform global mesh, while the high stress regions are discretized by fine local meshes. Local mesh is built independently from the global mesh, which greatly simplifies the model generation procedures. Strain energy release rate is calculated based on the modified virtual crack closure-integral method, which is used to describe the propagation of delamination in laminated composites. Mixed-mode bending tests are performed for unidirectional and cross-ply carbon fiber reinforced laminated composites to characterize the interlaminar fracture behavior under mixed-mode I/II loading conditions. The interlaminar fracture toughness is also given for different mixed-mode ratio. It is seen that fracture resistance for laminated composites exhibit R-curve behavior (increase as delamination propagation). However, once the delamination is sufficiently long, the interfacial fracture toughness changes slightly as the delamination extended and become almost independent of the delamination length. The results of finite element method are in good agreement with the experimental results and provides a basis for establishing failure criterion used in damage tolerance analysis of composite structures.

Effect of Bondline Thickness on Mixed-Mode Fracture of Adhesively Bonded Joints

The effect of bondline thickness on the critical strain energy release rate (CSERR) was investigated using aluminum adherends and an epoxy adhesive. Complete mixed Mode I/II fracture envelopes for adhesive thicknesses ranging from 0.203 to 1.52 mm were developed using double cantilever beam (DCB), mixed-mode bending (MMB), and end notch flexure (ENF) tests methods. Bondline thickness strongly affects the CSERR for different amounts of Mode II component. Pure Mode II had the largest CSERR and showed monotonic increase with bondline thickness, whereas pure Mode I had the lowest CSERR and exhibited non monotonic relationship with bondline thickness. The shape and size of the plastic zone that develops prior to crack propagation was predicted by finite element analysis. Variation of CSERR as a function of adhesive layer thickness was shown to be related to the size of the plastic zone for Mode I and MMB 50% fracture. No correlation was observed for the MMB 75% and Mode II, however.

Prediction of the cohesive strength for numerically simulating composite delamination via CZM-based FEM

The cohesive strength is an important parameter in numerically modeling composite delamination via CZM (cohesive zone model) based FEM. A micromechanical model is proposed to predict the cohesive strength based on the periodic RVE technique. A periodic displacement boundary condition has been presented on the assumption that the RVE is orthotropic in the sense of overall response. The cohesive strengths of T700/QY8911 and AS4/PEEK laminates at various fibers cross-angles are gained by FEM. With the predicted cohesive strengths the FEM simulations on Mixed-Mode bending (MMB) and seven-point bending test are presented, and the results are in fair agreement with experimental observation.

Face/core interface fracture characterization of mixed mode bending sandwich specimens

Debonding of the core from the face sheets is a critical failure mode in sandwich structures. This paper presents an experimental study on face/core debond fracture of foam core sandwich specimens under a wide range of mixed mode loading conditions. Sandwich beams with E-glass fibre face sheets and PVC H45, H100 and H250 foam core materials were evaluated. A methodology to perform precracking on fracture specimens in order to achieve a sharp and representative crack front is outlined. The mixed mode loading was controlled in the mixed mode bending (MMB) test rig by changing the loading application point (lever arm distance). Finite element analysis was performed to determine the mode-mixity at the crack tip. The results showed that the face/core interface fracture toughness increased with increased mode II loading. Post failure analysis of the fractured specimens revealed that the crack path depends on the mode-mixity at the crack tip, face sheet properties and core density.

Cryogenic delamination growth in woven glass/epoxy composite laminates under mixed-mode I/II fatigue loading

This paper investigates the fatigue delamination growth behavior in woven glass fiber reinforced polymer (GFRP) composite laminates under mixed-mode I/II conditions at cryogenic temperatures. Fatigue delamination tests were performed with the mixed-mode bending (MMB) test apparatus at room temperature, liquid nitrogen temperature (77 K) and liquid helium temperature (4 K), in order to obtain the delamination growth rate as a function of the range of the energy release rate, and the dependence of the delamination growth behavior on the temperature and the mixed-mode ratio of mode I and mode II was examined. The energy release rate was evaluated using three-dimensional finite element analysis. The fractographic examinations by scanning electron microscopy (SEM) were also carried out to assess the mixed-mode fatigue delamination growth mechanisms in the woven GFRP laminates at cryogenic temperatures.

Finite element analysis of delamination of a composite component with the cohesive zone model technique

PurposeThe purpose of this paper is to assess a numerical tool to simulate and predict the onset and the propagation of the delaminations in a composite structure.Design/methodology/approachThe approach to the work is done through the cohesive zone model technique applied to the finite element method.FindingsDouble cantilever beam, end notched flexure and mixed mode bending tests have been performed and correlated to benchmark cases, in order to validate the procedure. Numerical test campaign on specimens of the skirts with delaminations has been performed to analyze the behaviour under compressive load and the buckling.Originality/valueThis tool is applied to the study of the behaviour of some components in carbon/epoxy composite of a space structure in which one or more delaminations are eventually present following impact damage or manufacturing process. The components in particular are the booster's skirts of a small class launcher, subjected to a compressive load.

Influence of the Mode Mixity Ratio and Test Procedures on the Total Energy Release Rate in Carbon-Epoxy Laminates

In this work, the fracture behaviour under modes I, II and different mixed mode I/II ratios has been studied for a AS4/3501-6 carbon fibre epoxy resin laminate. Mixed Mode tests were carried out by means of two different procedures: MMB (Mixed Mode Bending) and ADCB (Asymmetric Double Cantilever Beam). ADCB specimens, in which the crack plane is out of the laminate midplane, are simple and useful test configurations to produce a mixed mode load state at the crack tip of the samples. The ADCB test is not still covered by international standards, so the calculations were performed by means of the Finite Element Modelling (FEM) and analytical formulation developed in previous works. FEM was used in order to analyze modes I, II and mixed I/II and to compare the experimental and numerical results. It was found a good agreement between ADCB and MMB tests. On the other hand, it was also observed that the critical energy Gc increased as the mode mixity ratio GII/Gc increased. Finally, experimental and numerical results showed a good agreement as the differences obtained from both procedures were generally lower than 10%.

フォームコアサンドイッチ梁の破壊靭性評価試験に関する解析

This study shows two fundamental aspects related to fracture characterization of sandwich beams for aerospace application; 1) formulation of energy release rates associated with face sheet debonding or core cracking in sandwich beams with residual thermal stresses, and 2) crack kinking analysis of foam core sandwich beams. Energy release rates are formulated using the bi-layer shear deformable beam model with consideration of residual thermal stresses. This formulation is specifically applied to double cantilever beam (DCB), end notched flexure (ENF) and mixed mode bending (MMB) tests of sandwich structures. The derived analytical results are verified by comparison with finite element analysis. Next, the present formulation is applied to the prediction of crack kinking behaviors in foam core sandwich beams. It is demonstrated that overall crack kinking behaviors in foam core sandwich beams are well predicted using the present method. Some discussions on the fracture toughness measurement considering residual thermal stresses are also provided.

Mixed-mode (I + II) fracture characterization of wood bonded joints

In this work fracture characterization of wood bonded joints is performed. The main objective is to define a fracture criterion under mixed-mode loading (I + II), in order to provide a safer and reliable design of wood bonded joints. Experimental fracture characterization tests were carried out. For mode I and mode II loading, the double cantilever beam and the end notched flexure tests were selected. Under mixed-mode I + II loading the mixed-mode bending test was used considering different mixed-mode ratios. A data reduction scheme based on the specimen compliance, the beam theory and on a crack equivalent concept was used to overcome the difficulties inherent to the above referred tests. The fracture linear energetic criterion showed to be adequate to describe the fracture envelop with an exception, as discussed in the paper.

Effects of Stitching on Delamination of Satin Weave Carbon-Epoxy Laminates Under Mode I, Mode II and Mixed-Mode I/II Loadings

The objective of the present study is to characterize the effect of modified chain stitching on the delamination growth under mixed-mode I/II loading conditions. Delamination toughness under mode I is experimentally determined, for unstitched and stitched laminates, by using untabbed and tabbed double cantilever beam (TDCB) tests. The effect of the reinforcing tabs on mode I toughness is investigated. Stitching improves the energy release rate (ERR) up to 4 times in mode I. Mode II delamination toughness is evaluated in end-notched flexure (ENF) tests. Different geometries of stitched specimens are tested. Crack propagation occurs without any failure of stitching yarns. The final crack length attains the mid-span or it stops before and the specimen breaks in bending. The ERR is initially low and gradually increases with crack length to very high values. The mixed-mode delamination behaviour is investigated using a mixed-mode bending (MMB) test. For unstitched specimens, a simple mixed-mode criterion is identified. For stitched specimens, stitching yarns do not break during 25% of mode I ratio tests and the ERR increase is relatively small compared to unstitched values. For 70% and 50% of mode I ratios, failures of yarns are observed during crack propagation and tests are able to capture correctly the effect of the stitching: it clearly improves the ERR for these two mixed modes, as much as threefold.

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.

Energy release rates of bi-material interface crack including residual thermal stresses: Application of crack tip element method

Crack tip element method is applied to the formulation of the energy release rate associated with interfacial crack growth of laminates with residual thermal stresses using the Timochenko beam model. Special attention is paid to the energy release rates of double cantilever beam and mixed-mode bending tests of bi-material specimens, and mode-I and mode-II energy release rates are formulated including residual thermal stresses. The derived results are verified by the comparison to finite element analysis, and the effect of residual thermal stresses on the mode mixity of the double cantilever beam and mixed-mode bending tests is discussed.

Failure criteria for mixed mode delamination in glass fibre epoxy composites

Critical strain energy release rate of glass/epoxy laminates using the virtual crack closure technique for mode I, mode II, mixed-mode I + II and mode III were determined. Mode I, mode II, mode III and mixed-mode I + II fracture toughness were obtained using the double cantilever beam test , the end notch flexure test , the edge crack torsion test and the mixed-mode bending test respectively. Results were analysed through the most widely used criteria to predict delamination propagation under mixed-mode loading: the Power Law and the Benzeggagh and Kenane criteria. Mixed-mode fracture toughness results seem to represent the data with reasonable accuracy.

A phantom node formulation with mixed mode cohesive law for splitting in laminates

A phantom node method with mixed mode cohesive law is proposed for the simulation of splitting in laminates. With this method, a discontinuity in the displacement field can be modeled at arbitrary locations. The micromechanical phenomenon that splitting cracks grow parallel to the fiber, is incorporated on the mesolevel, i.e., in the homogenized ply, by setting the direction of the crack propagation equal to the fiber direction. A new mixed mode cohesive law is introduced for increased robustness of the incremental-iterative solution procedure. The model is validated with mixed mode bending tests, and its utility is illustrated with examples for a single ply and for a laminate.

熱残留応力を考慮した層間き裂進展に関するエネルギー解放率：Ｃｒａｃｋ Ｔｉｐ Ｅｌｅｍｅｎｔ法による定式化

Crack tip element (CTE) method is applied to the formulation of energy release rate associated with interfacial crack growth of laminates with arbitrary layups and residual thermal stresses using the Timochenko beam model. Special attention is paid to the energy release rates of mixed mode bending (MMB) test, and mode-I and mode-II energy release rates are formulated including residual thermal stresses. The results derived are verified by the comparison to finite element analysis, and the effect of residual thermal stresses on the mode mixity of the MMB test is discussed.

A unified potential-based cohesive model of mixed-mode fracture

A generalized potential-based constitutive model for mixed-mode cohesive fracture is presented in conjunction with physical parameters such as fracture energy, cohesive strength and shape of cohesive interactions. It characterizes different fracture energies in each fracture mode, and can be applied to various material failure behavior (e.g. quasi-brittle). The unified potential leads to both intrinsic (with initial slope indicators to control elastic behavior) and extrinsic cohesive zone models. Path dependence of work-of-separation is investigated with respect to proportional and non-proportional paths—this investigation demonstrates consistency of the cohesive constitutive model. The potential-based model is verified by simulating a mixed-mode bending test. The actual potential is named PPR (Park–Paulino–Roesler), after the first initials of the authors’ last names.

Mixed-mode interlaminar fracture and damage characterization in woven fabric-reinforced glass/epoxy composite laminates at cryogenic temperatures using the finite element and improved test methods

The present research examines experimentally and analytically the mixed-mode interlaminar fracture and damage behavior of glass fiber reinforced polymer (GFRP) woven laminates at cryogenic temperatures. The mixed-mode bending (MMB) tests were performed with the improved test apparatus, at room temperature, liquid nitrogen temperature (77 K) and liquid helium temperature (4 K). The energy release rates at the onset of delamination crack propagation were evaluated for the woven GFRP specimens using both beam theory and finite element analysis. The fracture surfaces were also examined to verify the fracture mechanisms. In addition, the initiation and growth of damage in the specimens were predicted by a damage analysis, and the damage effect on the mixed-mode interlaminar fracture properties at cryogenic temperatures was explored.

Effective Simulation of Delamination in Aeronautical Structures Using Shells and Cohesive Elements

A cohesive element for shell analysis is presented. The element can be used to simulate the initiation and growth of delaminations between stacked, non-coincident layers of shell elements. The procedure to construct the element accounts for the thickness offset by applying the kinematic relations of shell deformation to transform the stiffness and internal force of a zero-thickness cohesive element such that interfacial continuity between the layers is enforced. The procedure is demonstrated by simulating the response and failure of the Mixed Mode Bending test and a skin-stiffener debond specimen. In addition, it is shown that stacks of shell elements can be used to create effective models to predict the inplane and delamination failure modes of thick components. The results indicate that simple shell models can retain many of the necessary predictive attributes of much more complex 3D models while providing the computational efficiency that is necessary for design.