Delamination buckling and propagation analysis of honeycomb panels using a cohesive element approach

The cohesive element approach is proposed as a tool for simulating delamination propagation between a facesheet and a core in a honeycomb core composite panel. To determine the critical energy release rate (G _c) of the cohesive model, Double Cantilever Beam (DCB) fracture tests were performed. The peak strength (_c) of the cohesive model was determined from Flatwise Tension (FWT) tests. The DCB coupon test was simulated using the measured fracture parameters, and sensitivity studies on the parameters for the cohesive model of the interface element were performed. The cohesive model determined from DCB tests was then applied to a full-scale, 914×914 mm (36×36 in.) debond panel under edge compression loading, and results were compared with an experiment. It is concluded that the cohesive element approach can predict delamination propagation of a honeycomb panel with reasonable accuracy.     

Panel stiffener debonding analysis using a shell/3D modeling technique

A shear loaded, stringer reinforced composite panel is analyzed to evaluate the fidelity of computational fracture mechanics analyses of complex structures. Shear loading causes the panel to buckle. The resulting out-of-plane deformations initiate skin/stringer separation at the location of an embedded defect. The panel and surrounding load fixture were modeled with shell elements. A small section of the stringer foot, web and noodle as well as the panel skin near the delamination front were modeled with a local 3D solid model. Across the width of the stringer foot, the mixed-mode strain energy release rates were calculated using the virtual crack closure technique. A failure index was calculated by correlating the results with a mixed-mode failure criterion of the graphite/epoxy material. The objective was to study the effect of the fidelity of the local 3D finite element model on the computed mixed-mode strain energy release rates and the failure index.     

复合材料机身曲板环向弯曲加载试验及失效机制

对复合材料机身曲板进行了环向弯曲加载试验,采用四点弯加载方式对考核段进行纯弯加载,设计一种加强连接方式避免加载段提前破坏,通过试验对机身曲板的环向稳定性和破坏模式进行了分析。同时,建立了基于内聚力单元的考虑长桁与蒙皮粘接界面损伤的有限元模型,分别使用Quads准则和Hashin准则作为界面和层合板的失效判据分析曲板结构的失效机制,计算结果与试验结果吻合较好。试验及有限元分析结果表明,长桁帽底蒙皮的局部屈曲引起长桁与蒙皮粘接的R区出现初始开裂,并最终扩展为长桁脱粘。随着蒙皮屈曲及长桁脱粘的扩大,蒙皮由局部屈曲变为整体失稳而失去承载能力,最终导致隔框承载过大而发生断裂。根据初始损伤模式,采取了长桁帽内全包工艺改进设计,改进后的曲板结构稳定性和承载能力分别提高了21.9%和16.8%。      

Post-buckling and debond propagation in sandwich panels subject to in-plane compression

Nonlinear finite element analysis is conducted to predict initiation of debond propagation in compression loaded foam cored sandwich panels containing a circular face/core debond embedded at the panel center. A three-dimensional geometrically nonlinear finite element model of the debonded sandwich panel combined with linear elastic fracture mechanics is used to determine the stress intensity factors K_I and K_II and energy release rate at the debond (crack) front parallel and perpendicular to the applied load. A range of core densities and debond sizes are analyzed. The opening mode (mode I) was found to dominate the fracture process. The critical load for crack propagation predicted using fracture mechanics concepts was found to agree with measured collapse loads for smaller debonds, but fell below measured debond propagation loads for larger debonds. In all cases the predicted direction of crack propagation was perpendicular to the loading direction, in agreement with experimental observations.     

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.     

Calculation of transient strain energy release rates under impact loading based on the virtual crack closure technique

This paper describes an interface element to calculate the strain energy release rates based on the virtual crack closure technique (VCCT) in conjunction with finite element analysis (FEA). A very stiff spring is placed between the node pair at the crack tip to calculate the nodal forces. Dummy nodes are introduced to extract information for displacement openings behind the crack tip and the virtual crack jump ahead of the crack tip. This interface element leads to a direct calculation of the strain energy release rate (both components G_I and G_II) within a finite element analysis without extra post-processing. Several examples of stationary cracks under impact loading were examined. Dynamic stress intensity factors were converted from the calculated transient strain energy release rate for comparison with the available solutions by the others from numerical and experimental methods. The accuracy of the element is validated by the excellent agreement with these solutions. No convergence difficulty has been encountered for all the cases studied. Neither special singular elements nor the collapsed element technique is used at the crack tip. Therefore, the fracture interface element for VCCT is shown to be simple, efficient and robust in analyzing crack response to the dynamic loading. This element has been implemented into commercial FEA software ABAQUS^® with the user defined element (UEL) and should be very useful in performing fracture analysis at a structural level by engineers using ABAQUS^®.     

Three-dimensional fracture analysis of thin-film debonding

A simplified mixed-mode fracture analysis combining nonlinear thin-plate stress solutions with crack-tip elasticity results has been developed to account for local variations of G _I, G _II and G _III in thin-film debond problems associated with large film deformations. Membrane and bending stresses from the plate analysis are matched with the crack-tip singularity solution over a small boundary region at the crack tip where the effect of geometric nonlinearity is small. Local variations in each of the individual components of the energy release rate are directly related to the jump in these stresses across the crack border.Specific results are presented for 1-D and elliptical planeform cracks. Deformations were induced either by a pressure acting normal to the film surface or biaxial compression or tension stresses applied to the substrate in which the loading axes and debond axes coincide. The latter type of loading involves buckling of the delaminated film. The model predictions compare well with more rigorous solutions provided the film thickness is small compared to the debond dimensions. In all cases analyzed, G _III was negligible. The ratio G _I/G _II typically decreases with increasing load or film deformation, the rate was moderate for pressure loading while generally sharp for compression loading. Film-substrate overlap may occur for certain debond geometry and loading conditions. Prevention of this by the substrate may critically increase the energy available for crack propagation.     

Enhancing mechanical and fracture properties of sandwich composites using nanoparticle reinforcement

Polyurethane (PU) foam is reinforced with SiC nanoparticles to develop core materials for sandwich composites. Isocyanate component (Part A) of PU foam was dispersed with SiC nanoparticles, and then mixed with polyol (Part B) to manufacture nanophased core materials. Nanoparticle reinforcement varied from 0.1 to 2.0 wt% of the total polymer. Both pristine and silane functionalized SiC nanoparticles were used in the investigation. Nanophased foams were tested in compression and flexure to determine the mechanical properties. Fracture toughnesses K _IC and G _IC were determined using the SENB test. Sandwich panels were fabricated and tested for face-core debond fracture toughness using the tilted sandwich debond test. The study has revealed that reinforcement of the foam by pristine nanoparticles substantially enhances mechanical properties but degrades fracture toughness. This loss in fracture toughness, however, may be recovered with the use of functionalized nanoparticles. Small concentrations (0.1–0.2 wt%) of functionalized nanoparticles provided large improvement in debond fracture toughness of sandwich specimens.     

On the analysis of a mixed mode bending sandwich specimen for debond fracture characterization

The mixed mode bending specimen originally developed for mixed mode delamination fracture characterization of unidirectional composites has been extended to the study of debond propagation in foam cored sandwich specimens. The compliance and strain energy release rate expressions for the mixed mode bending sandwich specimen are derived based on a superposition analysis of solutions for the double cantilever beam and cracked sandwich beam specimens by applying a proper kinematic relationship for the specimen deformation combined with the loading provided by the test rig. This analysis provides also expressions for the global mode mixities. An extensive parametric analysis to improve the understanding of the influence of loading conditions, specimen geometry and mechanical properties of the face and core materials has been performed using the derived expressions and finite element analysis. The mixed mode bending compliance and energy release rate predictions were in good agreement with finite element results. Furthermore, the numerical crack surface displacement extrapolation method implemented in finite element analysis was applied to determine the local mode mixity at the tip of the debond.     

Strain-life approach in thermo-mechanical fatigue evaluation of complex structures

This paper is a contribution to strain‐life approach evaluation of thermo‐mechanically loaded structures. It takes into consideration the uncoupling of stress and damage evaluation and has the option of importing non‐linear or linear stress results from finite element analysis (FEA). The multiaxiality is considered with the signed von Mises method. In the developed Damage Calculation Program (DCP) local temperature‐stress‐strain behaviour is modelled with an operator of the Prandtl type and damage is estimated by use of the strain‐life approach and Skelton's energy criterion. Material data were obtained from standard isothermal strain‐controlled low cycle fatigue (LCF) tests, with linear parameter interpolation or piecewise cubic Hermite interpolation being used to estimate values at unmeasured temperature points. The model is shown with examples of constant temperature loading and random force‐temperature history. Additional research was done regarding the temperature dependency of the K_p used in the Neuber approximate formula for stress‐strain estimation from linear FEA results. The proposed model enables computationally fast thermo‐mechanical fatigue (TMF) damage estimations for random load and temperature histories.     

Numerical prediction of notch bluntness effect on fracture resistance of SM490A carbon steel

The present work investigates the notch radius effect on fracture resistance using the finite element (FE) damage analysis based on the multiaxial fracture strain model. The damage model was determined from experimental data of notched bar tensile and fracture toughness test data using a sharp‐cracked compact tension specimen. Then, the FE damage analysis was applied to simulate fracture resistance tests of SM490A carbon steel specimens with different notch radii. Comparison of simulated results with experimental data showed good agreement. Further simulation was then performed to see effects of the specimen size, thickness, and side groove on J‐R curves for different notch radii. It was found that effects of the specimen size and thickness became more pronounced for the larger notch radius. Furthermore, it was found that without side groove, tearing modulus for notched specimens was similar to that for cracked specimens, regardless of the notch radius.     

含离散源损伤复合材料加筋板的拉伸特性

通过对含有离散源损伤的复合材料加筋板的拉伸试验和有限元模拟,研究了离散源损伤的损伤扩展与破坏特性。结果表明:复合材料加筋板的离散源损伤用穿透蒙皮切断桁条的切口来模拟是合适的,蒙皮上的穿透切口前端有很高的应力集中,桁条被切断导致加筋板传力路线改变;基于Hashin失效准则的渐进损伤有限元数值模拟方法,可以有效地模拟含切口加筋板的宏观损伤扩展和破坏过程,计算结果与试验值吻合较好。      

Mode III interlaminar fracture of carbon/epoxy laminates using a four-point bending plate test

A new four-point bending plate (4PBP) test was used for characterising the mode III interlaminar fracture of carbon/epoxy laminates. The specimen has a cross-ply lay-up and two edge delaminations whose propagation becomes visible at the edges. Although the test setup is very simple, determination of the mode III critical strain energy release rate G_IIIc requires finite element analyses (FEA). The virtual crack closure technique with an assumed initiation region was first proposed for computing G_IIIc. This scheme was subsequently validated by crack growth simulations with a cohesive zone model. The results showed an average G_IIIc = 1550 J/m², which is significantly higher than the G_IIIc = 850–1100 J/m² and G_IIc = 800 J/m² measured in previous studies.     

Bending modified J–Q theory and crack-tip constraint quantification

It is well known that the J–Q theory can characterize the crack-tip fields and quantify constraint levels for various geometry and loading configurations in elastic–plastic materials, but it fails at bending-dominant large deformation. This drawback seriously restricts its applications to fracture constraint analysis. A modification of J–Q theory is developed as a three-term solution with an additional term to address the global bending stress to offset this restriction. The nonlinear bending stress is approximately linearized in the region of interest under large-scale yielding (LSY), with the linearization factor determined using a two-point matching method at each loading for a specific cracked geometry in bending. To validate the proposed solution, detailed elastic–plastic finite element analysis (FEA) is conducted under plane strain conditions for three conventional bending specimens with different crack lengths for X80 pipeline steel. These include single edge notched bend (SENB), single edge notched tension (SENT) and compact tension (CT) specimens from small-scale yielding (SSY) to LSY. Results show that the bending modified J–Q solution can well match FEA results of crack-tip stress fields for all bending specimens at all deformation levels from SSY to LSY, with the modified Q being a load- and distance-independent constraint parameter under LSY. Therefore, the modified parameter Q can be effectively used to quantify crack-tip constraint for bending geometries. Its application to fracture constraint analysis is demonstrated by determining constraint corrected J–R curves.     

Mixed-mode fracture load prediction in lead-free solder joints

Double cantilever beam (DCB) fracture specimens were made by joining copper bars with both continuous and discrete SAC305 solder layers of different lengths under standard surface mount (SMT) processing conditions. The specimens were then fractured under mode-I and various mixed-mode loading conditions. The loads corresponding to crack initiation in the continuous joints were used to calculate the critical strain energy release rate, J_ci, at the various mode ratios using elastic–plastic finite element analysis (FEA). It was found that the J_ci from the continuous joint DCBs provided a lower bound strength prediction for discrete 2 mm and 5 mm long joints at the various mode ratios. Additionally, these J_ci values calculated from FEA using the measured fracture loads agreed reasonably with J_ci estimated from measured crack opening displacements at crack initiation in both the continuous and discrete joints. Therefore, the critical strain energy release rate as a function of the mode ratio of loading is a promising fracture criterion that can be used to predict the strength of solder joints of arbitrary geometry subject to combined tensile and shear loads.     

Fracture toughness of the fibre-matrix interface in glass-epoxy composites

The failure process arising at a broken fibre end in polymer matrix composite materials has been studied experimentally and analytically using the finite element method. A series of experiments were carried out using S-glass and E-glass single filaments, with different sizings and/or coupling agents, embedded in epoxy matrices with different moduli. A finite element analysis was used to simulate the experiments and calculate the change in strain energy accompanying the observed fracture mode. The strain energy release rate upon arrest of the crack, G _arrest, was then calculated. The measured interface debonding energies varied from G _arrest=57–342 J m^–2, depending primarily on the nature of the fibre sizing and the ratio of moduli of the fibre and matrix. Transverse and shear matrix cracks were characterized by G _arrest values of 58–103 J m^–2. Subtle changes in the constituent properties or fibre surface treatment resulted in a change in the fracture mode. This measurement and analysis technique may suggest reasons for the variability of previous measurements of interfacial adhesion, and provide a standard method for characterizing fracture modes at broken fibre ends.     

Two‐stage fatigue life evaluation of an aircraft fuselage panel with a bulging circumferential crack and a broken stringer

The article presents two‐stage fatigue life evaluation of a stiffened aluminium aircraft fuselage panel, subject to ground–air–ground pressure cycles, with a bulging circumferential crack and a broken stringer. As a worst‐case scenario, it is assumed that double cracks start at the edge of a rivet hole both in the skin and in the stringer simultaneously. In the first stage, fatigue crack growth analysis is performed until the stringer is completely broken with the crack on the fuselage skin propagating. After the stringer is completely broken, the effect of bulging crack on the fatigue life of the panel is investigated utilizing the stress intensity factors determined by the three‐dimensional finite element analyses of the fuselage panel with the broken stringer. It is concluded that bulging of the skin due to the internal pressure can have significant effect on the stress intensity factor, resulting in fast crack propagation after the stringer is completely broken.     

An updated continuum damage model to investigate fracture process of structures in DBTT region

In the Ductile–Brittle Transition Temperature (DBTT) region, it is not realistic to take unique fracture stress or fracture strain as the fracture criterion to investigate the fracture properties. In this paper, an updated continuum damage model was proposed, in which the fracture energy density, a function of the stress triaxiality, temperature and strain rate in the transition region was taken as the critical damage factor. Uniaxial tension tests were carried out to get the basic material properties at different temperatures, to calibrate the fracture model constants and verify the validity of the damage model. The fracture behaviour of pipes with penetrating cracks under the internal pressure was experimentally investigated with the load–deflection curves and the crack propagation length captured from tests. The J–R curves were obtained from the testing results for different temperatures. Based on the Finite Element Analyses (FEA) with the proposed fracture criterion of the updated continuum damage model, the loading level of pipes with penetrating cracks were estimated and compared with the experimental results. Meanwhile the fracture processes of the pipeline structures in the transition region were reproduced. The experimental and numerical results agreed very well in present calculations. It has been shown that the fracture process in the transition region strongly depends on both the stress and strain states, and could be effectively predicted using the continuum damage model.     

Application of decohesive model with mixed damage scale in fracture analysis of composite materials

A decohesive model using a mixed damage scale and using the total fracture energy to simulate the fracture process of composite materials has been developed in this article. The model assumes a bilinear interfacial decohesion function and is incorporated into an interface finite element developed as a user subroutine in the commercial FEA package ABAQUS. In comparison with traditional numerical methods in fracture mechanics, this approach can automatically predict the failure load, crack path and the residual stiffness of bodies undergoing the fracture process. Applications given in this paper are simulation of a typical fracture test with a double cantilever beam (DCB) specimen; modelling a stiffened composite laminated panel under four-point bending and modelling a repaired composite sandwich panel under four-point bending. Good correlation was seen between modelling predictions and experimental results.     

Investigation of fatigue crack growth and crack turning on integral stiffened structures under mode I loading

Integral structures have benefits compared to riveted structures, but they offer lower damage tolerance. This investigation analysed possible decrease of crack growth in integral structures by means of design analysis on stringer cross-sections. For this purpose the finite element analysis (FEA) was applied. First the reliability of FEA was proven by comparing calculated crack growth rates (CGR) to test results. Since CGR in linear elastic fracture mechanics is controlled by the stress intensity factors (SIF), different cross-sections were analysed. These configurations were evaluated regarding their crack turning behaviour (T-stress). The SIF was reduced about 18%. Crack turning is more probable when the crack is far away from stringer.