An investigation of Mode I fracture toughness using aligned carbon nanotube forests at the crack interface

This paper presents a novel approach for introducing aligned carbon nanotubes (CNTs) at the crack interface of pre-impregnated (prepreg) carbon fibre composite plies, creating a hierarchical (three-phase) composite structure. The aim of this approach is to improve the interlaminar fracture toughness. The developed method for transplanting the aligned CNTs from the silicon wafer onto the pre-preg material is described. Scanning electron microscopy (SEM) was used to analyse the effects of the transplantation method. Double Cantilever Beam (DCB) specimens were prepared, according to ASTM standard D5528- 01R07E03 [1] and aligned multi-walled carbon nanotubes (MWCNTs) were introduced at the crack-tip. Mode I fracture tests for pristine (control) specimens and CNT-enhanced specimens were conducted and an average increase in the critical strain energy release rate (GIc) of approximately 50 % was achieved.

An investigation of Mode I and Mode II fracture toughness enhancement using aligned carbon nanotubes forests at the crack interface

A novel approach for introducing aligned multi-walled carbon nanotubes (MWCNTs) in a carbon-fibre composite pre-impregnated (prepreg) laminate, to improve the through-thickness fracture toughness, is presented. Carbon nanotube (CNT) 'forests' were grown on a silicon substrate with a thermal oxide layer, using a chemical vapour deposition (CVD) process. The forests were then transferred to a pre-cured laminate interface, using a combination of pressure and heat, while maintaining through-thickness CNT alignment. Standard Mode I and four-point bend end-notched flexure Mode II tests were undertaken on a set of specimens and compared with pristine specimens. Mode I fracture toughness for T700/M21 laminates was improved by an average of 31% while for T700/SE84LV specimens, an improvement of 61% was observed. Only T700/M21 specimens were tested in Mode II which yielded an average fracture toughness improvement of 161%. Scanning Electron Microscopy (SEM) showed good wetting of the CNT forest as well as evidence of penetration of the forest into the adjacent plies. © 2013 Elsevier Ltd.

A correction to the analytical solution of the mixed-mode bending (MMB) problem

This paper addresses the analytical solution of the mixed-mode bending (MMB) problem. The first published solutions used a load separation in pure mode I and mode II and were applied for a crack length less than the beam half-span, a <= L. In later publications, the same mode separation was used in deriving the analytical solution for crack lengths bigger than the beam half-span, a > L. In this paper it is shown that this mode separation is not valid when a > L and in some cases may lead to very erroneous results. The correct mode separation and the corresponding analytical solutions, when a > L, are presented. Results, of force vs. displacement and force vs. crack length graphs, obtained using the existing formulation and the corrected formulation are compared. A finite element solution, which does not use mode separation, is also presented

Computation of stress intensity factors in functionally graded materials using partition-of-unity meshfee method

This paper describes the computation of stress intensity factors (SIFs) for cracks in functionally graded materials (FGMs) using an extended element-free Galerkin (XEFG) method. The SIFs are extracted through the crack closure integral (CCI) with a local smoothing technique, non-equilibrium and incompatibility formulations of the interaction integral and the displacement method. The results for mode I and mixed mode case studies are presented and compared with those available in the literature. They are found to be in good agreement where the average absolute error for the CCI with local smoothing, despite its simplicity, yielded a high level of accuracy.

Intralaminar toughness characterisation of unbalanced hybrid plain weave laminates

A numerical and experimental investigation on the mode-I intralaminar toughness of a hybrid plain weave composite laminate manufactured using resin infusion under flexible tooling (RIFT) process is presented in this paper. The pre-cracked geometries consisted of overheight compact tension (OCT), double edge notch (DEN) and centrally cracked four-point-bending (4PBT) test specimens. The position as well as the strain field ahead of the crack tip during the loading stage was determined using a digital speckle photogrammetry system. The limitation on the applicability of the standard data reduction schemes for the determination of intralaminar toughness of composite materials is presented and discussed. A methodology based on the numerical evaluation of the strain energy release rate using the J-integral method is proposed to derive new geometric correction functions for the determination of the stress intensity factor for composites. The method accounts for material anisotropy and finite specimen dimension effects regardless of the geometry. The approach has been validated for alternative non-standard specimen geometries. A comparison between different methods currently available for computing the intralaminar fracture toughness in composite laminates is presented and a good agreement between numerical and experimental results using the proposed methodology was obtained. 

A pseudo-transient solution strategy for the analysis of delamination by means of interface elements

Recent efforts in the finite element modelling of delamination have concentrated on the development of cohesive interface elements. These are characterised by a bilinear constitutive law, where there is an initial high positive stiffness until a threshold stress level is reached, followed by a negative tangent stiffness representing softening (or damage evolution). Complete decohesion occurs when the amount of work done per unit area of crack surface is equal to a critical strain energy release rate. It is difficult to achieve a stable, oscillation-free solution beyond the onset of damage, using standard implicit quasi-static methods, unless a very refined mesh is used. In the present paper, a new solution strategy is proposed based on a pseudo-transient formulation and demonstrated through the modelling of a double cantilever beam undergoing Mode I delamination. A detailed analysis into the sensitivity of the user-defined parameters is also presented. Comparisons with other published solutions using a quasi-static formulation show that the pseudo-transient formulation gives improved accuracy and oscillation-free results with coarser meshes

D3.1 Benefits Analysis of the Initial Operational Cruiser-Feeder Concept

The REsearch on a CRuiser Enabled Air Transport Environment (RECREATE) project is considers the introduction and airworthiness of cruiser-feeder operations for civil aircraft. Cruiser-feeder operations are investigated as a promising pioneering idea for the air transport of the future. The soundness of the concept of cruiser-feeder operations for civil aircraft can be understood, taking air-to-air refueling operations as an example. For this example, a comprehensive estimate of the benefits can be made, which shows a fuel burn reduction potential and a CO2 emission reduction of 31% for a typical 6000 nautical miles flight with a payload of 250 passengers. This reduction potential is known to be large by any standard. The top level objective of the RECREATE project is to demonstrate on a preliminary design level that cruiser-feeder operations (as a concept to reduce fuel burn and CO2 emission levels) can be shown to comply with the airworthiness requirements for civil aircraft. The underlying Scientific and Technological (S&T) objectives are to determine and study airworthy operational concepts for cruiser-feeder operations, and to derive and quantify benefits in terms of CO2 emission reduction but also other benefits.

Work Package (WP) 3 has the objective to substantiate the assumed benefits of the cruiser/feeder operations through refined analysis and simulation. In this report, initial benefits evaluation of the initial RECREATE cruiser/feeder concepts is presented. The benefits analysis is conducted in delta mode, i.e. comparison is made with a baseline system. Since comparing different aircraft and air transport systems is never a trivial task, appropriate measures and metrics are defined and selected first. Non-dimensional parameters are defined and values for the baseline system derived.

The impact of cruiser/feeder operations such as air-to-air refueling are studied with respect to fuel-burn (or carbon-dioxide), noise and congestion. For this purpose, traffic simulations have been conducted.
Cruiser/feeder operations will have an impact on dispatch reliability as well. An initial assessment of the effect on dispatch reliability has been made and is reported.

Finally, a considerable effort has been made to create the infrastructure for economic delta analysis of the cruiser/feeder concept of operation. First results of the cost analysis have been obtained.

Modified crack closure integral technique for extraction of SIFs in meshfee methods

A new approach for extracting stress intensity factors (SIFs) by the element-free Galerkin (EFG) class of methods through a modified crack closure integral (MCCI) scheme is proposed. Its primary feature is that it allows accurate calculation of mode I and mode II SIFs with a relatively simple and straightforward analysis even when a coarser nodal density is employed. The details of the adoption of the MCCI technique in the EFG method are described. Its performance is demonstrated through a number of case studies including mixed-mode and thermal problems in linear elastic fracture mechanics (LEFM). The results are compared with published theoretical solutions and those based on the displacement method, stress method, crack closure integral in conjunction with local smoothing (CCI–LS) technique, as well as the M-integral method. Its advantages are discussed.

Issues in fe modelling of FRP strengthened masonry arch bridges

Externally bonding of FRP composites is an effective technique for retrofitting historical masonry arch structures. A major failure mode in such strengthened structures is the debonding of FRP from the masonry. The bond behaviour between FRP and masonry thus plays a crucial role in these structures. Major challenges exist in the finite element modelling of such structures, such as modelling of mixed Mode-I and Mode-II bond behaviour between the FRP and the curved masonry substrate, modelling of existing damages in the masonry arches, consideration of loading history in the unstrengthened and strengthened structure etc. This paper presents a rigorous FE model for simulating FRP strengthened masonry arch structures. A detailed solid model was developed for simulating the masonry and a mixed-mode interface model was used for simulating the FRP-to-masonry bond behaviour. The model produces results in very close agreement with test results.

K&C局部损伤混凝土材料模型在精细有限元模拟中的应用

This paper presents a study on concrete fracture and the associated mesh sensitivity using the finite element (FE) method with a local concrete model in both tension (Mode I) and compression.To enable the incorporation of dynamic loading, the FE model is developed using a transient dynamic analysis code LS-DYNA Explicit.A series of investigations have been conducted on typical fracture scenarios to evaluate the model performances and calibration of relevant parameters.The K&C damage model was adopted because it is a comprehensive local concrete model which allows the user to change the crack band width, fracture energy and rate dependency of the material.Compressive localisation modelling in numerical modelling is also discussed in detail in relation to localisation.An impact test specimen is modelled.

Experimental and numerical study of debonding in composite adhesive joints

The mode I and mode II fracture properties of the FM300-2 adhesive bond between 5HS/RTM6 laminates are determined experimentally by DCB and ELS test. The crack propagation is studied numerically by means of interface elements based on the decohesive zone model. The latter is characterized by material degradation, which is usually assumed to be linear. In the present study it is shown that if a non-linear material degradation is used with an increased magnitude of the interface relative displacement at failure it is possible to model more correctly the experimentally observed significant non-linear behaviour before the start of crack propagation. An adhesive stepped flush joint is studied experimentally and numerically. A mixed mode interaction criterion is used together with the nonlinear material degradation of the interface. Sensitivity studies are performed to study the influence of the parameters defining it.

The role of material characterisation in the crush modelling of thermoplastic composite structures

The predictive capability of high fidelity finite element modelling, to accurately capture damage and crush behaviour of composite structures, relies on the acquisition of accurate material properties, some of which have necessitated the development of novel approaches. This paper details the measurement of interlaminar and intralaminar fracture toughness, the non-linear shear behaviour of carbon fibre (AS4)/thermoplastic Polyetherketoneketone (PEKK) composite laminates and the utilisation of these properties for the accurate computational modelling of crush. Double-cantilever-beam (DCB), four-point end-notched flexure (4ENF) and Mixed-mode bending (MMB) test configurations were used to determine the initiation and propagation fracture toughness in mode I, mode II and mixed-mode loading, respectively. Compact Tension (CT) and Compact Compression (CC) test samples were employed to determine the intralaminar longitudinal tensile and compressive fracture toughness. V-notched rail shear tests were used to measure the highly non-linear shear behaviour, associated with thermoplastic composites, and fracture toughness. Corresponding numerical models of these tests were developed for verification and yielded good correlation with the experimental response. This also confirmed the accuracy of the measured values which were then employed as input material parameters for modelling the crush behaviour of a corrugated test specimen.

Electrostatic mode envelope excitations in e-p-i plasmas - application in warm pair ion plasmas with a small fraction of stationary ions

The nonlinear propagation of amplitude-modulated electrostatic wavepackets in an electron-positron-ion (e-p-i) plasma is considered, by employing a two-fluid plasma model. Considering propagation parallel to the external magnetic field, two distinct electrostatic modes are obtained, namely a quasi-thermal acoustic-like lower mode and a Langmuir-like optic-type upper one. These results equally apply in warm pair ion ( e. g. fullerene) plasmas contaminated by a small fraction of stationary ions ( or dust), in agreement with experimental observations and theoretical predictions in pair plasmas. Considering small yet weakly nonlinear deviations from equilibrium, and adopting a multiple-scales perturbation technique, the basic set of model equations is reduced to a nonlinear Schrodinger (NLS) equation for the slowly varying electric field perturbation amplitude. The analysis reveals that the lower ( acoustic) mode is mostly stable for large wavelengths, and may propagate in the form of a dark-type envelope soliton ( a void) modulating a carrier wavepacket, while the upper linear mode is intrinsically unstable, and thus favours the formation of bright-type envelope soliton ( pulse) modulated wavepackets. The stability ( instability) range for the acoustic ( Langmuir-like optic) mode shifts to larger wavenumbers as the positive-to-negative ion temperature ( density) ratio increases. These results may be of relevance in astrophysical contexts, where e-p-i plasmas are encountered, and may also serve as prediction of the behaviour of doped ( or dust-contaminated) fullerene plasmas, in the laboratory.