3-D micromechanical model for predicting the elastic behaviour of woven laminates

This paper presents an analytical model for the prediction of the elastic behaviour of plain-weave fabric composites. The fabric is a hybrid plain-weave with different materials and undulations in the warp and weft directions. The derivation of the effective material properties is based on classical laminate theory (CLT).

The theoretical predictions have been compared with experimental results and predictions using alternative models available in the literature. Composite laminates were manufactured using the resin infusion under flexible tooling (RIFT) process and tested under tension and in-plane shear loading to validate the model. A good correlation between theoretical and experimental results for the prediction of in-plane properties was obtained. The limitations of the existing theoretical models based on classical laminate theory (CLT) for predicting the out-of-plane mechanical properties are presented and discussed. 

Numerical analysis of stiffener runout sections

The recent trend of incorporating more composite material in primary aircraft structures has highlighted the vulnerability of stiffened aerostructures to through-thickness stresses, which may lead to delamination and debonding at the skin-stiffener interface, leading to collapse. Stiffener runout regions are particularly susceptible to this problem and cannot be avoided due to the necessity to terminate stiffeners at rib intersections or at cutouts, interrupting the stiffener load path. In this paper, experimental tests relating to two different stiffener runout specimens are presented and the failure modes of both specimens are discussed in detail. A thinner-skinned specimen showed sudden and unstable crack propagation, while a thicker-skinned specimen showed initially unstable but subsequent stable crack growth. Detailed finite element models of the two specimens are developed, and it is shown how such models can explain and predict the behaviour and failure mode of stiffener runouts. The models contain continuum shell elements to model the skin and stiffener, while cohesive elements using a traction-separation law are placed at the skin-stiffener interface to effectively model the debonding which promotes structural failure.

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 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

Structural testing and numerical simulation of a 34 m composite wind turbine blade

A full-scale 34 m composite wind turbine blade was tested to failure under flap-wise loading. Local displacement measurement equipment was developed and displacements were recorded throughout the loading history.

Ovalization of the load carrying box girder was measured in the full-scale test and simulated in non-linear FE-calculations. The nonlinear Brazier effect is characterized by a crushing pressure which causes the ovalization. To capture this effect, non-linear FE-analyses at different scales were employed. A global non-linear FE-model of the entire blade was prepared and the boundaries to a more detailed sub-model were extracted. The FE-model was calibrated based on full-scale test measurements.

Local displacement measurements helped identify the location of failure initiation which lead to catastrophic failure. Comparisons between measurements and FE-simulations showed that delamination of the outer skin was the initial failure mechanism followed by delamnination buckling which then led to collapse. 

An automated hybrid procedure for capturing mode-jumping in postbuckling composite stiffened structures

This paper presents a robust finite element procedure for modelling the behaviour of postbuckling structures undergoing mode-jumping. Current non-linear implicit finite element solution schemes, found in most finite element codes, are discussed and their shortcomings highlighted. A more effective strategy is presented which combines a quasi-static and a pseudo-transient routine for modelling this behaviour. The switching between these two schemes is fully automated and therefore eliminates the need for user intervention during the solution process. The quasi-static response is modelled using the are-length constraint while the pseudo-transient routine uses a modified explicit dynamic routine, which is more computationally efficient than standard implicit and explicit dynamic schemes. The strategies for switching between the quasi-static and pseudo-transient routines are presented

Stiffener debonding mechanisms in post-buckled CFRP aerospace panels

This paper describes the fractographic analysis of five CFRP post-buckled skin/stringer panels that were tested to failure in compression. The detailed damage mechanisms for skin/stiffener detachment in an undamaged panel were characterised and related to the stress conditions during post-buckling; in particular the sites of peak twist (at buckling nodes) and peak bending moments (at buckling anti-nodes). The initial event was intralaminar splitting of the +45 degrees plies adjacent to the skin/stiffener interface, induced by high twist at a nodeline. This was followed by mode II delamination, parallel to +/- 45 degrees plies and then lengthwise (0 degrees) shear along the stiffener centreline. The presence of defects or damage was found to influence this failure process, leading to a reduction in strength. This research provides an insight into the processes that control post-buckled performance of stiffened panels and suggests that 2D models and element tests do not capture the true physics of skin/stiffener detachment: a full 3D approach is required.

Predicting the ultimate load of a CFRP wingbox

The finite element method in conjunction with the Soutis-Fleck model is used to predict the residual strength after impact of a carbon-fibre reinforced plastic wingbox subjected to a cantilever type loading. The maximum stress failure criterion further validates the Soutis-Fleck model predictions. The Soutis-Fleck model predicts that the wingbox fails at a tip load of 99.2 kN, approximately 5.5% less than the experimental observation

Capturing mode-switching in postbuckling composite panels using a modified explicit procedure

A postbuckling blade-stiffened composite panel was loaded in uniaxial compression, until failure. During loading beyond initial buckling, this panel was observed to undergo a secondary instability characterised by a dynamic mode shape change. These abrupt changes cause considerable numerical difficulties using standard path-following quasi-static solution procedures in finite element analysis. Improved methods such as the arc-length-related procedures do better at traversing certain critical points along an equilibrium path but these procedures may also encounter difficulties in highly non-linear problems. This paper presents a robust, modified explicit dynamic analysis for the modelling of postbuckling structures. This method was shown to predict the mode-switch with good accuracy and is more efficient than standard explicit dynamic analysis. (C) 2003 Elsevier Science Ltd. All rights reserved.

The Behavior of compressively loaded stiffener runout specimens - Part II: Finite element analysis

The termination of stiffeners in composite aircraft structures give rise to regions of high interlaminar shear and peel stresses as the load in the stiffener is diffused into the skin. This is of particular concern in co-cured composite stiffened structures where there is a relatively low resistance to through-thickness stress components at the skin-stiffener interface. In Part I, experimental results of tested specimens highlighted the influence of local design parameters on their structural response. Indeed some of the observed behavior was unexpected. There is a need to be able to analyse a range of changes in geometry rapidly to allow the analysis to form an integral part of the structural design process.

This work presents the development of a finite element methodology for modelling the failure process of these critical regions. An efficient thick shell element formulation is presented and this element is used in conjuction with the Virtual Crack Closure Technique (VCCT) to predict the crack growth characteristics of the modelled specimens. Three specimens were modelled and the qualitative aspects of crack growth were captured successfully. The shortcomings in the quantitative correlation between the predicted and observed failure loads are discussed. There was evidence to suggest that high through-thickness compressive stresses enhanced the fracture toughness in these critical regions.

The Behavior of compressively loaded stiffener runout specimens - Part I: Experiments

The development of the next generation of civil and military transport aircraft will inevitably see an increased use of advanced carbon fibre composite material in the primary structure if performance targets are to be met. One concern in this development is the vulnerability of co-cured and co-bonded stiffened structures to through-thickness stresses at the skin-stiffener interfaces, particularly in stiffener runout regions. These regions are a consequence of the requirement to terminate stiffeners at cutouts, rib intersections, or other structural features which interrupt the stiffener load path.

This work presents the results of an experimental programme investigating the failure of thick-sectioned stiffener runout specimens loaded in uniaxial compression. For all tests, failure initiated at the edge of the runout and propagated across the skin-stiffener interface. It was found that the failure load of each specimen was greatly influenced by intentional changes in the geometric features of these specimens. High frictional forces at the edge of the runout were also deduced from a fractographic analysis, indicating a predominantly Mode II initial failure mode.

The behaviour of damage tolerant hat-stiffened composite panels loaded in uniaxial compression

Damage tolerant hat-stiffened thin-skinned composite panels with and without a centrally located circular cutout, under uniaxial compression loading, were investigated experimentally and analytically. These panels incorporated a highly postbuckling design characterised by two integral stiffeners separated by a large skin bay with a high width to skin-thickness ratio. In both configurations, the skin initially buckled into three half-wavelengths and underwent two mode-shape changes; the first a gradual mode change characterised by a central deformation with double curvature and the second a dynamic snap to five half-wavelengths. The use of standard path-following non-linear finite element analysis did not consistently capture the dynamic mode change and an approximate solution for the prediction of mode-changes using a Marguerre-type Rayleigh-Ritz energy method is presented. Shortcomings with both methods of analysis are discussed and improvements suggested. The panels failed catastrophically and their strength was limited by the local buckling strength of the hat stiffeners. (C) 2001 Elsevier Science Ltd. All rights reserved.

Failure of thick-skinned stiffener runout sections loaded in uniaxial compression

Recent efforts towards the development of the next generation of large civil and military transport aircraft within the European community have provided new impetus for investigating the potential use of composite material in the primary structure. One concern in this development is the vulnerability of co-cured stiffened structures to through-thickness stresses at the skin-stiffener interfaces particularly in stiffener runout regions. These regions are an inevitable consequence of the requirement to terminate stiffeners at cutouts, rib intersections or other structural features which interrupt the stiffener load path. In this respect, thickerskinned components are more vulnerable than thin-skinned ones. This work presents an experimental and numerical study of the failure of thick-sectioned stiffener runout specimens loaded in uniaxial compression. The experiments revealed that failure was initiated at the edge of the runout and propagated across the skin-stiffener interface. High frictional forces at the edge of the runout were also deduced from a fractographic analysis and it is postulated that these forces may enhance the fracture toughness of the specimens. Finite element analysis using an efficient thick-shell element and the Virtual Crack Closure Technique was able to qualitatively predict the crack growth characteristics for each specimen

Fracture mechanics using a 3D composite element

The formulation of a 3D composite element and its use in a mixed-mode fracture mechanics example is presented. This element, like a conventional 3D finite element, has three degrees of freedom per node although, like a plate element, the strains are defined in the local directions of the mid-plane surface. The stress-strain property matrix of this element was modified to decouple the stresses in the local mid-plane and the strains normal to this plane thus preventing the element from being too stiff in bending. A main advantage of this formulation is the ability to model a laminate with a single 3D element. The motivation behind this work was to improve the computational efficiency associated with the calculation of strain energy release rates in laminated structures. A comparison of mixed-mode results using different elements of an in-house finite element package are presented. Good agreement was achieved between the results obtained using the new element and coventional higher-order elements

A simple non-linear global-local finite element methodology for composite structures

A simple non-linear global-local finite element methodology is presented. A global coarse model, using 2-D shell elements, is solved non-linearly and the displacements and rotations around a region of interest are applied, as displacement boundary conditions, to a refined local 3-D model using Kirchhoff plate assumptions. The global elements' shape functions are used to interpolate between nodes. The local model is then solved non-linearly with an incremental scheme independent of that used for the global model.