D. Hitchings

Compression after impact strength of composite sandwich panels

Abstract Two types of sandwich panels with carbon epoxy skins and aluminium honeycomb core were subjected to low velocity impacts and then the damaged panels tested for their compression-after-impact (CAI) strength. One type of panel was found to be a very robust energy absorber, i.e. a thick-skin thin-core option. The other panels with their thin skins and thick core were found to penetrate easily whereupon the impactor forced the back-face to debond massively. These panels then had the worst CAI strength. Both the impact damage and the CAI behaviour––to failure––were simulated using a finite element model of skins and core. The model gave very respectable agreements with the impact tests even though the damage in skin and core were extremely complex mechanisms, involving progressive fibre fracture in the skin and elasto-plastic deformation in compression and shear in the honeycomb core. The model for CAI strength predicted well the failure load and the mode of propagation from the damaged zone.

Delamination growth prediction using a finite element approach

Abstract Delamination can be a major problem for laminated composite structures. This paper summarises the computational methods for predicting delamination growth and gives details of a finite element (FE) approach that has been developed in the Aeronautics Department at Imperial College. In this technique, the delamination profile is sought so that the modal components of the energy release rate (G) satisfy a growth criterion along the advancing delamination front for a given applied load or displacement. The G values in the elements along the delamination front are calculated using the virtual crack closure method. An automatic mesh moving algorithm is used to update the delamination position in the FE model. The paper presents a number of examples showing the effectiveness of the delamination growth modelling technique. The examples include models containing single and multiple delaminations and growth in the presence of buckling. Comparison with experimental data is also presented. Difficulties in modelling delamination growth in more complex structures are discussed.

A FINITE ELEMENT MODEL FOR DELAMINATION PROPAGATION IN COMPOSITES

Abstract In this paper the theory and application of a modelling technique for three-dimensional planar delamination growth in laminated composites has been presented. The method is based on linear elastic fracture mechanics assumptions for delamination cracks and uses a strain energy release rate criterion. For a given component, strain energy release rate is considered to be a non-linear function of the location of the delamination front. Hence, satisfaction of the growth criterion reduces to the solution of a non-linear system of equations. A generalized secant method, by the Broydens update method, is used to solve the system of non-linear equations. Several examples of the application of the technique are presented.

Finite element modelling of delamination growth in the DCB and edge delaminated DCB specimens

This paper presents the results of a finite element investigation of delamination growth in a conventional Mode I double cantilever beam (DCB) specimen and in an edge-delaminated version of this specimen. The investigation was performed using a recently developed FE model for delamination growth prediction to which an approximate contact area detection method has been added. The results of the FE analyses are used to evaluate the existing data reduction techniques for calculation of interlaminar fracture toughness. It is shown that the conventional DCB data reduction schemes can be applied to the edge delaminated specimen but the results are dependent upon the difference between the measured apparent delamination length and the actual length being constant. An alternative data reduction method is presented in which the critical energy release rate is determined by comparison of the experimental data with finite element results and does not require measurement of the delamination length.

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.

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.

Fracture mechanics using a 3D composite element

Abstract 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.

FINITE ELEMENT MODELLING OF SEWER LININGS

Abstract In the course of renovating egg-shaped sewer linings, comparisons of stress/strain and deflection levels with their permissible values are complicated not only by their shape but also by their considerably variable material properties and the choice of intermediate restraint set-ups. Thus, the present attempt to model numerically two glass-reinforced plastic (GRP) linings (one of them segmental) and one glass-reinforced cement (GRC) lining (segmental) by using actual material data and structural test results carried out under uniform pressure aims at the validation of a suitable finite element model as a design tool capable of encompassing a wide range of parameters. These include arbitrary lining geometries, material properties, boundary restraint set-ups, and different load configurations resulting from the way in which the grouting pressure is applied.

FINITE ELEMENT SIMULATION OF GUST LOADING

SUMMARY In the structural design of civil aircraft the critical loads are often those encountered in a gust or atmospheric turbulence. The traditional ‘indicial’ solution is restricted to a simple plate. In this paper a finite element formulation is proposed for an aerofoil or arbitrary shape entering a uniform sharp-edged or sinusoidal gust. The thin rotational gust front and wake in an irrotational flow field are successfully modelled by a novel superposition technique. The finite element solutions are compared with the Kussner function and results by other numerical methods. The agreement is good.