G.A.O. Davies

Finite element modelling of low velocity impact of composite sandwich panels

Abstract This paper outlines a finite element procedure for predicting the behaviour under low velocity impact of sandwich panels consisting of brittle composite skins supported by a ductile core. The modelling of the impact requires a dynamic analysis that can also handle non-linearities caused by large deflections, plastic deformation of the core and in-plane degradation of the composite skins. Metal honeycomb, frequently used as a core material, is anisotropic and requires a non-standard approach in the elasto-plastic part of the analysis. A suitable yield criteria based on experimental observations is proposed. Comparisons of experimental and finite element responses are shown for sandwich panels with carbon fibre skins and aluminium honeycomb cores.

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.

Postbuckling behaviour of a blade-stiffened composite panel loaded in uniaxial compression

Abstract The postbuckling behaviour of a panel with blade-stiffeners incorporating tapered flanges was experimentally investigated. A new failure mechanism was identified for this particular type of stiffener. Failure was initiated by mid-plane delamination at the free edge of the postbuckled stiffener web at a node-line. This was consistent with an interlaminar shear stress failure and was calculated from strain gauge measurements using an approximate analysis based on lamination theory and incorporating edge effects. The critical shear stress was found to agree well with the shear strength obtained from a three-point bending test of the web laminate.

Impact damage with compressive preload and post-impact compression of carbon composite plates

Abstract This paper examines the effect on laminated composites of in-plane compression followed by impact damage, and the coupling between the two, on compression-after-impact (CAI) performance. It is found that preload can actually raise the CAI strength if the load approaches the initial buckling value, since the plate loses stiffness and the impact-induced force is reduced and so is the consequent damage. However, as the preload approaches the CAI strength the induced delamination can propagate catastrophically during the impact, but at a preload value below the CAI strength. The coupling between impact and preload is simulated using the equations of motion, and the same dynamic solver is then used to capture the snap-through when a plate is loaded beyond its initial buckling load. A special ‘dynamic relaxation’ routine is shown to be robust and reliable when handling these ‘snap-through’ problems which can be formidable challenges to conventional static incremental loading.

Impact damage prediction and failure analysis of heavily loaded, blade-stiffened composite wing panels

Within the framework of a European research programme to develop design methodology for the improvement of damage tolerance within composite materials, two heavily loaded, stiffened composite wing panels were designed, fabricated and tested. The panels were impacted at the vulnerable stiffener edges and the failure modes and mechanisms related to the infliction of impact damage and the subsequent compression after impact loading were determined. A capability to predict the occurrence of impact damage by finite element analysis was demonstrated and guidelines for the design of damage tolerant panels were established. The laminate composition of two panel skins was quasi-isotropic. The test results were compared with test results obtained earlier for two similar panels with soft skins, i.e., panel skins with a low axial stiffness. The latter panels were shown to be more damage tolerant, which is accredited to the much smaller number of 90° plies present in the soft skins. The failure mode was found to be a three stage phenomenon: a load eccentricity is present from the start causing local bending near the damage area, impact delaminated sublaminates then buckle out of plane and eventually propagate leading to global bending and to overall instability and collapse. Delamination growth occurred mainly in the lateral direction along 90° ply interfaces, but remained within the C-scan damage area until the final unstable propagation. The stability of the damage configuration, and in particular of the sublaminates formed by the impact and the subsequent compression loading, seems to be the key with respect to the damage tolerance of heavily loaded, stiffened panels.

A 3-D, co-rotational, curved and twisted beam element

Abstract The dominant motion in the large displacement analysis of a slender-bar space frame is attributable to finite rotations, the elastic strains remaining small. If this rigid body motion is eliminated from the total displacements, the deformational part which remains is always a small quantity relative to the local element axes. In the co-rotational (CR) formulation a local Cartesian coordinate system attached to each finite element continuously translates and rotates with the element as the deformations proceed. Thus the CR formulation incorporated with the small deflection beam theory would appear to be an efficient method for large displacement analysis. The present large displacement analysis developed by Bates [Ph.D. Thesis, University of London (1987)] uses Eulers theorem of rigid body rotation and the Polar Decomposition theorem of continuum mechanics to develop a rigorous finite rotation theory. A cubic, isoparametric, curved, composite beam element is proposed using the CR finite element formulation. Sample nonlinear problems have been solved using the Crisfield Arc-Length Method. The analysis has been found to be very efficient and reliable.

Shear driven delamination propagation in two dimensions

This paper investigates, theoretically and experimentally, the propagation of delamination in shear mode II between internal ply surfaces in a laminated composite plate. By considering two special cases the problem is approximated as an axisymmetric model amenable to analytical solutions. In one case the circular crack front expands and in the other it contracts. It is shown clearly that only a (linear) fracture mechanics approach will explain the mode and threshold of failure, but that a strength-based criterion can be used to initiate propagation without the need for an initial flaw. Apart from explaining some curious phenomena, the simple axisymmetric analytical solutions may be used as benchmarks for testing the ability of finite element models to predict plate delamination when the crack front is curved (at present only simple beam models are available for the standard DCB and ENF tests, but even these tests do not really develop straight crack fronts).

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

Abstract 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, thicker-skinned 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.

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.

An aeroelasticity beam model for flexible multibody systems under large deflections

Abstract Dynamic analysis of multibody systems is a subject of interest in a number of diverse disciplines. However, the modelling of multibody systems has only concentrated on structural dynamics so far. It is felt that there is another important class of problem needing to be simulated for multibody systems, especially in the aerospace industry: aeroelastic modelling for complex multibody systems. This paper presents a finite element aeroelasticity beam model as a first effort in developing a general multibody aeroelasticity model. A nonlinear finite element multibody structure dynamics model previously developed is further extended to a finite element aeroelasticity beam model in this paper. The aerodynamic loads are computed for a beam attached to a moving base using a two-dimensional quasi-steady thin airfoil theory, and is discretized by the finite element method. This general model can be used as a basic element to analyse the aeroelasticity problems of a beam and the aeroelasticity problems of some multibody systems by making use of the six rigid body degrees of freedom of the beam base. The algorithm is applied to evaluate the aeroelasticity stability of helicopter rotor blades in a companion paper.