P.D. Soden

Axial crushing of square tubes

Abstract The mechanics of the large deformation of a square tube under axial load is discussed. Theoretical results are substantiated by experimental results. The elastic buckling load is predicted by assuming the tube to be comprised of four plates simply supported at their edges. The highest load the tube can sustain is predicted by allowing for the development of plasticity near the corners. The mean crushing load is predicted from an incremental plasticity analysis which allows for travelling plastic hinges. Comparison with circular tube behaviour is considered and an attempt to explain some of the peculiarities is made.

Mode separation of energy release rate for delamination in composite laminates using sublaminates

Abstract Individual energy release rates for delamination in composite laminates do not exist according to two- or three-dimensional elastic theory due to the oscillatory characteristics of the stress and displacement fields near the delamination tip (Sun, C.T., Jih, C.J., 1987. Engng. Fracture Mech. 28, 13–20; Raju, I.S., Creus Jr., J.H., Aminpour, M.A., 1988. Engng. Fracture Mech. 30, 383–396.) In this paper, sublaminates governed by transverse shear deformable laminate theory are adopted to model such delamination. Oscillatory singular stresses around the delamination tip are avoided as a result. Instead, stress resultant jumps are found in the sublaminates across the delamination tip. It transpires that mode I, II and III energy release rates can then be obtained using the virtual crack closure technique. The results produced by this approach for a homogeneous double cantilever beam and an edge-delamination in a non-homogeneous laminate show good agreement with those available in the literature. The approach produces both total and individual components of energy release rate for delamination, which converge as the sublaminate division is refined and the sizes of the delamination tip elements decrease.

Experimental failure stresses for ±55° filament wound glass fibre reinforced plastic tubes under biaxial loads

Abstract Experiments have been carried out to determine the failure envelopes which describe the leakage and fracture strengths of thin walled ±55° filament wound E-glass fibre/epoxy tubes under a variety of biaxial stress states produced by applying combinations of internal pressure and axial tensile and compressive loads. The fracture strengths vary from 70 MPa to 900 MPa depending on the ratio of applied circumferential to axial stresses. For some combinations of loading leakage occurs at much lower stresses than final failure.

The strength of a filament wound composite under biaxial loading

Abstract This paper describes experiments in which filament wound glass/polyester tubes were loaded by internal pressure and simultaneous axial tension or compression. Failure envelopes are presented which describe the strength of ± 35° and ± 55° winding angle composites under a variety of biaxial stresses. The experimental results are compared with a semi-empirical failure criterion.

Application of a delamination model to laminated composite structures

Abstract A model for progressive interlaminar delamination is presented for laminated composite structures. Instead of a cumbersome 3D description, a computationally efficient 2D technique is adopted which models the laminated structure as an assembly of sublaminates connected through their interfaces. Constraints between sublaminates are removed to represent the presence of delaminations. The use of laminate theory results in jumps in stress resultants across the delamination tip and this helps to avoid dealing with the singular stress field at the delamination front. A stress-based failure criterion is used to predict delamination initiation. Delamination propagation is analysed by adopting a fracture mechanics approach. The major intralaminar damage mode, matrix cracking, is also included in the present analysis. This is detected by a stress-based failure criterion and a ply discount model is used to account for the effects of material degradation. Finite element analysis has been carried out to assess the deformation and the delamination development in a range of typical structures: a double cantilever beam, a cross-ply laminate and some filament-wound composite pipes. Good agreement has been achieved between the predictions and available experimental data. A study of the effect of mesh size shows that a relatively coarse mesh gives sufficiently accurate results. These examples give a useful indication of the versatility and feasibility of the present approach for real structural applications.

Damage, deformation and residual burst strength of filament-wound composite tubes subjected to impact or quasi-static indentation

Abstract Thin-walled filament-wound E-glass fibre-reinforced epoxy tubes were subjected to lateral indentation in quasi-static and low speed impact tests and were then tested under internal pressure to determine their residual burst strength. The behaviour of tubes subjected to quasi-static and low velocity impact loading tests was found to be the same. Experimental strain measurements in quasi-static indentation tests showed a large degree of redistribution of strain with increasing deflection which resulted in local buckling failure away from the indentation point. Damage in the form of matrix cracking resulted from low energy indentation but did not reduce the residual burst strength of the tube. Higher energy indentation, which produced buckling failure, reduced the tubes’ burst strength by 60%.

A finite strip analysis of cracked laminates

Abstract As a step towards the construction of a comprehensive model for damaged composites, the deformation of transversely cracked laminates is analysed. The approach is based on a generalised plane strain approach and uses the finite strip method which allows general lay-ups of laminates rather than just cross-ply to be considered. General loading is treated. In addition, the method permits a more flexible control to be exercised between accuracy and the extensiveness of the calculations than can be achieved using existing analyses. This method could be integrated with the finite element analysis of structures to allow for changes in the effective material properties of locally damaged regions. Results produced by the approach are compared with those available in the literature and good agreement is demonstrated.

Lamination theory in the prediction of failure envelopes for filament wound materials subjected to biaxial loading

Abstract This paper describes a theoretical approach to the prediction of failure envelopes for filament wound materials under biaxial loading. The failure is predicted from a ply-by-ply analysis allowing for progressive failure of the laminate, shear non-linearity and different properties in compression and tension. A maximum stress failure criterion is applied which also gives the mode of failure. Experimental results are compared with the theoretical failure envelopes and there is good correlation between theory and experiment.

Indentation of laminated filament-wound composite tubes

Abstract The finite element method has been used to analyse the behaviour of thin-walled, 100 mm diameter filament-wound GRP tubes supported on a flat plate and indented with a 50 mm diameter spherical indenter. The tube wall was treated as an angle-ply laminate and a half-tube model was employed with appropriate rotational symmetry conditions. The strain results were compared with those from a quarter-tube monolithic material model (homogeneous throughout and orthotropic with principal axes coincident with the axial and circumferential directions). The theoretical predictions were compared with experimental results. Local resin cracks occurred under the indenter. Two-cover (four-layer), 1 mm thick, ±55° and ±75° winding angle tubes finally failed at large indenter displacements by local shell buckling caused by the development of local axial compressive forces some distance away from the indenter. Four-cover (eight-layer), 2 mm thick, ±55° tubes delaminated under the indenter and failed by shell fracture, again some distance away from the indenter.

Theoretical through-thickness elastic constants for filament-wound tubes

Abstract A linear elastic analysis is presented for calculating the three-dimensional effective elastic constants for filament-wound fibre-reinforced composite tubes from the properties of unidirectional fibre-reinforced material. The tubes are analysed as balanced angle-ply laminates. Graphs are presented showing how all the elastic constants, including the through-thickness properties, vary with winding angle for Eglass/epoxy, carbon/epoxy and Kevlar/epoxy filament-wound tubes.