P.M.S.T. de Castro

A three-dimensional finite element model for stress analysis of adhesive joints

Abstract This paper presents a new model for three-dimensional finite element analysis of adhesive joints. The model considers geometric and material nonlinearities and uses solid brick elements as well as specially developed interface elements. The interface elements allow the calculation of stresses at the adherend–adhesive interfaces. The application of the model to a single-lap joint is presented. The results of a linear elastic analysis highlight the three-dimensional nature of the stresses and stress concentrations at interfaces. The influence of material nonlinearities on the behavior of the joint is also discussed.

Mode-I interlaminar fracture of carbon/epoxy cross-ply composites

Abstract Mode-I double-cantilever beam (DCB) tests were performed on carbon/epoxy [0°/90°]12 specimens. The starter crack was created at mid-thickness, between the 0 and 90° mid-layers. During the tests, however, the crack also propagated along the neighbouring 0°/90° interface and within the 90° mid-layer. Nevertheless, the test results were apparently consistent with the assumptions of the corrected beam theory (CBT) that was used to obtain the interlaminar critical strain energy release rate, GIc. The measured values were higher than those of unidirectional [0°]24 specimens, especially the final propagation values. A finite-element analysis confirmed the applicability of the CBT for interlaminar propagation along the two 0°/90° interfaces. The results also indicated that the intralaminar GIc is significantly smaller than the interlaminar GIc. This will prevent pure interlaminar propagation in multi-directional specimens with high interlaminar fracture toughness.

Interface element including point‐to‐surface constraints for three‐dimensional problems with damage propagation

An interface finite element for three‐dimensional problems based on the penalty method is presented. The proposed element can model joints/interfaces between solid finite elements and also includes the propagation of damage in pure mode I, pure mode II and mixed mode considering a softening relationship between the stresses and relative displacements. Two different contact conditions are considered: point‐to‐point constraint for closed points (not satisfying the failure criterion) and point‐to‐surface constraint for opened points. The performance of the element is tested under mode I, mode II and mixed mode loading conditions.

Modeling Compression Failure after Low Velocity Impact on Laminated Composites Using Interface Elements

Low velocity impact damage can significantly reduce the residual strength of laminated composites. This kind of damage (mostly delaminations) is very dangerous for the structures because it is not apparent to the naked eye and, in some cases, it can reduce the compressive residual strength up to 60%. In this work, a numerical model for predicting the compression failure of laminated composites containing delamination caused by low velocity impact was developed. An interface finite element, previously developed by the authors, was used. This element is compatible with twenty-seven node isoparametric hexahedral elements and enables modeling the behavior of the damaged interface, taking into account a three-dimensional stress state, the interpenetration constraint and the propagation of delamination. In order to verify the numerical model, some experimental work was done. The experimental work, performed on carbon-epoxy (04, 904)5 and (904, 04), laminates, included low velocity impact tests using a drop weight testing machine, followed by X-Ray damage characterization and compression tests using a fixture system similar to IITRI system. The numerical and experimental results were compared and good agreement was obtained.

Multiple-site damage in riveted lap-joints: experimental simulation and finite element prediction

Abstract The multiple-site damage (MSD) phenomenon is discussed, and exemplified by the behaviour of riveted lap-joint specimens of aluminium alloy 2024-T3 alclad. The tests performed, on which the paper is based, are part of the contribution of IDMEC to a project on the fatigue behaviour of ageing aeronautical structures—the BRITE-EURAM project ‘SMAAC’, partially funded by the European Union. The study involves fatigue testing under constant amplitude loading of 1.6-mm-thick riveted lap-joints, and includes examination of the specimens during and subsequent to testing (post-mortem analysis of the fracture surface in a scanning electron microscope) in order to determine the time of occurrence, location and extent of fatigue damage. Crack growth rates are determined from periodic crack length measurements with a travelling microscope. Stress measurements are made using extensometry and the SPATE infrared technique to determine loading distribution of the lap-joints and redistribution due to cracking of fastener holes. Data on the initiation and growth of cracks and on residual static strength are used to assess the predictive model based on the finite element method.

Prediction of compressive strength of carbon–epoxy laminates containing delamination by using a mixed-mode damage model

Abstract It is well known that composite laminates are easily damaged by low-velocity impact. The internal delaminations can drastically reduce the compressive strength of laminates. In this study, a numerical analysis for predicting the residual compressive strength of delaminated plates is proposed. The delaminated interfaces are modelled by using interface elements connecting the three-dimensional solid elements modelling the composite layers. Delamination propagation is modelled by using a damage model based on the indirect use of fracture mechanics. Due to the complex stress state of the problem, a mixed-mode analysis including the three modes of fracture was considered. Experimental studies were performed on carbon–epoxy [04, 904]s and [904, 04]s laminates. They included low-velocity impact tests, followed by X-ray damage characterisation and compression tests. Good agreement between experimental and numerical analysis was obtained.

A reduced integration mindlin beam element for linear elastic stress analysis of curved pipes under generalized in-plane loading

Abstract This paper presents a ring element for the analysis of in-plane bending of curved pipes. The element is derived from the arch bending theory using short, straight elements as an approach to the curved structure. Each curved pipe element is considered as a straight thin-walled C 0 -continuity beam element for the purpose of the derivation of the beam stiffness matrix terms. The assumption of the straight elements does not involve ovalization and warping of the transverse section; for the stiffness terms concerning the distortion of the transverse section, the pipe element is assumed curved. This method leads to the important advantage of generating a zero stress field along the curved centroidal line of the element under pure in-plane bending and to the satisfaction of the ‘patch test’.

Friction stir welding of T-joints with dissimilar aluminium alloys: mechanical joint characterisation

Abstract Friction stir welding (FSW) is a high reliability joining process creating excellent opportunities for new design concepts. This paper discusses T-joints composed by dissimilar aluminium alloys, a configuration suitable for reinforced panels where the skin is made of an aluminium alloy with higher toughness, and the web (reinforcement or stiffener) is made of a higher strength aluminium alloy, creating a good damage tolerant arrangement. A T-joint configuration was proposed non-including overlap interfaces between the workpieces. This T-joint also promotes a good flow among the materials of the different workpieces during the FSW process resulting in sound welds. Mechanical properties were measured achieving high efficiency values of joint static and dynamic strenght but with the drawback of the loss of elongation. Microstructural analyses of the weld zone were performed, and the results were compared with those of base materials and FSW butt joints evidencing the possibility of joining two dissimilar aluminium alloys in a T configuration. Additionally, the residual stress field, which is an important parameter for a more reliable design of integral structures, was evaluated with a semidestructive and a destructive method. The feasibility to weld T-joints with dissimilar aluminium alloys was demonstrated achieving good quality results, which can be used for structure reinforcement and optimisation.

Residual stress analysis near a cold expanded hole in a textured Alclad sheet using X-ray diffraction

In this paper we present the methods of determination and the stress obtained at the periphery of a cold expanded hole in a 2024-T3 Alclad aluminum alloy sheet. The measurements in the aluminum clad were performed by the sin2Ψ method, taking experimental precautions to deal with the texture effects. In the core aluminum a special method had to be implemented to determine the stress values in a direction not accessible to the X-ray diffraction. The strains were measured in sample orientations selected according to the texture characteristics and stress factorsFij were used to calculate the stress tensor. TheFij values were determined assuming a quasi-isotropic material behavior, after concluding that the stress results were not significantly affected by factors calculated for textured material. The residual stress profile, both in the clad and in the sheet, shows a nearly axisymmetric stress state. Compressive stresses were observed near the periphery of the hole, with values that are higher on the exit than on the entrance face. Residual stresses were also higher in the hoop direction than in the radial direction. They decreased with the radial distance to the hole and affected the previous stress state over a distance of 6 mm. The plastic deformation induced by the cold expansion is well evidenced by the FWHM values, which in the affected zone decrease with increasing distance from the hole edge.

The linear elastic stress analysis of curved pipes under generalized loads using a reduced integration finite ring element

Abstract This paper consists of a linear elastic stress analysis of curved pipes having all the possible boundary conditions in structural engineering and submitted to a generalized in-plane or out-of-plane loading. A semi-analytic displacement formulation ring element was developed, where simple first-degree polynomials were used to interpolate the global shell displacements along the longitudinal direction, and Fourier series were used along the meridional direction. The deformed shape of the curved pipe results from the superposition of the beam-type displacement to that of a toroidal shell. For the first case, the curved pipe was considered as being a short thin-walled straight beam element joining two nodal sections. In this case, as the pipe element is not curved, it is natural to consider that the transverse section undergoes no ovalization or warping. A C0-continuity reduced integration beam element was adopted for this purpose, leading to a simple and economic definition for the stiffness terms. In the second case, the displacement field was assumed to result from a stressed toroidal shell, where the transverse section could ovalize and warp. The stiffness terms following these assumptions are combined with those of the straight beam to give the complete stiffness matrix. This element has the important advantage of generating a zero stress field along the curved centroidal line when submitted to pure in-plane bending and, consequently, to the satisfaction of the ‘patch test’.