Keywords: composites, joints, contact, progressive damage, failure criteria, FEM.

When used in structural application, composites are commonly bonded either to composites or to metals by means of mechanical joints. Hence it is of mainly importance to understand the structural behaviour of this kind of joints in order to utilise advanced composites' full potential. Since most composite materials are characterised by brittle failure, with low margin of safety through ductility, the failure mechanisms in composite joints must be investigated and suitable prediction analysis tools need to be developed.

Due to its inherent complexity and its 3D nature, the problem under consideration needs to be investigated by means of a three-dimensional progressive damage approach able to take into account all the physical phenomena characterising the damage on-set and propagation until the final failure.

In the last years, the progression of damage in composite structures has been extensively studied. In [1] an effective overview of the basic steps to perform a progressive failure analysis is presented. The failure criteria and the properties degradation rules are identified as key-points for this kind of analysis.

Relatively few researchers have introduced 3D FEM models. In [2,3] the stress distribution at the pin-hole interface is investigated. However a full 3D progressive damage approach is necessary to reflect the physics of damage mechanisms and to obtain a realistic simulation of the structural behaviour of composite joints.

In the following a three-dimensional progressive damage approach for laminated composites is presented. This approach is based on the geometrically non-linear finite element formulation for stress calculation. To impose friction contact conditions the penalty method and the Coulomb friction law has been adopted. Finally, the FEM model has been integrated with Hashin's failure criteria to split fibre and matrix failure modes and with the ply discount method to simulate the stiffness degradation in each ply.

The two-dimensional progressive damage FEM procedure proposed in [4] was revised and adapted to the three-dimensional formulation here presented. As in [4] the ANSYS FEM code was used for the numerical implementations.

The progressive damage procedure can be summarised as follows. First, geometry, material lay out, boundary conditions and initial loads are defined. A first step linear analysis has also to be carried out in order to evaluate the stresses for each layer of each finite element in the Gauss points. Then the resulting values are used to obtain layer average stresses. The layer average stresses are checked according to the above mentioned failure criteria. If failure does not occur the load will be incremented while if failure occurs the material will be properly degraded in all the damaged elements according to the ply discount rules. In both cases the convergence of the Newton-Raphson method, for the presence of geometrical and contact non-linearity, is checked to find the new equilibrium position related to the local change of material properties or to the increasing of load. In case of no convergence the structural collapse occurs, otherwise a new stress evaluation is performed.

The implementation of this approach in the ANSYS FEM code makes it possible to take into account the failure of composites in each ply and in each element.

As application the structural behaviour of a single lap composite joint under in- plane tensile load was investigated. The comparison between numerical results and existing experimental data [5] has proved the effectiveness of the proposed progressive damage approach. In order to better understand the real structural behaviour of composite joints, some considerations on the failure mechanisms involved in the analysis and on the evolution of damage have also been provided.

The choice of penalty parameter for contacts and the choice of the reduction factor for the degraded material properties revealed themselves as critical points for the developments.

1

Ochoa, O.O., Reddy, J.N., "Finite Element Analysis of Composite Laminates", Kluwer Academic Publishers, Dordrecht, The Netherlands, 1992.

2

Matthews, F.L., Wong, C.M., Chryssafitis, S., "Stress Distribution Around a Single Bolt in Fibre-Reinforced Plastic", Composites, 13, 316-322, 1982. doi:10.1016/0010-4361(82)90016-7

3

Sperling, U.O., "Three-dimensional Stress Distribution Around Pin Loaded Holes in Composite Laminates", A"AA/ASME/ASCE/AHS 26th Structures, Structural Dynamics and Material Conference, 85-0826, 743-750, 1985.

4

Perugini, P., D'anna, G., Riccio, A., Scaramuzzino, F., Tessitore, N., "Progressive Failure Analysis of Composite Joints", ASME conference, Virginia US, 1999.

5

McCarthy, M., Stanley, W., "Bolt-Hole Clearance Test Specification", Deliverable D5-5, BOJCAS (Brite-Euram /Bolted Joints in Composite Aircraft Structures), 2000.

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