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CivilComp Proceedings
ISSN 17593433 CCP: 75
PROCEEDINGS OF THE SIXTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY Edited by: B.H.V. Topping and Z. Bittnar
Paper 129
Finite Element Analysis of Damaged Multilayered Composite Beams with Transverse Deformability M. Di Sciuva and M. Gherlone
Department of Aerospace Engineering, Turin Polytechnic, Turin, Italy M. Di Sciuva, M. Gherlone, "Finite Element Analysis of Damaged Multilayered Composite Beams with Transverse Deformability", in B.H.V. Topping, Z. Bittnar, (Editors), "Proceedings of the Sixth International Conference on Computational Structures Technology", CivilComp Press, Stirlingshire, UK, Paper 129, 2002. doi:10.4203/ccp.75.129
Keywords: zigzag models, transverse normal deformability, Hermitian degrees of freedom, sublaminates approach, damaged interfaces, sliplocking.
Summary
The use of advanced composite materials, typical of modern Aerospace
projects, leads to the need for theories capable to capture a number of
nonclassical effects: the transverse shear flexibility, the need for
fulfilling the continuity requirement of transverse shear stresses at the
layer interfaces, the possibility to model interfacial bonding damage
between the constituent laminae. The linear and cubic zigzag models
proposed by Di Sciuva [1] can fulfil the above described
requirements without increasing the number of degrees of freedom with
respect to the FSDT. An improvement of the model (the Hermitian zigzag
model) is presented in this paper; the term Hermitian is due to the fact
that the throughthethickness shape functions are a generalization of the
classical Hermite polynomials. The presented model offers some interesting
capabilities: (i) throughthethickness linear transverse displacement, (ii)
evaluation of the transverse normal deformability, (iii) traction
equilibrium condition on the external surfaces and (iv) use of the
displacements and transverse shear stresses of the external surfaces as
degrees of freedom. But, perhaps, the most important characteristic of the
Hermitian model is that it can be used to obtain a throughthethickness
description of displacements, strains and stresses (in particular of the
normal ones) that is more detailed than what is allowed by the displacement
field. Applying the sublaminates approach proposed by Averill
[2], a beam finite element based on the Hermitian model has been
formulated; then a discretizing and assembling procedure has been used that
enables to divide the laminate thickness in a number of
elementssublaminates. In this way, for example, we can study a laminated
beam using a piecewise linear transverse displacement instead of a simply
linear one (that is what we can do with the Hermitian model by itself).
The problem of interlayer slip is a big challenge for 2D laminate models. The classical cubic zigzag model can be used to study damaged beams and plates [1]: it is in fact possible to introduce jumps in the inplane displacements at the damaged interfaces and, moreover, these jumps are proportional to the interlaminar transverse shear stress (linear slip law). This capability is still present in the Hermitian model. It is to be said that this way to describe damage is not valid when high levels of debonding are experienced. As we will show in this work, in fact, when the interlaminar damage is severe, the classical zigzag models experience what we have called sliplocking: we use the term locking because the laminated structure behaves in a stiffer and stiffer way when the slip damage level is increasing. In this work the origin of the phenomenon is explained. When we use the classical zigzag model or the Hermitian one but with only a sublaminate, the throughthethickness distribution of the transverse shear stress exhibits a shape that does not change with the damage level and this is an incorrect behaviour; as a consequence, when the damage is very high, the whole transverse shear stress distribution vanishes. The correct behaviour should be characterized by the vanishing of the shear stress only in correspondence to the damaged interface and this can be obtained only if the shape of the throughthethickness distribution changes with the intensity of the slip defect. The use of the sublaminates approach allow to divide the thickness in such a way that the damaged interface is a boundary between adjacent elementssublaminates. The damage effects are introduced imposing a particular relation (not only linear) between the inplane displacement jump and the transverse shear stress for the nodes where the debonding defect is present. This procedure can be easily introduced because the degrees of freedom used for the elements are the displacements and the shear stresses of the external surfaces of each sublaminate. In this work it is shown that the Hermitian model is valid in describing local throughthethickness responses (in particular in terms of transverse quantities) when used together with the FEM/sublaminates approach. A particular assembling scheme is used to describe localized or diffused interlayer slips; a comparison between the results obtained with the sublaminates approach and those obtained with the classical and Hermitian (one sublaminate) zigzag models show that the latter are unable to describe severe damages because of the sliplocking phenomenon. Some numerical results are presented to show the potentialities of the method. References
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