Finite element modelling of delaminated composite plates

1.3 Presentation

Due to the anisotropy of composite laminates and non-uniform distribution of stresses in lamina under flexural bending as well as other types of static/dynamic loading, the failure process of laminates is very complex.

Large differences in strength and stiffness values of the fiber and the matrix lead to various forms of defect/damage caused during manufacturing process as well as service conditions. In shipbuilding, many structures made of composite laminates are situated such that they are susceptible to foreign object impacts which can result in barely visible impact damage. Often, in the form of a complicated array of matrix cracks and interlaminar delaminations, these barely visible impact damages can be quite extensive and can significantly reduce a structure’s load bearing capability.

Delamination or separation of two adjacent plies in a composite laminate is one of the most common modes of damage. The presence of delamination may reduce the overall stiffness as well as the residual strength leading to structural failure. A clear understanding of the influence of delamination on the performance of the laminates is very essential to use them efficiently in structural design applications.

Since such damage is in general difficult to detect, structures must be able to function safely with delamination present.

Although several studies are available in the literature in the field of delamination prediction and growth, effect of delamination on buckling, post-buckling deformation and delamination propagation under fatigue loading, etc. the work on the effect of delamination on the first ply failure of the laminate is scarce.

However, there clearly exists the need to be able to predict the tolerance of structures to damage forms which are not readily detectable (Chirica & al, 2006).

(Ambarcumyan, 1991, Adams & al, 2003) have analysed experimental characterization of advanced composite materials. When a laminate is subjected to in-plane compression, the effects of delamination on the stiffness and strength may be characterized by three sets of results, (Finn & Springer, 1993):

a. Buckling load;

b. Postbuckling solutions under increased load;

c. Results concerning the onset of delamination growth and its subsequent development. Many of the analytical treatments deal with a thin near surface delamination. Such approaches are known as "thin-film" analysis in the literature (Kim & al,1999, Thurley & al, 1995). The thin-film analytical approach may involve significant errors in the post-buckling solutions.

(Naganarayana & Atluri, 1995) have analysed the buckling behaviour of laminated composite plates with elliptical delaminations at the centre of the plates using finite element method. They propose a multi-plate model using 3-noded quasi-conforming shell element, and use J-integral technique for computing point wise energy release rate along the delamination crack front.

(Pietropaoli & al, 2008) studied delamination growth phenomena in composite plates under compression by taking into account also the matrix and fibers breakages until the structural collapse condition is reached.

The aim of the work presented in this chapter is to present the studies on the influence of elliptical delamination on the changes in the buckling behaviour of ship deck plates made of composite materials. This problem has been solved by using the finite element method, in (Beznea, 2008). An orthotropic delamination model, describing mixed mode delaminating, by using FEM analysis, was applied. So, the damaged part of the structures and the undamaged part have been represented by well-known finite elements (layered shell elements). The influence of the position and the ellipse’s diameters ratio of delaminated zone on the critical buckling force was investigated.

If an initial delamination exists, this delamination may close under the applied load. To prevent the two adjacent plies from penetrating, a simple numerical contact model is used. Taking into account the thickness symmetry of the plates, only cases of position of delamination on one side of symmetry axis are presented. The variations of the transversal displacement of the point placed in the middle of the plate versus the in-plane applied pressure are plotted for each position of delamination. Buckling load determination for the general buckling of the plate has been done by graphical method. The post-buckling calculus has been performed to explain the complete behaviour of the plate.

Only cases with one delamination placed between two laminas is presented here.

There are several ways in which the panel can be modeled for the delamination analysis. For the present study, a 3-D model with 4-node shell composite elements is used. The plate is divided into two sub-laminates by a hypothetical plane containing the delamination. For this reason, the present finite element model would be referred to as two sub-laminates model. The two sub-laminates are modeled separately with shell composite elements, and then joined face to face with appropriate interfacial constraint conditions for the corresponding nodes on the sub-laminates, depending on whether the nodes lie in the delaminated or undelaminated region.

The delamination model has been developed by using the surface-to-surface contact option (Fig. AA11). In case of surface-to-surface contact, the FE meshes of adjacent plies do no need to be identically. The contact algorithm used in the FEM analysis has possibility to determine which node of the so-called master surface is in contact with a given node on the slave surface. Hence, the user can define the interaction between the two surfaces.

Finite element modelling of delaminated composite plates

Fig. 17.11. The FEM delamination model

The condition is that the delaminated region does not grow. These regions were modeled by two layers of elements with coincident but separate nodes and section definitions to model offsets from the common reference plane. Thus their deformations are independent. At the boundary of the delamination zones the nodes of one row are connected to the corresponding nodes of the regular region by master slave node system.

Typically, a node in the underlaminated region of bottom sub-laminate and a corresponding node on the top sub-laminate are declared to be coupled nodes using master-slave nodes facility. The nodes in the delaminated region, whether in the top or bottom laminate, are connected by contact elements. This would mean that the two sublaminates are free to move away from each other in the delaminated region, and constrained to move as a single laminate in the undelaminated region.

The material characteristics presented in previous chapter are used.

Two material models were used: quasi-nonlinear model and non linear model.

A quasi-nonlinear model means that the material behaviour is not according to a failure criterion.

The non-linear model is the material fulfilling Tsai-Wu failure Criterion.

The ellipse’s diameters of the delamination area placed in the middle of the plate are considered from the condition of the same area for all cases. In the parametric calculus, the following diameters ratios were considered:

– Case 1 (Dx/Dy=0.5): transversal diameter Dy=141mm, longitudinal diameter

Dx= 70.5mm;

– Case 2 (Dx/Dy=1): transversal diameter Dy= 100 mm; longitudinal diameter

Dx = 100mm;

– Case 3 (Dx/Dy=2): transversal diameter Dy= 70.5 mm; longitudinal diameter

Dx = 141mm.

In this chapter the following cases (in numerical and experimental ways) are presented: compressive buckling, shear buckling, mixed compressive and shear buckling. The results (for linear, and nonlinear model) are presented as variation of the buckling loads function of maximum transversal displacement (buckling and post-buckling behaviour).

The buckling analysis of delaminated plates was done on square plates (320x320mm), made of E-glass/epoxy (biaxial layers having the thickness t=0.32mm).

These layers are grouped into macro-layers as are presented in table AA1. The position of the delamination is considered between two neighbors layers i and i+1, (i=1,10). The calculus was done for the all 9 cases. Only results obtained for a specific case of position of delamination (i=4) are presented in the chapter.