PhD Project  Multilayer modelling 
Start / End:  November 2011 to November 2015 
Contact  TPRC Palatijn 15 7521 PN Enschede P.O. Box 770 7500 AT Enschede The Netherlands Phone: +31 88 877 38 13 Email: devi.wolthuizen[a]tprc.nl 
 University of Twente Faculty of Engineering Technology Chair of Production Technology P.O. Box 217 7500 AE Enschede The Netherlands Email: d.j.wolthuizen[a]utwente.nl List of publications 
Funding  This project is funded by the Thermoplastic Composite Research Centre (TPRC). The support of the Region Twente and the Gelderland & Overijssel team for the TPRC, by means of the GO Programme EFRO 20072013, is gratefully acknowledged 
TPRC Founding Partners  
TPRC Supporting Partners 

Motivation  Nowadays the finite element method is a wellestablished method for the design and layout of composite structures. However, there are still a number of drawbacks in predicting the feasibility of the part with respect to the thermoforming process for thermoplastic composites. State of the art simulations take each ply separately into account in order to capture the complex mechanisms of intraply and interply behaviour during forming. This is computationally very expensive and susceptible to instabilities. In this research a new finite element is to be developed that implicitly takes multilayers into account. In this way the aforementioned mechanisms can be accounted for without the drawbacks of current methods. 
Introduction  With the increasing use of fibre reinforced polymers in the aviation and automotive industries there is a high demand for automation. This is to increase production volume and reducing labour costs and time. With automation reproducibility is guaranteed and human errors are minimised. Press forming of preconsolidated flat laminates is most appropriate for high volumes due to its fast production process and the lack of curing time needed for thermoplastic material. The total time from flat laminate till end product can be in the range of minutes. In the case of (rubber)press forming the laminate is heated with the use of infrared and is transferred to the mould. The female mould can be made of rubber or steel. The process is schematically indicated in Figure 1. 
 Fig. 1: The rubber pressing process [1] CFRP are highly anisotropic which may induce unwanted distortions during press forming of (double) curved products, among others springback and forward, buckling and wrinkling, resulting usually in far from ideal products. Besides anisotropy induced distortions external parameters can play a role e.g. geometry of the product and friction between the tools and the product. Multiple trialanderror iterations are commonly necessary to develop the designed product, resulting in extra costs in terms of labour hours and waste material. To reduce the number of trialanderror iterations numerical tools such as the Finite Element Method (FEM) can be used. For FEM to become an attractive tool to simulate deformations in highly anisotropic materials like CFRPs the program should be accurate, robust and fast. Nowadays forming of composite laminates is well established, but still time consuming. This originates from the discrete modelling of each ply in the laminate (Figure 2). Each ply consists of multiple element layers; two for the intraply properties (membrane elements for the in plane deformation and DKT elements for bending), and two for contact on the top and bottom side of the ply (toolply and plyply interaction). This makes the model to grow rapidly with the increase of number of plies, which is one cause of the large simulation time. The other cause is contact logic between the different plies, which is computational very expensive. When plyfolding as well as delamination is occurring stability issues arise. These bottlenecks make it hardly feasible to simulate complete structures with all plies, let alone to do a full optimisation study on the design parameters. Fig. 2: Discrete modelling of each ply for thermoforming simulation [2] 
Objectives  To make designing and optimising with the aid of finite element method more attractive the computational time should be reduced. The model can be reduced in size with a multilayer approach instead of discrete modelling of the separate plies. In this approach all the in plane properties per ply (intraply shearing and bending) are combined in one element through the thickness. Besides reducing the model in size contact logic between the plies is avoided. The interaction of the plies is replaced by an accurate interply shear and friction model. The absence of contact logic between the plies should also increases stability of the system. On top and bottom of the multilayer element contact logic should be implemented for the interaction between the laminate or structure and the tools. Elements with a linear displacement field should be used for modelling contact to ensure overall stability and good convergence. Higher order elements are poor in contact modelling. Before a multilayer approach can be achieved the numerical problem of intraply shear locking should be solved. This numerical artefact can be avoided when the finite element mesh is aligned with the fibre directions. For simulations with a single ply aligning the mesh is the most appropriate solution. This is no longer possible when a multilayer element is used to avoid discrete modelling of each ply. While a multilayer element can contain more than two fibre directions, an element can align with up to two fibre directions. Furthermore automatic mesh generation is prohibited when aligned meshes are required. 
Intraply shear locking  During forming processes of doubly curved products intraply shearing is the dominant deformation mode. This mode, which can be visualised by a trellis frame, is the main deformation mode due to the near inextensible fibres. Each crossing of the fibre bundles is used as a hinge point, as in a Pin Jointed Net assumption. These hinge points can divide the material in areas with different shear angles when certain boundary conditions are applied. A good example to visualise this is the bias extension experiment, see Figure 3. The fibre directions are indicated by the dark lines in the left picture and are initially at ±45° The short edges are gripped and the fabric is stretched. Due to the applied boundary conditions the upper and lower triangle in the fabric (region I) stay undeformed. Pure shear can be seen in region II and region III has intermediate shear. The lines in the right figure indicate lines of discontinuous shear angles. Standard finite elements are of at least C^{1} continuity and thus are unable to capture this discontinuity correctly, except when it lies exactly on the element boundary. By aligning the mesh with the fibre directions this can be accomplished. Figure 4 shows the normalised force of two finite element simulations of a bias extension experiment with an aligned and unaligned mesh (respectively mesh A and mesh B) of linear triangles (LTR). In the simulation with the unaligned mesh the discontinuous shear angles lie inside the element. During deformation the fibres are therefore stretched instead of sheared, resulting in unrealistic high stresses and forces. This is the origin of the intraply shear locking. With increasing number of elements the locking can be reduced, but this will lead to unacceptable simulation times. Fig. 4: Two simulations of the bias extension experiment. Mesh A with aligned mesh correctly predicts tensile forces while mesh B exhibits intraply shear locking and overpredicts the tensile force [3] 
References  [1] R. H. W. ten Thije, Finite element simulations of laminated composite forming processes. PhD thesis, University of Twente, Sept. 2007. [2] S.P. Haanappel et al., Forming of Thermoplastic Composites, Key Engineering Materials, vol. 504506, p. 237242, 2012. Volume: Material Forming ESAFORM 2012, ed. by M. Merklein and H. Hagenah. [3] R. ten Thije and R. Akkerman, Solutions to intraply shear locking in finite element analyses of fibre reinforced materials" Composites Part A: Applied Science and Manufacturing, vol. 39, pp. 11671176, July 2008.
