Simulation of continuous fibre reinforced thermoplastic forming using a shell finite element with transverse stress

A shell finite element with transverse stress is presented in this paper in order to simulate the forming of thermoplastic composites reinforced with continuous fibres. It is shown by an experimental work that many porosities occurs through the thickness of the composite during the heating and the forming process. Consequently the reconsolidation i.e. the porosity removing by applying a compressive stress through the thickness is a main point of the process. The presented shell finite element keeps the five degrees of freedom of the standard shell elements and adds a sixth one which is the variation in thickness. A locking phenomenon is avoided by uncoupling bending and pinching in the material law. A set of classical validation tests will prove the efficiency of this approach. Finally a forming process is simulated. It shows that the computed transverse stresses are in good agreement with porosity removing in the experiments.

[1]  J. C. Simo,et al.  On a stress resultant geometrically exact shell model , 1990 .

[2]  K. E. Bisshopp,et al.  Large deflection of cantilever beams , 1945 .

[3]  E. Ramm,et al.  A unified approach for shear-locking-free triangular and rectangular shell finite elements , 2000 .

[4]  T. Chou,et al.  Compaction of woven-fabric preforms in liquid composite molding processes: single-layer deformation , 1999 .

[5]  E. Ramm,et al.  On the physical significance of higher order kinematic and static variables in a three-dimensional shell formulation , 2000 .

[6]  D. Bhattacharyya,et al.  A direct comparison of matched-die versus diaphragm forming , 1998 .

[7]  J. C. Simo,et al.  On stress resultant geometrically exact shell model. Part I: formulation and optimal parametrization , 1989 .

[8]  Philippe Boisse,et al.  Analysis of the Interply Porosities in Thermoplastic Composites Forming Processes , 2002 .

[9]  Carlo Sansour,et al.  An exact finite rotation shell theory, its mixed variational formulation and its finite element implementation , 1992 .

[10]  E. Ramm,et al.  Shear deformable shell elements for large strains and rotations , 1997 .

[11]  Jerry I. Lin,et al.  Explicit algorithms for the nonlinear dynamics of shells , 1984 .

[12]  F. Cogswell,et al.  Thermoplastic structural composites in service , 1992 .

[13]  Neng-Ming Wang,et al.  Analysis of bending effects in sheet forming operations , 1988 .

[14]  Thomas J. R. Hughes,et al.  Nonlinear finite element analysis of shells: Part I. three-dimensional shells , 1981 .

[15]  Anthony K. Pickett,et al.  Numerical and experimental investigation of some press forming parameters of two fibre reinforced thermoplastics: APC2-AS4 and PEI-CETEX , 1998 .

[16]  H. Parisch,et al.  An investigation of a finite rotation four node assumed strain shell element , 1991 .

[17]  E. Ramm,et al.  Three‐dimensional extension of non‐linear shell formulation based on the enhanced assumed strain concept , 1994 .

[18]  Jan-Anders E. Månson,et al.  Prediction of the consolidation of woven fibre-reinforced thermoplastic composites. Part I. Isothermal case , 1998 .

[19]  G. Springer,et al.  A Model of the Manufacturing Process of Thermoplastic Matrix Composites , 1987 .

[20]  Vijay K. Stokes Thermoplastics as Engineering Materials: The Mechanics, Materials, Design, Processing Link , 1995 .