The fatigue behaviour of injection moulded short fibre reinforced polymers depends upon fibre orientation, as shown in experiments conducted with notched specimens injected through different injection gates. The different fatigue behaviour is mainly related to the different local elastic properties, as determined by the different fibre orientation patterns, resulting into different strain distributions. In order to quantify the relationship between fibre orientation and elastic constants, the Cell Method was applied to volumes extracted from the specimens, reconstructed by micro-tomography

Andrea Bernasconi

Francesca Cosmi

COSMI, Francesca

Bernasconi A.

Archivio istituzionale della ricerca - Università di Trieste

ELASTICITY OF SHORT FIBRE REINFORCED POLYAMIDE:  MORPHOLOGICAL AND NUMERICAL ANALYSIS OF FIBRE ORIENTATION EFFECTS

F. Cosmi

BERNASCONI, ANDREA

Archivio istituzionale della ricerca - Politecnico di Milano

Elasticity of short fibre reinforced polyamide: morphological and numerical analysis of fibre orientation effects

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Materials Engineering, Vol. 17, 2010, No. 2   6 ELASTICITY OF SHORT FIBRE REINFORCED POLYAMIDE:  MORPHOLOGICAL AND NUMERICAL ANALYSIS OF FIBRE ORIENTATION EFFECTS  Francesca Cosmi, Andrea Bernasconi  Received 1st  April 2010; accepted in revised form 12th  October 2010   Abstract          The fatigue behaviour of injection moulded short fibre reinforced polymers depends upon fibre orientation, as  shown  in  experiments  conducted  with  notched  specimens  injected  through  different  injection  gates.  The different  fatigue  behaviour  is  mainly  related  to  the  different  local  elastic  properties,  as  determined  by  the different  fibre  orientation  patterns,  resulting  into  different  strain  distributions.  In  order  to  quantify  the relationship between fibre orientation and elastic constants, the Cell Method was applied to volumes extracted from the specimens, reconstructed by micro-tomography.   Keywords: short fibre reinforced polyamide, Fatigue, Micro computed tomography.   1. Introduction The  mechanical  behaviour  of  short  fibre reinforced  polymers  (SFRP)  strongly  depends  upon fibre orientation. Moreover, fibre orientation is related to  the  manufacturing  process,  usually  injection moulding. During injection, fibres are dispersed into the  molten  matrix  and  their  final  orientation  is  the result of complex phenomena related to viscosity of the  melt  polymer,  velocity  profiles,  shear  flow  and interactions with mould walls. In  the  perspective  of  metal  replacement  by SFRP  in  mechanical  parts,  the  importance  of  the fatigue behaviour is increasing. Like other mechanical properties,  e.g.  tensile  modulus  and  strength,  the fatigue behaviour depends upon fibre orientation. In the case of simple geometries and for short glass fibre reinforced (SGFR) polyamide 6, this dependence was experimentally investigated and expressed through a relationship derived from the Tsai-Hill criterion [1]. This  relationship  was  verified  for  off-axis  uniaxial tests on specimens extracted from injection moulded plates  and  assuming  that  mean  fibre  orientation coincided with the plate’s axis. Real parts display a more complex geometry, and their fatigue strength is influenced  by  other  factors  like  weld  lines  [2]  and notches [3,4]. The importance of the manufacturing process is evidenced by the different fatigue behaviours which can  be  observed  when  notched  specimens  of  same geometry  are  injection  moulded  through  different gates [4]. This appears to be due to the different fibre orientation  patterns  obtained  [5].  It  is  therefore important to be able to predict the fibre orientation in real parts, and to take into account of the effect of fibre  orientation  when  modelling  the  material’s behaviour,  e.g.  when  performing  finite  element analysis.  Commercial  software  packages  exist,  which allow  for  this  operations.  However,  it  is  also necessary to define proper experimental  methods to validate fibre orientation predictions, to characterize the micro structure and to relate fibre architecture to the mechanical properties of the material. Recently,  a  novel  technique  based  on  micro computed tomography (micro-CT) 3D reconstruction of  the  fibre  structure  has  been  introduced  and quantification of fibre orientation preferred directions has  been  shown  possible  by  means  of  a  global parameter, the Mean Intercept Length (MIL) [6]. By this method it is possible to analyze fibre orientation in  the  perspective  of  validating  predictions  by software packages simulating the injection moulding process,  which  often  also  provide  estimates  of  the elastic  constants  to  be  assigned  locally  to  each element in a subsequent finite element simulation. In fact, mean fibre orientation alone is not sufficient to determine the material’s elastic constants, as the local the  full  fibre  orientation  distribution  must  be  taken into account. In this work, in order to study the effect of injection point location upon the fatigue strength of the specimens used in [4, 5] (see Fig. 1), we applied an analysis method combining micro CT and a micro- F. Cosmi, Dipartimento di Ingegneria Meccanica, via A. Valerio 10, 34127 Trieste, Italy. A. Bernasconi, Politecnico di Milano, Dipartimento di Meccanica, via La Masa 34, 20156 Milano, Italy. Materials Engineering, Vol. 17, 2010, No. 2    7 mechanical  model  based  on  the  Cell  Method,  first introduced in [7] to examine the local properties of biological materials, subsequently [8, 9] applied to the same short glass fibre reinforced polyamide studied in [1].  2. Experimental Results  The  experimental  results  of  the  tensile  and fatigue  tests  are  presented  in  [4,  5]  and  they  are summarized  in  Fig. 2  and  Fig. 3,  respectively.  It  is clearly  shown  that  longitudinal  injection  yielded higher tensile fatigue strength than lateral injection. A reduction  in  strength  is  observed  with  reference  to standard ISO 527 specimens. The tensile strength of standard and non-standard specimens is performed by plotting the stress-time history (it is not possible to compare strain in notched and un-notched specimens if local strains at the notch root are not measured).   Fig. 2. Tensile stress-strain curves of the specimens with lateral notches, compared with that of a standard ISO 527 specimen.  Fig. 3.  S-N curves for specimens with lateral notches.  The  comparison  of  the  fatigue  behaviour  of notched specimens with that of standard specimens is carried  out  by  dividing  stress  values  by  σW,  the fatigue strength of standard specimens at one million cycles.  The  strength  decreases  with  reference  to standard specimens is mainly due to the notch effect, but  also  to  the  orientation  has  to  be  taken  into account: the fibre distribution in a standard specimen may differ from that of a notched specimen because of  the  changes  in  the  mould  thickness  and  shape. Conversely,  the  decrease  of  strength  of  specimens injected laterally with reference to specimens injected longitudinally  is  only  related  to  the  different  strain distribution  induced  by  the  differences  in  fibre orientation. A different strain pattern was shown by experimental  observations  using  Digital  Image Correlation techniques [5]. Moreover, different fibre orientation  patterns  were  observed  in  the  gauge sections  of  two  specimens  injected  through longitudinal and lateral gates [5, 10]. Fig. 1.  Specimens type, dimensions and injection gates; position and size of micro-CT examined samples. ISO 527 standard specimen Longitudinal injection  Lateral injection Materials Engineering, Vol. 17, 2010, No. 2  8 The local fibre architecture was reconstructed by Micro-CT on samples extracted form the specimen in their gauge section. Micro-CTs with a resolution of 9  µm  were  obtained  at  the  SYRMEP  beamline  of Elettra synchrotron light source (Trieste, Italy) using Phase  Contrast  (PHC)  imaging  techniques  and  the morphological  characterization  was  conducted  by means of the Mean Intercept Length (MIL) parameter and  the  MIL  related  fabric  tensor  using  Quant3D software  [11].  The  details  of  the  procedure  are reported  in [6].  In order to investigate whether the effect of the observed differences in fibre orientation distributions upon elastic modulii, samples extracted in the location A of fig.1, close to the notch, were analyzed over a 5 mm portion of the gauge section. A comparison was performed among sample A of the specimen injected longitudinally and sample A of the specimen injected through  the  side  gate.  These  samples  displayed  the common  layered  structure,  characterized  by  the presence of a shell layer, where fibres tend to align parallel to the polymer flow during injection, and a core  layer  usually  found  in  the  mid  section  of  flat specimens, where under certain conditions fibres may rotate  and  deviate  from  the  flow  direction.  In  this layer  the  most  significant  differences  in  fibre orientation  distributions  were  observed.  A longitudinal section, corresponding to the core layer, of the reconstructed volumes is reported in Fig. 4 for both specimen types. The  core  layer  (mid  plane)  of  each reconstructed  sample  was  divided  into  a  series  of cubic  Volumes  Of  Interest,  VOI,  80x80x80  voxel3, that  were  singularly  analyzed  using  Quant3D software. From the properties of the MIL fabric tensor evaluated  by  this  method  it  is  possible  to  define  a preferred  fibre  orientation  angle  and  an  Index  of Anisotropy IA: IA = =1 – MIN(eigenvalues)/ MAX(eigenvalues)     (1) so that IA values can vary from IA = 0 for perfect isotropy to IA =1. Results are shown in Fig.5. It clearly appears that the location of the injection gate influences both the preferred  fibre orientation angle and the index of anisotropy. In the core layer of the laterally injected specimen, it can be seen that fibres tend to make an almost  full  180°  rotation  when  observed  from  the notch root inwards. In order to evaluate the effect of the observed differences  in  fibre  orientation  and  degree  of anisotropy  upon  the  local  elastic  constants  of  the material, a Cell Method model was built for each VOI. The Cell Method model has already been used for this material in [8,9] and it allowed for estimating  Fig. 4.  Lateral and longitudinal injection, point A, core layer: µ-CT reconstruction.  Fig. 5.  Preferred fibre orientation with respect to specimen y axis (above), and Index of Anisotropy IA (below), at different z positions (mm), core layer.  the local values of the elastic modulii Ex, Ey and Ez. Moreover,  a  correlation  between  the  values  of  the elastic modulii and the morphological parameters was found in different samples. Material properties in each cell of a 812905 cells mesh were scaled based on the base material (matrix and glass fiber) properties and the  apparent  elastic  modulii  along  the  x,y  and  z Materials Engineering, Vol. 17, 2010, No. 2    9 directions of the reference frame of Fig. 1 (Ex , Ey and Ez  respectively)  were  computed  by  simulation. Results are shown in figures from 6 to 8. It appears that  the  differences  in  mean  fibre  orientation  and index  of  anisotropy  shown  in  Fig.  5  result  into different local values of the local elastic moduli, as predicted  by  the  Cell  Method  applied  to  the reconstructed  micro-structure  of  the  samples, particularly in the case of the Ex modulus.  Fig. 6.  Apparent elastic modulus Ex (MPa) along specimen x axis, at different z positions (mm), core layer.  Fig. 7.  Apparent elastic modulus Ey (MPa) along specimen y axis, at different z positions (mm), core layer.  These results indicate that by this method it is possible to estimate the local values of the material’s elastic  modulii  and  relate  them  to  the  fibre distribution. Further research is required in order to explain  the  different  fatigue  behaviour.  In  this perspective,  the  information  deriving  from  the analysis  method  presented  herein  could  be  used  to validate the values of the elastic modulii used in finite element models, as defined on the basis of numerical simulations of the injection moulding process.  Fig. 8.  Apparent elastic modulus Ez (MPa) along specimen z axis, at different z positions (mm), core layer.  3. Conclusions Differences have been observed in the fatigue behaviour of short fibre reinforced polyamide notched specimens  depending  on  injection  point  location. These  experimental  results  might  be  attributed  to different strain distributions due to variations of the local apparent elastic properties along the specimen section, which in turn are closely related to changes in fibre orientation occurring during the manufacturing process  and  consequently  to  different  local  elastic constants. In order to precisely quantify these effects, the  Cell  Method  applied  to  the  micro-structure reconstructed by micro tomography was successfully applied.  Further  investigation  is  needed  to  confirm these preliminary results.  Acknowledgements The  authors  thank  Diego  Dreossi  and  the SYRMEP staff at Sincrotrone Trieste. Radici Plastics, Italy,  kindly  provided  the  specimens  used  in  this research. The research work is funded by the MIUR Prin 2007 program.  References [1]  Bernasconi A., Davoli P., Basile A., Filippi A.: Effect of fibre orientation on the fatigue behaviour of a short glass fibre reinforced polyamide-6. Int J Fatigue, Vol. 29 (2007) 199-208. [2]  Zhou  Y.,  Mallick  PK.:  Fatigue  performance  of  an injection-molded  short  E-glass  fiber-reinforced polyamide  6,6.  I.  Effects  of  orientation,  holes,  and weld line. Polym. Compos., 27: 230–237, 2006. Materials Engineering, Vol. 17, 2010, No. 2  10 [3]  Sonsino  CM,  Moosbrugger  E.:  Fatigue  design  of highly  loaded  short-glass-fibre  reinforced  polyamide parts in engine compartments. Int J Fatigue , 30:1279-1288, 2007. [4]  A.  Bernasconi,  P.  Davoli,  C.  Armanni,  A.  Filippi.: Effect of notches and fibre orientation on the fatigue behaviour of a short glass fibre reinforced polyamide 6. 4th Int. Conf. on Fracture of Polymers, Composites and Adhesives. Les Diablerets (CH), 2007. [5]  Bernasconi A., Cosmi F.: Combined effect of notches and fibre orientation on fatigue behaviour of short fibre reinforced polyamide. Strain (2009) in press. [6]  Bernasconi A., Cosmi F., Dreossi D.: Local anisotropy analysis in injection moulded fibre reinforced polymer composites. Composites Science and Technology, Vol. 68 (2008) 2574-2581.  [7]  Cosmi,  F.,  Dreossi,  D.:  Numerical  and  experimental structural  analysis  of  trabecular  architectures. Meccanica, Vol. 42 (2007) 85-93. [8]  Cosmi,  F.:  Morphological  and  numerical characterization of a PA6-GF 30 sample, 25th Danubia Adria Symposium, Ceske Budejovice, Czech Republic, 24-27.09.2008. [9]  Cosmi F.: Local anisotropy and elastic properties in a short glass fibre reinforced polymer composite. Strain (2009) in press. [10] Bernasconi, F. Cosmi: Fibre orientation at notches and fatigue behaviour of short fibre reinforced polyamide. 17th  Int.  Conf.  on  Composite  Materials,  July  27-31, 2009, Edinburgh, UK. [11] Ketcham  RA,  Ryan  TM.:  Quantification  and visualization of anisotropy in trabecular bone. Journal of Microscopy 213 (2004) 158-171.  

ELASTICITY of SHORT FIBRE REINFORCED POLYAMIDE: MORPHOLOGICAL AND NUMERICAl ANALYSIS OF FIBRE ORIENTATION EFFECTS

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ELASTICITY of SHORT FIBRE REINFORCED POLYAMIDE: MORPHOLOGICAL AND NUMERICAl ANALYSIS OF FIBRE ORIENTATION EFFECTS

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