1. Simulation of the hemispherical
forming process of a woven fabric
with two different material models
Ankara Yildirim Beyazit University
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4. Preforming Defects
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• Another important point in the design stage
is that the angular distortions occurring in
part after the forming process should be
predicted accurately.
• The formation of defects is inevitable in the
production of some parts with complex geometry
during preforming process. Especially in the
production of double-curved parts, the most
common problem is wrinkling.
5. Deformation mechanisms during forming
• Finite element analysis (FEA) is an efficient method at the design stage of composite parts
since trial and error methods to estimate possible defects are often expensive and time-
consuming.
7. The importance of simulation
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The commercial FEM software LS-DYNA offers many options for modeling dry fabrics or
fabric-reinforced thermoplastic prepregs. Anisotropic Hyperelastic Model (MAT_249) and Non-
Orthogonal Model (MAT_293) are the best candidates in the LS-DYNA material library.
8. MAT_249
● -The total stress response of the model is calculated by summation of the matrix stress and
the fiber stress as follows:
𝜎 = 𝜎𝑚 + 𝜎𝑓
● -The matrix material in the MAT_249 material model is assumed that the material is
isotropic, and Young’s modulus 𝐸 = 𝐸 𝑇 and Poisson’s ratio 𝑣 = 𝑣 𝑇 is temperature-
dependent values. von Mises yield criterion is used in the model of the matrix material. The
yield criterion can be stated as the following:
𝜑 𝝈, 𝜎𝒚 = 𝝈 − 𝜎𝑦 𝜀𝑃
, 𝑇 ≤ 0
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12. Laminate modelling methods in FEA
In this study, a hemispherical stamping simulation was used to evaluate the potential of two material
models developed for woven fabrics based on different approaches in LS- DYNA. The validation of the
simulation was tested by using experimental work in the literature.
The geometry consists of four parts: Punch, Blank Holder, Die, and Blank.
13. Finite element model
● E-glass woven fabric reinforcement
● Punch radius: 97 mm
● 4 x 4 mm shell elements (MAT_249 model)
● 3.2 x 3.2 mm shell elements (MAT_293 model)
● Blank holder force: 97 N
● Tool-to-ply friction coefficient: 0.2
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Fabric thickness (mm) 0.58
Areal density (kg/m2) 0.529
Ends/10 mm 1.1
Picks/10 mm 1.2
14. MAT_249 Parameters
The MAT_249 model requires the following parameters to be defined:
● Mass density
● Tensile modulus or the associated tensile curve
● Shear modulus or the associated shear curve
● Resin parameters at forming temperature
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15. MAT_249 Parameters
● The parameters in the material card requiring extensive experimental work are obtained
from an experimental work available in the literature.
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Figure 1. Axial stress vs. axial strain curve of the fabric reinforcement
0
200
400
600
800
1000
1200
1400
0 0.01 0.02 0.03
Axial
stress
(MPa)
Axial strain
axial stress vs.
axial strain
Figure 2. Shear stress vs. shear strain curve of the fabric reinforcement
0
20
40
60
80
100
0 0.5 1 1.5
Shear
stress
(MPa)
Shear strain
Shear stress vs.
Shear strain
16. Material Model Parameters
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Description Variable Value
Mass Density (kg/m3) RO 2540
Number of fiber families to be considered NFIB 2
Young's modulus for 1st fiber family (GPa) EF1 3.98
Young's modulus for 1st fiber family (GPa) EF2 3.98
Transversal shear modulus orth. to direction of fiber 1
(GPa)
G23_1 0
Transversal shear modulus in direction of fibre 1 (GPa) G31_1 0
Transversal shear modulus orth. to direction of fiber 2
(GPa)
G23_2 0
Transversal shear modulus in direction of fibre 2 (GPa) G31_2 0
Curve ID for shear stress vs shearing between of 1st &
2nd fiber
LCG12 Curve
Option for shear between fiber 1 and 2 METH12 10
Description Variable Value
Mass Density (kg/m3) RO 2540
Tensile modulus along the fiber yarns (GPa) ET 3.98
Compression modulus along the fiber yarns (GPa) EC 0.01
Shear locking angle, in degrees GAMMAL 60
Fiber volume fraction in the prepreg composite VF 1
Transverse compression modulus of the dry fiber
(GPa) EF3 7.5
Transverse Poisson’s ratio of the dry fiber VF23 0.2
Young’s modulus of the cured resin (GPa) EM 0.01
Poisson’s ratio of the cured resin VM 0.1
Stretch ratio at the end of undulation stage during the
uniaxial tension test
EPSILON 0.01
Coefficients for the bias-extension angle change-
engineering stress curve
Curve
Non-orthagonal Model (MAT_293) Parameters
Anisotropic Hyperelastic Model (MAT_249) Parameters
18. Wrinkles on deformed composite laminate with [0/90,-15/75] lay-up
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Deformed shapes obtained with 97 mm punch stroke: a) The MAT_249 material model b) The MAT_293 material model
19. Wrinkles on deformed composite laminate with [0/90,-15/75] lay-up
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Deformed shapes obtained with 61.5 mm punch stroke: a) The MAT_249 material model b) The MAT_293 material model
20. Wrinkles on deformed composite laminate with [0/90,-15/75] lay-up
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Shear angle contour plots obtained with 61.5 mm punch stroke: a) The MAT_249 material model b) The MAT_293 material
model
21. Conclusion
● In this study, hemispherical forming simulations of a plain woven fabric are performed
using the MAT_249 and MAT_293 material models available in the LS DYNA material
library. Both models produce similar results up to a certain punch stroke regarding the
boundary profile and shear angle distribution. However, after a certain punch stroke is
reached, high mesh distortions are observed, and then the wrinkling formation begins in the
simulation performed with MAT_293. In addition, as a result of the analysis, it is seen that
MAT_293 is more sensitive to mesh size than MAT_249. For this reason, smaller-sized
meshes are used in simulations performed with MAT_293.
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22. References
● [1] Vanclooster, K., Forming of multilayered fabric reinforced thermoplastic composites, Katholieke
Universiteit Leuven, 2010.
● [2] Dörr, D., Brymerski, W., Ropers, S., Leutz, D., Joppich, T., Kärger, L., & Henning, F. (2017). A benchmark
study of finite element codes for forming simulation of thermoplastic UD-tapes. Procedia CIRP, 66, 101-
106.
● [3] Ziegs, J. P., Weck, D., Gude, M., & Kästner, M. (2020). Thermo‐mechanical modeling of the temperature
dependent forming behavior of thermoplastic prepregs. Engineering Reports, e12373.
● [4] Yildirim, H., & Ozturk, F. (2022). A benchmark study of the material models for forming simulation of
woven fabrics. The Journal of The Textile Institute, 113(6), 1027-1038.
● [5] Mohammed, U., Lekakou, C., & Bader, M. G. (2000). Experimental studies and analysis of the draping of
woven fabrics. Composites Part A: Applied science and manufacturing, 31(12), 1409-1420.
● [6] Peng, X., & Ding, F. (2011). Validation of a non-orthogonal constitutive model for woven composite
fabrics via hemispherical stamping simulation. Composites Part A: Applied Science and Manufacturing,
42(4), 400-407.
● [7] Livermore Software Technology Corporations (LSTC). LS-DYNA Keyword User’s Manual -Volume II.
2018
● [8] Zhang, W., Ren, H., Liang, B., Zeng, D., Su, X., Dahl, J., ... & Cao, J. (2017). A non-orthogonal material
model of woven composites in the preforming process. CIRP Annals, 66(1), 257-260.
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