This document discusses using LS-DYNA software to simulate the thermoforming process. It introduces the geometry and finite element model created in HyperMesh and LS-Prepost. Shell elements are used to model the thin structures. Material models are defined for the rigid tools and deformable fabric. The forming process is defined through contact definitions, prescribed motion of the punch, and blank holder force. Results of the fiber orientation and shear angle distribution are compared to previous work. Parameters like yarn thickness and friction could not be exactly determined and may contribute to differences in results.

1. THERMOFORMING ANALYSIS
IN LS-DYNA

2.  In this study the geometry created by HyperMesh for the analysis
will be introduced first. Then, The definitions used in the finite
element model created by using LS-Prepost will be introduced.
During the process, the blank holder apply a constant force of 2 Mpa
while the punch moving in –z direction. At the end of the process, the
blank shape turn into the hemisphere.

3. Geometry
Figure : Geometry of deep drawing tools
The geometry consists of 4 parts : Punch,
Blank Holder, Die, Blank. The dimensions
are shown in the Figure.

4.  In this study, symmetry is used to shorten the solution time. The generated
quarter models are shown in the figure below. The geometry and the meshes were
created in HyperMesh. Almost the all meshes were created with quad elements
having the good quality.

5. Element Selection
 Selecting shell elements instead of solid elements for modeling thin
structures are more suitable due to reducing the number of elements that
should be used during the modeling. In this study, Shell type 16 (a fully
integrated shell) in LS-Dyna with 3 integration points in thickness direction
was chosen in order to decrease locking effect.

6. Unit System
 LS-Dyna does not allow to define any unit. So the values used in the
analysis should be entered according to a suitable unit system. In this
study Table 1 (c) compatible unit system was used [4].

7. Keywords Defined for LS-DYNAAnalysis
 The creation of the finite element model in Ls-Dyna is done by a set of
keywords. These definitions includes simulation time, simulation
speed, contact state and friction force, material model and type,
moment of inertia, wall thicknesses, degrees of freedom, loading
conditions and various simulation control parameters. These keywords
can be entered in the system manually or by using the LS-Prepost
interface [5].

8. Defining of the Materials
 Defining of the materials in Ls-Dyna is implemented within *MAT keyword.
In this study, punch, blank holder and die are accepted as rigid and MAT_RIGID_020
material model is used for these parts. The following figure shows how to define
MAT_RIGID keyword for rigid elements.

9.  In this study, fabric is accepted as deformable and
MAT_VISCOELASTIC_LOOSE_FABRIC_234 material model is used for fabric. E-glass
fiber fabric was defined for fabric material in the first analysis.

10.  In the second analysis of the study, fabric material and the matrix material (PPS) are combined.
Material properties of the resin are defined using the keyword
*MAT_ELASTIC_PLASTIC_THERMAL as follows.

11. Defining of the Thermal Properties

13.  Section definition is made within the *SECTION keyword in LS-Dyna. In this study, all
parts are represented by shell elements. Shell elements are identified by the keyword *
SECTION_SHELL. Some definitions such as element formulation and wall thickness
are made with this keyword. The following figure shows *SECTION keyword created to
define the shell elements assigned for rigid parts.

14.  The following figure shows *SECTION keyword created to define the shell elements
assigned for the fabric.

15. Defining of the Part
 Ls-Dyna defines the part within the keyword *PART. Sections and materials are associated
with the parts by entering the numbers of related keywords. *PART keyword used in the
study is shown in the figure below.

16.  In the second analysis of the study, the fabric and the resin are combined using the
keyword *PART_COMPOSITE. In fact, this keyword was created to define a laminate at
each integration point to form a composite laminate. However, it is used to combine the
fabric and the thermoplastic resin in the study as follows.

17. Contact Definitions
 Ls-Dyna offers several contact algorithms for the users. The determination of the
suitable contact algorithm is of great importance in the analysis. Ls-Dyna defines the
contacts in the keyword *CONTACT.
 *CONTACT_FORMING_ONE_WAY_SURFACE_TO_SURFACE keyword is used to
define contact interactions between the parts in this study because the commonly used
contact type for stamping analysis is the FORMING contact. The parameters used in this
keyword is shown the figure below.

19. Movement Constraints
 The curve that the punch will follow along its movement is defined using the keyword
DEFINE_CURVE as follows.

20.  The movement of the punch is established by using the keyword
BOUNDARY_PRESCRIBED_MOTION_RIGID as follows.

21. Load Definition
 A force is applied by the blank holder to create a pressure of 2 MPa on the fabric during
the process. This force was calculated as 91.835 kPa at the beginning of the process. The
force applied by punch to the material is defined by the keyword LOAD_RIGID_BODY
keyword as follows.

22.  The curve defining the change of loading status of the punch over time is shown below.

23. Time Definition
 Simulation times must be defined by the user. The simulation time is defined as 35 ms by
using the keyword CONTROL_TERMINATION as follows.

24. Defining of Initial Temperatures and Temperature Regions

25. Hourglass Control

26. Defining of the Solution Procedure

27. Determination of the Thermal Solver

28. Thermal Timestep Control

29. Contact Control

30. Energy Control

31. Results
 The simulation is applied for two initial fiber orientations of E-glass fiber fabric, 0˚/90˚
and -45˚/+45˚. The final shape of the draped fabric is compared with the Tabiei’s result.
 Comparison of draped shapes for 0˚/90˚ orientation a) Tabiei’s result [3] b) Simulation result

32. Comparison of draped shapes for -45˚/+45˚ orientation a) Tabiei’s result [3] b) Simulation result

33.  Distortion angles were determined along the diagonal axis starting from the center point
for 0˚/90˚ orientation, along the horizontal axis starting from the center point for -
45˚/+45˚ orientation.
Comparison of the angular distortions for 0˚/90˚ orientation a) Tabiei’s result [3] b) Simulation result

34. Comparison of the angular distortions for -45˚/+45˚ orientation a) Tabiei’s result [3] b) Simulation result

35.  In the next study, carbon fabric and resin were combined using PART_COMPOSITE
keyword. A material and thickness value was assigned to each of the 3 integration points
used. The material and thickness values ​​assigned to the integration points are shown
below. Thicknesses were determined according to fiber volume fraction of Tabiei’s
sample.

36.  The shear angle distribution obtained in the simulation is shown below.

37.  Apart from Tabiei's work, a parametric study was performed to see the effect of
blankholder force on maximum shear angle distortion. Dry glass fabric with 0˚/90˚
orientation was used in the study. Following results was obtained from the analysis.
Blank holder force (kN) Max. Angular distortion (°)
30 38,98°
50 39,24°
70 40,52°
90 40,7°
110 41,44°
Table 2. Variation of max. angular distortion according to the blank holder force

38. It has been tried to duplicate Tabiei’s study using Ls-Dyna FEA package. Although
the results are close to that of Tabiei, some deviations are observed. Yarn thickness,
transverse shear modulus and coefficient of friction between the fibers are not given
for glass fiber fabric in Tabiei's article. In addition, yarn thickness and coefficient of
friction between the fibers are not given for carbon fabric. These parameters
couldn’t be found because there are many conflicting values in the literature. So, the
estimated values ​​were used for these parameters. This is thought to be one of the
most important reasons for the discrepancy in the results. Micro-mechanical and
meso-mechanical models like MAT_234 represents the fabric behaviour
successfully however too many parameters are needed to obtain for the simulation.
It is necessary to carry out too many tests to be able to determine the input values in
the model and these tests can be quite expensive and time consuming.
CONCLUSION

39.  For the next thesis progress following studies will be held :
 Coupled thermo-mechanical analysis for hemispherical forming of fabric reinforced
thermoplastic prepreg will be carried out by using MAT_249. The results will be
compared with the results obtained using MAT_234.
 Thermoforming process simulation of a laminate will be carried out.
 Effects of laminate sequencing and interlaminar friction on thermoforming will be
studied.
 Experimental studies related to thermoforming process will be carried out.
FUTURE WORK

40. REFERENCES
 [1] Ivanov I., Method development for finite element impact simulations of composite materials, University of
Cincinnati, 2002.

 [2] Ivanov I., Tabiei A., Loosely woven fabric model with viscoelastic crimped fibres for ballistic impact simulations,
International Journal for Numerical Methods in Engineering, 61, 1565-1583, 2004.

 [3] Tabiei A., Murugesan R., Thermal structural forming simulation of carbon and glass fiber reinforced plastics
composites, International Journal of Composite Materials, 5(6), 182-194, 2015.

 [4] Sözen L., Boru bükme operasyonu sonucunda meydana gelen geri yaylanma miktarının öngörülmesi, TOBB ETÜ,
2011.
 [5] Livermore Software Technology Corporations (LSTC), LS-DYNA Keyword User’s Manual - Volume I, 2018.
 [6] Livermore Software Technology Corporations (LSTC), LS-DYNA Keyword User’s Manual - Volume II, 2018.