numerical analysis and optimal design of composite
TRANSCRIPT
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Ph. D. Defense Computational Mechanics Laboratory
Numerical Analysis and Optimal Design ofComposite Thermoforming Process
by
Shih-Wei Hsiao
Department of Mechanical Engineering and Applied Mechanics The University of Michigan March 25, 1997
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Ph. D. Defense Computational Mechanics Laboratory
Outline
• Introduction
• FEM Analysis of Composite Thermoforming Process
– Rheological Characterization of Continuous fiber Composites
– Global FEM Analysis of Thermoforming Process
– Residual Stress Analysis
• Optimal Design of Composite Thermoforming Process
• Conclusions and Future Work
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Ph. D. Defense Computational Mechanics Laboratory
Schematic of Thermoforming Process
Microstructure
Die
Blankholder
Before forming After forming
Laminate
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Ph. D. Defense Computational Mechanics Laboratory
Motivations of this research
Deep drawing (stamping) of woven-fabric thermoplastic composites is amass production and precision shaping technology to produce compositecomponents.
Objectives of this research
• Develop a FEM model to analyze this thermoforming process.
• Develop an optimization algorithm based on this FEM model to optimize this forming process.
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Ph. D. Defense Computational Mechanics Laboratory
Why Thermoplastic Composites?
From the manufacturing viewpoints
• Thermosetting Resins– Hand layed up into structural fiber preform and impregnation after shaping– Need chemical additives to cure after shaping and very long cure cycle time– Labor intense
• Thermoplastic Resins– Shaping only depends on heat transfer and force without chemistry– In a preimpregnated continuous tape form– High processing rate– Drawback: higher processing viscosity and forming temperature (320~400 C), and higher equipment cost
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Ph. D. Defense Computational Mechanics Laboratory
Advantages of the composite stamping process
u Deep drawing (stamping) of woven-fabric thermoplastic compositesis a mass production technology to produce composite components.
u This stamping process is also a precision shaping process.
u Woven-fabric composites possess a balanced drawability, and canavoid the excessive thinning caused by the transverse intraplyshearing.
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Ph. D. Defense Computational Mechanics Laboratory
Related work
• Under the kinematic consideration, the draping behavior of woven fabrics over 3-D spherical, conical or arbitrary surfaces was simulated by solving the intersection equations numerically.
• This approach provides a preliminary prediction of fiber buckling and final fiber orientation.
• This approach can be used as a design tool fot selecting suitable draped configurations for specific surfaces.
• Kinematic approach
Potter (1979)Robertson et al. (1981)Van West et al. (1990)
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Ph. D. Defense Computational Mechanics Laboratory
• Diaphragm and blowing forming processes.
• Newtonian viscous flow formulation with the fiber inextensibility constraint
• Inplane prediction of macroscopic stress and strain.
• Isothermal forming processes.
• Unidirectional composite sheets.
• FEM Analysis
O’Bradaigh and Pipes (1991)
O’Bradaigh et al. (1993)
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Ph. D. Defense Computational Mechanics Laboratory
Goals of this FEM Analysis
A 3-D numerical modeling of thermoforming process on woven-fabricthermoplastic composite laminates:
• Characterization of the processing rheology of woven-fabric thermoplastic composite materials by the homogenization method.
• Coupled viscous flow and heat transfer FEM analyses for forming.– Predictions of global and local stress, temperature and fiber
orientation distribution.
• Residual stress FEM analysis for cooling.– Predictions of macroscopic and microscopic residual stress and warpage after cooling.
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Ph. D. Defense Computational Mechanics Laboratory
Governing equations for thermoforming process
Momentum and continuity equations Thermal equation
Viscosity equation
Coupled
• Impossible to solve these equations at each microcell to obtain obtain the global response.
• Homogenization method is used to overcome this difficulty.
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Ph. D. Defense Computational Mechanics Laboratory
Homogenization Method for Composite Materials
X
Y
ΓΩb
t
Γt
Γg
Unit cell
Unit cell
Review• Under the assumption of periodic microstructures which can be represented by unit cells.
• Using the asymptotic expansion of all variables and the average technique to determine the homogenized material properties and constitutive relations of composite materials. • Capable of predicting microscopic fields of deformation mechanics through the localization process.
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Ph. D. Defense Computational Mechanics Laboratory
Digitized woven-fabric unit cell
Woven fabric laminateUnit cell
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Ph. D. Defense Computational Mechanics Laboratory
Thermal conductivity prediction for unidirectional composites vs volume fraction
0
1
2
3
4
5
6
0 10 20 30 40 50 60 70 80
The
rmal
con
duct
ivit
y (W
/m-K
)
Fiber volume fraction (%)
Axial conductivity
Transverse conductivity
Experimental (axial)
Experimental (transverse)
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Ph. D. Defense Computational Mechanics Laboratory
Implementation of Global FEA
• 3-D sheet forming FE analysis coupled with heat transferFE analysis using ‘Viscous shell with thermal analysis’.
vz
vy
vx
ωx
ωy
ωz
x
yz
Membrane element
+
Bending element
Shell elementX
Y
Z
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Ph. D. Defense Computational Mechanics Laboratory
Viscous shell with thermal analysis
• Plane stress asumption-- the incompressibility constraint can beachieved by adjusting the thickness of each shell element.
• Large deformation process divided into a series of small time step.
• Complicated geometry, friction and contact considerations.
v (i ) → Ý ε (i ) ⇔ µ
(i ) ⇔ T(i )
At i-th time step
Coupled thermal analysis
Viscous shell
• Transient heat transfer FEM to solve temperature at each node.
are solved.
• At each step, solve nodal temperature and velocity iteratively until convergence.
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Ph. D. Defense Computational Mechanics Laboratory
Fiber Orientation Model
Purposes:
• Update the fiber intersection angle of each global finite element by the global strain increment at every time step.
• Change material properties according to updated fiber orientation.
Assumptions:
• The fiber orientation of all the microstructures in one global finite element is identical.
• The warp yarn and weft yarn of woven-fabric composites can be represented by two unit fiber vectors.
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Ph. D. Defense Computational Mechanics Laboratory
Schematic of lamina coordinate
X
Y ZX
Y
X
Y
Layer A
Layer B
Fiber
Matrix
Lamina
Warp yarn
Weft yarn1
2
1
2
a
b
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Ph. D. Defense Computational Mechanics Laboratory
Updating Scheme
.
FEM mesh
Weft vector
Warp vector
X
Y
Z
∆ t
∆ε
a n
a n+1
b n+1
b n
φnθn
θn+1
φn+1
x x
y y
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Ph. D. Defense Computational Mechanics Laboratory
Global-local solution scheme
Global finiteelement analysis
Fiber orientationmodel
Obtain homogenizedmaterial properties
Construct unit cells
Check if forming is doneEnd
No
Yes
Local finite elementanalysis (PREMAT)
Localization(POSTAMT)
Begin
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Ph. D. Defense Computational Mechanics Laboratory
Comparison with experiments(cylindrical cup)
55
60
65
70
75
80
85
90
0 5 10 15 20 25
Simulation (Diagonal)Simulation (Median)Experiment (Diagonal)Experiment (Median)
Fib
er in
ters
ecti
on a
ngle
(de
g)
Distance from the origin (mm)
Punch zone Free zone
Diagonal
MedianMedian
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Ph. D. Defense Computational Mechanics Laboratory
P
Laminate Unit Cell
Effective stress of laminate and unit cell at P.
Effective stress prediction(square box)
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Ph. D. Defense Computational Mechanics Laboratory
Temperature distribution
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Ph. D. Defense Computational Mechanics Laboratory
Stamped body panel
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Ph. D. Defense Computational Mechanics Laboratory
Residual Stress Analysis
• Three levels of residual stresses are generated during cooling– Microscopic stress: Due to CTE mismatch between matrix and fiber
– Macroscopic stress: Due to stacking sequence of laminates
– Global stress: Due to thermal history along laminate thickness
• Warpage due to the release of residual stresses after demoulding.
• In this study, homogenization method based on incremental elasticanalysis with thermal history is adopted.
• Thermoelastic properties are dependent on temperature and crystallinityfrom the thermal history.
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Ph. D. Defense Computational Mechanics Laboratory
Thermal history along thickness
100
150
200
250
300
350
400
0 0.1 0.2 0.3 0.4 0.5 0.6
Tem
pera
ture
( C
)
Location (mm)
10 sec
20 sec
40 sec
60 sec
90 sec
0
0.1
0.2
0.3
0.4
0 0.1 0.2 0.3 0.4 0.5 0.6
Location (mm)
10 sec
20 sec
30 sec
40 sec50 sec
60 sec
65.1 sec
Vol
ume
frac
tion
cry
stal
linit
y
Z
oSym.
Laminate
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Ph. D. Defense Computational Mechanics Laboratory
Curvature prediction compared with experimental data
[0/90] asymmetric laminate Compared with experimental data
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Ph. D. Defense Computational Mechanics Laboratory
Stress prediction compared with experimental data
0
20
40
60
80
100
0 50 100 150 200 250 300
Res
idua
l str
ess
(MP
a)
Temperature ( C)
-40
-30
-20
-10
0.0
10
20
-1 -0.5 0 0.5 1
5 C/s15 C/s25 C/s
Glo
bal r
esid
ual s
tres
s (M
Pa)
Location (mm)
Macroscopic stress prediction for cross-ply laminatecompared with experimental data.
Global stress prediction for unidirectionallaminates with various cooling rates.
Macroscopic stress Global stress
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Ph. D. Defense Computational Mechanics Laboratory
Warped shapes of square box and cylindrical cup
DeformedUndeformed
Square box Cylindrical cup
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Ph. D. Defense Computational Mechanics Laboratory
Warped body panel with its microscopic residual stress
Unit cell
Fiber part
Laminate
DeformedUndeformed
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Ph. D. Defense Computational Mechanics Laboratory
Conclusions
• The thermoforming process of woven-fabric thermoplastic composite laminates was analyzed by the 3-D thermo-viscous flow FEM.
• The constitutive and energy equations of the composites forming were formulated by the Homogenization Method.
• The global-local analysis of the Homogenization Method enables us to examine the macro and microscopic deformation mechanics.
• An optimization algorithm is developed to obtain uniform distribution by adjusting preheating temperature field.