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SuCoHS project, Grant Agreement N° 769118
EASN2019 Athens, 2019-09-06
Martin Liebisch1, Tobias Wille1, Georgios Balokas2, Benedikt Kriegesmann2 1German Aerospace Center (DLR) 2Hamburg University of Technology (TUHH)
Robustness analysis of CFRP structures under thermomechanical loading including manufacturing defects
10/10/2019 2
Motivation
Robustness analysis of CFRP structures under thermomechanical loading including manufacturing defects
Exploitation of thermal and mechanical potentials
Robust design
Stiffness/
Strength
Temperature
Current Design
Point
Thermal Potential
Me
ch
an
ica
l P
ote
nti
al
Future Design Curve
Current
Composite
SHEFEX II at re-entry
Aircraft tailcone section with
APU marked in orange
Future aircraft concept
(September 2010): www.spiegel.de
http://www.google.de/url?sa=i&rct=j&q=&esrc=s&source=imgres&cd=&cad=rja&uact=8&ved=2ahUKEwig1Z6n_LDhAhWEb1AKHb5JDh8QjRx6BAgBEAU&url=http://www.spiegel.de/fotostrecke/konzepte-fuer-die-luftfahrt-september-2010-flugzeuge-der-zukunft-fotostrecke-59417-2.html&psig=AOvVaw1Yb_fysPShifBI2UCKST1J&ust=1554279408639012
10/10/2019 3
General aspects
Surrogate-boosted Monte Carlo
Design of Experiments
Deterministic analyses
Surrogate model creation
Probabilistic analysis
Various assessment aspects
Robust design
Tolerance restrictions
Maintenance scheduling
Parameter 1
Para
mete
r 2
Design of Experiments
Design points
Analysis results
Surrogate model
Defintion
Phase DOE Deterministic
Analyses
Probabilistic
Analysis
Surrogate
creation
Timeline of the analysis procedure
uncertainty propagation
inverse uncertainty
quantification
Surrogate-boosted Monte Carlo
1) Balokas et al., Neural network assisted multiscale analysis for the elastic prediction
of 3D braided composites under uncertainty, Comp.Struct. 183, 550-562, 2018.
2) Kriegesmann et al., Fast probabilistic design procedure for axially compressed
composite cylinders, Comp. Struct., 93, 3140-3149, 2011.
Statistical result
Output measure
10/10/2019 4
Curing analysis
Material curing properties
Process conditions
Thermal analysis
Thermal material properties
Manufacturing Defects
Thermal loading
Thermal deformation
analysis
Mech. material properties
Manufacturing defects
Boundary Conditions
Mechanical load analysis
Mech. material properties
Manufacturing defects
Boundary conditions
Mechanical load Conditions Preforming defect
analysis
Individual
FE-Analysis
Relevant topic & Parameter input
Legend
Deterministic FE-analysis procedure
Process simulation
Preform behavior
10/10/2019 5
Preforming defects I - Motivation & Objectives
Typical manufacturing induced deviations:
Fuselage section cycle time distribution:
According to reference 1)
Twisted tow
Gap
Overlap
41%
32%
27%
Layup
Inspection & rework
Anything else
According to reference 2)
1) B. Denkena, C. Schmidt, K. Völtzer, and T. Hocke, “Thermographic online monitoring system for Automated Fiber
Placement processes,” Compos. Part B Eng., vol. 97, pp. 239–243, 2016.
2) T. Rudberg, J. Nielson, M. Henscheid, and J. Cemenska, “Improving AFP Cell Performance,” SAE Int. J. Aerosp., vol.
7, no. 2, pp. 2014-01-2272, 2014
3) R. Hein und F. Heinecke. „Digitaler Zwilling - ein dynamisches Abbild und nicht nur eine digitale Kopie“. In:
Innovationsbericht 2018 (2018), S. 93.
DLR‘s AFP facility called GroFi at ZLP Stade, according to reference 3)
10/10/2019 6
Preforming defects II – Implemented defects
Parameters:
• Location
• Width, Length
• Wavelength
• Amplitude
• Defect impact factor
• Defect shape propagation
• Optional: Contour
Undulation
Parameters:
• Location
• Width, Length
• Defect impact factor
• Defect shape propagation
• Resin properties
• Optional: Contour
Gap
Parameters:
• Location
• Width, Length
• Defect impact factor
• Defect shape propagation
• Optional: Contour
Overlap
Parameters:
• Location
• Angle
Angle deviation
Parameters:
• Location
• Thickness
Thickness deviation
Parameters:
• Location
• Properties
Material deviation
Defects, which have to be analyzed using a detailed
geometric representation
Defects, which can be directly considered via finite
element properties
Preforming defect
analysis 1) Heinecke, F.; Willberg, C. Manufacturing-Induced Imperfections in Composite Parts Manufactured via Automated
Fiber Placement. J. Compos. Sci. 2019, 3, 56.
10/10/2019 7
Name Symbol comment
Deformation
u,
v,
w
Local value; f(x,y,z)
Residual stresses
σres, x σres, x σres, x
Local value; f(x,y,z)
Cure defects are a result of
The materials resulting degree of cure
Thermal expansion and chemical shrinkage
Orthotropic material behavior
Curing analysis I
Name Symbol comment
Cure times t1, t2, … Depend on the
materials cure cycle Cure temperatures T1, T2, …
Materials cure behavior Pcure Property development Curing
analysis
Te
mp
era
ture
Time
Nominal
Variation 1
Input parameters of the curing analysis Output parameter from curing analysis serves as
input parameters for the thermomechanical analysis
Process parameters and
an exemplaric variation
Geometrical imperfection
that results from curing
10/10/2019 8
Local defects
Geom. Imperfection,
Residual stresses
10/10/2019 9
Simplifications
Symmetric behavior wrt to hotspot
One-sided heating
Spatially constant conditions at back side
Requirements
Spatially constant heating
Spatially distributed heating
Variations of the thermal load in
Shape
Magnitude
Thermal load conditions I
𝑇𝑎𝑖𝑟 𝑥, 𝑦 = ∆𝑇 ⋅ 𝑒𝑏𝑥⋅𝑥+Δ𝑥
2− 𝑏𝑦⋅𝑦+Δ𝑦
2
+ 𝑇𝑐𝑜𝑛𝑠𝑡
Name Symbol
convective sink
temperature TConv,cooled
Functional relation for
temperature
distrbution
Tconst. ΔT
Δx, Δy bx, a
Heat transfer
coefficient
kconv,heated kconv,cooled
x y
T in °C
𝑎 = 𝑏𝑥𝑏𝑦
Thermal loading function derived
from typical gaussian function
Shape parameter
Exemplaric temperature
distribution
200°C
180°C
190°C
185°C
195°C
Parameters used to define thermal loading
conditions
10/10/2019 10
Exemplaric thermal load distributions
Thermal load conditions II
Circular shape, high width
Circular shape, small width
Ellipsoidal, centered
Ellipsoidal, offset to center 200°C
180°C
190°C
185°C
195°C
10/10/2019 11
Temperature dependent behavior of thermal properties
Orthotropic behavior of UD-CFRP plies
Fitting based on experimental data
Linear temperature dependency assumed
Thermal material properties I
Name Symbol
Thermal
conductivity
λ11
λ22
λ33
Heat capacity cp
Density ρ
Overview to thermal properties
parameter space
More general overview; no details
Maybe some bullet points which
dependency or specific behavior will
be considered later on
1) Hein, R. (2019): Vorhersage und In-Situ Bewertung fertigungsbedingter Deformationen und Eigenspannungen von Kompositen.
Dissertation, TU Braunschweig. Insitut für Faserverbundleichtbau und Adaptronik, DLR Braunschweig.
Temperature [°C]
Th
erm
al C
on
du
cti
vit
y [
Wm
-1K
-1]
He
at
cap
ac
ity [
Jg
K-1
]
10/10/2019 12
Temperature
distribution
10/10/2019 13
Temperature dependent behavior of mechanical properties
Load direction has to be distinguished
Strength properties are more sensitive to temperature effects than elastic properties
Mechanical material properties II
Temperature dependency of mechanical
properties for unidirectional EP-CF
100%
80%
60%
40%
20%
0%
Temperature
No
rma
lize
d p
rop
ert
y
Tension strength
Compression strength
Shear strength
Young‘s modulus fibre direction
Young‘s modulus transverse direction
Name Symbol
Thermal expansion
coefficients
α11,
α22,
α33
Young’s modulus E11,
E22,
Shear Modulus
G12,
G13,
G23
Poisson ratio ν12,
Strength
S1T,
S2T,
S1C,
S2C,
S12, Overview to mechanical material
properties parameter space
10/10/2019 14
Boundary and load conditions
Thermal strain locking (in-plane)
0% 100% Fully locking of thermal
expansion
Additional stresses reduces
buckling load
Ideal thermal expansion
possible
Deformation only due to
temperature gradients
Picture of the panel and the FE-model!?
Test conditions
Realistic conditions
Name Symbol
Thermal Strain locking TSLL
TSLT Load direcftion φ 𝜀𝑇
𝑡ℎ
Constantly heated
Structure
Not heated structure
Thermal expansion
allowed
Evtl als 1/… darstellen
um 100% bei
freierausdehnung zu
erlauben
10/10/2019 16
Overview
Exemplaric results: Implementation panel
Only thermal load conditions varied
Axial thermal strain locking 0% (free)
One-sided thermal
loading
Axial compression
loading
Constant ambiance
conditions at backside
10/10/2019 17
Implementation panel at room temperature (RT)
Results
0
20
40
60
80
100
Ax
ial
forc
e [
kN
]
0.0 0.5 1.5 2.5 3.5 1.0 2.0 3.0 4.0
Axial displacement [mm]
1
2
3
1
2
3
Local Buckling
Global Buckling
1) Zimmermann, R.; Klein, H.; Kling, A. (2006): Buckling and postbuckling of stringer stiffened fibre composite
curved panels – Tests and computations. In: Composite Structures 73 (2), S. 150–161.
10/10/2019 18
Results
Constant temperature applied to the whole part Temperature 𝑬𝑳 𝑻
𝑬𝑳,𝑹𝑻
𝑬𝑻 𝑻𝑬𝑻,𝑹𝑻
25°C 100 % 100 %
180°C 96.7 % 84.0 %
195°C 85.8 % 62.8 %
210°C 53.3 % 33.3 %
0
20
40
60
80
100
Ax
ial
forc
e [
kN
]
0.0 0.5 1.5 2.5 3.5 1.0 2.0 3.0 4.0
Axial displacement [mm]
RT
180°C
195°C
210°C
RT
180°C 195°C 210°C
Material stiffness reduction in dependence on
the used analysis temperature
Similar deformation behavior at different thermal
load conditions
10/10/2019 19
Thermal behavior and thermal deformation
Results
T [°C]
220
200
210
T [°C]
Thermal load distribution Stationary temperature distribution Thermal deformation
Elastic properties at the
hotspot compared to RT:
EL = 90%; ET = 70%
U [mm]
10/10/2019 20
Comparison of behavior at RT and thermal loads
Results
0
20
40
60
80
100
Ax
ial
forc
e [
kN
]
0.0 0.5 1.5 2.5 3.5 1.0 2.0 3.0 4.0
Axial displacement [mm]
Hinweis auf Buckling
als Design-Kriterium
Reduction of
Buckling-Load 1
2
3
No thermal loads
Thermal loaded
3
2
1
Comparison of the structural deformation due to axial
compression lod: at const. room temperature (left)
and at spatial temperature distribution (right)
10/10/2019 21
Probabilistic analysis of the implementation panel
Sensitivity studies and parameter range definition
Robustness analysis
Inverse tolerance quantification
Apply the probabilistic analysis to SuCoHS use cases
Update material models by novel material solutions
Experimental validation
Outlook: next steps
10/10/2019 22
This project has received funding from the European Union’s Horizon 2020 research and
innovation programme under grant agreement N° 769178.
www.sucohs-project.eu
https://www.linkedin.com/company/sucohs-project/
https://www.google.de/url?sa=i&rct=j&q=&esrc=s&source=imgres&cd=&cad=rja&uact=8&ved=2ahUKEwj_w9rev5zdAhXDbFAKHYQkBu8QjRx6BAgBEAU&url=https://de.wikipedia.org/wiki/Datei:Bombardier_Logo.svg&psig=AOvVaw0Ys0Cq9Iqf5WIyVW76v8yI&ust=1535983814770656http://www.l-up.com/index.phphttps://www.google.de/url?sa=i&rct=j&q=&esrc=s&source=imgres&cd=&cad=rja&uact=8&ved=2ahUKEwiW6IDTv5zdAhVNalAKHT9sBhIQjRx6BAgBEAU&url=https://twitter.com/nlr_nl&psig=AOvVaw1vLAHfpDCyfB1JIEu1FRdp&ust=1535983790016837http://www.sucohs-project.eu/http://www.sucohs-project.eu/http://www.sucohs-project.eu/https://www.linkedin.com/company/sucohs-project/https://www.linkedin.com/company/sucohs-project/https://www.linkedin.com/company/sucohs-project/