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/

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