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Simulation of process induced deformations (spring-back)

Mathias Hartmann

Simple Methods for Strain Anisotropy Evaluation on a Generic

I-Profile Frame Structure

„A Comprehensive Approach to Carbon Composites Technology“

Symposium on the occasion of the 5 th anniversary of the Institute for Carbon Composites

Research Campus Garching, September 11th - 12th 2014

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Conclusions and Future Work 5

PID on generic I-profile structure 4

Spring-In: Root Causes 3

Process induced deformations: phenomena and methods for quantification 2

Motivation: Dimensional Control on Stiff Structures 1

Agenda


09/11/2014 | M. Hartmann | Simulation of process induced deformations (spring-back)

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Methods evaluation on a frame structure



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Geometrical deviations on stiff structures result in

Additional rework effort and / or high mounting forces required,

Expensive iterative tooling adaption.

Motivation: Dimensional Control on Stiff Structures


Picture: A350 fuselage structure [Airbus]

Deformed frame after curing

Magnification factor: 30

Deformed frame section

Magnification factor: 30

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6

Catagorization on most prominent deformations appearent on parts

Spring-In due to strain anisotropy is one of the major drivers of PID reported in literature

Process Induced Deformations


Phenomena

- -

-

-

-

Fig.1: Main phenomena of PID

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Process Induced Deformations


Approaches

Fig.1: Approaches for PID quantification, illustrated for an L-shaped subcomponent

Experimental: Iterative optimization of final part shape

Analytical: Estimation of deformation for simple geometries

Phenomenological: Summarization of different mechanisms with one actuating variable (e.g. enhanced CTE)

Curing simulation: Simulation of all relevant mechanisms (e.g. reaction kinetics, modulus development,…)

Dimensional Control through PID Quantification

Evaluation of Residual Stresses, Optimization

of Process Control

Le

ve

l o

f d

eta

il a

nd

ac

cu

rac

y /

ve

rsa

tility

Number of input parameters

Focus of

presentation

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Laminas have very different thermal and cure shrinkage behavior in fiber and transverse

direction

On changes in temperature, plies built in the laminate build up residual stress due to constraint

strains

Laminate homogenization captures effective expansion and mechanical properties in equilibrium

state of the laminate

Approach:

In-plane homogenization:

„virtual“ loads due to constrained ply

strains are calculated using CLT

Out-of-plane homogenization:

Poisson effects are captured utilizing

orthotropic Hook‘s law (Pagano [1])

Spring-In


Root cause of strain anisotropy

wTCx ,

tTplyr 2,3

lTCy ,

are typical dimensions of the laminatesection (ply thickeness, width, length)

lwt ,,

ply 2tT 3

ply 3

ply 4

wT 1

ply 1

wT 2

Fig. 1 Illustration of the effect of lamina built in the laminate [1] N. J. Pagano, “Thickness expansion coefficients of composite laminates”,

Journal of Composite Materials 1974 8:310

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In curved sections inplane and out-of-plane strains are not compatible

For the free expansion case a change in curvature is the result

Quantification of change in included angle well established utilizing the Radford equation [2]

Spring-In


Effect of strain anisotropy

x y

z

Ri,0

0

1

Ri,1

z

zx

10

Fig. 1 Geometrical situation and result for the effect of strain anisotropy in curved sections

[2] Radford DW, Diefendorf RJ. “Shape instabilities in composites resulting from laminate anisotropy”. Journal of Reinforced Plastics and Composites 1993;12:58–75

zII RRI 1)( 0,1,

xII RRII 1)( 0,01,1

01

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Options for adoption of (enhanced) matrix CTE to cover effective cure shrinkage

Measured corner spring-in component as target variable using Radford equation

Measured deflection of a bi-material beam (e.g. steel and prepreg)

Enhanced matrix CTE has been determined for material system of concern

Spring-In


Input parameter: thermal and cure shrinkage strains

chemthermeq mmm

Cu

re

Fig. 1: Thermal and effective chemical shrinkage are projected on the matrix coefficient of thermal expansion

z

zx

10eqm→

Fig. 2: Experimental Spring-In data presents target variable for determination of αM,eq

1.000

1.050

1.100

1.150

1.200

1.250

1.300

1.350

Position1 Position2 Position3 Position4 Position5

[°d

eg]

"Reiner" Spring-In, MS1-17, MS1-18, MS1-19

w

[1] Clyne T W, Key Engineering Materials, vol.116/117 (1996) p.307-330

22 4

81

ws

w

r

eqm

Keqm

78Km

55

HexPly M18/1:

Fig. 3 Deflection measurement on cured bi-material sample in DMA

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Simplified Finite Element Analysis 4.3

Analytical spring-in estimate 4.2

Sample case setup 4.1








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Monolithic I-beam structure, 180°C curing system

Effective properties to account for anisotropic thermal and cure shrinkage strains have been

generated based on L-shaped specimen

Goal: Assessment of the global Deformations of the

structure with the focus on anisotropic strains

Steps:

Development of a methodology to evaluate

effect of global strain anisotropy (analytical)

Phenomenological finite element based

assessment of deformations

Case Study: Generic I-Profile Frame Structure


Setup

Fig. 1 Generic frame structure [Airbus Helicopters Germany]

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Setup loosely based on real structure

Two representative layups have been picked: one including patch reinforcements and one

containing continuous plies for the areas of interest only

Changes in cross section have been neglected

Profile has been simplified to represent the main geometric features (curvatures) with swept

cross section



Simplification of setup in terms of geometry and layup

+ =

Fig. 1 CAD representation of simplified frame geometry [Airbus Helicopters]

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Precondition:

Analytical formulae describing homogenized strain behavior for composite laminates utilizing

CLT are applicable also for sandwich setups [3] as long as the transvers shear deformation is

negligible.

Steps

Cross section homogenization

Application of Nelson & Cairns / Radford equation

Description of profile change



Analytical strain anisotropy evaluation: Approach

[3] Y. Mahadik, K. Potter. “Experimental investigation into the thermoelastic spring-in of curved sandwich panels”, Composites: Part A, Vol. 49, pp 68-80, 2013

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I-Beam can be homogenized applying equivalent (smeared) properties for the web, e.g.

Strains in local 3-direction of the web are assumed to be

decoupled from strains in the skin

Ex,web set close to zero (10Pa)

Only membrane stiffnesses of web are relevant

Layup of the web is symmetric and quasi-isotropic

web can be homogenized as an orthotropic ply with

main direction in global x-axis

Strain anisotropy between strains in y- (global

in-plane) direction and z- (global through thickness)

direction is considered.



Analytical strain anisotropy evaluation: Homogenization

z

x

Fig. 1 Actual and homogenized cross section of the frame

wweb

wflange

Outer Flange

Web

Inner Flange

1

2

3

1

2

3

y

flange

webwebweby

w

wEE ,1,

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Area of interest of the I-beam profile has been described as a section wise defined curve

Changes in angles are applied as calculated spring-in

Change in radii have been evaluated applying the effective out-of-plane expansion of the

homogenized cross section, changes in length of straight sections accordingly with the

concerning in-plane strains

Deviations are calculated as the difference between the local y coordinates in deformed and

un-deformed state



Analytical strain anisotropy evaluation: Quantification of deviation

Fig. 1 Geometrical representation of guide curve for analytical evaluation

sym

me

try a

xis

y

x

Section 1 Section 2 Section 2

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-3.500

-3.000

-2.500

-2.000

-1.500

-1.000

-0.500

0.000

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Del

ta [

mm

]

y/yt

ota

l [m

m]

x/xtotal [-]

undeformed profile

Delta, representative cross section

Delta, continous plies at radii

Initial deviation of ~0.5mm due to contraction of transverse section of the structure

Maximum deviation amounts total of ~5.8mm “closing” the legs

Difference between representative cross section and continuous plies is ~0.7mm in total.



Analytical strain anisotropy evaluation: Results

Fig. 1 Undeformed profile and calculated delta (analytical)

Deformation

tendency

measured 3mm

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Solid model has been set up to best engineering practice

~800000 elements in total

Run time ~1hour of CPU, but (detailed) FE model setup took ~ weeks

2 load cases: „mounted“ and free (statically determined boundary conditions)



Finite Element Cool Down Analysis: Setup

Fig. 1 Fraction of FE mesh: top view (left) and cross section (right) [Airbus Helicopters]

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2 deformation modes: closing of leg and global torsion

Magnitude of deformation due to global strain ansisotropy ~30% of maximum deflection due to

torsion

„Closing“ of leg amounts 3.5mm

(vs. 5.8mm spring-in analytical)



Finite Element Cool Down Analysis: Results for free deformation

Fig. 1 Deformations on frame [Airbus Helicopters]

Additional curvature

component present not captured

in analytical model.

measured 3mm

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Effect of strain anisotropy on global profile (“leg closing”) leads to high rigging forces

critical deformation mode.

Rigging forces to constrain bending of the transverse section amount ~60%

If edges of profile are critical interfaces

the torsional deformation mode plays

a minor role on required clamp up

forces.



Finite Element Cool Down Analysis: Results “mounted”

Fig. 1 Reaction forces for load case “mounted” [Airbus Helicopters]

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Global spring-in has been identified as critical deformation mode for a generic I-Profile frame structure

based on expected rigging forces.

Approach to quantify the effect of global strain anisotropy analytically has been customized for I-beam

profile and captures main deformation tendency

Provides a test bed for fast evaluation of cross section and laminate variants for qualitative evaluation

Analytical results overestimate deformation in comparison to FEA by ~60% for presented case study

Model should be enhanced with section asymmetry (layup) effects to capture additional curvature

component appearent in FEA results.

Simplified FEA shows good agreement to experimental results. Still tool adaption based on results derived

might not suffice in order to achieve tight tolerance requirements.

Process simulation should be carried out and compared to measured deformation field in order to quantify

contribution of additional phenomena tool-part interaction and cure gradients and clarify relevance of

different drivers on overall deformations.

Conclusions and Future Work


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Acknowledgements


The authors would like to thank Airbus Helicopters Germany for funding the work within

the project CompTAB, a Lufo IV venture with financial support of the German Federal

Ministry of Research and Technology. The generative collaboration with Jordy Balvers

throughout the project is particularly acknowledged.

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Thank you for your attention!


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Technische Universität München

Institute for Carbon Composites

Boltzmannstraße 15

85748 Garching

www.lcc.mw.tum.de

Contact

Address

Fax

Email

Tel

Room

+49 89 /

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Institute for Carbon Composites donated by

Mathias Hartmann

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802.03.104

289-15097

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