tailored stacked hybrids â an optimization-based

TAILORED STACKED HYBRIDS – AN OPTIMIZATION-BASED APPROACH IN MATERIAL DESIGN FOR FURTHER IMPROVEMENT IN LIGHTWEIGHT CAR BODY STRUCTURES Alan A. Camberg*, Thomas Tröster Automotive Lightweight Design (LiA) ILH, Paderborn University Tagung Faszination Hybrider Leichtbau

29 & 30 May 2018 MobileLifeCampus Wolfsburg, Germany

Multi-Material Design. • “The best material for the best application” Multi-material design is a common approach in latest BIW concepts, but … Audi A8 D5

BMW 7 G11

Aluminum sheet

Aluminum castings

UHS hot-formed steel

Aluminum section

Magnesium

Conventional steel

CFRP

Source: Audi MediaCenter

30/05/18

TAILORED STACKED HYBRIDS – AN OPTIMIZATION-BASED APPROACH IN MATERIAL DESIGN FOR FURTHER IMPROVEMENT IN LIGHTWEIGHT CAR BODY STRUCTURES

UHS hot-formed steel

Aluminum

Multiphase steels

CFRP

Source: BMW Group, Technical Training G12 Introduction

2

Other steels

Common Structural Materials. • Pros and cons of common structural materials … the lightweight potential of established materials is limited. Steel + high strength + high stiffness due to high elasticity modulus - high density - buckling problems due to reduced sheet thickness

FRP

combine established materials in a manner to offset the drawbacks of every single material and reach an optimum of mechanical properties and costs

Aluminum + good strength to weight ratio - limited formability - low stiffness potential due to relative low elasticity modulus

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+ superior lightweight characteristics + high energy absorption - catastrophic failure - high production costs

3

Multi-Layer Materials. • Multi-material design in thickness dimension Structural and semi-structural materials with a property gradient in thickness direction: litecore®

LEIKA

CAPAAL®

tribond®

There is a dozen of multi-layer materials but are they really optimal for every application?

FOREL 2017: LEIKA Abschlussbericht

bondal® Kroll 2017: Kombination großerientauglicher Basistechnologien zur ressourceneffizienten Herstellung von Leichtbaustrukturen für den Automobilbau

ATZ extra 10/2014: Das Projekt ThyssenKrupp InCar plus

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Optimum?

GLARE Pieronek et al. 2016: Virtuelle Produktentwicklung und Crashauslegung von Stahl-Werkstoffverbunden

de Vries 2001: Blunt and sharp notch behavior of Glare laminates


4

?

LHybS Project Approach. • Development of new hybrid materials with tailored through-thickness properties

Identification of critical components and their requirements

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Material

Component

Subdivision in layers

Suitable optimization methods

Parametric material models

In detail analysis of the local stress / strain conditions and an optimization-based investigation of an ideal through-thickness property profile


5

Multi-layered material with tailored through-thickness properties for a particular application

Reference Structure Analysis. • Benchmarking the InCar® plus* reference structure Global Bending Stiffness

Global Torsion Stiffness

InCar®plus

𝑐𝐵 = InCar plus – an OEM independent executive class station wagon structure (E segment)

σ 𝐹𝑧 𝑢𝑧,𝑚𝑎𝑥.𝑟𝑜𝑐𝑘.𝑐𝑜𝑟𝑟.

*courtesy of thyssenkrupp Steel Europe AG

30/05/18


6

𝑀𝑥 𝑁𝑚 𝑐𝑇 = Φ𝑥 𝑑𝑒𝑔

Modal Analysis

Component Determination. • Clustering: classification of BIW-components into functional groups Percentage of a component at the BIW deformation:

Strain energy of a single element:

𝑊𝑖,𝑒

1 1 = 𝜎 dA 𝜀 𝑑𝑡 = 𝜎 𝜀 𝑑𝑉 2 2

𝑊𝑖%,Κ = ෍

𝑒∈Κ

𝑊𝑖%,𝑒

Specific prorate strain energy of a single element :

𝑊𝑖%,𝑒

𝑒𝑎

𝑊𝑖,𝑒 = ∗ 100% σ𝑒∈𝜃 𝑊𝑖,𝑒

𝜎 = 𝜎𝑥 𝜎𝑦 𝜏𝑥𝑦 𝜀 = 𝜀𝑥 𝜀𝑦 𝛾

𝑇

𝑎 ≥𝑏,

∧

𝐾𝑏

𝑏=1,…,𝑛

Κ𝑏 ∩ Κ𝑚 = ∅

∀𝑎 = 1, … , m ∃! 𝑏 = 1, … , n with 𝑒𝑎 ∈ Κ 𝑏

𝑇

𝑊𝑖 = ෍


𝑊𝑖,Κ = ෍

Κ∈Θ

Camberg & Tröster 2018: Optimization-Based Material Design of Tailored Stacked Hybrids for Further Improvement in Lightweight Car Body Structures; Proceedings of 3rd Int Conf on Hybrid Materials and Structures, 2018

30/05/18

𝑎=1,…,𝑚

7

𝑊𝑖,𝑒

𝑒∈Θ

Evaluation quantity: Component specific prorate strain energy The ratio between the strain energy of the component 𝐾 and the whole strain energy of the BIW 𝜃 is used to quantify the relevance of structural BIW for particular load cases

Demonstrator Definition. • Sensitivity analysis of load-case specific components on the global response

Energy method

Demonstrator Stiffness: Rear Cross Member Domain reduction – stiffness scaling of components with high prorate strain energies

Sensitivity analysis – evaluation of the component‘s impact on global BIW characteristics

Component-wise prorate strain energy distribution

Element-wise strain energy distribution

CR240IF t2 = 2.0 mm

DP-K®330Y590T-GI t1 = 1.0 mm

CR240IF t2 = 2.0 mm

Component rating – comparison and comparative assessment of global characteristics Dominance-Matrix based rating of demonstrator candidates by taking into account several criterions

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8

Demonstrator „Stiffness“

Material Design. • Determination of ideal layer properties with a modified SIMP method Classical SIMP Method:

SIMP approach from topology optimization (solids) …

𝐸 𝜌 = 𝜌𝑝 𝐸0 ,

𝜌 ∈ 0; 1 ∧ 𝑝 > 1

Modified SIMP Method for two-phase materials: 𝐸 𝜌 = 𝜌𝑝 𝐸1 + 1 − 𝜌𝑝 𝐸2 ,

… modified and applied for integration point layers of shell elements

Ordered Multi-Material SIMP Method: 𝑝

𝐸𝑒 𝜌𝑒 = 𝜌𝑒 𝐴𝐸 + 𝐵𝐸 , 𝐴𝐸 =

𝑇

𝑂𝑏𝑗𝑒𝑐𝑡𝑖𝑣𝑒:

min 𝐶 = 𝑢 𝐾𝑢 𝜌

𝑀 ≤ 𝜑𝑀 𝑀0 𝐾𝑢 = 𝑃

𝑁𝑒

𝑆𝑢𝑏𝑗𝑒𝑐𝑡 𝑡𝑜: 𝐾 = ෍ න

𝑚=1 𝑉

𝑒 𝐾𝑚 , 𝑁𝑒

𝑚=1

𝐸𝑖 − 𝐸𝑖+1 𝑝

𝑝

𝜌𝑖 − 𝜌𝑖+1

𝜌𝑒 ∈ 𝜌𝑖 , 𝜌𝑖+1 ∧ 𝑝 > 1, 𝑝

∧ 𝐵𝐸 = 𝐸𝑖 − 𝜌𝑖 𝐴𝐸

LHybS Ordered Multi-Material SIMP Method:

𝑁𝑙

𝑇 𝐵𝑘𝑙

𝑒

𝐾 = ෍න

𝑒 𝑀 = ෍ 𝑀𝑚 ,

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𝜌 ∈ 0; 1 ∧ 𝑝 > 1

𝑘=1 𝑉

𝐶𝑘𝑙 𝐵𝑘𝑙

𝐸 𝜌𝑖 = 𝑎 ∗ 𝑒 𝑏∗𝜌𝑖 + 𝑐 ∗ 𝑒 𝑑∗𝜌𝑖 , 𝑑𝑉 𝐸𝑖 =

𝑁𝑙

𝑀𝑒 = ෍ 𝑉𝑘𝑙 𝜌𝑘𝑙 𝑘=1


9

𝐸𝑖𝑡𝑒𝑐ℎ , 𝐸𝑚𝑎𝑥

𝑖 = 1, 2, 3, … , 𝑚

𝜌𝑖 =

𝜌𝑖𝑡𝑒𝑐ℎ , 𝜌0

𝑖 = 1, 2, 3, … , 𝑚

Material Design. • Determination of an optimal hybrid layer design

LHybS Ordered Multi-Material SIMP Method is still limited to optimize material distribution problems and additional design variables, such as material thickness or orientation have to be optimized in a separate optimization run

1st optimization run: Optimize material distribution in a constant cross section

2nd optimization run: Optimize layer thicknesses and material orientation (only for orthotropic materials)

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Direct in-BIW Material Design. • Determination of optimal layer properties directly in the BIW simulation: 𝑚𝐵𝐼𝑊 𝐿= 𝑐𝑇 ∗ 𝐴

Variant A

Variant B

Variant C

Restrictions: CFRP UD tapes 0.1, Steel 0.5

Restrictions: CFRP fabric 0.35, Steel 0.5

Restrictions: CFRP fabric 0.35, Steel 0.6

Steel 0.5 mm CFRP UD 0.2 mm 40°

Steel 0.5 mm

CFRP UD 0.1 mm -55°

CFRP 0.35 mm +45°/-45°

CFRP 0.35 mm +45°/-45°

CFRP 0.35 mm +45°/-45° CFRP 0.35 mm +45°/-45° Steel 0.6 mm

Steel 0.5 mm

CFRP UD 0.1 mm -50° Steel 0.5 mm

Objective: Increase of the BIW Lightweight Index Multi-objective → left and right turning BIW torsion

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Lightweight Index

Component Mass


Lightweight Index

Component Mass


Lightweight Index

Component Mass

+ 0.03 %

- 0.42 %

- 25 %

+ 0.37 %

- 0.60 %

- 23.2 %

+ 0.37 %

- 0.49 %

- 14.64 %


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1.90 mm

CFRP UD 0.2 mm -55°

CFRP 0.35 mm +45°/-45°

2.05 mm

CFRP UD 0.3 mm 0°

1.90 mm

Steel 0.6 mm

Geometry Redesign. • Adapting the reference geometry for FML forming Reference Geometry

Package Model

Variant D

Topology Optimization

CFRP 0.35 mm +45°/-45° CFRP 0.35 mm +45°/-45° Steel 0.6 mm

Material Variant C, “worst-case” in terms of lightweight

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1.90 mm

Steel 0.6 mm

Variant D Global Torsion Stiffness

Lightweight Index

Component Mass

+ 5.89 %

- 5.38 %

- 0.45 %


A further improvement in lightweight potential can be gained by performing a full material design process. This will be the subject of future work.

12

Forming simulations carried out at LUF, Chair of Forming and Machining Technology, Paderborn University

Numerical Validation. • Validation of different material designs in BIW simulations: Variant A

Variant B

Variant C

Variant D

Component Mass

-25 %

-23.2 %

-14.64 %

-0.45 %

Bending stiffness

-0.71 %

-0.71 %

-0.72 %

-0.40 %

Torsional stiffness

+0.03 %

+0.37 %

+0.37 %

+5.89 %

Lightweight index

-0.42 %

-0.60 %

-0.49 %

-5.38 %

1st bending mode

unchanged

unchanged

unchanged

+0.02 %

1st torsion mode

+0.27 %

+0.40 %

+0.33 %

+2.32 %

2nd bending mode

+0.07 %

+0.07 %

+0.04 %

+0.02 %

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Conclusions & Outlook. • To sum up: • •

The lightweight potential of established materials is limited Numerical processes developed within LHybS allowed to design novel requirement-optimal hybrid materials

•

The tailored hybrid stacks lead to a weight reduction of up to 25 % while maintaining or even improving the overall vehicle properties

•

The developed materials were hitherto investigated only in numerical simulations and coupon-based experimental tests

•

The experimental validation on real component geometries is still pending

•

US-NCAP Full Width

IIHS Small Overlap

EuroNCAP ODB


Global Bending Stiffness

Free-Free Modal Analysis

EuroNCAP Oblique Pole

Crashworthiness is the subject of current investigations. Due to high non-linearity, numerical noise and nonconvex objective functions the optimization problem is even more complex

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IIHS Roof Crush


14

Contact

#Leichtbau18

Thanks for your attention! Alan A. Camberg Paderborn University Faculty of Mechanical Engineering Chair of Automotive Lightweight Design (LiA)

Phone: +49 (0) 5251/60-5961 E-mail: [email protected] Web: http://www.leichtbau-im-automobil.de

www.tecup.de/lhybs/

This project is founded by the European Union and the State North Rhine-Westphalia.

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tailored stacked hybrids â an optimization-based

tailored stacked hybrids â an optimization-based

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