sorg thesis 2008

Baustatik und Baudynamik

Universitt Stuttgart

Institut fr Baustatik und Baudynamik Prof. Dr.-Ing. habil. Manfred Bischoff

Crashworthiness Assessment

of Automobile Front Ends

using Explicit Finite Element

Formulations

submitted by

Annika Sorg

in

May 2008

Master Thesis

Crashworthiness Assessmentof Automobile Front Ends

using Explicit Finite ElementFormulations

November 23rd, 2007 May 23rd, 2008

Author Annika SorgMatr.-Nr.: 2380825

1st Supervisor Prof. Dr.-Ing. habil. Manfred BischoffInstitute of Structural MechanicsUniversitat StuttgartPfaffenwaldring 7, 70550 StuttgartGermany

2nd Supervisor Dr.-Ing. habil. Fabian DuddeckSchool of Engineering and Materials ScienceQueen Mary, University of LondonMile End Road, London E1 4NSUnited Kingdom

Abstract

The primary topic of this dissertation is the general safety of road trafficand especially the safety of cars; with emphasis on the assessment of crashsimulations modelled using finite element software.The main aspects leading to safer road traffic are presented, focussing onhigh speed frontal impacts and on the contribution to car safety afforded bythe design of the cars structure - particularly the design of the two enginemounts towards the front end of a car (the main components to considerduring a crash). These are designed to deform, such that they absorb thelargest part of the released crash energy without penetrating the passengercompartment. An example of an aluminium extrusion frontal side memberwas chosen in order to evaluate the capability of crash simulations with finiteelements to predict real crash test results. Analysis was performed to deter-mine the sensitivity of the model to changes made to individual modellingparameters, allowing statements on the reliability of the computational re-sults to be proposed.Parameters altered during these assessments were the element size, the num-ber of integration points along the thickness of the shell elements, the typeof numerical integration used, and the manner of meshing. Computationsthat included three different types of failure modelling, and computationsthat didnt, were both considered. In addition the strain rate dependencywas analysed. While the work focused more heavily on dynamic computa-tions, quasistatic computations were also performed, and results from eachcompared.The final outcome of the study are recommendations where to pay specialattention when FE software is used for crash simulations; limitations andpossibilities are identified and critically summarized.

v

Declaration

I, Ms. Annika Sorg, declare that this masters thesis is written independentlyand no sources have been used other than the stated references.

.................................................. ..................................................P lace/Date Signature

vii

Contents

Abstract v

Declaration vii

List of figures xiii

List of tables xvii

Nomenclature xix

Indices xxi

Abbreviations xxiii

1 Introduction 1

1.1 Topic of the Masters Thesis . . . . . . . . . . . . . . . . . . . 1

1.2 Structural Outline . . . . . . . . . . . . . . . . . . . . . . . . 2

2 Safety of Road Traffic 3

2.1 History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.2 Active and Passive Safety . . . . . . . . . . . . . . . . . . . . 4

2.2.1 Passive Safety . . . . . . . . . . . . . . . . . . . . . . . 5

2.3 Structural Concept of the Car Body . . . . . . . . . . . . . . 6

2.4 Compatibility . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.5 Deformation Zones . . . . . . . . . . . . . . . . . . . . . . . . 8

ix

x CONTENTS

2.5.1 Pedestrian Safety and Urban Crash . . . . . . . . . . 8

2.5.2 Self and Partner Protection . . . . . . . . . . . . . . . 9

2.6 Overview of Existing Tests . . . . . . . . . . . . . . . . . . . 11

2.6.1 Frontal Impact Test . . . . . . . . . . . . . . . . . . . 11

2.6.2 Obligatory Tests after the Law . . . . . . . . . . . . . 12

2.6.3 Consumer Tests . . . . . . . . . . . . . . . . . . . . . . 16

2.6.4 Other Tests . . . . . . . . . . . . . . . . . . . . . . . . 21

3 The Structure of a Car Body 23

3.1 The Main Structural Elements . . . . . . . . . . . . . . . . . 23

3.1.1 Occupant Cell . . . . . . . . . . . . . . . . . . . . . . 23

3.1.2 Front End . . . . . . . . . . . . . . . . . . . . . . . . . 24

3.1.3 Rear End . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.2 Load Paths through the Car . . . . . . . . . . . . . . . . . . . 25

3.3 Front Side Members . . . . . . . . . . . . . . . . . . . . . . . 26

3.3.1 Evaluation of Energy-Absorbing Structures . . . . . . 28

3.3.2 Deformation of the Front Side Members . . . . . . . . 29

4 Crash Computation using FEM 31

4.1 Time Integration . . . . . . . . . . . . . . . . . . . . . . . . . 32

4.1.1 Implicit Time Integration . . . . . . . . . . . . . . . . 32

4.1.2 Explicit Time Integration . . . . . . . . . . . . . . . . 33

4.2 Contact Definition . . . . . . . . . . . . . . . . . . . . . . . . 37

4.2.1 Definition of Contact in ABAQUS/explicit . . . . . . 38

4.3 Adaptive Meshing . . . . . . . . . . . . . . . . . . . . . . . . 39

5 Underlying Computer Simulation Model 41

5.1 Model Description . . . . . . . . . . . . . . . . . . . . . . . . 42

5.2 Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

5.3 Element Model . . . . . . . . . . . . . . . . . . . . . . . . . . 44

5.3.1 Double Chambered Extrusion Beam . . . . . . . . . . 44

CONTENTS xi

5.3.2 Impactor and Base Support . . . . . . . . . . . . . . . 44

5.4 Material Model . . . . . . . . . . . . . . . . . . . . . . . . . . 45

5.4.1 Elastoplasticity . . . . . . . . . . . . . . . . . . . . . . 45

5.4.2 Mechanisms for Failure Initiation . . . . . . . . . . . . 46

5.5 Contact Definition . . . . . . . . . . . . . . . . . . . . . . . . 51

5.6 Boundary and Initial Conditions . . . . . . . . . . . . . . . . 52

5.7 Time Step Definition . . . . . . . . . . . . . . . . . . . . . . . 52

6 Sensitivity Examination of the Model 53

6.1 Procedural Method . . . . . . . . . . . . . . . . . . . . . . . . 53

6.2 Without Considering Failure . . . . . . . . . . . . . . . . . . 56

6.2.1 Reference model . . . . . . . . . . . . . . . . . . . . . 56

6.2.2 Reduction of Number of Integration Points . . . . . . 65

6.2.3 Comparison of an Integration after Simpsons Ruleand a Gauss Point Integration . . . . . . . . . . . . . 71

6.2.4 Comparison of a Mesh with only Quad-Elements anda Mesh where Quad- and Tri-Elements are Mixed . . . 73

6.2.5 Comparison to a Quasistatic Computation . . . . . . . 75

6.3 Including Failure . . . . . . . . . . . . . . . . . . . . . . . . . 79

6.3.1 Reference model . . . . . . . . . . . . . . . . . . . . . 79

6.3.2 Reduction of Number of Integration Points . . . . . . 86

6.3.3 Comparison of an Integration after Simpsons Ruleand a Gauss Point Integration . . . . . . . . . . . . . 86

6.3.4 Comparison of a Mesh with only Quad-Elements anda Mesh where Quad- and Tri-Elements are Mixed . . . 87

6.3.5 Comparison of a Dynamic and a Quasistatic Compu-tation . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

7 Conclusions and Outlook 93

xii CONTENTS

A Input File 97

A.1 Preliminary Definitions . . . . . . . . . . . . . . . . . . . . . 97

A.2 Nodal Point Data . . . . . . . . . . . . . . . . . . . . . . . . . 97

A.3 Element Data . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

A.4 Material Definition . . . . . . . . . . . . . . . . . . . . . . . . 99

A.5 Rigid Body Data . . . . . . . . . . . . . . . . . . . . . . . . . 102

A.6 Contact Surface Data . . . . . . . . . . . . . . . . . . . . . . 103

A.7 Boundary Condition Data . . . . . . . . . . . . . . . . . . . . 104

A.8 History Definition . . . . . . . . . . . . . . . . . . . . . . . . 104

A.9 Contact Interaction Data . . . . . . . . . . . . . . . . . . . . 105

A.10 Initial Condition Data . . . . . . . . . . . . . . . . . . . . . . 106

A.11 Output Request . . . . . . . . . . . . . . . . . . . . . . . . . . 106

B Stress-Strain-Curves 109

C Damage Criterion Ductile 113

D Damage Criterion Shear 117

E Damage Criterion MSFLD 121

F Tracking Approach 123

G Total Energy over Time Curve 125

Bibliography 131

List of Figures

2.1 Comparison of driven vehicle kilometres and casualty rate inthe United Kingdom, after [DOT07]. . . . . . . . . . . . . . . 4

2.2 Different approaches for improving road safety, after [Kra98]. 5

2.3 Subsections of passive safety. [Ada95] . . . . . . . . . . . . . 6

2.4 Weaker car hits stiffer truck. [Tan] . . . . . . . . . . . . . . . 8

2.5 Crash of two cars with a different stiffness. [ADA] . . . . . . 8

2.6 Deformation zones, after [Ada95]. . . . . . . . . . . . . . . . . 9

2.7 Failure performance of a beam under axial loading, after[Wal05]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.8 Distribution of types of collision according to their frequency,after [Ada95]. . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.9 Different types of car-to-car collisions, after [Kra98]. . . . . . 13

2.10 Frontal impact after ECE-R 94, after [Wal05]. . . . . . . . . . 14

2.11 Deformable barrier for frontal impact testing (ECE-R 94).[UNEb] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.12 Frontal impact after EuroNCAP. [NCAa] . . . . . . . . . . . 17

2.13 Evaluation after EuroNCAP. [ENC] . . . . . . . . . . . . . . 18

2.14 Smart ForTwo front crash. [NCAb] . . . . . . . . . . . . . . . 18

2.15 Testing record for the Smart ForTwo. [NCAb] . . . . . . . . . 19

2.16 ATZ-test settings top and side view. [AZT] . . . . . . . . . 20

3.1 Design junction between front side member and occupant cellinvolving three-axis forked beams. [Ans00] . . . . . . . . . . . 25

xiii

xiv LIST OF FIGURES

3.2 Bow-shaped design of the front side member and flow offorces. [Ans00] . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.3 Possible profile geometries for the front side members, after[Ada95]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3.4 Front side member deformation aids (crush initiators). [Ans00] 30

4.1 Visualisation of the forward difference scheme. [Dud08] . . . 32

4.2 Visualisation of the central difference method, after [Dud08]. 36

5.1 Geometry and finite element mesh. . . . . . . . . . . . . . . . 42

5.2 Cross section. . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

5.3 Side view. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

5.4 True stress-strain-curves for different plastic strain rates. . . . 46

5.5 Damage criterion ductile. . . . . . . . . . . . . . . . . . . . . 48

5.6 Damage criterion shear. . . . . . . . . . . . . . . . . . . . . . 49

5.7 Transformation of the forming limit curve from traditionalFLD representation (a) to MSFLD representation (b). Lineardeformation paths transform onto vertical paths. [ABAb] . . 50

5.8 Forming limited curve. . . . . . . . . . . . . . . . . . . . . . . 51

6.1 Flowchart for the analyses without considering failure. . . . . 54

6.2 Flowchart for the analyses including failure. . . . . . . . . . . 54

6.3 Mesh with mixed Quad- and triangular elements. . . . . . . . 55

6.4 Mesh with only Quad-elements. . . . . . . . . . . . . . . . . . 55

6.5 Displacement over time curves for different mesh sizes. . . . . 58

6.6 Unfiltered reaction force over time curve (2.50mm mesh). . . 59

6.7 Filtered reaction force over time curves with different cutofffrequencies (2.50mm mesh). . . . . . . . . . . . . . . . . . . . 60

6.8 Unfiltered and filtered reaction force over time curve with acutoff frequency of 300Hz (2.50mm mesh). . . . . . . . . . . 61

6.9 Filtered reaction force over time curves for different mesh sizes. 61

6.10 Deformed structure of a 10.00mm mesh. . . . . . . . . . . . . 62


LIST OF FIGURES xv




6.15 Building of the first fold with a mesh of 2.50mm-elements. . . 64

6.16 Displacement over time curves for 3, 5 and 9 SIMP (5.00mmmesh). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

6.17 Reaction force over time curves for 3, 5 and 9 SIMP (5.00mmmesh). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

6.18 Deformed structure of a 5.00mm mesh with 3 SIMP. . . . . . 68



6.21 Reaction force over time curves for 3, 5 and 9 SIMP (2.50mmmesh). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70



6.24 Displacement over time curves GP vs. SIMP (5.00 mm-mesh). 72

6.25 Reaction force over time curves GP vs. SIMP (5.00 mm-mesh). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

6.26 Displacement over time curves Quad vs. mixed (5.00mmmesh). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

6.27 Reaction force over time curves - Quad vs. mixed (5.00mmmesh). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

6.28 Simulation of a quasistatic (left) and a dynamic (right) crashof a double chambered extrusion (no failure). . . . . . . . . . 75

6.29 Deformation over time curves from a dynamic and a qua-sistatic computation (no failure). . . . . . . . . . . . . . . . . 76

6.30 Stress-strain-curves for different plastic strain rates in therange of small strains. . . . . . . . . . . . . . . . . . . . . . . 77

6.31 Stress-strain-curves in the rank of 0.90 1.60 for plasticstrain rates between 0 and 1. . . . . . . . . . . . . . . . . . . 78

6.32 Deformation over time curves from a dynamic computationwith all stress-strain-curves, a dynamic computation withstress-strain-curves for strain rates between 0 and 1 and aquasistatic computation (no failure). . . . . . . . . . . . . . . 78

xvi LIST OF FIGURES

6.33 Result of a computation on 1 CPU (2.50mm mesh). . . . . . 81

6.34 Result of a computation on 2 CPUs with domain level paral-lelisation (2.50mm mesh). . . . . . . . . . . . . . . . . . . . . 81

6.35 Displacement over time curves for 1 and 2 CPU (2.50mmmesh). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

6.36 Reaction force over time curves for 1 and 2 CPU (2.50mmmesh). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

6.37 Result of an experiment. [HHW04] . . . . . . . . . . . . . . . 83

6.38 Displacement over time curves for different mesh sizes. . . . . 85

6.39 Reaction force over time curves for different mesh sizes. . . . 85


6.41 Simulation of a quasistatic (left) and a dynamic (right) crashof a double chambered extrusion (failure included). . . . . . . 88

6.42 Quasistatic and dynamic compression tests. [HHW04] . . . . 88

6.43 Deformation over time curve from a dynamic and a qua-sistatic computation (failure included). . . . . . . . . . . . . . 89

6.44 Fracture with respect to the individual failure criteria for qua-sistatic and dynamic compression. . . . . . . . . . . . . . . . 91

6.45 Dynamic (upper) and quasistatic (lower) failure diagram forextrusion EN AW-7108 T6. [HHW04] . . . . . . . . . . . . . 92

F.1 Two-dimensional global contact search [ABAa]. . . . . . . . . 123

F.2 Two-dimensional local contact search [ABAa]. . . . . . . . . . 124

G.1 Total energy for a mesh of different sizes with only Quad-elements (Dynamic computation with 9 SIMP, failure excluded).126

G.2 Total energy for a mesh of different sizes with only Quad-elements (Dynamic computation with 9 SIMP, failure included).126

G.3 Energy components for a 2.00mm mm mesh (no failure). . . 127

G.4 Energy components for a 2.50mm mesh (no failure). . . . . . 128

G.5 Energy components for a 5.00mm mesh (no failure). . . . . . 128

G.6 Internal energy for different mesh sizes (no failure). . . . . . . 129

G.7 Kinetic energy for different mesh sizes (no failure). . . . . . . 129

List of Tables

6.1 Computation time for different mesh sizes without failure. . . 65

6.2 Computation time for a different number of integration points(5.00mm mesh). . . . . . . . . . . . . . . . . . . . . . . . . . 70

6.3 Computation time for a different numerical integration - GPvs. SIMP (5.00mm mesh). . . . . . . . . . . . . . . . . . . . . 73

6.4 Different approaches for refining the mesh (failure included). 84

B.1 Data for the stress-strain-curves for the respective plasic strainrate pl. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

C.1 Data for the ductile damage initiation criteria curves. . . . . 115

D.1 Data for the shear damage initiation criteria curves. . . . . . 119

E.1 Data for the MSFLD damage initiation criteria curve. . . . . 121

xvii

xviii LIST OF TABLES

Nomenclature

a acceleration ratio of principal strain rates inclination of the barrierB widthC damping matrixcd wave speedl incrementd strain incrementE Energy absorptionE elastic modulus strainpl equivalent plastic strain at fracturepl equivalent plastic strain rate strain rate stress triaxialityF force vectorF forceF vehiclefi field variablesH heightI vector of internal element forcesK stiffness matrixk stiffnessks material parameterl lengthm massM mass matrix friction coefficient Poissons ratio frequency integral criterion for damage initiationp pressureR rounding off

xix

xx NOMENCLATURE

densitys deformation path stress1 principal stress in 1-direction2 principal stress in 2-direction3 principal stress in 3-directioneq von Mises equivalent stressm hydrostatic stressy yield stresst time shear stress temperatures shear stress ratiou displacementu velocityu accelerationu acceleration vectoru velocity vectorU offsetu displacement vectorv velocityW width fraction of critical damping

Indices

crit criticalD damage criterion ductilee elementmajor majormax maximumminor minorMSFLD damage criterion MSFLDn at time nn+ 1 at time n+ 1S damage criterion shearstable stablet at time t

xxi

xxii INDICES

Abbreviations

AZT Allianz Zentrum fur TechnikCPU Central Processing UnitDMP Distributed Memory Parallel ProcessingDOF Degrees Of FreedomECE Economic Commission for EuropeEU European UnionFEM Finite Element MethodFFC Femur Force CriterionFLD Forming Limited DiagramFMVSS Federal Motor Vehicle Safety StandardsGP Gauss Point(s)HIC Head Injury CriteriaHPC Head Protection CriterionIIHS Insurance Institute for Highway SafetyMSFLD Muschenborn and Sonne Forming Limited DiagramNCAP New Car Assessment ProgramNHTSA National Highway Traffic Safety AdministrationNIC Neck Injury CriterionSIMP Integration points with Simpsons ruleSMP Shared Memory Parallel ProcessingTCC Thoracic Compression CriterionTCFC Tibia Compression Force CriterionTI Tibia IndexUS United StatesUSA United States of AmericaV*C Viscous Tolerance Criterion

xxiii

xxiv ABBREVIATIONS

Chapter 1

Introduction

The design and development of automobiles involves various aspects com-bining the expertise of engineers, designers, test centres and productionfacilities. Strict legislations and standards, especially the safety standards,dictate the design of the vehicles. This results in the design and designmethodologies being regularly updated. Aspects related to better designwhich improve passenger safety, especially the crashworthiness of an auto-mobile, have been of intense scrutinity in the recent years. This has led tothe design departments of automobile industries to employ novel method-ologies which help in cutting costs and more importantly time. Highly ex-pensive and time intensive experimental tests have given way to computersimulations using algorithms which would accurately represent the dynam-ics involved in such tests. Algorithms using finite elements are commonlyused in these commercial codes. It is very important therefore to un-derstand the intricacies of the way these codes work. This would help usdesign algorithms which are better suited for such commercial purposes thatare accurate (in representation of the dynamics) and also not time inten-sive, as time is money for large commercial establishments like automobileindustries. The present work is a small step forward in this direction.

1.1 Topic of the Masters Thesis

Commercial finite element programs offer an almost infinite number of vari-ations to settings designed to model realistic environments and situations,yet not all options are suited for the same things. In large companies, theyusually have standard protocols that describe how they are to setup pro-grams for any given simulation, for instance in terms of the kind of elementsand the size of the elements required for a specific task etc. Clearly, how-ever, these protocols are only guidelines for specific crash conditions, and

1

2 CHAPTER 1. INTRODUCTION

not valid for all crash computations. Generally, the user does not know themeans by which a particular set of recommendations has been generated -they are unaware of the analyses that lead to the respective protocols, andtypically wont have the time to find out. The aim of this work was to findout how sensitive present crash simulations are to changes made to singlecomputation parameters, like the element size, the meshing technique, theintegration method etc. This sensitivity analysis was performed on a verysimple model, of a so-called front side member which was crashed into a wall.This model represents the main component in terms of energy absorptionduring a crash, and is therefore very important to model correctly.

1.2 Structural Outline

Safety of road traffic is the primary topic of this dissertation. Anoutline relating to this, with attention to active and passive safety,is provided in Chapter 2 with the role of the front side members asmain safety components shown. Finally various testing procedures arepresented with focus on front crashes.

Chapter 3 concentrates on the structure of a car body. The mechanismof load transfer through the car, and kinetic energy transform (throughdeformation) until the vehicle stops is described.

The basics and some specifics of a non-linear finite element computa-tion related to crashes are shown in Chapter 4. The use of the explicittime integration method is justified and the differences with the im-plicit method explained. Additionally, explanation is given regardinghow a FEM-program like ABAQUS handles contact definitions.

Chapter 5 describes in detail the underlying computer simulation mod-el which is used as the basis for all further computations and changesmade in Chapter 6.

The main part of this dissertation can be found in Chapter 6, whereanalyses relating to how sensitive a computer simulation model in crashcomputation is, on certain changes of single parameters. It is differ-entiated between a computation including and one excluding failurecriteria, and gives descriptions of how the influence of parameters, likethe element size and the number of integration points, is analysed.

In Chapter 7 follows a summary and a conclusion of Chapter 6, as wellas describing what future work still has to be done.

Chapter 2

Safety of Road Traffic

2.1 History

The word automobile is derived from the Greek word for self, auto, andthe Latin word for moving, mobilis. An automobile, therefore, is a self-moving vehicle - rather than one that is moved by another vehicle or ananimal. The alternative title motor car (or just car) is also widely used,and implies a wheeled passenger vehicle that carries its own motor.

The question of who invented the first automobiles does not have a straight-forward answer, and is more a matter of opinion. The first self-propelledautomobiles were invented at some point during the 18th and early 19th cen-turies by various people, and had different kinds of engines, such as steamor internal combustion engines, the early forms of which were fuelled by amixture of hydrogen and oxygen. The invention of our present-day cars,however, began in 1885/86 with Karl Benzs patent for a three-wheeled ve-hicle with a gasoline engine. One year later, independently of Benz, GottliebDaimler and Wilhelm Maybach constructed a motor-driven vehicle, basedon a carriage, with a maximum speed of 16 km/h. This was followed in1888/89 by Siegfried Marcus, again independently, with the release of thefirst petrol driven four-stroke engine, displaying all of the key features of ourpresent-day cars [Wika].

The spread of cars on the roads was accompanied by increased traffic acci-dents, especially with the rise in vehicle speeds. Bridget Driscoll is known asthe first person to die in a traffic accident involving an automobile when, onAugust 17th 1896, she and her daughter crossed the grounds of the CrystalPalace in London [Wikb].

Already by the 1930s, death rates due to automobile crashes in the UnitedStates had surpassed 15.6 fatalities per 100 million vehicle miles, and contin-

3

4 CHAPTER 2. SAFETY OF ROAD TRAFFIC

ued to climb [BIR01]. It was time for the designers to find ways of makingtheir products safer.

Greater discussion of these safety precautions can be found in the subse-quent section, but its worth noting just how effective these safety measureswere. As displayed in Fig. 2.1, the casualty rate (number of accidents in-volving casualties) continuously decreased over the last 50 years despite thenumber of registered cars increasing over the same period (corresponding toan increase in the number of kilometres driven on the road).

Figure 2.1: Comparison of driven vehicle kilometres and casualty rate in theUnited Kingdom, after [DOT07].

2.2 Active and Passive Safety

There are different ways of making road traffic safer, cf. Fig. 2.2. One cangenerally distinguish two main categories which are active (primary) andpassive (secondary) safety. Active safety is concerned with accident preven-tion measures, i.e. safety instructions, traffic steering and driving assistancesystems, whereas passive safety deals with the reduction of accident sever-ity and the consequences of accidents. Passive safety systems include thedevelopment of safety belts, air bags, and the design of a cars structure tobe able to plastically deform, thus allowing the absorption of crash energywhile ensuring a sufficient survival space for the occupants.

2.2. ACTIVE AND PASSIVE SAFETY 5

Figure 2.2: Different approaches for improving road safety, after [Kra98].

While the focus of this work is on passive safety, it is important to mentionthat active safety measures have become and are becoming more and moreimportant. Whereas the possible options for further improvement of passivesafety systems have been exhausted, development of active safety still holdsgreat potential.

2.2.1 Passive Safety

Passive safety can be split into self and partner protection (Fig. 2.3), if oneconsiders that not only a cars own occupants may be injured, but also thosein another vehicle. Elements of passive self protection include, for example,the stiffness of the passenger compartment, a good energy-absorbing defor-mation zone, and the compliance of biomechanical limit values. Partnerprotection is mainly afforded through adjustment of the deformation char-acteristics of a vehicle to the safety requirements of other participants in theaccident, e.g. occupants of the other car, pedestrians or cyclists.


Figure 2.3: Subsections of passive safety. [Ada95]

2.3 Structural Concept of the Car Body

To mitigate injuries in car accidents, the structure of the car body has to bedesigned according to rules for crashworthiness. One of the most importantrequirements is that the car should have different deformation zones in thefront. The basic idea of this comes from Bela Barenyi who was awarded apatent in 1952 for his description of the decisive features of passive safety.He divided the car body into three sections, a rigid non-deforming passengercompartment in the middle and a front and rear crumple zone that are ableto absorb the impact energy by deformation during collision. Newer carsare also designed for side impacts, enabled by smaller deformation zones onboth sides as well.

2.4. COMPATIBILITY 7

Generally one can say that there are three basic requirements on the struc-ture of the car body:

sufficient rigidity of the passenger compartment,

sufficient deformation zone to transform the kinetic energy,

compatibility for other road users.

In the early stages of developing a new car, structural values, such as a limitfor the deformation of the engine mounts, are taken to evaluate the safetyquality of the new car. These values are used instead of biomechanical valuesmeasured on dummies, when simulations involving crash test dummies arenot yet possible. However, the structural values are generally chosen suchthat subsequent biomechanical values are kept within their limits.

2.4 Compatibility

Regarding compatibility, it is desirable to have cars that are able to absorbthe energy they contribute to the crash. Every car is tested for its responseto crashing against a rigid wall, and is constructed to absorb the energyreleased in that test. The energy released when a very stiff car crashesagainst the wall is much higher than for a car with lower stiffness. Herethe problem of compatibility arises. If a stiff car crashes not against a rigidwall, but against a weaker car, the weaker car experiences a greater releaseof energy than if it had hit against a rigid wall because the kinetic energyof the stiffer car is now dissipated not only by its own structure, but also bythe weaker front structure of the other car. Longer and softer deformationzones for vehicles with higher mass are therefore recommended to reducetheir overall stiffness. Weaker, generally smaller cars must be designed withgreater rigidity, cf. [EEV07]. In terms of compatibility, the stiffness of theengine mounts and the level of forces where they start to plastify is thusmost important. It is best if this level is the same for all vehicles on theroad.

To avoid severe accidents of the severity shown in Fig. 2.4 and 2.5 a littlemore has to be taken into account. It is important that the bumpers of bothcars and also the internal structures behind, like the front side members, area good match in terms of height. The height of the absorbing beams shouldbe the same for all vehicle variants with a close tolerance, such that theycan best absorb the energy. This is not always easy to achieve, as bestexemplified in a car-truck-crash. A truck, in particular, has to be carefullydesigned to accommodate these crashes with the bumper and the respectivebeams being very low compared to the total height of the vehicle.


Figure 2.4: Weaker car hits stiffertruck. [Tan]

Figure 2.5: Crash of two cars witha different stiffness. [ADA]

2.5 Deformation Zones

In current concepts for car bodies, the front longitudinal chassis beams arethe primary energy absorbing structures of a car, accounting for 60 70%of the total energy [Ada95]. Therefore engineers focus on these beams withrespect to safety when designing new car bodies.

To optimise the front structure of the car (including with regard to com-patibility), the part of the car in front of the passenger compartment (thesurvival space) is divided into 4 deformation zones (Fig. 2.6) depending onthe different crash-conditions, and the respective average deformations foreach situation (and therefore also the velocities that usually lead to thecrash). The four deformation zones are for:

Pedestrian protection: the car should be constructed in such a waythat pedestrians remain as unscathed as possible.

Protection at low velocities / urban crash: to maintain a structuresuch that the repair costs are kept low.

Partner protection / compatibility: to observe the protection criteriafor the occupants of the other car.

Self protection: to observe the protection criteria for the occupants ofthe principal car.

2.5.1 Pedestrian Safety and Urban Crash

To reduce the accident severity for pedestrians and cyclists, the geometryof the vehicles front structure comes into play. The effects on pedestriansduring accidents can be kept low by using broad bumpers, filled with energy

2.5. DEFORMATION ZONES 9

Figure 2.6: Deformation zones, after [Ada95].

absorbing foam material where the loads are not concentrated on just a singlepoint on the leg. Nevertheless, the deformations should not be excessive inorder to keep the cost of repair as low as possible. This is a difficult situation,where the goals are conflicting and compromises must be made. Pedestriansafety is therefore tested in various ways. To name a few, there is

a lower leg test,

a test for pelvis and thigh (upper leg test),

a test for head impact of a normal adult and a child.

Regarding the last test, it is recommended not to fix anything rigid justbeneath the bonnet and to keep at least 6 7 cm space between bonnet andengine components to make sure the bonnet can deform, and thus absorb theimpact energy. For further information on pedestrian safety refer to [MK06].

Urban crash testing is conducted according to the AZT-test (or Danner test)where the focus is on the repair costs. It is a test the insurance companies inparticular are interested in. Levels for physical damage insurance are basedon this test. For more on this see Section 2.6.3.3.

2.5.2 Self and Partner Protection

If a car crashes against a barrier, or even worse if two cars crash head-on,the possible relative velocities are extremely high, as are the requirements to


save the occupants. While the front comes to an abrupt halt during crash,the remainder of the vehicle is still undergoing high deceleration. Substantialcompression forces develop between the front and rear of the vehicle thathave to be absorbed by the structure.

Generally, hollow sections are used for the front longitudinal chassis beams.For those kinds of beams, two types of failure for axial loading exist: Thebending of the beam or the formation of a crumple zone.

In bending, the beam buckles just to one side without much deformationto the other parts. The energy absorption is only high at the beginning,until failure, at which point the load decreases considerably. So the energyabsorption is a mere E 2 kJ/kg for steel, refer Fig. 2.7 and [Ada95].

Figure 2.7: Failure performance of a beam under axial loading, after [Wal05].

The energy absorption is much better in the formation of a crumple zonethan in pure bending, making the former the more desirable failure mode.After energy transformation, lots of folds appear in the beam. The sameenergy can be absorbed in the regular crumple mode (that usually does notinclude bending) (E 10 12 kJ/kg for steel) as in the irregular crumplemode (E 2 12 kJ/kg for steel). The probability of absorbing up to12 kJ/kg is much higher in the formation of a regular crumple zone and thuscan be seen as the optimal failure mode. But usually one has a combinationof both, e.g. due to inhomogeneities like changes in the cross section. The

2.6. OVERVIEW OF EXISTING TESTS 11

aim is to achieve the crumple mode in the beginning and allow the beam tobend for larger deformations only.

The force level required for deformation is strongly influenced by the mate-rial of the beam, the thickness, the shape of the hollow section and hencethe cross-sectional area.

2.6 Overview of Existing Tests

Generally, all tests a car has to pass until it can be released are represen-tations of real accident situations in which the interaction of the occupantsand the car is measured. In addition to these interactions, some technicalmeasurements like the impermeability (and thus fire-resistance) of the tankafter a crash, or the displacement of the steering column after the crash areconsidered. There are quite a lot of combinations one can imagine. Hence,it is probably easy to see that there are many different tests even for theassessment of frontal impacts alone. Since the focus of this work is on thefront side members, only those tests relating frontal impact will be consid-ered further.

Two main categories of tests are differentiated. The ones that are obligatoryunder the law and the those that are optional, but more oriented to the usersinterests. See the explanations and differences in the example of the frontalimpact test in the following sections.

2.6.1 Frontal Impact Test

Frontal impacts, where a car crashes with a maximum inclination of 30,are the most frequent, accounting for 55% of all crashes. Thus, the maindeformation zone of a car has to be at the front, cf. Fig. 2.8.

Frontal impacts concern car-to-car crashes and car-to-barrier crashes, e.g.a crash against a tree or a bollard. As in Fig. 2.9 displayed, for car-to-carcrashes one further distinguishes between crashes where the car hits theother car frontally, on a side or in its rear, or whether the crash occursperpendicularly, with or without an offset, and whether they hit under acertain angle.

Severe frontal impacts occur when two cars with opposite driving directionscrash frontally into each other, because their relative velocity reaches a max-imum. This is further worsened if there is an offset, because then the wholeenergy has to be absorbed by a smaller part of the structure.

Due to national differences in road traffic and varying development trendsfor passive safety, legal standards for the main market areas differ worldwide.


Figure 2.8: Distribution of types of collision according to their frequency,after [Ada95].

In the context of the EU, the standards of all member countries were mergedinto a new standard, valid throughout Europe. Further regulations exist forthe USA, Australia, Canada and Japan, where the last three are gearedto those of Europe and the USA. To be able to sell a car in a country,the respective standards have to be fulfilled. It is advisable to look to theEuropean and US regulations for guidance, since they are the leading ones.The big advantage of these standardised tests is that all vehicles are testedunder the same conditions and thus test give comparative information.

2.6.2 Obligatory Tests after the Law

In the following the main aspects of the legal standards for Europe andfor the USA are named. That they are legal standards means they are


Figure 2.9: Different types of car-to-car collisions, after [Kra98].

mandatory under the law. To sell a car, or any other vehicle, these testsat least have to be passed, and the respective requirements fulfilled. Later,in Chapter 2.6.3, it will be shown that there are further voluntary tests,apart from the legal requirements and based on the users interests, wherethe requirements are a little bit higher.

2.6.2.1 Europe: ECE-R 94

The decisive test in the European norm, released by the Economic Commis-sion for Europe [UNEa], is the 40% offset impact test, named ECE-R 94[UNEb], where the car crashes against a deformable barrier which covers40% of the cars front side (Fig. 2.10). The barrier face is deformable to rep-resent the deformable nature of the cars. The main requirements of this testare related to values obtained from crash dummies. The values measured onthe dummies are compared to the biomechanical limit values. All settingsare exactly regulated to make the test as reproducible as possible. Specifiedin the regulation one can find forms for communication, the arrangementsof the approval mark, an instruction on how to determine the performancecriteria, everything that has to be looked for regarding the dummies (e.g.how to install them and how to adjust the restraint system), where to placethe points for the measurements, what has to be measured and how etc.The test procedure with all its settings is described in annex 3 of regula-tion no. 94 and the properties and conditions of the deformable barrier inannex 9. In the following, just the main characteristics are mentioned.

The test vehicle shall be a representative of its series production and innormal running order. Some components may be replaced by equivalent


Figure 2.10: Frontal impact after ECE-R 94, after [Wal05].

masses, as for example the tank is not filled with fuel but with water. Thetest is carried out with two Hybrid III-dummies, each of them on one of thefront seats. The doors shall be closed, not locked, and should remain closedduring the test. For a successful test, one criterion is that they have to beable to be opened afterwards to assist quick rescue. The vehicle shall overlapthe barrier face by 40%20mm. The speed of the vehicle at the moment ofimpact shall be 56 km/h with no tolerance downwards and 1 km/h upwards.

The barrier is divided into two parts, the main honeycomb block and thebumper element. The geometry can be determined from Fig. 2.11. Bothparts are made of the same kind of aluminium, but with a different structure,such that the density of the bumper element is higher than the density ofthe main honeycomb block, yielding a different crush strength. The wholeblock is fixed to a rigid wall, 200mm above the ground.

The front face of the deformable structure is perpendicular within 1 tothe direction of travel of the test vehicle (Fig. 2.10). [...] The orientation ofthe barrier is such that the first contact of the vehicle with the barrier is onthe steering-column side. Where there is a choice between carrying out thetest with a right-hand or left-hand drive vehicle, the test shall be carriedout with the less favourable hand of drive as determined by the TechnicalService responsible for the tests. ([UNEb] Annex 3, Sections 1.2 and 1.3)The whole barrier should not deform, such that the car is able to crashagainst the wall behind it. The wall does not represent anything in this testand would distort the results. But since the barriers were designed in themid 1990s and meanwhile the vehicles became much more rigid, this in notfulfilled anymore in most of the cases. Hence, there are activities to improvethe barrier design.


Figure 2.11: Deformable barrier for frontal impact testing (ECE-R 94).[UNEb]

2.6.2.2 USA: FMVSS 208

In the USA the regulations are formulated in the Federal Motor VehicleSafety Standards (FMVSS), provided by the National Highway Traffic SafetyAdministration (NHTSA) [NHT]. The decisive tests for frontal impact aregiven in the FMVSS 208. The tests in there differ considerably from theones in the European norm, cf. [NHT97]. The car here crashes into a rigidbarrier at any speed up to 48 km/h (30mph) and at any angle between per-pendicular and 30 to either side. But it is planned to increase the maximumspeed up to 56 km/h, similar to the European norm, but only for crashesperpendicular to the barrier, cf. [NHT]. As in the ECE-R 94, the main re-quirements of this test are related to values obtained from crash dummies two 50th percentile male Hybrid III-dummies, seated at the front of the car,and then compared to biomechanical limit values. But, while in the EU, thedummies must be belt restrained, in the USA the test has to also be passedwith unrestrained dummies. Thus the requirements for the occupant pro-tection systems, like air bags and restraint systems, are higher in the USA,since there they also have to protect the not-belted passenger. In the EUone concentrates more on the structural safety of the car. The FMVSS 208includes threshold criteria for the head (1,000 HIC), chest deceleration (60g),chest deflection (76mm) and femur (proximal) lower leg (10 kN), while theECE-R 94 includes additionally viscous criteria (V*C) and threshold criteriafor the neck, the knee, lower leg bending (tibia index), foot/ankle compres-sion and compartmental intrusion. In the European 40% offset impact test


a smaller area of the structure must manage the crash energy, while thedemand on the structure in the American full width frontal impact test isless, but in return the restraint system is put under particular strain (whilethe reverse is true in offsets).

Since this thesis is about crashworthiness and in particular about the energyabsorption of the front longitudinal chassis beams and their design, thedecisive test here will be the test after the European norm with 40% offset.

Apart from the aforementioned test at 48 km/h and the 50th percentilemale Hybrid II-dummies, the US-norm also foresees the same test with 5thpercentile adult female dummies at a speed between 32 and 40 km/h, andone at 48 km/h with the same 5th percentile adult female dummies butonly perpendicular to the barrier. A 40% offset test perpendicular to thebarrier is also part of the US standard, but with 5th percentile adult femaledummies and at a reduced speed of 40 km/h, cf. [NHT] and [CRA].

2.6.3 Consumer Tests

Apart from the legal standards, some other testing programmes have beenestablished. These tests, designated as the New Car Assessment Program(NCAP), are largely based on the users interests and should help the cus-tomer at making her/his decision regarding buying a new car. In countrieswhere they are used, they are based on the legal standards, but are evenmore stringent. If a vehicle wants to get a good evaluation, it has to fulfil(at least partially) these considerably higher requirements. To assert itselfon the world market, it is therefore important to fulfil these criteria. In theUSA they are called US-NCAP and in Europe, EuroNCAP. The EuropeanNCAP [ENC] was founded by a consortium of ten members (governmen-tal and non-governmental like motoring organizations). In both, US- andEuroNCAP, the tests are evaluated in stars (max. 5, which means safe).

2.6.3.1 EuroNCAP

As in the legal standards, there is more than one test to be passed for avehicle. In the EuroNCAP one can find (amongst other tests for frontalimpact) side impact, pole impact and pedestrian tests. In the following onlythe frontal impact test is described, which is again a test with 40% offset(Fig. 2.12).

In this test, the car crashes with a velocity of 64 km/h against a deformablebarrier; this is hence an even more severe test of the cars ability to en-sure sufficient survival space during an impact (without suffering passengercompartment intrusion) compared to the ECE-R 94. Contact between the


Figure 2.12: Frontal impact after EuroNCAP. [NCAa]

occupant and intruding parts of the passenger compartment is the maincause of serious and fatal injuries, for restrained adult car occupants. Thetest speed of 64 km/h represents a car to car collision with each car trav-elling at around 55 km/h. The difference in speed is due to the energyabsorbed by the deformable face. Accident research has shown that thisimpact speed covers a significant proportion of serious and fatal accidents.By preventing intrusion, the chances of the occupant impacting the carsinterior is minimised with space remaining for the restraint system to op-erate effectively. [NCAa] The EuroNCAP frontal impact test also requirestwo Hybrid III-dummies on the front seats, but additionally a P1/2- anda P3-child-dummy on the backseats strapped in by the respective restraintsystems for children. The dummies represent children of 18 months and3 years. The main requirements of this test are again related to valuesfrom dummies that are compared to the biomechanical limit values. Theresults are then summarised, as e.g. in Fig. 2.13 or in the Testing record ofthe Smart ForTwo, Fig. 2.15. The body regions are coloured correspondingto the result, while the scale ranges from good to poor, with three furthersubsections.

In addition to the values obtained from the dummies, the displacement ofthe steering column towards the drivers head is, for example, evaluated neg-atively, as well as any intrusion of the passenger compartment. The abilityto open the door after the crash influences the result, the existence and qual-ity of safety equipment like airbags and restraint systems, the protection ofchildren etc. And the test provides extra points for the availability of a seatbelt reminder, since a lot more people are heavily injured or die if they donot use a seat belt.

In Fig. 2.15, a testing report for the Smart ForTwo is shown, released in 2007.


Figure 2.13: Evaluation after EuroNCAP. [ENC]

Smart ForTwo This car belongs to the category supermini and it mightbe surprising that it received four out of five stars in EuroNCAPs AdultOccupant protection rating [NCAb]. But first of all, the Smart ForTwo hasno rear seats and consequently has not been assessed for child protection[NCAb]. And secondly, it is essential that no attempt is made to comparethe ratings between cars in different segments or mass groups. The frontalcrash test aims to measure the performance of the car impacting anothercar of similar mass. There is no capability to determine what would happenif cars of widely different masses impact each other, cf. Section 2.4. It isnot primarily the mass difference that has the effect, but the effect thatmass has on the structural stiffness combined with the relative height of thestructures from the ground.

Figure 2.14: Smart ForTwo front crash. [NCAb]


Figure 2.15: Testing record for the Smart ForTwo. [NCAb]


2.6.3.2 IIHS

In the US, they also have an optional test based on the users interests. Itis released by the Insurance Institute for Highway Safety (IIHS) [IIH] andis comparable to the EuroNCAP, explained in the previous chapter.

2.6.3.3 AZT-Test / Danner Test

The AZT test, also called the Danner test, is not an obligation accordingto the law but, in addition to the legal regulations for low and high veloc-ity tests, it is a supplementary test of a cars performance during accidentsthat cause average damage. The test was invented by the technical centreof the German insurance company Allianz and evaluates whether a car isrepair friendly, (i.e. consideration given to repair costs) while it does notevaluate values from dummies. The car should be easy to recondition afteran accident, for example via beating out or through partial replacements.The results are used by insurance companies to classify the car type regard-ing the levels of physical damage insurance for new car models. During thetest, the principal structures should remain undeformed, that means in re-turn that there are no plastic strains allowed. Particular elements, like theengine mounts already mentioned, are designed to reduce the deformations.

The settings of the test are illustrated in Fig. 2.16 and the main testingconditions listed below.

Figure 2.16: ATZ-test settings top and side view. [AZT]

The vehicle crashes with a velocity of 15 1 km/h onto a rigid barrier with40% offset (generally) on the drivers side. The barrier has inclination of = 10 and has to be considerably higher than the front of the car. Thecar should not be able to hit against the wall behind the barrier. Therehas to be a belted 50% male dummy in the drivers seat, the tank must be


fully filled, the vehicle has to be ready to drive and the battery connected.Additionally some measurements have to be carried out before and after thecrash, for example the length of the axis and the car body itself. Currently,there are activities to design additional repair tests to gather informationon the bumper matching problem.

2.6.4 Other Tests

Aside from the tests for frontal impact described above, there are variousfurther tests. Some for side impact, for rear impact, as well as so-called poleimpact tests for the side and front of a car. They simulate, for example,the collision of a vehicle against a bollard, a street light or a pillar in a carpark. Also, special rollover tests are developed and real car-to-car crashesfor the sake of compatibility checks. But there are still a lot more tests notdescribed here.

Chapter 3

The Structure of a Car Body

In his book, Anselm [Ans00] differentiates between two kinds of car bodies.A car body can either be a self-supporting body or a skeleton construction.The self-supporting body is generally a combination of pressings and steelsections, in other words shell constructions and structural elements. In askeleton construction, the body is mainly a steel carcass that gives basicstrength and all the other parts are welded, bolted, riveted or bonded tothe skeleton. This construction is slightly heavier, but offers more flexibilityin the external design, and makes it cheaper to repair and to change thedesign because there are no supporting elements involved. This design ismore popular for small to medium production volumes, especially sportscars and hand-built models.

3.1 The Main Structural Elements

3.1.1 Occupant Cell

As already described in Chapter 2, the occupant cell is designed as a survivalbox for the passengers and has to remain undeformed during a crash, whichmeans it has to be a strong, rigid box. Since this dissertation focuses on thefront end, only the main parts of the occupant cell are mentioned, withoutany further description. These are: the bulkhead, the front and rear seatsections, the side frames, and the side panels (as vertical elements), and thefloor assembly, the centre tunnel, the sills, and the roof (as the horizontalelements).

23

24 CHAPTER 3. THE STRUCTURE OF A CAR BODY

3.1.2 Front End

The front end is the most complicated part of a car with respect to the struc-tural elements and their respective functionalities. The different automotivemanufacturers follow various concepts for the structure of their cars and itis therefore hard to describe the general front end. However, one can saythat the front end is essentially built of two wheel-houses, the front top andbottom cross members, sometimes a motor cross member, sometimes upperside members, the fenders, the front hood, and the two front side members.

The wheel houses are the most complex elements of a cars front end, yetdespite their size they are very stiff due to their curved shape.

If the car has a cross member design and no other appropriate connectionsbetween the body structure, adjacent assemblies and engine, both sides ofthe upper cross members are welded to the wheel houses and the lowercross members are welded to the side members. The function of the crossmembers is to transfer the forces from one side of the vehicle to the other,such that the loads are about the same level on either side. This is especiallyimportant in a one sided crash impact, as tested in the 40% offset test, cf.Section 2.6.

The motor cross member/chassis underframe is a highly profiled sheet-metalsection that carries the engine and serves to make the structure of the frontend stronger, with more twisting stiffness, but is not part of every car. Someautomobile manufacturers prefer to mount the engine on an underframe.

Also the upper side members are not included in the structure of all manu-facturers cars. Cars produced in the Far East are especially likely to havethem. They are located below the upper fender strip and provide additionalbending strength, and absorb additional energy in a severe frontal collision,but they also increase the repair costs of a car.

The fenders play just a subordinate roll in the overall stability of the frontend. Their shape and mounting have to be designed such that the spacebetween them and the door is not immediately eliminated in a slight crash.The bumpers are attached to the lower front part of the fenders.

The largest pressing of a car is the front hood. The hood itself is veryunstable and has to be supported on all four sides by the hood frame, aspecially formed strengthening section. The main requirement of the hoodis that it has to yield during a collision with pedestrians, to keep the damageas low as possible, cf. Section 2.5.1.

The most important structural elements of a car body when speaking abouta crash, are definitely the front side members. Since they are the centralpart of this dissertation, their function is described separately in Section 3.3.

3.2. LOAD PATHS THROUGH THE CAR 25

3.1.3 Rear End

The rear of a car usually has a very simple design, compared to the otherparts. The rear ends of notchback cars comprise two side sections behindthe C-pillars, the trunk floor, the rear apron and the trunk lid. Hatchbackvehicles are generally built the same. The main difference is the trunk lid,which is a door design, and hinged on the roof. The two side members areoften conjoint with the trunk floor for mounting and supporting the rearbumper system. According to Anselm [Ans00] energy can be strategicallydissipated by strong profiled interior panels below the edge of the windowfrom the tail lamp to the C- or B-pillar. Panels around the rear wheel houseprovide mutual support to the front in a structure where longitudinal andcross members are combined. Strengtheners are often welded to the rearside member to ensure good deformation behaviour during a rear impact.

3.2 Load Paths through the Car

As this work concentrates on a front crash, the forces one is mainly interestedin lead longitudinally through the car. During a front crash, a huge masspushes from the back of the car. The released energy has to be absorbedby the two main energy-absorbing structures in the front of a car, the twofront side members.

Figure 3.1: Design junction between front side member and occupant cellinvolving three-axis forked beams. [Ans00]

To transmit the forces from the rear to the front of the car and vice versa,there has to be a continuous load path through the whole car. Usually thereare two paths, one on either side. All the load paths have to come togetherin the two front side members. Therefore they have to continue under the


floor of the vehicle with several transverse supports to the centre tunnel,the A-pillar and especially to the longitudinally stable structural zone ofthe sills. This can be achieved, for example, by a three-axis forked beamas depicted in Fig. 3.1. The solutions again differ between the automobilemanufacturers.

To have a continuous flow of forces, all junctions must be linked harmo-niously and any inconsistencies, like steps, bends, taperings, reinforcements,changes in thickness, cut-outs, drill holes and notches, are to be avoidedas far as possible, especially the ones introduced subsequently and in high-stress regions. They disrupt the moment of resistance and thus weaken thestructure. The incorporation of holes into simulation programmes is thusvery important. Introducing only one hole into a primary component like afront side member can completely change the energy dissipation behaviour.To join the members, most commonly spot welding is used. Although insome cases there are only a few welds needed, it is better to have more toget a smoother transition.

In an optimally designed vehicle, the impact forces introduced at singlepoints are transferred to other areas of the front structure, such that locallysevere deformations are prevented. This is very important in overlap tests,where the velocity is reduced only by a small part of the front structure.To protect the passengers, an intrusion of the front side members into thepassenger compartment has to be avoided by all means. The front sidemembers are thus strongly connected to the floor assembly. In such a waypenetration of the bulkhead can be avoided as far as possible.

3.3 Front Side Members

The front side members are the most important part of a car in terms ofenergy absorption in a front crash. In Anselm [Ans00] one can find severaldifferent references of how much energy is absorbed by the front side mem-bers, compared to the total crash energy. After Anselm, Betz/Laschetstate that they absorb at least 45% of the impact energy in the entire defor-mation zone by transformation to deformation energy, under FMVSS 208.On the other hand, Rauser/Grossmann are mentioned, who used a bal-ance of energy determined from a dual-mass model to reach the conclusionthat 79% of the kinetic energy in a 50 km/h frontal impact test is absorbedby the vehicle front end structure, 12% by the powertrain and 9% by thebulkhead. Within the front end structure, the energy absorption is furtherdistributed; 72% to the front side members, 22% to the wheelhouses and6% to the fenders. Finally Anselm refers to Piech/Behles, who describethat in a frontal collision, about 70% of the transformation of energy is as-

3.3. FRONT SIDE MEMBERS 27

sumed by the front side members over a deformation travel of up to 300mmbefore any other component comes into play. Therefore a designer primaryhas to pay attention to the front side members. The aim is to optimise theirdeformation behaviour. The total deformation space is limited to about50 60 cm and should be kept within these limits as far as possible, withregard to safety and repair costs.

Figure 3.2: Bow-shaped design of the front side member and flow of forces.[Ans00]

Optimising the front side members means first of all optimising the shape ofthe structure, and secondly the properties of the material used. To be able tobest convert the kinetic energy, they are usually straight with a continuouslyincreasing cross section, and thus moment of resistance, from the bumper tothe bulkhead. Tailored increasing material thickness additionally supportsthis effect as well as strengtheners and beads. Instead of straight front sidemembers, their external shape can also be single-offset, double-offset or bow-shaped (see Fig. 3.2), which is usually worse, since they favour bending. Forthe design of the front side members several shapes of cross sections areused. Some are displayed in Fig. 3.3.

In terms of material, a standard high strength steel of deep-drawing qualityis mostly used. Steel has a high level of plastic absorption of energy and foran acceptable price a high quality finish can be achieved. High strength steelhas higher energy absorption properties compared to normal steel and, due


Figure 3.3: Possible profile geometries for the front side members, after[Ada95].

to the higher strength, even a weight reduction is possible, which is goodfor the consumption behaviour. But using high strength steel also meansa decrease in stiffness due to the higher porosity, as well as a reduction offormability, weldability and corrosion resistance. Nevertheless, it is usedbecause the mass specific energy absorption increases with the elastic limitof the material. Other materials like aluminium, magnesium or plastic havea substantially lower specific weight, but bigger dimensions due to theirlower material strength. Using those materials is thus hardly a reductionof weight. It is, however, possible to build a whole profile at once withoutneeding any joints that disrupt the load paths. Especially for the front sidemembers this is a big advantage, since the way they deform is crucial andstrongly influenced by joints, in a negative way.

The optimisation process is an iterative process because there are at leasttwo main conflicting goals: on the one side one wants to find a structure thathas minimum weight in order to attain optimum utilisation of the material,but on the other side one simultaneously has to observe the boundaries formaximum stresses and displacements.

3.3.1 Evaluation of Energy-Absorbing Structures

In order to evaluate energy-absorbing structures, Anselm [Ans00] providesfour objectives:

3.3. FRONT SIDE MEMBERS 29

Deformation Characteristics This describes the conversion of energyby plastic deformation. Good deformation characteristics cause the severestpossible deformation to a limited part of the structure. For sheet metalstructures, that means a large number of tight folds are formed withoutbuckling of the entire structure. Closed cross sections should not open as aresult of edge stresses.

Mass-Specific Absorption of Energy This characterises the absorbedenergy with respect to the mass of the deformed structure. A good materialhas a high mass-specific absorption of energy.

Force-Travel Curve The integral value of force and travel represents theenergy absorption properties of the structure. The aim is to get a struc-ture that attains the highest possible value which remains constant for anaverage folding force. The basic presupposition for optimal consumption ofenergy would be a right-angled force-travel curve, which theoretically couldbe achieved by a structure that transforms energy constantly during thewhole deformation process.

Energy-Travel Curve This is a measure to estimate the deformationstiffness and is obtained by integration of the force-travel curve. The steeperthe curve rises, the stiffer the structure.

The length-specific energy absorption depends on the impact speed. Thehigher the speed, the more energy is absorbed along the same travel. Thus,different structures can only be compared for the same testing and respectivesimulation conditions.

3.3.2 Deformation of the Front Side Members

An optimised front structure has to absorb as much energy as possiblethrough controlled folding and buckling of the front section of the front sidemembers. Preferably, they should form regular foldings (Fig. 2.7) ratherthan a pure bending of the whole structure, where the energy absorptioncapability is not exploited. However, bending additional to crushing of thestructure to some degree is usually not avoided, e.g. due to non-axial impactforces. Vehicle structures are frequently a compromise of several require-ments and cannot be designed as ideal deforming bodies.

The goal is to design a structure which is able to absorb as much energy aspossible from the very beginning, that means immediately when the front


side member contacts the opposing structure. To support the specific de-formation behaviour of building regular folds, the front side member mustbe given a design element such that the folded buckle really commences atits beginning, a so-called crush initiator. This could be a preformed foldor crease, or can be achieved by means of adding a bolted or welded railextension with reduced panel thickness, see Fig. 3.4.

Figure 3.4: Front side member deformation aids (crush initiators). [Ans00]

Also, tapered sections in the front side-member cross-section along thelength, with constant panel thickness, act as crush initiators and shouldtherefore be avoided where the folding is not to be initiated. The individ-ual components must be optimally matched because all anomalies demon-strate effects on the deformation characteristics. Even the location of weldpoints, the metal thickness and the cross-sectional shape affect the foldingbehaviour.

The structure behind the front side members must be strong enough to resistthe bearing load and the average buckling force. Thus, the transition fromthe front side members to the bulkhead and floor area must be well planned.Round transitions are preferred to angular ones. A slight curvature in thefront side members towards outside takes account of conditions in a diagonalimpact. The front side members should be extended by means of additionalrail sections attached to the floor panel, to take up forces introduced intothe floor pan.

Chapter 4

Crash Computation usingFEM

As real crash tests can only be performed on a finished vehicle, and thus costa lot of money, and due to the increasing number of regulations and thus thenumber of tests required, computational methods in car designing have be-come more and more important. By using computer simulations things canbe optimised during their development already, revealing any weak pointsin the body at a very early stage. Although computational crash calcula-tions are not a substitution for real tests, they allow engineers to make validpredictions about the deformation behaviour of a structure, if they are welldefined. A computation with non-linear deformation characteristics can becarried out quasistatically or dynamically using the Finite Element Method(FEM)1, but the results must always be confirmed through testing. As a re-sult, one wishes to get data for the development of structural improvementswith selection of material thicknesses, strategically located strengtheners,beads and welding point positions.

Crash computation using FEM has some specialities which this chapter dealswith. However, the scope of this will be restricted to aspects that the au-thor considers important. These are the two ways of time integration inSection 4.1, the definition of contact in Section 4.2 and adaptive meshingwith respect to parallel computations in Section 4.3.

In this thesis all computations are done using the commercial programmeABAQUS (Version 6.6) and, to be more precise, only its explicit solver.The following explanations for how crash computations work using FEM-programmes are basically related to ABAQUS, and might be dealt withdifferently in other FEM-codes. The information given here is taken fromthe ABAQUS online documentation [ABAa].

1For information on FEM: [TB00], [OCZ00b], [OCZ00a], [Bat02]

31

32 CHAPTER 4. CRASH COMPUTATION USING FEM

4.1 Time Integration

Especially when solving nonlinear problems, the solution cannot be calcu-lated by solving a single system of equations, as in linear problems. Usuallyseveral iterations are needed to determine an acceptable solution for thenonlinear analysis. There are generally two ways of doing computations,the implicit way, which ABAQUS/standard uses to solve, and the explicitway, used in the ABAQUS/explicit solver. The main principles of bothstrategies will be explained in the following.

4.1.1 Implicit Time Integration

To solve nonlinear problems, ABAQUS/standard uses the Newton-Raphsonmethod, where the solution is found by applying the specified load grad-ually and incrementally working toward the final solution (following theload-displacement path). The simulation is broken into a number of loadincrements where the approximate equilibrium configuration is found at theend of each load increment. It is thus a combination of incremental anditerative procedures. The dynamic equilibrium equation at a certain timetn+1 (here exemplarily for a one-dimensional single degree of freedom singlemass oscillator without damping)

mun+1 + kun+1 = Fn+1 (4.1)

is integrated at the end of the time step (tn+tn). By applying a forwarddifference scheme (implicit time integration), the following relations are ob-tained and visualised in Fig. 4.1.

t

u(t)

t

u(t)

t

u(t)

tn1 tn tn+1

tn

un

un+1

unun+1

unun+1

Figure 4.1: Visualisation of the forward difference scheme. [Dud08]

4.1. TIME INTEGRATION 33

un+1 =un+1 un

t, (4.2)

un+1 =un+1 un

t, (4.3)

un+1 =Fn+1 + mt2 (2un un1)

mt2

+ k. (4.4)

In (4.1) to (4.4), m is the mass, k the stiffness, F the external force, uthe displacement, u the velocity and u the acceleration at time tn+1. Thisscheme works independently of the time step size and is thus unconditionallystable. But as one can see in (4.4), the stiffness matrix has to be invertedand therefore the scheme requires many cost intensive iterations.

4.1.2 Explicit Time Integration

4.1.2.1 Characteristics and Advantages of Explicit Time Integra-tion

While ABAQUS/standard with an iterative time integration scheme mustiterate to determine the solution to a nonlinear problem, ABAQUS/explicitdetermines the solution to the dynamic equilibrium equation

Mu+Cu+Ku = F. (4.5)

M : nodal mass matrixC : nodal damping matrixK : nodal stiffness matrixu : nodal displacementu : nodal velocityu : nodal accelerationF : external forces

I = Cu+Ku : internal element forces

without iterating by explicitly advancing the kinematic state from the pre-vious increment, see later on in Section 4.1.2.2. Since there is no necessaryinversion of the stiffness matrix, the global set of equations does not haveto be solved in each increment and even highly nonlinear procedures can becalculated easily with the explicit method.

But unlike the implicit scheme, the explicit finite element method is onlyconditionally stable, that means that numerical stability is only guaranteed if


the time increments are smaller than the time a material wave needs to crossthe smallest element in the finite element mesh. The increment size dependssolely on the highest natural frequency of the model and is independent ofthe type and duration of loading, see later on in Section 4.1.2.3.

Thus, one can say that the smaller the elements used, the smaller the timeincrements have to be and the more time is needed for the whole compu-tation. The computational cost is proportional to the number of elementsand roughly inversely proportional to the smallest element dimension. Byrefining the mesh in all three directions (in 3D) by a factor of two, the com-putational costs thus increase by a factor of 2 2 2 due to the increase ofthe number of elements and by a factor of 2 as a result of the decrease inthe smallest element dimension, which increases the stable time increment(cf. Section 4.1.2.3). This means an increase of the computational costs by afactor of 24 = 16. Disk space and memory requirements are proportional tothe number of elements with no dependence on element dimensions. There-fore, by refining the mesh by a factor of two in 3D, disk space and memoryrequirements increase by a factor of 23 = 8.

But even though the time increments in the explicit method are smaller andmore timesteps are needed, the computation is more efficient as the standardimplicit solution method. Due to the immensely increasing stiffness matricesof large models (about 1.5 million elements in current models), the explicitmethod shows great cost savings as the model size increases, compared tothe implicit one, as long as the mesh is relatively uniform. It uses less diskspace and memory [ABAa].

The explicit dynamics method was originally developed to analyse high-speed dynamic events, such as the crash problem at hand, where many smallincrements are required to obtain a high-resolution solution. As rapidlyas the load is applied, the structure has to deform. Accurate tracking ofstress waves through the metal sheet is important for capturing the dynamicresponse. Since stress waves are related to the highest frequencies of thesystem, obtaining an accurate solution requires many small time increments.

By using the explicit method, also contact conditions are formulated moreeasily because this method can readily analyse problems involving complexcontact interaction between many independent bodies. Using an implicitscheme, contact cannot be easily controlled, cf. Section 4.2.

4.1.2.2 Central Difference Method

In the explicit solver, the central difference method is used to integrate theequations of motion explicitly through time, using the kinematic conditionsat one increment to calculate the kinematic conditions at the next increment.

4.1. TIME INTEGRATION 35

That means the accelerations calculated at time t are used to advance thevelocity solution to time t + t/2 and the displacement solution to timet+t, as described in the following, cf. Fig. 4.2.

At the beginning of the increment the programme solves for dynamic equi-librium, which means solving

Mu = F I (4.6)

for the nodal acceleration u at the beginning of the current increment (timet). One then gets for the acceleration at time t:

ut=M1 (F I)

t. (4.7)

This equation is easy to compute, since the explicit procedure always usesa diagonal mass matrix (lumped mass approach). The acceleration of anynode is determined completely by its mass and the net force acting on it.There are no equations to solve simultaneously. The accelerations are in-tegrated through time using the central difference method, which calcu-lates the change in velocity assuming that the acceleration is constant. Thechange in velocity is added to the velocity from the middle of the previousincrement to determine the velocities at the middle of the current increment:

ut+t

2= u

tt

2+

tt+t

+tt

2u(t). (4.8)

The velocities are integrated through time and added to the displacementsat the beginning of the increment to determine the displacements at the endof the increment:

ut+t

= ut+t

t+t

ut+t

2(4.9)

Since the method integrates constant accelerations exactly, the elementsshould be quite small, such that the accelerations within an increment arenearly constant. The element stresses and consequently the internal forcesare determined by applying material constitutive relationships on the deter-mined element strains. Besides the effect for the contact algorithm, most ofthe computational expense lays here.

1. Compute the element strain increments (d) from the strain rate (),

2. Compute the stresses () from constitutive equations

t+t = f(t,d), (4.10)

3. Assemble nodal internal forces, I(t+t).

The term explicit refers to the fact that the state at the end of the in-crement is based solely on the displacements, velocities and accelerations atthe beginning of the increment.


t

u(t)

t

u(t)

t

u(t)

tt t t + t

t

t

ut

ut+t

utt/2

ut+t/2

utt

ut

Figure 4.2: Visualisation of the central difference method, after [Dud08].

4.1.2.3 Definition of the Stability Limit

The stability limit dictates the maximum time increment. For computa-tional efficiency it is worth to choose a time increment as close as possibleto the stability limit, but without exceeding it. It is defined in terms of thehighest frequency in the system, max, by the expression [ABAa]

tstable =2

max

(1 + 2

)(4.11)

where is the fraction of critical damping in the mode with the highestfrequency. According to [ABAa], it can be shown that the highest elementfrequency determined on an element-by-element basis is always higher thanthe frequency in the assembled finite element model. Due to the minor com-plexibility, it is thus more computationally feasible to calculate the stabilitylimit based on an element-by-element estimate, where it can be defined us-ing the element length (Le) and the wave speed (cd) as a property of a linearelastic material with a Poissons ratio of zero:

tstable =Le

cd, (4.12)

cd =

E

. (4.13)

Thus, if one knows the length of the shortest element and the wave speedof the material, one can estimate the stability limit, which is smaller theshorter the element and the stiffer the material, and larger the higher themass density.

In nonlinear problems (with large deformations and/or nonlinear materialresponse), the highest frequency of the model changes continuously and con-sequently also the stability limit. ABAQUS/explicit has two strategies for

4.2. CONTACT DEFINITION 37

time incrementation control: fully automatic time incrementation, wherethe code accounts for changes in the stability limit and fixed time incremen-tation, where the fixed time increment size is either determined by the initialelement-by-element stability estimate or directly by the user. While usingthe latter, the user has to check if the result is reasonable or not, whereasthe former works adaptive and is calculated by the following:

An analysis always starts by using the element-by-element estimation meth-od (described above, where the time increment is always smaller than thetrue stability limit based upon the maximum frequency of the entire model)and may switch to the global estimation method under certain circum-stances. The latter is an adaptive algorithm that determines and contin-uously updates the estimate for the maximum frequency using the currentdilatational wave speed. This will usually allow time increments that exceedthe element-by-element values.

Mass Scaling to Control Time Incrementation The stability limit isinfluenced by the mass density, as can be seen clearly in (4.12) and (4.13).Therefore scaling the mass density is sometimes used to increase the effi-ciency of an analysis, e.g. if one has very small elements and thus needs verysmall time increments, one can compensate that by simply increasing themass density. By doing that on only a few elements, which lay in certainregions complex to discretise and thus with small elements, or elements witha poor shape, the effect on the overall dynamic behaviour of the model maybe negligible. However, one has to be careful when employing mass scaling.

4.2 Contact Definition

In a computation where the deformations are large and two parts are likelyor even meant to hit each other, contact has to be defined wherever this canhappen during the process of deformation. The programme therefore has tobe able to detect automatically if two surfaces are contacting each other, andwhenever they do it has to apply the previously defined contact constraintsaccordingly. Similarly, it has to detect when two surfaces separate andremove the contact constraints.

First of all, contact surfaces have to be created from the faces of the un-derlying elements. They can either be defined single-sided or double-sided,depending on which side of the element forms the contact or if both sidesdo. In ABAQUS, the general contact algorithm (Section 4.2.1) and self-contact in the contact pair algorithm enforce contact on both sides of allshell, membrane, surface and rigid surface facets, even if they are definedsingle-sided.


The interaction between contacting surfaces consists of two components, onenormal to the surfaces and one tangential, where the tangential componentrepresents the relative motion of the surfaces and frictional shear stresses.Regarding the contact normal to the surfaces, the programme checks if thereis a certain distance between the two surfaces, the so-called clearance. If theclearance is positive, there is no contact and the pressure automatically iszero. The contact constraint is just applied, when the clearance is zero.There is then no limit of contact pressure. The dramatic change in contactpressure that occurs when a contact condition changes from open (positiveclearance) to closed (clearance equal to zero) makes it difficult for theimplicit method to complete contact simulations due to the huge amount ofiterations, which is not true for the explicit method.

When surfaces are in contact, they usually transmit also shear forces acrosstheir interface. To simulate this, Coulomb friction is a simple common modelthat uses a coefficient of friction . The tangential motion is then zero untilthe surface traction reaches a critical shear stress value crit, which dependsalso on the normal contact pressure p:

crit = p. (4.14)

Tie constraints can be used to tie two surfaces together such that the nodeson the surfaces have the same motion on either side. This means thatthe translational and optionally the rotational degrees of freedom are con-strained. For general contact information see e.g. [Wri06].

4.2.1 Definition of Contact in ABAQUS/explicit

ABAQUS/explicit provides two different algorithms for contact simulations,the general (automatic) contact algorithm and the contact pair algorithm.The general (automatic) contact algorithm allows very simple definitionswith very few restrictions on the types of surfaces that are involved and theinteractions are typically defined by specifying self-contact as a default.

The contact pair algorithm has more restrictions on the types of surfacesinvolved and often requires more careful definition of contact, but it alsoallows for some additional interaction behaviours. All contact pair interac-tions are defined by specifying each of the individual surface pairs that caninteract with each other.

Constraint Enforcement Method In ABAQUS/explicit, there are twoso-called constraint enforcement methods, the kinematic contact formulationand the penalty contact method. The latter searches for node-into-face pene-trations and edge-into-edge penetrations and is enforced by general contact.

4.3. ADAPTIVE MESHING 39

Equal and opposite contact forces with magnitudes equal to the penaltystiffness times the penetration distance are applied to the master and slavenodes at the penetration points. The penalty stiffness is chosen automati-cally by the programme and is dependent on the stiffness of the underlyingelement.The kinematic contact formulation searches for surface-to-surface contact.It uses a predictor/corrector method, which means, that it is first assumedthat contact does not occur and that if there is an overclosure at the end ofan increment, it will be corrected by modifying the acceleration.

Contact Evaluation In the pure master-slave approach one of the sur-faces is the master and the other one the slave. When they come into contact,the penetrations are detected and the respective contact constraints are ap-plied. This approach will resist only penetrations of slave nodes into masterfacets, penetrations vice versa may remain undetected.The balanced master-slave contact applies the pure master-slave approachtwice, reversing the surfaces on the second pass and can thus resist penetra-tions of either case.For the contact pair algorithm ABAQUS/explicit chooses automatically amaster-slave approach based on the nature of the two surfaces involved andthe constraint enforcement method used (kinematic or penalty). The generalcontact algorithm however uses balanced master-slave weighting wheneverpossible, while for node-based surfaces pure master-slave weighting is used.

Appendix F provides an explanation of the algorithm ABAQUS uses fortracking the motions of the contact surfaces in the case of a contact pairalgorithm. The general contact algorithm uses a more sophisticated trackingapproach that does not require user control and was thus not explained there.

4.3 Adaptive Meshing

Adaptive meshing is not used in crash computation. The main problemlies in the parallelisation of the computations