Computer aided fatigue design.

YAZDANPANAH, Amir.

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YAZDANPANAH, Amir. (1990). Computer aided fatigue design. Doctoral, Sheffield Hallam University (United Kingdom)..

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COMPUTER AIDED FATIGUE DESIGN

by

AMIR YAZDANPANAH B.Sc, M.Tech

A thesis submitted in partial fulfilment of the requirements of the COUNCIL FOR NATIONAL ACADEMIC AWARDS for the degree of

DOCTOR OF PHILOSOPHY

Sponsoring Establishment: Sheffield City Polytechnic,Sheffield, SI 1WB.

Collaborating Establishment: nCode International Limited,230 Woodbourn Road, Sheffield, S9 30Q.

May 1990

(Ao-cbu 1*5') \> <* ./ J>

0 SlTlttT

TO MY WIFE AND FRIEND,

CHRISTINE,

THANK YOU FOR YOUR PATIENCE AND UNDERSTANDING.

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ACKNOWLEDGEMENTS

The author wishes to express his gratitude to Mr D E Eaton, Mr G Cockerham, Dr K Morton, and Dr L Lack for their helpful supervision during the course of this project. Thanks are also expressed to Dr S R Bradbury and other research assistants for their constructive suggestions and comments.

The technical assistance offered by Mr R Teasdale and his staff was much appreciated and in particular the author wishes to thank Messrs J Stanley, K Wright, D Allen, R Sidebottom and R Wilkinson for their valued contribution at various stages of this work. Finally, my gratitude to members of staff at nCode International Limited for technical assistance offered.

(ii)

DECLARATION

The author declares that no part of this work has been submitted in support of another degree or qualification to this or any other establisHment- The author further declares that he has not been a registered candidate or enrolled student for another award of CNAA or other academic or professional institution during the course of the research programme

A Yazdanpanah

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NOMENCLATURE

A = Area

b = Fatigue strength exponent

c = Fatigue ductility exponent

b = Fatigue strength in bending

Ci = t = Fatigue strength in twisting

E = Modulus of elasticity

f = Functional relationship

F = Force

G = Modulus of rigidity

Kt = Theoretical elastic concentration factor

K<j = True Stress Concentration factor

Ke = True Strain Concentration factor

K' = Cyclic Strength coefficient

Nf = Cycles to failure

n' = Cyclic strain hardening

AS = Nominal Stress range

cjyt = Yield strength

Oeq = equivalent stress

A a = Stress at notch root

o f ' = Fatigue strength coeficient

Gi, G 2 , G3 = Principal Strains

Ae = Nominal strain

ea = AJE = Axial strain amplitude 2

Ge = Elastic strain

ep = Plastic strain

G t = Total strain

G f ' = Fatigue ductility coefficient

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Tensile strain normal to the plane of maximum shear.• • • ayBiaxial strain ratio.-, —7 Ae

Poisson's ratio

Axial stress amplitude

(73 = Principle stresses

Maximum shear strain

Shear stress amplitude on plane of maximum range of shear stress

Normal Stress amplitude on plane of maximum range of shear stress

Density

The elastic strain energy per unit due volume to the nominal remote stress

The strain energy per unit volume due to local stress and strain at the notch root.

ABSTRACTCOMPUTER AIDED FATIGUE DESIGN

A Yazdanpanah B.Sc, M.Tech

Today's competitive market requires engineers to produce reliable light weight products at low cost. This can be achieved by more effective use of computer aided engineering tools during early stages of the design process.

A research programme has been undertaken to investigate the data requirements of integrating commercially available software packages (finite element analysis and fatigue life evaluation) to evaluate the integrity and durability of engineering components at the conceptual design stage.

A real engineering component, in the form of a steering arm, supplied by a European truck manufacturer was used as a basis for the investigation. This is a typical vehicle component, in which, under service loading conditions, a multiaxial state of stress occurs.A geometric model of the component was created using the Prime "MEDUSA" software suite. The model was used to locate the boundary co-ordinates necessary for the development of a PAFEC Finite Element model. By imposing the conditions experienced during the service, the critical areas of the component were identified by analysing the F.E. model and a detailed description of the elastic stress/strain fields were also established. These were incorporated in an energy density approach and Neuber's uniaxial analysis to predict total local elastic/plastic strains at these critical- locations. These were compared with strain gauge measurements. The calculated results were used to plot a num b e r of l o a d / l o c a l s t r a i n c a l i b r a t i o n c u r v e s f o r the development of a load history, suitable for experimental fatigue life assessment.Fatigue crack initiation tests were performed on the steering arm using a computer controlled DARTEC multiaxial fatigue testing machine. Fatigue life assessment based on full service loading was carried out using a software package based on the critical location approach. A comparison of computerised, experimental and actual test circuit fatigue lives has been made.The work enabled a specification to be produced for the integration of the two items of software. This i n t e g r a t e d software was developed by third parties and used to produce a computerised life map of the steering arm.

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CONTENTS PAGE

ACKNOWLEDGEMENTS iiDECLARATION iiiNOMENCLATURE ivABSTRACT viCONTENTS viiINDEX TO FIGURES xiCHAPTER 1 - INTRODUCTION1.1 The Engineering Design Process 11.1.1 Background 11.1.2 Design Philosophy 21.1.3 Marketing Stage 4

1.1.4 Product Specification 41.1.5 Conceptual Design 51.1.6 Detailed Design 6

1.1.7 Application Of Computers In The Design Process 71.2 Computer Aided Engineering 91.3 Historical Perspective of Fatigue 111.4 Scope Of The Present Work 151.5 Principal Objectives Of Research Programmes 17 CHAPTER 2 - FATIGUE LIFE EVALUATION TECHNIQUES2.1 Introduction 232.2\ Neuber1s Rule 242.3 ) The Cyclic Stress/Strain Curve 27

.2.4 ) Methods Of determining The Cyclic Stress/Strain Curve 302.4.1 Multiple Step Tests 302.4.2 Incremental Step Tests 30^T5\ Analysis Of Strain-Life Curve 312.6/ Extracting Hysteresis Loops (Cycle Counting) 34

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CONTENTS (contd.)2.7 Energy Density Approach For Elastic/Plastic

Stress/Strain Calculation At the Notch Root2.8 Multiaxial Fatigue2.8.1 Principle of Static Yield Criteria to Fatigue2.9 Critical Location Approach CHAPTER 3 - STEERING ARM DESCRIPTION3.1 Introduction

3.2 Steering Arm3.2.1 Function Of A Steering Arm System3.3 Chemical And Mechanical Properties3.4 Micro-Structure Examination3.5 Manufacturing Processes

3.6 Test Track Trails3.7 Durability Assessment3.8 DiscussionCHAPTER 4 - COMPUTER BASED ANALYSIS OF STEERING ARM4.1 Introduction

4.2.4 FAMbuild4.3 Two and Three Dimensional Geometric Modelling4.4 Finite Element Analysis4.4.1 Component Geometry and Material Properties

4.4.2 Development Of The Finite Element'Model4.5 Results and Discussion4.6 Conclusions

PAGE

36384144

5960 61 61 62646566 68

93949596 .97 98 98 101 101 102 105 110

4.2 \Software Summary4.2.1 MEDUSA

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CHAPTER 5 - STATIC STRAIN MEASUREMENT OF THE STEERING ARM5.1 Introduction 1265.2 Test Equipment 1265.3 Experimental Rigs 1295.4 Strain Measurements 1305.4. 1 Strain Gauge Specification 1305.4. 2 Static Loading Results 1305.5. Conclusions 134

CHAPTER 6 - COMPUTER BASED FATIGUE LIFE CALCULATIONS6.1 Aims And Objectives 143

6.2 Software Summary 1456.3 Measured Strain-Time History 1466.4 MaterialX 146

6.5 yFatigue Reduction Factor 147v_x6.6 Fatigue Life Evaluation 1476.6. 1 FATIMAS Fatigue Life Assessment:

Measured strain-time Service History 147

6.6. 2 Fatigue Life Assessment:Load calibrated measured strain-time Service History 148

6.7 Conclusion 151CHAPTER 7 - FATIGUE TESTING OF THE STEERING ARM7.1 Introduction .1677.2 Test Equipment 167

7.3 Fatigue Testing 167

7.3. 1 Crack Detection Methods 1687.3. 2 Fatigue Crack Initiation Tests 171

7.4 Visual Examination Of The Fracture'Surface 172

7.5 Fractrography Investigation 173

7.6 Microstructure 174

7.7 Discussion 174

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CHAPTER 8 - INTEGRATED F.E. AND FATIGUE COMPUTATIONS8.1 New Software Structure 1948.2 Steering Arm Fatigue Predictions 1958.3 Discussion 1978.4 Conclusions 198 CHAPTER 9 - DISCUSSION9.1 Introduction 2099.2 Computer Based Modelling and Analysis 2119.3 Theoretical and Experimental Life Evaluation 215

CHAPTER 10 - CONCLUSIONS AND SUGGESTIONS FOR FUTURE WORK10.1 Computer Based Analysis 21810.2 Practical Applicability of the Technique 22010.4 Scope for Future Work 222REFERENCES 224

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INDEX TO FIGURES PAGECHAPTER 11.1 French's Model Of The Design Process 201.2 Archer's Model Of The Design Process 211.3 Pugh And Smith's Model Of The Design Process 22

CHAPTER 22.1 Variation Of Stress Concentration Factor

And Strain Concentration Factor As StressIncreases 47

2.2 Solving The Neuber Equation 48

2.3 Monotonic And Cyclic Stress/strain Curve 492.4 Stable Stress/Strain Hysteresis Loop 502.5 Strain Control Programmes For Obtaining An

Approximate Cyclic Stress/Strain Curve FromOne Specimen 51

2.6 Strain-Life Curves Showing Total ElasticAnd Plastic Strain Components 52

2.7 Rainflow Cycle Counting 532.8 Example Of Rainflow Cycle Counting Method 542.9 A Load Versus Time History Repeatedly

Applied To A Notched Component And TheResulting Notch Strain Response 55

2.10 Mohr's Circle Of Strain 562.11 Case A And Case B System Of Crack Extension 572.12 A Typical r Plot 58CHAPTER 33.1 The Steering Arm 703.2 Steering Arm Dimensional Details 713.3 The exploded View Of The Steering System 723.4 Unetched Micro-Structure Showing The Inclusions 763.5 Etched Micro-Structure Showing Bainite In A

Matrix Of Martensite 773.6 The Spectra Of Inclusion ^lot 78

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3.7 Time Temperature Transformation Curve 7 93.8 Manufacturer's Test Track Surfaces 803.9 Recorded Stubaxle Strain-Time Service History 813.10 Cyclic Stress/Strain Curve (SAE 1046 V) 823.11 Strain/Life Curve (SAE 1046 V) 833.12 STW/Life Curve (SAE 1046 V) 843.13 Cyclic Stress/Strain Curve (41 Cr S4) 853.14 Strain/Life Curve (41 Cr S4) 863.15 STW/Life Curve (41 Cr S4) 873.16 Cyclic Stress/Strain Curve (41 Cr 4V) 883.17 Strain/Life Curve (41 Cr 4V) 893.18 STW/Life Curve (41 Cr 4V) 903.19 Stubaxle Cycle Distribution 913.20 Stubaxle Damage Distribution 92CHAPTER 44.1 Three Dimensional Geometric Model Of

The Steering Arm 111

4.2 Shaded Image Of The Steering Arm 1124.3 Element Types 1134.4 A Mesh Used For Three Dimensional Finite

Element Analysis Of The Full Component 1144.5 Stress Contours Of The Full Component 1154.6 A Mesh Used For Three Dimensional Analysis

Of The Critical Part Of The Component 116

4.7 Streiss Contours Of The Critical Part Of The Component 1174.8 Example Of Solving Neuber's Equation 1234.9 Monotonic Estimated Load/Notch

Root Strain Calibration Curves 1244.10 Cyclic Estimated Load/Notch

Root Strain Calibration Curves 125

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CHAPTER 55.1 Dartec Fatigue Testing Machine Showing The Swivel

Joints, Rig And Component In Position 1355.2 Exploded View Of The Rig 1365.3 Location Of Post-Yield Strain Gauges 1375.4 Monotonic, Measured And Estimated Load/Notch

Root Strain Calibration Curves 1415.5 Comparison Of Monotonic, Predicted And

Measured Strain 142

CHAPTER 6

6.1 Washboard Strain-Time Service History 1536.2 Fatigue Life Assessment 1576.3 Hysteresis Loops 158

6.4 Cycle Distribution For Washboard History 1596.5 Damage Distribution For Washboard History 1606.6 Load Versus Life Comparison Of The FE Predicted

Fatigue Lives 1636.7 Load Versus Life Comparison Of The FATIMAS Measured

History, and FE Predicted Fatigue Lives 166

CHAPTER 7

7.1 Washboard Strain-Time Service History 1787.2 Washboard Load-time Service History 1797.3 Load Versus Life Comparison Of The Experimental

And FATIMAS Predicted Fatigue Lives 1827.4 Comparison Of Experimental And FATIMAS Predicted

Fatigue Lives 1837.5 The Fracture Surface Of The Component 1847.6 The Surface Immediately Surrounding The

Initiation Point 1857.7 Crack Propagation Region 186

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7.8 The Transition Area Between Slow Crack GrowthAnd Ductile Shear Failure 187

7.9 An Area Of Ductile Shear Failure 188

7.10 An Area Of Ductile Fracture, Showing MixedFracture Modes 189

7.11 An Area Of Ductile Fracture, ShowingNon-Metallic Inclusions 190

7.12 Final Brittle Fracture, Showing Two ModesOf Fracture (a) Intergranular (b) Cleavage 191

7.13 Brittle Fracture, Showing IntergranularAnd Cleavage Fracture 192

7.14 Brittle Fracture Region, Final CatastrophicFailure 193

CHAPTER 8

8.1 An Overview Of The FALCON Structure 2008.2. Fatigue Life Contours For The Steering Arm (Maximum

Principal Stress Method) 201

8.3 Fatigue Life Contours For The Steering Arm(Tresca Method) 202

8.4 Fatigue Life Contours For The Steering Arm(von Mises Method) > 203

8.5 Fatigue Life Contours For The Steering Arm(oxx Method) 204

8.6 Comparison Of The Experimental FALCON And FATIMASPredicted Fatigue Lives 207

8.7 The Flow Chart Showing An Overview Of The RoutesTaken To Assess The FAtigue Life Of The Steering Arm 208

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CHAPTER 1INTRODUCTION1.1 The Engineering Design Process

1.1.1 BackgroundDesign engineers in many industries today are expected to produce reliable products of light weight and low cost. This can be achieved by more effective use of computer aided engineering tools during the design process.[1, 1]*. However, an understanding of the design processes is necessary before computers can be used to support them. Understanding these processes is the first and probably one of the most important steps in the development of an integrated computer aided design and durability assessment package. Such insights certainly make the designer more aware of the advantages and pitfalls of advanced and sophisticated computer software packages.

The designer must consider a whole variety of events and circumstances before attempting to use c o m p u t e r s to enhance the process. Presently, computer systems assist in

the development of geometric modelling and can be linked to finite element software for load analysis. This produces elastic stress fields and guides thedesigner in his endeavours and quite often fatigue life assessment is necessary using separate soft w a r e or physical prototype.

.* Numbers refer to references given at the end of this text.

1

This chapter briefly describes the different stages of the d e s i g n p r o c e s s and i d e n t i f i e s the areas w h e r e an integrated CAD system might be successfully used. A brief historical development of fatigue life evaluation methods is also presented for completeness.

.1.2 Design Philosophy

It is now widely accepted that a systematic approach to problem solving is needed, if a high pr o p o r t i o n of problems are to be solved in the best way [8].

In the past most designers' approach to problem solving has been intuitive rather than systematic. When they have exercised their art, native wit has been relied upon to produce a design and they would possibly find it difficult to explain how the design evolved [9].

The designer must implement a set of specific objectives for investigating the needs and circumstances of the design activity, and synthesising these design objectives into an optimum solution. The failure to -consider all aspects of the design in a systematic way may possibly lead to a workable solution, however, the designer will have little justification of the design solution. There are many structured design strategies available to the designer the following being typical [10-12] (see figures

1.1 to 1.3):-

2

i) French procedureii) Archer procedureiii) Pugh and Smith procedure

Any systematic strategy may be selected during the design activity. The decision as to which strategy or tactic to use will depend upon the industry and the circumstances of the problem.

The following factors should be considered irrespective of approach:- market needs, specification, conceptual design, detail design, manufacture, and sales. The above phases

are applicable to any area of design be it construction, industrial product, or consumer product. It must be appreciated that design processes are highly interactive and iterative [10, 13].

Two further inputs are required to enable the design

processes to work, these being technology and techniques.

Technological and other relevant information are dependent upon the industry and the product area in w h i c h the designer is working. The informational inputs are the 'life blood' of design. This is an are a w h i c h is continuously changing and expanding through new material development and methods of storage and retrieval.

The traditional techniques of designers are creativity, evaluation, costing, analysis, sketching, scale drawing,

3

perspectives, models and the like. These techniques are used to manipulate the information inputs to a suitable form which then can be integrated into the design process.

1.1.3 Marketing Stage

Marketing can be defined as directing all the activities

of an organisation (men, machine, material, money and building) towards satisfying the potential need of consumer. The ultimate objective being to pr o d u c e a competitive, cost effective product that fits a market or creates a market of its own [10]. To achieve this an organisation must consider the following factors

"population, technology, consumer taste and fashion, politics, income, and competition", although changes in need reflect changes in one or more of these factors. The aim of the market research activity is to clarify the design objectives and to identify the course of actions that are capable of bringing about a fully definitive product specification.

1.1.4 Product Specification

The starting point for any design is, or should be a fully definitive product specification. This is formulated in conjunction and as a result of the information obtained in the marketing phase. This should be a clear document outlining all the design objectives and c o n s t r a i n t s related to the product attributes and performance.

4

1.1.5 Conceptual Design

The conceptual stage of any design should be concerned with synthesis, which Collins Dictionary defines as: "combination, composition, putting together, building up of s e p a r a t e e l e ments, e s p e c i a l l y of c o n c e p t i o n or propositions or facts into a connected whole, especially a theory or system" [87]

From the above definition it is clear that creative tactics are used in the conceptual (synthesis) stage of the design process and are for the purpose of generating functional solutions to the problem stated. Most designers are involved in the creative process in their search for the optimum solution to a design problem.

Conceptual design is about identifying possible solutions to a design problem within the scope of the design s p e c i f i c a t i o n but w i t h o u t n e c e s s a r i l y a n y d e t a i l commitment to individual component shapes, sizes or m a t e r i a l s . M a n y e m i n e n t d e s i g n e r s b e l i e v e t h a t a systematic approach helps to generate many alternative c o n c e p t s w h i c h then n e e d to be e v a l u a t e d t h r o u g h comparison with the requirements of the specification.

Computers can be used in a limited fashion to explore alternatives but only in circumstances where the solution has fairly tight technical boundaries. If a wide range of alternative solutions are possible and therefore need to

5

be explored, then computer aided draughting and design can be useful in the early stages of evaluation for techniques of geometric acceptability. Rapid determination through CAD of volumes, areas or enclosing envelopes are all helpful in eliminating unsuccessful concepts. If technical issues are not resolved it may be necessary to carry forward several concepts or at the technical evaluation stage, good concepts fail, therefore we have to start

again [13].

1.1.6 Detailed Design

Upon completion of the concept design, the detail design activity begins. At this stage the commitment to the development is very high, although no hardware has yet

been produced.

The conceptual and detailed design activities are highly interactive processes. The level of interaction is dependent upon the simplicity or complexity, nature and type of p r o d u c t w h i c h is b e i n g d e s i g n e d . The simplicity/complexity are directly related to the number of elements which an artefact contains, the ultimate in simplicity being only one component.

This is the last phase, in which all the essential detail drawings and analytical procedures are decided. In this p h a s e the u l t i m a t e o b j e c t i v e is or s h o u l d be the production of a product which contains the minimum number

6

of c o m p o n e n t s , h e nce m i n i m u m c o m p l e x i t y - m a x i m u m simplicity. Additionally the reliability is built into each component through the understanding of service loads, materials and stress distributions. Finite element analysis tends to be used when component geometry is established to a large extent and provides opportunities for detail analysis and redesign.

Linking C.A.D, finite element analysis and fatigue life p r e d i c t i o n g i v e s an o p p o r t u n i t y for e v a l u a t i o n of

alternative concepts some way into the detail design phase and therefore reduces the time spent in the development

and testing of prototypes.

1.1.7 Application Of Computers In The Design Process

Now that "the design activities have been explored it is necessary to examine the applicability or otherwise of computer software packages at e.txcV\ stage of design.

During the market research phase the computers may be used to store the information on the existing product range, level of competition, etc. This information can then be a n a l y s e d m a n u a l l y or u s i n g a p p r o p r i a t e c o m p u t e r techniques.

The application of computers in the specification phase of the design activity is again limited to the compilation of information. The decision, whether or not to use computers

7

d e p e n d s on the j u s t i f i c a t i o n of the time and cost involved.

The application of computers in the conceptual and detail stages of the design activity is dependent upon the industry and the type of product being designed.

There exist numerous separate computer software packages (e.g. computer aided draughting, finite element analysis and fatigue life evaluation etc.) which can be employed successfully to define the shape and assess the integrity and durability of components very quickly and accurately. Therefore, computers are used successfully as part of the

analytical tools of the designer.

The introduction of computers already has improved the efficiency of the design process. CAD has improved the quality of detailing and reduced the occurrence of errors. F i n i t e E l e m e n t A n a l y s i s techniques have b e e n u s e d successfully to assess the integrity of the components and hence reduce the static testing time. In the past these computer software packages have been used individually.

The t r a n s f e r and e x c h a n g e of i n f o r m a t i o n f r o m one a p p l i c a t i o n to a n o t h e r was o f t e n t e d i o u s if n o t ; .feasible. With ever increasing use of computer solid modellers for design of engineering components the natural progression has been to generate finite element meshes automatically so that the solid modelling and analysis processes are integrated. This avoids the tedious and

8

error-prone manual transfer of data, hence saving both time and money [6,7],

The next logical step is or should be the integration of finite element output data with fatigue life analysis so f t ware. This e n a b l e s the d e s i g n e r to a s s e s s the integrity and durability of the components in the design stage before any commitment to prototype manufacture and testing has been made.

1.2 Computer Aided Engineering

In many engineering situations components are subjected to variable amplitude multiaxial stresses under service loading conditions. The engineer often uses traditional theories from strength of materials to analyse and stress the load bearing components under such complex loading conditions. However, because of the limitations of the theoretical methods and techniques used, the above procedure almost always requires the manufacture and • testing of prototype components. Therefore, a m ajor proportion of engineering time is used in the building and testing of prototypes. To shorten the development cycle time and minimise the associated costs it is necessary to reduce the number of prototypes produced for testing. Consequently, the initial prototype should be close to the

final product. The manufacturers have an urgent need for a reliable method to assess the fatigue life of such components at the pre-prototype design stage. Computer

9

aided engineering methods offer possible techniques [1, 2].

The overall aim of this project is to evaluate the engineering requirements of combining computer based geometric modelling, finite element analysis and fatigue

life prediction software packages. A system of this type c o u l d a l l o w e n g i n e e r s to p r o c e e d from c o n c e p t to manufacture at the CAE workstation reducing the need for expensive and time consuming prototype build and test programmes.

The three areas of computer aided engineering mentioned previously are well established as separate entities. At the p r e s e n t tim e c o m m e r c i a l l y a v a i l a b l e li n k s are established between the first two processes. However, as yet no effective link exists between finite element analysis and computerised fatigue life assessment. The manual transfer and exchange of information from finite element to fatigue life assessment systems is often tedious and time consuming, if feasible. Indeed, the precise form that the finite element analysis should take to produce data relevant for fatigue life analysis is not clear. Therefore, computerised fatigue life prediction

methods are primarily used during the development stage as they rely on a prototype being available to give strain or stress histories. Once these stress and strain histories are known, alternative methods of predicting fatigue life are p o s s i b l e i.e. c r i t i c a l l o c a t i o n [ 3 ] , f r a c t u r e

10

mechanics[4], S-N curves[5]. Each method is complicated by

multiaxial loading and random loading conditions. For this work the critical location approach will be used, because it is extensively used in the ground vehicle industry and also can be incorporated into a computer program.

The next step in this overall process is the integration of finite element analysis and fatigue life assessment to assess the durability of engineering components at the design stage.

If successful, this approach could significantly reduce the need for prototype testing but at the same time ensure high component reliability.

1.3 Historical Perspective of Faticrue

As e a r l y as the 1840's, m a n y r e s e a r c h e r s w e r e investigating the behaviour and properties of engineering materials undergoing fatigue failure. In the 1850's August Wohler [14] performed many laboratory fatigue tests under repeated stresses. He showed from stress versus life (S-N) diagrams how fatigue life decreases with higher stress amplitudes and that below a certain stress amplitude the test specimens' did not fracture. Thus Wohler introduced the concept of the S-N diagram and the fatigue limit. He pointed out that for fatigue the range of stresses is more important than the maximum stress. Wohler's (S-N) curve

is still widely jused today as one of the m e thods of quantifying fatigue resistance. During the 1 8 7 0 's and

11

1890's Gerber [15] investigated the influence of the mean stress, and Goodman [16] proposed a simplified theory concerning mean stress. Another notable contributor of this p e r i o d was B a s q u i n [17] w h o i n t r o d u c e d the exponential relationship between stress and fatigue.

The next important step . was the work by Bairstow [18, 19]

at the National Physical Laboratory. His 1909 paper contains the earliest published hysteresis loops. This work indicates the phenomenon of materials undergoing cyclic softening. He also demonstrated that "the maximum width of any loop measured parallel to the axis of extension added to the elastic extension of the specimen is the total change of length in each cycle". In the 1920's Gough [20] and associates performed studies of the fatigue limit on bending and torsion and found that the ratio of the fatigue limit in torsion to that of bending v a r i e d wit h m a t e r i a l . In 1 9 2 9 / 1 9 3 0 H a i g h [21] investigated the difference in the response of high tensile strength steel and mild steel to fatigue when notches are present. He used the concept of notch strain analysis and s e l f - s t r e s s e s . During the 1930's an i m p o r t a n t p r a c t i c a l a d v a n c e was a c h i e v e d by the introduction of shot-peening in the automobile industry. Almen [22, 23] correctly explained the s p e c t a c u l a r

improvements by compressive stresses produced in the surface layers of peened parts and promoted the use of peening and other processes that produce beneficial self stresses.

12

In 1937 Neuber [24] introduced stress gradient effects at notches and the elementary block concept, which consider that the average stress over a small volume at the root of the notch is more important than the peak stress at the notch. N e u b e r 's Rule is now an essential part of most modern computer based methods of fatigue life predictions. In the same period the development of the bonded wire resistance strain gauge by Ruge and De Forest at MIT and S i m m o n s and C l a r k at the C a l i f o r n i a I n s t i t u t e of Technology revolutionised the technique of service load measurements. In 1945 Miner [25] formulated a linear

cumulative fatigue damage criterion suggested by Palmgren in 1924 [26]. This linear damage criterion is now recognised as the Palmgren Miner Law. It has been used extensively in fatigue life calculations involving random load histories.

In the 1950's Gassner [27] recognised the complex nature of service loading. To overcome the pitfalls of constant amplitude testing he suggested the variable-loading test be carried out for both ground vehicles and air craft. He proposed the use of block programming, tuhere the service data are analysed and broken down into blocks of loading to be applied sequentially.

Major contributions to the subject of fatigue in the

1950's included the introduction of closed-loop electo- hydraulic test systems, which allowed better simulation of

13

load h i s t o r i e s on s p e c i m e n s , c o m p o n e n t s and t otal mechanical systems. Electron microscopy revealed new horizons to a better understanding of fatigue mechanisms. Irwin [28] introduced stress intensity factor, Ki which has been accepted as the basis of linear elastic fracture mechanics (LEFM) and of fatigue crack growth predictions. Low cycle strain- controlled fatigue behaviour became

prominent with the Manson-Coffin[29, 30] relationshipbetween plastic strain amplitude and fatigue life. These ideas are the basis for current local strain fatigue analysis.

Many multiaxial fatigue life prediction theories have been proposed by many eminent researchers. However, as yet no universally acceptable method exists. The traditional approach to multiaxial fatigue life evaluation has been based on the extension of the static yield criteria to fatigue [53, 64]. This is used to reduce the multiaxial component of stress or strain to a single equivalent p a r a m e t e r , w h i c h can then be a n a l y s e d u s i n g the conventional techniques developed. More recently, it has become clear that single parameter description of fracture is inadequate, but two parameters are required for more accurate fatigue analysis. Among the leaders in this school of thought are Brown and Miller [42]. The theory is based on critical plane approaches, which postulate that cracks initiate and grow on certain planes and that the strain normal to those planes assist in the fatigue crack growth process.

14

With the development of finite element techniques by the aerospace industry in the 1950's and 60's stress analysis of complex structures was made possible. Prior to this all components had to be analysed by extremely complex and often tedious techniques. Indeed, some methods became so complex that they were impossible to solve. Empirical data

and past experience were often the most useful tools at the engineer's disposal and as a consequence, large factors of safety were incorporated resulting in large and over weight components.

The availability of low cost, high performance computers

and associated fatigue software packages, together with advancement in load measurement and analysis method can n o w s i g n i f i c a n t l y aid the e n g i n e e r and e n a b l e the development of efficient, effective and economic products. Application of these tools to component design can also reduce the need for expensive prototype 'build and test' programmes [31].

1.4 Scope Of The Present Work

Major advances have been made during the last 150 years in the development of analytical procedures to assess structural damage resulting from repetitive loadings. However, failures due to fatigue still occur in many areas of engineering with disastrous consequences in terms of both human life and cost. It is for this reason that the

15

analytical procedures used during the design stage are supported with full scale prototype build and test programmes. There are two weaknesses in this approach. First of all,.once the most suitable concept is selected, the detail design and analysis procedures are followed. In this phase, quite often the static load analysis is carried out and peak stresses are limited to fatigue s t r e n g t h of the m a t e r i a l but are not t o t a l l y representative of the service environment. Secondly, upon completion of the above procedures, prototype build and test begins. This is used to identify durability weaknesses in a given prototype. Obviously this process of build and test takes place very late in the design stage. Any limitations in the design analysis lead to repetition of the above procedures. This makes the process of design time consuming and prohibitively expensive [1, 2].

The p r e s e n t i n v e s t i g a t i o n into the i n t e g r a t i o n of geometric modelling, finite element analysis and fatigue life p r e d i c t i o n s o f t w a r e is b e i n g c a r r i e d out in association with nCode International Limited, suppliers of the FATIMAS [32] software which uses the critical location approach to estimate fatigue lives from a service strain history. Other software packages used are geometric modelling software (MEDUSA) [33] and finite element analysis software (PAFEC) [34, 35]. The above software has all the necessary capabilities to support the project. It

should be pointed out that already a link exists between MEDUSA and PAFEC, ie FEGS software[36] which will be used and evaluated as a minor element of the project.

16

Although the project concentrates on providing a link between PAFEC and FATIMAS, it is intended that any final conclusions will be applicable to other finite element and fatigue life prediction packages.

In this programme of work, the actual component used for evaluating the procedures developed was a steering arm of a 32 ton track supplied by a European manufacturer. This was evaluated for a real service load h i s t o r y supplied by the manufacturer, which had been recorded during the prototype testing of the vehicle driven on

mixed test road surfaces at their test track. Material data was also supplied.

.5 Principal Objectives Of Research Programmes

The principal objectives of the work pro g r a m m e are therefore

To use a CAD software package to create a two and three dimensional geometric model of the steering arm, which will be used to select the boundary co­ordinates for development of a finite element niesh.

To use a finite element package to develop a model and to identify the critical stress points in the s t e e r i n g arm t o g e t h e r w i t h the e l a s t i c s t r e s s / s t r a i n data.

i)

ii)

17

iii) To use the local elastic stresses and strains generated in (ii), together with both the energy density approach [37] and Neuber's uniaxial equation [38], to give the total elastic/plastic strains at the critical points. Other inputs r e q u i r e d for the a n a l y s i s are the m a t e r i a l properties, an appropriate geometric stress concentration factor, Kt, and service loading history. The analysis will include biaxial loading.

iv) To use strain gauge measurements under staticloads to monitor the total elastic/plastic strains at these critical areas in the component in order to examine the validity of the application of the analysis outlined above (iii).

v) To use the total elastic/plastic strains obtainedin (iii) to develop load/strain c a l i b r a t i o n curves for the component. These can be used to create a load history, suitable for experimental fatigue life analysis.

vi) To experimentally monitor fatigue life measurementof the steering arm using a load controlled DARTEC computer controlled servo hydraulic multiaxial testing machine.

18

v i i )

v i i i )

ix)

To use computerised fatigue life software FATIMAS

to predict the fatigue life of the steering arm under service loading conditions.

To compare the experimental, computerised and actual test track fatigue lives to examine the validity of the technique proposed.

To p r o p o s e the data r e q u i r e m e n t s for the i n t e g r a t i o n of the fin i t e e l e m e n t e l a s t i c stress/strain output data file with that of fatigue life software package to produce a life map of the component.

To critically evaluate the proposed procedures.

19\

iE

Need

Selectedschemes

Workingdrawings,etc.

Conceptualdesign

Analysis of problem

Detailing

Embodiment of schemes

Fig. 1.1 French's model of the Design Process(H).

20

Brief

Training

+

Solution

Programming

iData CollectionI

Analysis

ISynthesis

iDevelopment

ICommunication

Experience

Fig. 1.2 Archer's Model of the Design Process CSV

21

DESIGN CORE BOUNDED BY PRODUCT SPECIFICATION

TECHNOLOGY TECHNIQUE

ACTIVITYTOTAL

MARKET< MARKET ANALYSISMATERIALS

SPECIFICATION s FORMULATIONELEMENTS OF

SPECIFICATIONi P E C I F I C A T J O I

SYNTHESISCONTROLCONCEPTUAL DESIGN EQUATES TO SPEC

CONCEPT

o < DECISION MAKINGinUJMECHANISMS

DETAIL

< STRESS ANALYSISPATENTS

QUALITY RELIABILITY > COSTING

DESIGN IN BALANCE WITH SPECIFICATION

MANUFACTURE

SPECIFIC ENG INFOR > MANUFACTURE

SELL

ORGANISEDPLANNED

Fig. 1.3 Pugh and Smith’s Model of the Design Process(12.^15).

CHAPTER 2FATIGUE LIFE EVALUATION TECHNIQUE2.1 Introduction

It is generally accepted that fatigue analysis based upon a knowledge of strain in a component is more logical than one based upon stress, since strain is the phenomenon deemed more appropriate for modelling the plasticity which the component undergoes at the site of failure [39],

The local stress/strain method places emphasis on the local cyclic stresses and strains at the root of the notch where failure originates. Normally local values are

derived from nominal values, by applying Neuber's rule [24] as determined by Topper, Wetzel, and Morrow [38, 39], and the cyclic properties of the material are used instead of the monotonic values. Multiaxiality causes complications and one approach is to reduce the complex stresses to a single equivalent parameter [53, 64].

The critical location method has been established as realistic for predicting the durability of engineering components. This approach is finding wide-spread use by many manufacturing companies [40, 41], in particular the automotive industry.

Alternative methods of multiaxial fatigue evaluation have been based on critical plane approaches as proposed by Brown and Miller [42]. These theories are based on crack initiation and growth on specific geometric planes. One advantage suggested foj^ this theory is the opportunity for

physical interpretation of fatigue damage accumulation. However, this approach is insufficiently developed to deal with non-proportional loading or accumulation of damage under random out-of-phase biaxial histories. Furthermore, the guidelines to deal with stress concentration factors, stress gradients etc, are not available. Thus it's usefulness in the automotive field is at present very limited.

2.2 Neuberfs Rule

The fatigue behaviour in a notched component can be predicted on the basis of known behaviour of a simple

smooth specimen. The basis of the prediction is Neuber's rule [24], which takes into account the possibility of non-linear deformations at the root of the notch. Neuber developed a mathematical expression of the stress and strain concentration at a notch root.

£Kt = (Ko. Ke ) - 2.1

Where:-

Kt = Theoretical elastic concentration factor.JCd = True stress concentration factor.Ke = True strain concentration factor.

Equation 2.1 is exact when the notch root remains elastic. In this case, any concentration of stress is accompanied by the same c o n c e n t r a t i o n of strain, w h i c h c a n be calculated using Hookas law.

24

Thus K o = Ke and from equation 2.1 Ko = K t as shown in figure 2.1. The validity of N e u b e r 's expression is not necessarily obvious when yielding takes place at the notch root. However, it suggests that as K o decreases, K e

increases in non-linear deformation, so their product could be constant.

For fatigue application equation 2.1 is usually altered by replacing Kt with Kf and defining K o and Ke as the ratio of the ranges of stress and strain which result in:-

Aa A sK f = ( — . — ) - 2.2

A S A e

Where:-act = Stress range at notch root AS = Nominal stress range a g = Strain range at notch root Ae = Nominal strain range Kf = Fatigue concentration factor

Equation 2.2 may be transposed giving

% £Kf (A s. Ae) = ( A ct. a s ) - 2.3

25

All terms on the left side are determinable for each reversal from the load history and cyclic stress-strain curves, and all terms on the right side represent the local stress/strain behaviour of the material at the notch root.

If the nominal conditions away from the notch are elastic then:-

A SAe = --- - 2.4

. E

Giving:-

i’Kf . AS = (Act. A g .E) - 2.5

*

The r ight h a n d side of the a b o v e e q u a t i o n is a determinable constant for each half-cycle of load. The equation is of the form, X.Y = C, which is a rectangular hyperbola [39, 43].

For simulations of the material at the notch root, the smooth specimen must be strained until the product of the stress and the strain equal the constant C, where C = (Kf.AS)2/E as shown in figure 2.2.

26

2.3 The Cyclic Stress-Strain Curve

The cyclic stress/strain curve which provides a measure of the steady-state cyclic deformation r e s istance of a material can be different from the monotonic stress/strain curve. The cyclic stress/strain curve, is the locus of tips of the stable hysteresis loops from several companion tests at different completely reversed constant strain amplitudes [43]. Such a steady-state stress-amplitude strain-amplitude curve can be compared directly with the monotonic stress/strain curve. Cyclically induced changes in d e f o r m a t i o n r e s i s t a n c e then b e c o m e i m m e d i a t e l y apparent. If the cyclic stress/strain curve is above the monotonic curve the material is said to cyclically harden; if the cyclic curve is below the monotonic curve the material is said to cyclically soften [44].

Cyclic stress/strain properties are determined by testing smooth polished specimens under axial cyclic strain control. The cyclic stress/strain curve is defined as the locus of tips of stable "true stress/strain hysteresis loops" obtained from companion test specimens. A typical stable hysteresis loop with a cyclic stress/strain curve drawn through the loop tips is shown in figure 2.3.

As shown in figure 2.4 the height of the loop from tip-to- tip is defined as the stress range (Act). For completely reversed testing one half of the-stress range is generally equal to the- stress amplitude. While one half of the width from tip-to-tip is defined as the strain amplitude

( A 6 T /2). The plastic strain amplitude is f ound by

27

subtracting the elastic strain amplitude (Ae4 /2 ) from the total strain amplitude.

A Gp A GT

2 2

For elastic conditions:

a se A ct = — - 2.72 2E

Where;

E = modulus of elasticity

Then:A Gp A 6T A <j = - - 2.82 2 2E

The relation between cyclic stress and plastic strain can be described mathematically by a power function similar to that used for the monotonic curve [44, 45].

A ct A Gp n 1— = k' ( ) - 2 . 92 2

A G.2.6

28

w h e r e :A a— = Sta b l e S t r e s s A m p l i t u d e

2

A e P = S t a b l e p l a s t i c s t r a i n a m p l i t u d e2

n' = Cyclic strain hardening exponent

k' = Cyclic strength coefficient.

The value of n' is found to be between 0.05 and 0.30 and usually close to 0.15 for most metals regardless of their initial condition [44, 45].

In many field test conditions it is desirable to convert measured strains to the corresponding stresses in order to estimate fatigue life. Equation 2.8 can be rewritten

A g t A a A e p = — + - 2.102 2E 2

Equation 2.9 may be rearranged givingA e P A a 1 / n 1

= ( — ) - 2.11 2k'

Substituting equation 2.11 into equation 2.10 yields an equation relating cyclic stress amplitude in terms of the p r e v i o u s l y d e f i n e d p r o p e r t i e s and the m o d u l u s of elasticity.

Aet • Act Ao 1/n1 -— = — + (— ) - 2.12 2 2E 2k'

29

2.4 Methods of Determining the Cyclic Stress/Strain Curve

2.4.1 Multiple Step Tests

In 1910 Bairstow [46] and the later Dugdale [47] showed that the hysteresis loop rapidly adjusts to a stable steady state following sudden changes in cyclic strain amplitude. This makes it possible to obtain several points on the cyclic stress/strain curve from a single specimen by cycling at different strain amplitudes. Such a program is shown in figure 2.5a. Each strain amplitude step and the corresponding stable stress amp l i t u d e provides one point on the cyclic stress/strain curve. Cycling to about 20 percent of the life at a given strain amplitude normally gives a reasonable indication of the stable behaviour. The effect of strain sequence can be important. A high-to-low strain sequence is generally preferable. To avoid mean stress effects the strain amplitude should be decreased incrementally to zero stress and strain between blocks.

2.4.2 Incremental Step Tests

A specimen may be subjected to blocks of g r a d u a l l y increasing and then decreasing strain amplitudes as shown in f i g u r e 2.5b, to q u i c k l y d e t e r m i n e the c y c l i c stress/strain curve. After a number of these blocks, the metal cyclically stabilises. A continuous plot of the hysteresis loops through a block results in a series of superimposed loops with a clearly defined locus of tips corresponding to the cyclic stress/strain curve [48].

30

2.5 Analysis of Strain-life CurveAn analysis of the stable stress/strain hysteresis loops show that the strain is made up of elastic and plastic components, so that at any given fatigue life these two components are present. At large strains or short lives, the plastic strain component is predominant, and at small strains or longer lives the elastic strain component is predominant [39, 48]. This is indicated by the straight lines and the hysteresis loop sizes in figure 2.6. The intercepts of the two straight lines at 2N = 1 are e'f for the plastic component and a ' / E for elastic component. The

slopes are c and b respectively. This provides the following equations for strain-life data of small smooth specimens:-

A G t A Ge+ 2.13

2 2 2

A GT(2Nf )b + g 'f (2Nf )c 2.14

2 E

31

Where:-

A GT 6a = total strain amplitude

2 2

A G e = Elastic strain amplitude

2

A Gp

2P l a s t i c strain a m p l i t u d e

g 1f = Fatigue ductility coefficient

a'f = Fatigue strength coefficient

c = Fatigue ductility exponent

b = Fatigue strength exponent

2Nf = number of reversals to failure

The above relationship does not take mean stress into account; to overcome this disadvantage two laws have been proposed.

a) Morrow's law, which empirically reduces thefatigue strength coefficient by an amount equal to the mean stress [48, 49].

A gt a'f - am = (--------- )(2Nf )b + G ' f (2Nf )c - 2.15

32

b) Smith-Watson-Topper parameter [50]

Zc ' f

Qm a x . 6a — ( 2Nf ) 2 b + O'f ,6'f ( 2Nf )b + c 2.16E

Where:-

C7m a x maximum stress of the reversal.

The number of cycles Nf before failure at a certain level of strain range can be calculated using the above laws. The damage caused by one reversal is assumed to be equal to l/2Nf. This stems from the Palmgren-Miner theory for linear cumulation damage [39, 51]. The formal statement of the linear damage concept is that the summation of all fractions of life equals one.

Zni/Ni =1 - 2.17

Where n± is the total number of cycles applied during the fatigue life at a strain level corresponding to a fatigue life of Ni cycles.

The damage Di caused by a sequence of cycles or "loading block" can therefore be estimated from:-

Di = m / N i - 2.18

Obviously using equations 2.17 and 2.18 failure occurs when Di =1

If the component is subjected to a number of loading blocks then the number of loading blocks to cause failure is 1/Di [51] .

33

2.6 Extracting Hysteresis Loops (Cycle Counting)

The objective of all cycle counting methods is to reduce an i r r e g u l a r load h i s t o r y to a series of c o n s t a n t amplitude cycles and to compare these with the S-N or e-N curves obtained with uniformly repeated simple load cycles. The application of the linear damage rule D = 1/N requires a knowledge of the condition (mean and amplitude

of stress or strain) to which the damaging event should be compared.

The only meaningful method among those which are currently used to extract hysteresis loops from a strain signal is the "Rainflow Count" method proposed by M. Matsuiski and T. Endo [39, 52]. The operation of the rainflow method is shown in Fig. 2.7 for a history consisting of four peaks and four valleys.

The rules are:

1. Rearrange the history to start with the highest peak.

2. Starting from the highest peak go down to the nextreversal, proceed horizontally to the next downward range, if there is no range going down from the level of the valley at which you have stopped, go upward to the next reversal.

3. Repeat the same procedure upward instead of downwardand continue these steps to the end.

4. Repeat the procedures for all the ranges and partsof a range that were not used in previous procedure.

34

Thus assume that the highest peak is more extreme than the lowest valley. If not, start with the lowest value and go up instead of down. In figure 2.7a, the first traverse is shown. Remaining ranges are in figures 2.7b. The procedure applied to figure 2.7b again leaves a pair of range unused. They are shown in figure 2.7c.

Another technique which gives the same results of cycle counting is that of imaginary rainflow on fictitious multi-farious overlapped pagoda roofs[48] as shown in figure 2.8. The strain-time history is plotted so that the time axis is v e r t i c a l l y d o w n w a r d s , and the lines connecting the strain peaks are imagined to be a series of pagoda roofs so that cycles and half cycles are defined,

the rain starts at the top of the history and also at the inside of each peak and trough. The flow is stopped by striking flow descending from above, or passing a point opposite a peak or trough with a greater magnitude than that which the flow started. Flow also stops when it reaches the bottom of the history. Each flow is a half cycle, and there is a complementary half cycle of opposite sign elsewhere in the complete history, except for the beginning or the end of the history.

The advantage of a rainflow count comes when it is combined with a strain analysis as shown in figure 2.9. The damage can then be computed -for each cycle as soon as it has been identified in the counting procedure and the corresponding reversal points can be discarded.

35

Energy Density Approach For Elastic/Plastic Stress AndStrain Calculation At The Notch Root

An alternative method to N e u b e r 's equation for the calculation of local stresses and strains is based on the energy density approach developed by Glinka [37, 62, 63].

Due to non-uniform stress distribution at a notch root, each point of the notched body absorbs different strain energies. Assuming uniaxial stress conditions at the notch root and linear elastic behaviour of the material we can calculate that:-

EW ct = E (— )

2

a2W ct — 2.20

2E

Where:-

WS = The elastic strain energy per unit volume due tothe nominal remote stress S.

W ct = The strain energy per unit volume due to localstress and strain at the notch root.

In entirely elastic cases the stress at the notch tip can be calculated as:-

ct = Kt . S 2.21

The following equation is obtained by s u b s t i t u t i n g equations 2.19 and 2.20 in equation 2.21.

Wct £kt = ( — ) - 2.22

WSIt means that the elastic energy density Wa at the notch

tip is equal to the strain energy WS due to the nominal s t r e s s s m u l t i p l i e d by the s q u a r e of the s t r e s s concentration, K t .

In the presence of localised yielding at the notch tip, the stra i n energy, Wa is c a l c u l a t e d u s i n g c y c l i c stress/strain relationship.

37

a2 a a 1/n'W ct = — + ( — )

2E n'+l k'2.23

If plastic yielding occurs equation 2.22 is given in the form:-

ct2 ct ct 1/n1— + ( )2E n'+l K'

Kt = - 2.24s22E

Equation 2.24 can be rearranged into:-

(Kt .s2 ) ct2 ct ct 1/n1------- = — + ( — ) - 2.25

2E 2E n'+l k'

For fatigue applications the strain energy equation is written in terms of the ranges of stress and strain which results in:-

(Kt.As2 ) A ct2 A ct A ct 1/n' = + ( ) - 2.26

4E 4E n'+l 2k'

Equations 2.26 and 2.12 make it possible to calculate the

local elast i c / p l a s t i c s t r e s s e s and strains needed for fatigue life evaluation.

2.8 Multiaxial Fatigue

A number of approximation methods for multiaxial fatigue life evaluation have been proposed, but as yet no univer­sally acceptable approach exists [57]. The traditional approach relies on characterisation of^multiaxial fatigue process by a single parameter (e.g. equivalent stress).

IThis equivalent stress dr strain is subsequently processed

38

with an appropriate fatigue life prediction technique [53,64,59]. Therefore, the fatigue damage is accounted for by a single stress or strain variable without regard to the simultaneous presence of other stresses and strains. The modern approach to fatigue life evaluation adopts two parameters. These parameters may be stress or strain based. Uniaxial fatigue data is then used in the form of stress-life or strain-life curves to obtain a relationship between fatigue life and calculated stress or strain amplitude. Obviously fatigue life estimation based on strain is more appropriate than that based on stress since the former is more suitable for modelling the plasticity which the component undergoes at the critical site of failure.

Multiaxial fatigue theories can be generally divided into three categories [57, 64]. One commonly used approach is based on the extension of static yield criteria to fatigue life- evaluation. The most often used criteria in this group include the maximum shear theory (Tresca), the octahedral energy criterion (von Mises), and the maximum principal stress theory (Rankine). In order to improve the accuracy of the results, modifications have been developed by other researchers and incorporated in the analyses. These have included consideration of such factors as hydrostatic stress effect, normal stress effect and surface anisotropy [57]. Another approach to fatigue life prediction has been the use of energy as a correlating parameter for multiaxial data. A third and more recent

39

method of multiaxial fatigue life evaluation has been the critical plane approach [37, 63], described earlier.

Close examination of the published data shows that successful multiaxial fatigue life assessment requires r e p l a c e m e n t of u n i a x i a l q u a n t i t i e s a and e by the equivalent quantities aeq and eeq, by consideration of the following steps [53, 59]:-

i) Knowledge of external loads or nominal stresses and strains which causes failure.

ii) A yield criterion (e.g. Tresca or von Mises') to reduce the multiaxial elastic/plastic stress system

to an equivalent stress or strain.

iii) An approximation formula (e.g. Neuber's equation)to relate the external loads or nominal stresses and strains to notch root stresses and strains causing failure.

iv) Geometric information, Kt.

v) The material fatigue properties.

Since there are no universally acceptable s t a n d a r d techniques for fatigue life assessment, a brief review of some of the more popular traditional and more radical modern techniques are out-lined below:

40

2.8.1 Principle Of Static Yield Criteria To Fatigue

This approach has been developed from theories of strength of materials under static biaxial loading [53, 54]. When using these techniques the Multiaxial stresses are reduced at some critical location on the structure, to three principal stresses, the failure criterion is then applied which will reduce these principal stresses to a

single equivalent stress, aeq or strain, eeq . This is then used in conjunction with an approximation formula and material fatigue properties to obtain the fatigue life of engineering components. Therefore, principle of static yielding criteria has been adopted for dynamic loading of the structures. For random loading of the structure, the first step is to calculate an equivalent stress/strain from the principal stress histories. This equivalent h i s t o r y is s u b s e q u e n t l y p r o c e s s e d w i t h any of the available uniaxial techniques. A brief description of each method is outlined below.

a ) Tresca1s Method: (Maximum Shear Stress Theory)

This theory states that failure can be assumed to occur when the maximum stress in the complex stress system

becomes equal to that at yield in the simple tensile test. Since the m a x imum shear stress is half the g r e a t e s t

difference between two principal stresses the criterion of failure become [55, 56]:-

41

cti CT 3

2

And for yield

CT 1 03 CT y t

2 2

(cti - CT3 ) CTy t 2.27

b) von Mises' Method (Shear or Distortion Strain Energy

The total strain energy, Ut, of an element of material is made up of two parts, that due to change in volume and that due to change in shape. These will be termed volumetric strain energy, Uv and distortion or shear strain energy, Us. The conditions are determined by equating the strain energy of distortion at yield in the general case with the strain energy of distortion under simple tension thus [55, 56]:—

1 CTy t 2 (CTI ~ CT 2 ) 2 + (CT 2 ~ CT 3 ) 2 + ( CT 3 — CT 1 ) 2 = ------12G . 6G

(CTI - 02 )2 + (CT 2 - CT3 )2 + (CT 3 - CT l) 2 = 2(Jyt2 - 2.28

In two-dimensional systems,

Theory)

CT 3 = 0

42

Therefore:-

CTI2 + CT2 2 - CTI . CT2 = CTy t 2 = CTeq2 - 2.29

c ) Rankine's Method: (Maximum Principal Stress Theory)

This theory states that yielding will occur in a material under complex stress when cti attains a value equal to the yield stress, o Y t , measured in a simple tension test on the same material [55, 56].

CTI = CTyt = CTeq — 2.30

For yielding to occur.

Rankine's method defines the fatigue limit in terms ofmaximum principal stress. The component is judged safe ifthe principal stress remains below that of the yield stress under uniaxial tension. A cumulative damage sum under random loading can be calculated by u s ing the principal stress and the service history [53].

The maximum principal stress theory has successfully been used for brittle materials, while both the Tresca and von M i s e s ’ c r i t e r i a have bee n shown to r e s u l t in g o o dcorrelations for ductile materials at long lives [53, 64].

The above techniques a, b and c, can be used to reduce.the multiaxial stress system to an equivalent stress ceq which can then be used in conjunction with an approximation equation to calculate the local stress/strain values needed for fatigue life estimation.

43

2.9 Critical Plane Approach

Brown and Miller [42] have postulated that cracks initiate and grow on certain planes and that the normal strains to those planes assist in the fatigue crack growth. The general form of this theory is expressed with the aid of figure 2.10.

El + £ 3(ei - e3 )/2 = f ( ) - 2.31

2

Where:-

ei, E 2 , e 3 are principal strains (ei>e2 >£3 )

(£i - e3 )/2 = maximum shear strain

(ei + £3 ) = £n tensile strain normal to the plane of 2

maximum shear.

f = Functional relationship

There are two possible cases of crack growth under biaxial fatigue conditions [64, 65]. Case A arises for negative

values of x = ct2 /a 1 where the crack propagates along the surface and the surface strains are ei and £3 . Case Barises for positive values of x = <J2 /a 1 wherev crackpropagate inwards and the surface strains are ei and £2 .

44

Case B is more severe than case A as shown in figure 2.11. Brown and Miller have shown that data from all kinds of biaxial and multiaxial fatigue tests can be plotted on r pl anes. It is to be n o t e d that for all p o s s i b l e combinations of biaxial loading, no points can lie outside a wedge shaped area, the top edge of which corresponds to the uniaxial loading. The horizontal axis is the plane strain state and pure torsion condition and lastly the bottom edge of the wedge corresponds to equiaxial loading as shown in figure 2.12.

A similar approach has been proposed by McDiarmid [66, 67,

68] although his approach is based on maximum shear and normal direct stress. McDiarmid has proposed that the i m p o r t a n t p a r a m e t e r s for long life f a t i g u e in the unnotched specimens are the alternating and mean stresses, both normal and shear, occurring on the plane of maximum range of shear stress.

McDiarmid has shown that:-

1-5......t a = Cl - C 2 (ctt) - 2.32where:-

Ta = Shear stress amplitude on plane of maximum range of shear stress.

or = Normal stress amplitude on plane of maximum range of shear stress.

45

Cl = t = Fatigue strength in twisting.

1-5C2 = (t-b/2)/(b/2)

b = Fatigue strength in bending

Hence:-

1-5 1-5TTa = t- [ (t-b/2) / (b/2) ] . Or - 2.33

The allowable amplitude of shear stress on the plane of maximum shear stress can be predicted using equation 2.33.

46

Elostic region

4-£UaV -o

Nominal stress

Fig. 2.1 Variation of Stress Concentration Factor and Strain Concentration Factor as Stress Increases.

47

b< Solution point to be computed

ocrVIV)

Line representing

Ao. AE = constont

to

Cyclic stress-stra in line

Strain range AE

Fig. 2.2 Solving the Neuber Equation.

48

Stress

Cyclic CT-«

Curv«

0.01 ,n/m

Strain

Loops

A Cyclic Stress/Strain Curve. Fig. 2.3 Monotonic and

49

60-

Fig. 2

4 0 -

20-

-0004 0004

4 Stable Stress/Strain Hysteresis Loop,

50

Str

ain

Time

a) Multiple Step Test Program

Time

b) Incremental Step Test Program

Fig. 2.5 Strain Control Programmes for Obtaining An Approximate Cyclic Stress/Strain Curve From One Specimen

51

Stra

in

ampl

itude

(lo

g sc

ale)

TotalStrainoj/E

Elasticstrain

Plastic ’ strain

1Reversals to failure (log scale)

Fig. 2.6 Strain-Life Curves Showing Total Elastic and Plastic Strain Components.

52

25

-12

0

•14(a)

A0 o-

( b ) ( c

Fig. 2.7 Rainflow Cycle Counting.

53

strain

Fig. 2.8 Example of Rainflow Cycle Counting Method,

54

P. lo

ad

P

1

2.2'

4(c)

Fig. 2.9 A Load Versus Time History Repeatedly Applied To A Notched Component and the Resulting Notch Strain

' Response.

55

Fig. 2

Shear Strain

Tensile Strain

.10 Mohr's Circle of Strain.

56

PRINCIPALSTRAINS£ l = e 2 = e 3

Planes of maximum shear strain and direction of stage I

Plane and direction of Stage II crack . growth

crack growth

SURFACE PLANESURFACE STRAINS:

ESURFACE PLANE

CASE B: X = c ^ / a ^ V E )

A

SURFACE STRAINS: ei,e2

Fig. 2.11 Case A and Case B Systems of Crack Extension

57

2

CASE A1Plane

Strain N.-T 5 7 5 oTT-y— — Case B

Torsion0Nf-3000

;1000

Fig. 2.12 A Typical T Plot.

58

CHAPTER 3

STEERING ARM DESCRIPTION

3.1 Introduction

The selection of a material that gives the longest fatigue life under a given service loading is one of the most important aspects of the design analysis process. The designer must be able to match the material behaviour to the expected loading condition. This is only possible if a great deal is known about every proposed material and the required service conditions. Therefore, a full knowledge of all aspects of the mechanical properties of proposed m a t e r i a l s is e s s e n t i a l before they can be u s e d efficiently.

This chapter discusses the important properties that should be considered during the design process to predict the f a t i g u e life of the compo n e n t . M a c r o / M i c r o examination and the chemical analysis of the component material was undertaken to identify the following aspects:

a) Non-uniform composition due to the segregation of alloying elements.

b) Non-metallic inclusions such as slag, sulphides and oxides.

c) Method of manufacture.

d) Mechanical properties.

59"

e) Physical defects due to manufacture and uniformityof heat treatment.

f) The distribution of phases.

g) The number of micro-constituents present.

h) Identification of the equivalent British Standardspecification.

3.2 Steering Arm

During prototype testing of a new 32 ton truck the heavy goods vehicle manufacturer identified a fatigue problem with the steering arm shown in figure 3.1. This is a

typical problem faced by the automotive industry. To analyse the fatigue behaviour of the component, basic s o f t w a r e was o b t a i n e d from e n g i n e e r i n g s o f t w a r e

specialist, nCode International Limited. In the current work the possibility of combining finite element analysis and durability assessment software packages are under investigation.

The steering arm has been used to test the validity of the proposed approach in the design and development stage before commitment to expensive prototype development is made. S t u d y of this c o m p o n e n t w i l l lead to an understanding of the application of the proposed method to a wider range of components experiencing uniaxial, biaxial and triaxial states of stress during service.

60

3.2.1 Function Of A Steering System

The function of a steering system is to enable a vehicle to change its direction of travel and negotiate corners. The main requirement of a good steering system is to ensure geometrically precise rolling of the wheels (without slip) when travelling in bends. Figures 3.2 and 3.3 show the overall dimensions and an exploded view of the kingpin steering system for a 32 ton truck. In this steering system each wheel has its own pivot point, namely, kingpin, to which is attached the stub axle on

which the wheel rotates. Each stub axle is connected to the steering arm. The two track arms are inter-connected by the track rod.

3.3 Chemical And Mechanical Properties

The steering arm was manufactured of forged 41 Cr 4V material (DIN standard). The equivalent British Standard specification for the above material was found to be BS 970 530 M40 (EN 18). This is a general purpose steel which

may be heat treated to produce a tensile strength of 700 MPa and upwards depending on the section size, with good ductility and resistance to shock. It is used in the

automobile industry for gears, connecting rods, steering levers, spindles, axles and crank shafts. Table 3.1 compares the range in chemical com p o s i t i o n for the steering arm tested with standard data for actual material EN 18. The typical monotonic mechanical properties of the material are listed in table 3.2.

61

The fatigue test data for the component material was provided by the manufacturer. The cyclic properties are described in tabular form in table 3.3, and the cyclic stress/strain, strain-life and STW (Smith-Topper-Watson)- life curves are shown in figures 3.16 tb ' 3.18. The

material has a considerable amount of plasticity. The cyclic strain hardening exponent of the material is less than 0.1 (n'=0.097), and under the experimental cyclic loading conditions the material softens [72].

3.4 Micro-structure Examination

The micro-structure examination of the component was

undertaken to identify the phases present, and their shape and size distribution.

A Zeiss Ultraphot metallurgical microscope was used for this purpose. The magnification was set at X500 for all the tests. When investigating the properties of a metal it is essential that the specimens used be representative of the whole mass. The usual procedure is to obtain samples in two directions; longitudinal and transverse. These were obtained from the critical location of the component and mounted in bakelite. Fine grinding of the specimens was carried out on a series of silicon carbide papers of increasing fineness. The fine scratches were then removed by polishing on an alumina loaded selvyt stretched on a flat disc. The polished specimens were mounted on a glass slip with plasticine. These were examined under an optical microscope. A uniform bright surface with some small dark

62

areas were observed as shown in figure 3.4. M i c r o ­structure examination of the surface showed the dark areas to be non-metallic inclusions such as oxides and manganese sulphides as can be seen from the X-ray spectra produced for manganese sulphides inclusion as shown in figure 3.6. The specimens were then immersed in etching solutions for 30 seconds, removed, swilled in running water, rinsed in methylated spirits and dried in hot air. These were examined under the microscope, and the structure of the material was found to be upper bainite as shown in figure 3.5.

The time for the b e g i n n i n g and c o m p l e t i o n of the transformation of austenite have been plotted against t e m p e r a t u r e to give the " S - c urve" k n o w n as t ime- temperature-transformation (T T T) curve of figure 3.7. The T T T c u r v e was then used to p r e d i c t the transformation and heat tiredtment operations undertaken to form the bainitic micro-structure.

Acl and Ac3 lines represent the equilibrium transformation temperature Austenite is completely stable above Ac3, partially unstable between Ac3 and Acl, and below Acl it is completely unstable and transforms in time.

The decomposition of austenite occurs according to three separate but sometimes overlapping mechanisms and results in three different reaction products, pearlitic (700°c to 500°c), bainitic (500#c to 350"c) and martensitic (350°c

to 250°c). For detailed account of each reaction product see [73, 74].

63

At quench temperatures slightly above Ms (Martensite start), a m i c r o-structure forms that is d i s t i n c t l y different from fine pearlite. This micro-structure is called bainite. Bainite has a two-phase micro-structure composed of ferrite and iron carbide. There is avariation in the morphology of bainite and in the type of carbide (Fe3 C or e carbide Fe2.5 C) depending upon the quench temperature and composition.

A distinct change in morphology occurs between high and low quench temperature. These two morphologies are referred to as upper bainite (high quench temperature) and lower bainite (lower quench temperature). The mi c r o ­

structure of lower bainite is finer than that of higher bainite.

The centre scale in figure 3.7 represents the logarithmic scale bar dimensions of oil quenched materials.

The maximum sectional dimensions of the component body is 42 x 46 mm. A line is projected vertically from the appropriate point along the scale to the undersection of the T T T curve. This determines the percentage bainite available with in the martensitic matrix, which is found to be approximately 50%.

3.5 Manufacturing Processes

It is difficult to establish precisely the manufacturing processes carried out to produce the aforementioned micro­structure. However, examination of the component material suggested that the following m a n u f a cturing and heat

64

treatment processes must have been carried out.

a) Forging 1200 ° C finish above 850°Cb) Hardening 850°C - 880°C oil quenchc) Tempering air coold) Surface treatment sand-blasted surface cleaning

.6 Test Track Trials

Several methods are available for assessing the fatigue of engineering components prior to their incorporation into products in the market place. At the conceptual stage simple calculations can be performed to give approximate load and stress histories, which in conjunction with material data such as S-N curves, provide an estimate of fatigue life. These can be refined by the manufacture of prototype products which when subjected to realistic loading can provide accurate component measured load

histories. For new components where previous load histories have been established then simulated testing can take place on laboratory equipment and data thus generated be used to predict the real fatigue life of the component using computer methods such as the FATIMAS program. F i n a l l y real life tests w o u l d n o r m a l l y f o l l o w for confirmation.

The importance of component testing was recognised as

early as the 19th century. One of the earliest published papers by Albert, 1838, discusses tests carried out to investigate the fatigue life of mine cables [70]. Other

65

examples of component testing are reported in the work by Wohler [14], 1860, and Andrew, 1890, which investigated the effect of fatigue damage on railway axles [71].

The concept of component testing on proving grounds can be traced to The Dodge brothers, who built the earliest test track in 1915 [31]. The construction was built of split logs, which is known today as a corrugated surface. The pu r p o s e of the test t r a c k was to i n v e s t i g a t e the s u s p e n s i o n s y s t e m s of a u t o m o b i l e s . This f o r m of accelerated testing is a feature of all proving ground tests today.

Todays test track constructions contain a mixture of surfaces designed to represent typical customer usage. The criterion is often based on the vehicle surviving a given distance, usually 1000 miles, over such surfaces.

3.7 Durability Assessment

Automotive industries have numerous road endurance test routes which they use for evaluating components and vehicles. The test circuits contain a number of different surfaces. These routes have all been prepared following past experience and historical usage. The general feeling being that the routes simulate closely conditions met. in service.

It is the manufacturer's practice to select a mix of test track surfaces as shown in figure 3.8 to evaluate ride and

handling, noise, vibration and harshness of prototype v e h i c l e s .

66

D u r i n g the d u r a b i l i t y a s s e s s m e n t of a n e w 32 ton prototype truck on manufacturer's proving grounds in 1983, fatigue failure of the steering arm occurred. The expected life was specified to be 10,000 circuits of the test track. However, failure occurred after approximately 120 circuits; considerably less than that desired for the life of the component. Figure 3.9 shows the recorded strain­time history from the road test.

The component was manufactured from forged SAE 1046 V with a tensile strength of 890 MPa. The test information was fed back to the material engineering department to initiate modifications to the component. It was decided to change the material. Two alternative materials were considered, namely; 41 Cr 4V and 42 Cr S4 with tensile strength of 940 and 1100 MPa, respectively. These were fitted to the truck and the above test was repeated. The life remained approximately 120 circuits of the test

track.

Tests were then undertaken to consider the p o s s i b l e changes in mechanical properties that cyclic loading may induce. The test results showed the cyclic p^opprties of the above materials to be almost the same as shown in figures 3.10 to 3.18 consequently th$ materials selected were unsatisfactory. The chemical composition of the three materials are shown in tabulated form in table 3.1.

Examination of the chemical composition of the three materials shows that they are almost identical.

67

Geometric modifications were implemented by engineers in an attempt to overcome the above problem. Material 41 Cr 4V was selected. The blend radii around the bosses were increased at the critical location and consequently the desired fatigue life was achieved.

3.8 Discussion

The procedure followed by the manufacturer in developing the steering arm component is typical of many industrial organisations, where decisions on physical shape and

m a t e r i a l are not c o n f i r m e d u n t i l very late in the development cycle. Clearly the ultimate confirmation of any component is the final road test but it is necessary to increase the reliability of the decision making process at the early stages of the design cycle, where costs accrue at a relatively slow rate. Having decided upon the best available concept, detailed design and analysis procedures follow. At this stage of the design process the level of commitment to the development of a new artefact is high. Consequently, long term decisions for the

manufacturing processes and tooling are made. At this stage in the design process the rate of spending is very high. It is at this late stage when the' e n g i n e e r i n g p r o t o t y p e s are m a d e and t e s t e d for i n t e g r i t y and durability that any design changes are expensive, since modifications will lead to further testing and may even lead to major tooling changes.

During the analysis process the manufacturer had made a number of wrong decisions which led to the premature

68

failure of the steering arm. They fell into the trap of

endless material changes and repeated testing without asking the question, why? After much research it emerged that a design modification of the steering arm at the critical location was required.

It is difficult to be specific concerning which method of analysis has been used by the designer. However, it is suggested that because a material with a higher tensile stress was usually selected, then one can conclude that the designer used a S-N curve approach to estimate the fatigue life of the component.

Figures 3.19 and 3.20 show the three dimensional outputs

of cycle distributions and associated fatigue damage distributions for the above materials for the recorded data shown in figure 3.9. Several comments can be made of the graphs.

1) Figures 3.19 and 3.20 shows that in all cases only a small number of the cycles caused any damage.

2) Figure 3.20 shows that all the fatigue damage was caused by the washboard road surface.

It is clear that the company should have recognised that only the washboard road surface was causing damage and the follow up tests should have been carried out only on that surface. This would have reduced the testing time.

69

70

The Steering Arm.

009*

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71

Fig. 3.2 Steering Arm Dimensional Details.

18/5

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72

Fig. 3.3 The Exploded View of the SteeringSystem of a 32 Ton Truck. (Item 1 Steering Arm)

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73

Yield Point, MPa : 813Tensile Strength, MPa : 940Elongation : 24%Reduction in Area : 63.5%Hardness, Vickers : 250

Table 3.2. Mechanical Properties

74

MATERIALS ENVIRONMENT

Fatigue Strength Coefficient (MPa) Sf 1 = 840Fatigue Strength Exponent b = -0.041Fatigue Ductility Exponent e = -0.694Fatigue Ductility Coefficient 6 f ' = 0.387Elastic Modulus (MPa) E - 2.148x10sCyclic Strain-Hardening Exponent n' = 0.097Cyclic Strength Coefficient (MPa) k' = 944Cut-off (reversals) Rc = 1E7

Table 3.3 Cyclic Properties of the Steering Arm(41 CR 4V)

75

#«

6I

Fig. 3.4 Unetched Micro-Structure Showing The Inclusions.

77

Etched Micro-Structure Showing Bainite in a Matrix of Martensite.

Rfi 0 - 20 keU 40 s P re s e t; 40 s Rema i n » n*

D e a d

IHCUJSION IN MAN STEERING RRi

4 ,640 k eU

MEM1

Fig. 3.6 The Spectra Of Inclusion Plot.

78

CONTINUOUS COOLING TRANSFORMATION DIAGRAM

I C r AUSTliNITISED AT 870°C

START.

xr— i

COOLING RATE AT 750 C

mm O IL

mm WATER

PREVIOUS TREATMENT ROLLED

ANALYSIS Wt% (See note on page 8)

C Si Mn P S Cr Mo Ni A1 Nb V0.39 0.20 0.70 0.020 0.020 1.05 — — — — —

Fig. 3.7 Time Temperature Transformation Carve.

79

80

Fig. 3.8 Manufacturer's Test Track Surfaces.

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82

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85

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50

Cycles

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CYCLE DISTRIBUTION FOR HISTORY = stubaxle Maximum touer height : 3095 Units : Local Strain

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nCode NSOFTTurning point hlstor stubaxle.dac

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Fig. 3.19 Cycle Distribution (Micro-strain).91

DAMAGE DISTRIBUTION FOR HISTORY = uash.boardMaximum touer height : 30.22 Units = Local Strain

40

Damage V.

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Turning point history = washboard.dacNumber of cycles used : 479Fatigue life •• 58 repeats of history

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30

Damage ’/ .

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Fig. 3.20 Damage Distribution (Micro-Strain).

92

CHAPTER 4

COMPUTER BASED ANALYSIS OF STEERING ARM4 .1 Introduction

The aims of this section of the programme of work were:-

i) To develop two and three dimensional computer modelsof the steering arm. The former was used to locate the relevant boundary co-ordinates as required for the development of a finite element mesh and the latter was for automatic mesh generation using the FAMbuild software package [82, 6].

ii) To undertake a full three dimensional elastic finite element analysis to identify the most critically stressed areas of the component, and also establish a full description of the static load stresses and strains under elastic conditions.

iii) To use the elastic stress field information obtained to predict local elastic/plastic strains in the component for inclusion in a fatigue life prediction

computer package [83].Typical of available methods for determining the plastic strains is the one associated with Neuber [3, 38]. This uses the nominal stress, the stress concentration factor and Young's Modulus of Elasticity to d e t e r m i n e the plastic strains as follows;

(Rf ; S )2a . e = ---- ------

E

93

For an elastic finite element analysis a is the plastic stress at the critical location and Kt = 1 ;

(S)2e =

EAnother approach which can be used to determine the local

elastic/plastic strain behaviour is the energy method [37, 63]. This also uses the nominal stress, the stress concentration factor and Young's Modulus of Elasticity; (S)2 (a)2 a a 1/n'4E 4E n'+l 2 K 1

The results obtained from the above techniques were used to develop a series of critical location load/strain calibration curves for the component. These were used to load scale the washboard service strain history. The fatigue life evaluation package FATIMAS was then used to assess the fatigue life of the steering arm through a range of scaled load histories. The lowest factored load history was 20 kN and the highest factored load history was 40 kN which resulted in respective strain fields which varied from totally’ elastic to highly plastic. These are discussed in chapter 6.

4.2 Software Summary

Three individual software packages were used in this phase of the project. A brief description of each is outlined.

94

4.2.1 MEDUSA

A Prime 9750 mini computer using Medusa [33] software is typical of commercially available CAD systems. The work station consists of a graphics screen and keyboard, and a graphics menu. The screen displays the drawing, as it is being developed or modified. The menu is divided into segments, each labelled with the name of a frequently used command. A command is activated by moving a pen to the relevant entry in the menu and pressing the pen. The screen cursor can be moved by means of a joy-stick. The keyboard can also be used to enter commands, instructions and data to the system, and to input any text, labelling,

titles or notes which are to be appear in the drawing. Completed drawings are stored as a data file on magnetic tape and paper copies made on plotters or printers.

A solid model consists of one or more objects. An object is a single c o n t i n u o u s p i ece of m a t e r i a l or, m o r e formally, a number of polygons that bound part of space. A

complex model is usually created by a build up of simple primitives (blocks, cylinder, cone, wedge, sphere etc), with Boolean operations.

Prime Medusa geometric modelling systems consist of three programs the modeller, the viewer and the reconstructor. A model is created by processing a three dimensional file through the modeller. The modeller scans the sheet and interprets the primitives on the sheet and creates a model. The viewer generates one or more orthogonal and isometric views of a specific model. The orientation of

95

the model and the direction from which it will be viewed are d e t e r m i n e d by the v i e w p r i m in that box. The reconstruction program projects the generated views back on to the sheet.

4.2.2 PAFEC

The finite element package PAFEC (Program for Automatic Finite Element Calculation) [34, 35] together with PIGS (PAFEC I n t e r a c t i o n G r a p h i c s Suite) is t y p i c a l of commercially available finite element systems. The package consists of ten definite phases, each carrying out a specific task, towards a solution. In phase one the data modules are read in, the other nine phases including the

solution, determination of the stresses, etc. can be included depending on the output required.

The PAFEC program is modular in nature, and due to its flexibility, requires a control file to guide a particular problem towards the required solution. The control m o d u l e starts w i t h the w o r d C O N T R O L and e n d s w i t h CONTROL.END. In between these a number of co m m a n d statements can be entered. This informs the computer what will be required in the subsequent analysis. Each module within the data file is defined by its heading. After this there will normally be a 'contents' card giving the headings for the information columns . There are over one hundred data modules available and descriptions of each m o d u l e is o u t l i n e d in P AFEC M a n u a l [34, 35].However, some of the most frequently used modules are:-

96

geometry, mesh, restraints, loading, material.

PAFEC data validation takes place in phase 2; here each element is checked for distortions from the basic shape. Limited distortions are acceptable, and these limits vary with the element type. Four basic checks are made;

i) Angles between adjacent element sides.

ii) Ratio of longest to shortest sides.

iii) Radius of curvature on each side.

iv) Nodes out of the plane of the elements.

If any of the above fails, warnings or errors result.

PIGS is a powerful and valuable pre-processing and post­processing package. It is used for the production of F.E. models and files and also examination of the PAFEC output profiles. The following advantages are associated with

4.2.3 PIGS

PIGS: -

a) Fast F.E. data production

b) Mistakes can be viewed and rectified on the screenat all times

c) Results can be processed quicker than throughPAFEC plots.

97

4.2.4 FAMbuild

FAMbuild is a finite element mesh generation program [36]. It may be used to interface almost any CAD to finite element analysis program. The interface between FAMbuild and CAD systems is achieved by FAM from CAD system commands.

The first level of the problem is the transformation from a CAD model into a numerical model suitable for finite element analysis. The second level of the problem is the

actual transfer of geometry between the systems.

Any data transferred must be selected carefully in CAD systems and must represent information that can be used in FAMbuild. The processing in FAM from CAD can not add geometrical information that is not supplied to an unstructured sequence of points and lines.

For a well prepared numerical model, the FAM from CAD processor can significantly contribute to the building of a finite element model in FAMbuild and avoid the extremely labour intensive manual inputting of data, hence saving time and money.

4.3 Two And Three Dimensional Geometric Modelling

The Medusa software package was used to create both a two and three dimensional model of the steering arm. These were then used to accurately locate the boundary c o ­ordinates needed for the development of the finite element mesh.

98

Initially a two dimensional drawing of the steering arm was produced as shown in figure 3.2. This was found to be a relatively easy task. A three dimensional solid model of the component was also generated as shown in figure 4.1. Due to the complexity of the component geometry, in particular the blend radii surrounding the bosses, it was necessary to create the model in two separate stages.

To reduce the degree of complexity, the component was modelled in three separate parts, namely; the steering control shaft, and the two regions surrounding the two bosses. Three separate facilities were used to create the model:-a) Volume of revolution

b) Slidec) Surface network.

A Boolean addition operation was then u n d e r t a k e n to combine the individual models to form the c omplete component.

Overall, the software package was found to be user friendly. However, the creation of a 3-D model was found to be a very complicated and time consuming process. It was found impossible to create an exact replica of the actual shape of the component. This was mainly due to the limitation of the Medusa software package. It was found that the software is incapable of handling coincident faces of the p r i m i t i v e shapes d u r i n g the B o o l e a n op e r a t i o n . To o v e r c o m e this m a j o r d e f i c i e n c y the primitives had to be overlapped, which was then accepted

99

by Medusa software. This is a very serious problem particularly when combining a number of three dimensional solid models at common faces or edges.

The accuracy of a solid model is dependent upon chord tolerance selected for cylindrical primitives in the model. The finer the chord tolerance given to a model the better the accuracy. However, more time is consumed by the

computer to generate such a model. For the steering arm the chord tolerance was set at 0.1 mm.

In order to avoid the tedious manual inputting of data, an integrated solid modelling and finite element analysis software package (CAD-FAM) was used to transfer the solid model of the component and carry out finite element analysis using the automatic mesh generator p a c kage (FAMbuild). This was unsuccessful due to the complex geometry at the change of section around the bosses. An attempt was made to produce a simplified solid model of the component. However, further problems were encountered with coincident face of the primitive shapes during the Boolean operation. Therefore this technique was abandoned. Manual data input to the F.E. package was then undertaken. The three dimensional solid model of the steering arm was found to be of no real value at the later stages of the project.

Having created a solid model, the colour shader facility was used to produce a shaded image of the component as shown in figu r e 4.2.

100

4.4 Finite Element Analysis

4.4.1 Component Geometry And Material Properties

Due to the complexity of the component g e o m e t r y in p a r t i c u l a r the b l e n d ra d i i a r o u n d the b o s s e s , the generation of a three dimensional finite element model was necessary. There were however, considerable constructional difficulties in undertaking such a task. Restrictions on element geometry presented the largest problem. Within such a c o m p l e x me s h it was d i f f i c u l t to a v o i d the generation of elements which violated the basic elemental rules.

Distorted elements even far removed from the region of immediate interest can lead to the introduction of quite considerable inaccuracies.

The biggest problems encountered were at the changes of section around the bosses, where the adjacent angles were outside the acceptable limit. To minimise the above difficulties some geometric modifications were necessary. These will be described in the next section.

The material properties used for input to PAFEC data file were: -

Young's Modulus, E 214800 MPa

Poisson's ratio, v 0.3

Density, p 7850 Kg/mm

101

4.4.2 Development Of The Finite Element Model

Initially the full component was modelled. To overcome the d i f f i c u l t i e s p o s e d by the c o m p l e x g e o m e t r y of the component the geometric model in Medusa was modified in order to simplify the finite element dis c r e t i s a t i o n process. The diameter of the bosses were made the same (40 mm), this increased the blend radii around the bosses from 25mm to 25.73mm.

The component was split into several suitable blocks [82]

and the boundary co-ordinates were entered using a global axis set. PIGS was used to fill these blocks with 892

individual elements.

The elements used were standard twenty noded isoparametric brick elements (37110) and fifteen noded isoparametric p rism elements (37210) as shown in figure 4.3 [82].These elements have three degrees of freedom at each node and the stress/strain varies linearly in each direction. This also has the advantage that the displacement and boundary shapes are .quadratic in nature. The midside nodes allow curved boundaries to be represented accurately if necessary.

A point load of 20 kN was applied to the area XY in figure

4.4. Since the stress/strain varies linearly, unit load may be applied. This value of load was chosen to obtain reasonable stress values for comparison with strain gauge results.

102

The lower surfaces AB and GH of the component were restrained in the Z direction. The end AC was fully restrained in the X direction. The upper surface CD and EF were subjected to a uniform pressure of 87 MPa in Z direction representing fastening bolt pressure in both the rig and the real location. This value was derived using the following method:-

The c l a m p i n g force of bolt and w a s h e r = 2 ay3

where:-

ay = yield stress of the bolt * 640 MPaClamping force of the bolt •= 2/3 x 640 = 427 MPabolts diameter = 18mmArea of bolt = n r 2 = 254.54 mm2Load = F = a.ALoad = 108.6 x 103 NDiameter of the washer = 40 mmArea of the washer = 1256 mm2P r e s s u r e = a = F_ = 86.5 « 87 MPa

• AThe data file was. created in PIGS and the m a t e r i a l properties were entered via the keyboard.

The basic output from the computer was in digital form. For every node or element in the structure the print out gave the values of stress and displacement in X, Y and Z directions. The computer also calculated the principal stresses and their directions. Whilst the printed output was required for detailed analysis, a clear picture of the state of stress was given on the graphics terminal. The

103

results were also plotted as stress contours, to highlight the highly stressed regions as shown in figure 4.5.Close examination of the stress contours and stress data file revealed that the component does not carry any appreciable load between A-A and B-B. Hence, this part was discarded and the component was restrained in the X direction at the section of cut to enable a finer mesh to be produced at the critical location.

Again the blend radii were increased from 25 mm to 25.73 mm to enable the element geometry to be within acceptable limits of PAFEC. At this point the remainder of the •component was remodelled. A point load of 20 KN was applied to the kingpin, area XY shown in figure 4.6.

To ensure the accuracy of the solution a finer mesh was defined at the section of the component which exhibited high stress gradients, identified by the previous model. The new model resulted in a total of 600 elements and 3156 nodes.

The lower surface of the component, AB, was restrained in the Z direction as shown in figures 4.6. The section of cut, AC, was clamped in the X direction. The upper surface, CD, was subjected to a uniform pressure of 87 MPa to represent the fastening pressure exerted by the bolt. The data file was created in PIGS and material properties were input via the keyboard.

104

4.5 Results And Discussion

Contours of the maximum principal stresses were plotted using the facility within PIGS. The 'rainbow' plots highlighted the areas of high stress gradients, referred to as 'hot spots', which are shown in figure 4.7.

Output from the FE analysis is shown in Table 4.1 in the form of principal stresses.

At the point of highest principal stress (node 12) a triaxial state of stress p r e vails. The p e r c e n t a g e biaxiality was found to be 9% for principal stress values of G| = 355 MPa, and c2 = 32.2 MPa and = 2 3 . 3 MPa.

Since maximum principal stress/strain values at the surface of the component are of interest in fatigue life evaluation, only these were initially considered. The elastic stress/strain relations given by equations 4.1 to4.3 were used to calculate the elastic principal strains from the F.E calculated principal stresses and are shown in Table 4.2.

1G, = — { ai - V (<J2+ <73 ) } - 4.1

E1

G 2 = — { CT2 - V (<73+ <71 ) } 4.2E1

G 3 = — { <73 “ V (<71+ C72 ) } - 4.3E

105

For an applied end load of 20 kN the finite element analysis predicted a maximum principal strain value of 1571 micro-strain at node 12.For prediction of the elastic/plastic strain values at the critical location both Neuber's rule and the energy density approach were used. Since the measured strains were obtained using the unstabilised component, the initial plastic strain calculations were carried out using the monotonic stress/strain curve, listed in table 4.4. These strains were then compared to measured strains. For use in fatigue life predictions the met h o d was repeated using the cyclic stress/strain curve, listed in table 4.5.

The elastic finite element critical location principal stress values, listed in table 4.1, were reduced to an

equivalent stress (aeq) using maximum principal stress, Tresca, von Mises1 and maximum principal strain methods and the results are listed in table 4.3 [55, 56].

The elastic finite element principal stresses vary within the region of the critical location. Consequently when equivalent values are calculated there is a degree of variation in magnitude and position of the critical node. Using the maximum principal strain and the m a x i m u m principal stress methods node 12 is the most critical node, whereas using the other two methods node number 19 is the most critical node.

Neuber's rule was then applied to each equivalent stress to construct Neuber's hyperbola. The intersection of

106

N e u b e r ' s h y p e r b o l a and the u n i a x i a l m o n o t o n i c stress/strain curve gives the required elastic/plastic strain values. As an example the procedure for solving the Neuber's equation for a 30 kN load is shown in figure 4.8.

The energy density approach was also used in conjunction with the monotonic stress/strain curve to calculate the plastic strain values using the equivalent stresses (aeq) described above. A number of calculations were carried out in load increments of 10 kN from 10 kN to 70 kN and the results are included in table 4.4.

The component monotonic load/notch root strain calibration curves using F.E. calculated equivalent values and both Neuber's rule and the energy density method are shown in figure 4.9. It is apparent that for low values of load, both methods give results very close to each other. For high values of load the calibration curves obtained from both methods deviate from each other. As the amount of plasticity increases the degree of correlation decreases between Neuber’s estimated strains and the energy density estimated strains.

For a load of 10 kN, the estimated total strain values obtained using maximum principal stress, Tresca, von Mises and maximum principal strain methods toget h e r wit h Neuber's rule were found to be respectively 845, 763, 734 and 783 micro-strain. For a 70 kN load these v a l u e s increase to 7077, 6539, 6494 and 6679 micro-strain. For the same load variation the calculated strain values using

107

maximum principal stress, Tresca, von Mises and maximum principal strain methods together with energy density technique were found to be 815, 776, 771 and 789 micro­strain and 6070, 5731, 5678 and 5822 micro-strain. Thus, the lowest 70 kN total micro-strain of 5678 is obtained using the energy density and von Mises method, whilst the highest value of 7077 micro-strain occurred with Neuber's method and maximum principal stress equivalent. The latter is 20% greater than the former.

The above calculations were repeated using the F.E. calculated equivalent values and the cyclic stress/strain curve. The results are shown in tabulated and graphical form in table 4.5 and figure 4.10.

For a load of 20 KN, the estimated elastic/plastic strain values obtained, using maximum principal stress, Tresca, Von M i s e s and m a x i m u m p r i n c i p a l s t r a i n m e t h o d s in conjunction with the cyclic s t r e s s /strain curve and

Neuber's rule were found to be respectively 1800, 1665, 1640 and 1730 micro-strain. This variation increased with increasing load to 4415, 4095, 3955 and 4150 micro-strain for a 40 KN load. For the same load v a r iation the calculated strain values using maximum principal stress Tresca, Von Mises and maximum principal strain methods together with the energy density method and cyclic stress/strain curve were found to be 1653, 1547, 1539 and 1569 micro strain, and 3276, 3079, 3064 and 3127 micro­strain .

108

The onset of cyclic yielding (ay) appears to occur at a load of approximately 20 KN. At this load the material experiences slight plastic deformation as shown in figure 4.8. Close agreement was found between the Neuber's estimated strains and those obtained using the energy

density method for a 20 KN load (the elastic range). However, it can be seen that the estimated strains based on Neuber's rule and equivalent methods are grossly over­estimated for a 40 KN load in the plastic range when compared to those obtained using the energy d e nsity method.

In the case of the 20 kN load, the highest elastic strain (approximating the cyclic yielding) of 1800 micro-strain is obtained with Neuber's method and maximum principal

stress method, whilst the lowest value of 1539 m i c r o ­strain occurred with the energy density and von Mises equivalent method. The former is 14.5% greater than the latter. The highest strain of 4415 micro-strain comes from using Neuber's method with maximum principal stress for 40 kN. For the. same load inbrement the lowest plastic strain of 3064 micro-strain is produced by combination of

the energy method and von M i s e s 1 equivalence. This represents a 31% increase between minimum and maximum values.

The above results show that the accuracy of the above methods depends in general on the extent of the plastic zone at the notch root. The smaller the plastic zone in comparison with the elastic area surrounding the notch

109

root, the closer agreement exists between the two methods. The perecentage strain difference of 14.5% and 31% for 20and 40 kN load i n c r e m e n t show that N e u b e r ' s rule

a 5overestimates local strains, ajt the amount of plasticity increases with increasing load in comparison with the energy density method.

Conclusions

For low values of nominal stress, Kt.S, both Neuber's and the energy density methods give results which are in close agreement. For high nominal stress values, Neuber's method in general overestimates the local strains when compared to those obtained using the energy d e n sity method. As the load increases to give high levels of plasticity the degree of correlation reduces as shown in figures 4.9 and 4.10.

Fig. 4.1 Three Dimensional Geometric Model Of The Steering Arm

112

Shaded Image of the Steering Arm.

Eight Noded Isoparametric Quadrilateral Element (36210)

Twenty Noded Isoparametric Brick Element (37110)

Six Noded Isoparametric Triangular Element (36110)

Fifteen Noded Triangular Prism Element (372.10)

Fig. 4.3 Element Types.

113

Restraints

Load

y

20 kN

Fig 4.4. A Mesh Used For Three Dimensional Finite Element Arullysis M The Full Component.

114

F'lg 4.5 Stress Contours Of The Full Component.

Fig. 4.X

Mesh Used For Three Dimensional Analysis Of The Critical Part Of The Component.

117

Fig 4.7. Stress Contours Of The Critical Part Of The Component..

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125

CHAPTER 5

STATIC MEASUREMENT OF STEERING ARM STRAINS

5.1 Introduction

The static testing of the component was undertaken to verify the accuracy of the finite element results. Up to the y i e l d - p o i n t of the c o m p o n e n t m a t e r i a l , the experimental results were compared with the elastic finite element results. For points where the material yield stress had been exceeded, plastic strains were obtained using both Neuber's rule and the energy method. The resultant elastic-plastic values were compared with post­yield measured data.

5.2 Test Equipment

1) Dartec 9500 Computer Controlled Multiaxial Testing Machine:-

This machine can be used for the a p p l i c a t i o n of dynamic or static loading of engineering components. The machine can be programmed to run under load, stroke or extension control. For this work it was decided to operate under load control because the actuator has a capacity of +/-250 and +/-200 kN. in

static and dynamic mode, respectively. The test programme on the 9500 system was p r o g r a m m e d and monitored by a IBM A T (E) microcomputer. This was used to apply loading to a test specimen and to store the test r e s u l t s and a s s o c i a t e d data on disk.

126

The following modules were used during the testingprogram.

i) Profile Generator:- This unit was used to generatecommand profiles from a large number of turning points. These points were loaded into the memory from the supervisory computer. The origin of the profile was input from a keyboard (manual) or data obtained from service measurement. This program was used to input the load history into the 9500 system.

ii) Load Program:- This was used to convert the strain based service history supplied by the manufacturer to a load history suitable for the profile generator.

iii) X-Y program:- This was used to capture and plot thedata during the test programme.

iv) Trip Program:- This facility provided control ofthe bounds tests, error tests and external tests. Theparameters for these tests were read from the 9500 or from a file, as and when required. M a x i m u m and minimum load values were entered and stored if required, also a means of resetting the trip and identifying the cause of a trip was provided. This program was normally loaded before starting a test.

There are several limitations associated with the above facility:-

127

a) In its present form the dartec machine will not test under strain control conditions, hence the need to generate a load history from the strain history supplied.

b) Over heating is a major problem. The pump would often stop, with the profile generator continuing. This made it impossible to run the test program continuously.

3) Solartron Data Acquisition System:- This system was micro-processor based. It offered a setting for single gauges as well as rosettes. The system can be programmed to give the principal strains and their directions. This unit allowed 24 individual bridge circuits to be balanced and switched to an output separately. A print out facility was also provided.

4) Ferranti Merlin 750 Metrology system:- This machineprovided measurements in the X, Y, and Z directions.A horizontal bridge X, and a longitudinal granite worktable Y, and a vertical column Z, p r o v i d e d movements of 750, 750, and 500 mm respectively. To ensure precision of movement all axes were fitted with air bearings. The machine was also fitted with an optical scale which allowed measurements to be determined to a resolusion of 0.5 micro-metres.

The Merlin machine is micro-processor based, this

being fitted and operated as a combined counter and data processing unit. The machine can be part-

128

programmed by a personal computer. A print-out facility was also provided.

Measurement was carried out by probing the workpiece with a spherically-ended stylus. This operation was carried out manually under Joy-stick control, or computerised using the part-programming facility when undertaking repetitives routines, such as inspection.

This system was used to define the exact position of the strain gauges. Care was taken to position the gauges at points corresponding to the nodal positions of the finite element model around the critical location.

5) Dial Test Indicator:- This was used to measure the deflection values at the unsupported end of the steering arm under varying load increments.

5.3 Experimental Rigs

The steering arm was loaded to examine the effects on fatigue life of the stress fields which approximated the actual loading conditions. This was achieved by applying the load through the kingpin, as shown in figure 5.1.

The experimental rig designed to carry out both the static and fatigue tests consisted of two rectangular plates, a

circular plate, a T-section and a kingpin manufactured of EN18. The rectangular plates were fastened together with the steering arm bolted securely to the rig. This was then secured to the Dartre 9500 testing machine bed. The

129

T-section was fastened to the circular plate and this assembly was then secured to the actuator. The kingpinwas used to connect the above assemblies. Figures 5.1 and 5.2 show the exploded and the assembled views of the rig.

5.4 Strain Measurements

5.4.1 Strain Gauge Specification

SINGLE GAUGE ROSETTEType Reference YFLA -2 FRA -2 -11Length 2 mm 2 mmGauge factor 2.12 2.07Wire resistance 120 I 0.3 ohm 120 I 0.5 ohmOrientations _ 0°, 45°, 90°

5.4.2 Static Loading Results

In order to identify the principal planes for attachment of post yield strain gauges, two strain gauge rosettes were attached to the steering arm at the critical location identified from the finite element analysis. One gauge was attached to the radius of the component at a distance of 37 mm to the right of the centre of the middle boss. The

second gauge was fixed at an angle of 22° from the first gauge, conforming to the arrangement stipulated by the manufacturer, as shown in figure 5.3. The Dartec 9500 testing machine was used to apply loads from 5 kN to 40 kN in increments of 5 kN, and the strain and deflection values were recorded. The results are shown in table 5.1. A comparison of the measured maximum principal strains

130

with those obtained from elastic finite element analysis at the highest stressed node (node 12) was made. For a 20 kN load the maximum principal strains were found to be 1608 and 1571 m i c r o - s t r a i n for m e a s u r e d a n d F.E. calculated results, respectively. Therefore the F.E. result was about 2.3% lower than the measured strain.

To obtain the strain values in the plastic range the rosette strain gauges were replaced by two post-yield strain gauges. The post yield strain gauges were attached to coincide with the plane of the maximum principal strain identified by the rosette strain gauges. The Ferranti

Merlin 7 50 Metrology system was used to defined the exact position of the strain gauges. Loads were applied in increments of 10 kN up to a maximum load of 70 kN and the strain values were recorded at each load increment, as listed in table 5.2. Plastic collapse of the component occurred when a load of 80 kN was applied. Two values are useful for comparison; at 20 kN load 1425 micro-strain was recorded and at 70 kN load, 5668 micro-strain was

recorded.The measured strains were compared with the m a x i m u m principal strain values obtained using the elastic F.E. analysis at the highest stressed node (node 12), listed in table 4.2 and shown in figure 4.7. For an applied end load of 20 kN in the elastic range the finite element analysis gave a maximum principal strain value of 1571 micro-strain. For the same load the single gauge measured strain was found to be 1425 micro-strain. Thus, the F.E.

131

calculated results were 9% higher than the m easured strains in the elastic region. This is somewhat lower than the strain measured using the rosette and this appears to be true for all experimental strains, which are on average around 10% lower by the single strain gauge than those from the rosette.

Table 5.3 lists the measured and finite element based estimated strains based on both the energy density method and Neuber's equation. The component monotonic load/local strain calibration curves were used with the elastic finite element calculated equivalent values and both

Neuber's rule and the energy density method, and the

results are compared to the measured load/local strain

calibration curve in figure 5.4. It is apparent that for low values of load, both methods give results which are very close to the measured strains. For high values of load, the calibration curves obtained from both method

deviate from the measured strain curve. As the amount of plasticity increases the degree of correlation between

measured and Neuber's estimated strains decreases. A range of 6494 to 7077 micro-strain is at least 15% higher than the measured value of 5668 micro-strain. However, the degree of correlation between the measured and the energy density predicted strains remains of the same order of m a g n i t u d e t h r o u g h o u t the e l a s t i c and p l a s t i c

deformation. A measured value of 5668 m i c r o - s t r a i n

compares well with the energy method upper and lower

values of 5822 and 6070 micro-strain.

132

Figure 5.5 shows a plot of measured strains versus F.E estimated strains. The strain values obtained using both Neuber's and the energy based method fall above the 100% correlation line in all cases, showing both methods to overestimate the strain values in both the elastic and plastic range. Close agreement was found between the m e a s u r e d and p r e d i c t e d strains b a s e d on m o n o t o n i c stress/strain curves up to a 20 KN load (the elastic

range). However, it can be seen that the p r e d i c t e d strains based on F.E. calculated equivalent methods and Neuber's equation are grossly overestimated in the plastic range. This contrasts with the close agreement that exist between the measured and predicted strains based on the energy density method.

A reasonable correlation between the measured, and elastic finite element results using both Neuber's and the energy d e n s i t y p r e d i c t e d s t r a i n s has been a c h i e v e d w h e n

considering that the geometry of the finite element model was modified, as described in chapter 4.4.2. It was considered that the discrepancy between the results could be influenced by the following factors:

i) The misalignment of the single gauges w i t h the

direction of the principal planes during attachment.

ii) The strain gauge gives the average strain valuesunder the gauge whereas the finite element analysisgives the strain values at a nodal point.

133

5.5 Conclusions

i) The predicted strains based on F.E. analysis together with Neuber's rule and the energy density method are overestimated in both elastic and plastic ranges when compared to the measured strains.

ii) For low values of nominal stress, (Kt.S), both methods give results very close to the measured strains. For high nominal stress values, both Neuber's rule and

the energy density method over-estimate the local strains, however, better correlation is achieved with the latter.

iii) The plastic local strains estimated using the energy density method and von Mises equivalent stress exhibit closest correlation to the measured strains. T hose e s t i m a t e d u s i n g N e u b e r ' s e q u a t i o n and e q u i v a l e n t p r i n c i p a l stre s s e x h i b i t l e a s t

correlation.

134

135

Fig. 5.1 Dartec Fatigue Testing Machine Showing The Swivel Joints, Rig and Component in Position, (detailed position of the component shown schematically in fig 5.2).

136

Exploded View of the Testing Ri

LOAD

ROSETTE GAUGE (2)ROSETTE GAUGE (1)

22'

Fig. 5.3 Location of Post Yield Strain Gauges.

137

LOAD (KN) ROSETTE 1 (M STRAIN) ROSETTE 2 (U STRAIN)5 407 -60 400 -63

10 793 -114 777 -11615 1204 -108 1174 -16820 1608 -231 1561 -23825 2050 -279 2001 -28030 2435 -328 2382 -32535 2889 -438.8 2750 -38140 3295 -502 3195 -482

Table 5.1 The Measured Strains Using RosetteStrain Gauges.

138

LOAD(KN)

DEFLECTION(mm)

STRAIN GAUGI (1)

S (m STRAIN) (2)

10 1.43 714.4 711.620 2.71 1425 140430 3.72 2193 214440 4.82 2952 287650 5.96 3760 305660 7.55 4685 4533.670 ---- 5668 5633

Table 5.2 Experimental Strain Values UsingStrain Gauges.

139

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CHAPTER 6COMPUTER BASED JFATIGUE LIFE CALCULATIONS

6.1 Aims And Objectives

The critical location technique used to p r edict the fatigue life of engineering components from the "fatigue environment" (loads, stress, strain, etc) has been discussed in detail in chapter 2. Based on this method, a commercially available computer package (FATIMAS) has been applied to predict the fatigue life of the steering arm. The objectives of this programme of work were:-

i) To simulate the test circuit fatigue failure of the s t e e r i n g arm u s i n g the n C o d e fa t i g u e a n a l y s i s software package FATIMAS.

ii) To assess the components sensitivity to design and manufacturing variables, (Kf) and service loading variables.

iii) To compare the FATIMAS measured strain-time based

service history predicted fatigue life results with full scale load controlled fatigue testing of the component.

iv) To compare the FATIMAS measured strain-time based service history fatigue life results with FATIMAS predicted fatigue lives based on load calibrated strain-time service histories.

143

v) To compare the experimental results with FATIMAS predicted fatigue lives based on load calibrated measured strain-time service histories.

vi) To compare the experimental results with the Falcon predicted fatigue lives.

It should be pointed out that both the Neuber and theenergy density estimated cyclic notch root load/straincalibration curves, figure 4.10, were used to calibratethe washboard measured strain-time history for use inFATIMAS. For the applied load/strain calibration curvesan equation of the following form exists.

P P 1/de = — + ( — )

Ci C2where C i , C2 , and d are constants.

Ideally the calibration of the strain-time service history should be governed by the above equation and would take account of the non-linear stress strain relationship. However, it was not possible to include this equation intothe FATIMAS package since it is a commercial package and

can not be altered without permission. Therefore, .for both the experimental and FE estimated applied load/strain curves an approximate linear extrapolation was used. The load-time history for experimental fatigue life evaluation

is based on the measured monotonic load/strain curve. An arbitrary reduction in strain of approximately 10% on

36.5 kN load value obtained from the measured monotonic load/strain calibration curve was imposed to compensate for cycle-dependent softening of the component material.

144

This ensured reasonable lives were likely in tests. The 33 kN load value was used to scale the measured strain­time service history for a maximum strain value of 2734 micro-strain for experimental fatigue life evaluation.

Before discussing the fatigue analysis results, the FATIMAS software is described to present the reader with an understanding of the techniques involved [84].

6.2 Software Summary

The FATIMAS program is modular in nature and consists of the following modules signal display, data manipulation, signal analysis, fatigue analysis, material properties, etc.

The p r o g r a m r e q u i r e s three inputs, the f a t i g u e

environment, appropriate materials data, and geometric information.

The fatigue loading on a component is a s s umed to be obtained from service measurement, or by generation of artificial histories using statistical techniques. An edit facility is also available to remove spikes and gate out

noise before extracting the turning points.

Properties for a number of materials are included in the data base and further materials can be added.

The f o l l o w i n g m a t e r i a l p r o p e r t i e s are u s e d in the analysis:- K ’> n 1, E, of 1 , e f 1, b and c. The module MDT e n a b l e s the g r a p h i c a l d i s p l a y of the f o l l o w i n g r e l a t i o n s h i p s [32].

145

1) stress amplitude versus life

2) strain amplitude versus life

3) Smith-Topper-Watson (S.T.W) parameter versus life

4) cyclic stress/strain curve

Following input of the elastic stress concentration factor, Kt, fatigue damage is calculated u s ing the critical location approach by rainflow and the cycle counting using the cyclic stress/strain curve.

The following output modules are also available SLP - Display of stress/strain hysteresis loops P3D - Display of cycle and damage histograms H3D - Formation of cycle and damage histograms

6 .3 Measured Strain-Time History

The Washboard signal for the steering arm contains 13705 data points, at a sampling rate of 370.4 points per second. The turning point history contained 884 turning points (442 cycles). Figure 6.1 shows the details of the complete signal.

6.4 Material

The material used for the manufacture of the steering arm was a forging steel DIN 41 CR 4V. The fatigue data was generated by constant amplitude, strain controlled axial p u s h - p u l l t e s t i n g of c y l i n d r i c a l s p e c i m e n s by the manufacturer. For full material specification see chapter

3.3, table 3.1 and f i g u r e s 3.16 to 3.18.

146

6.5 Fatigue Reduction Factor

A data acquisition exercise has been carried out by the manufacturer using four strain gauges, two of which were affixed at the critical location of the component. Hence, the fatigue strength reduction factor, Kf = 1, was used for the analysis.

6.6 Fatigue Life evaluation

6.6.1 FATIMAS Fatigue Life Assessment: Measured Strain-Time Service History

Table 6.1 shows the fatigue life predictions together with a list of the set-up conditions. In this case a life was predicted consisting of 58 repeats (25636 cycles) of

signal.

Table 6.2 and figure 6.2a display the t a b u l a t e d and grapical output showing the effects of adjusting the

magnitude of the signal by a "strain factor". Successive 10% reductions were made down to 70% of the strain range. The reduction in strain factor reduced the amount of plasticity which the material experienced.

Table 6.3 shows the sensitivity of fatigue life to variations in stress concentration factor, Kf. Figure 6.2b

displays a graphical output of the data from which it is evident that the component is sensitive to small changes in K f . For example by increasing Kf from 1 to 1.1, an increase in fatigue life of 36% would be achieved.

147

Figure 6.3 shows the hysteresis loops traced by the material during cycling. It is evident that the material is capable of withs t a n d i n g a considerable amount of plasticity, by the relatively wide hysteresis loops shown. The life to crack initiation was very short, (58 repeats of strain history), which was not unexpected since the strain data was acquired from the worst durability course. Figures 6.4 and 6.5 show the three dimensional graphical histogram of the cycles and associated fatigue damage

using rainflow. It is evident that only a small number of cycles caused most of the fatigue damage. It can be seen that two cycles in particular were responsible for most of the damage.

6.6.2 Fatigue Life Assessment: Load Calibrated Measured Strain- Time Service History

In order to appreciate the potential limitation of the techniques described in section 4.5, it was decided to

assess the fatigue life of the steering arm through a range of service histories. Each has the same pattern of loading as the known service history, with the lowest applied load of 20 kN having all strains less than yield and the highest applied load of 40 kN incorporating high yield strains. In all cases the FATIMAS predicted fatigue lives based on FE calculated strains were compared with the FATIMAS washboard history lives and experimental fatigue lives. These are shown in table 7.1. The maximum

strain value identified from the washboard service history data was 2734 micro-strain, which was used in subsequent c a l i b r a t i o n e x e rcises.

148

The fatigue life evaluation package FATIMAS was used to predict the life of the component for a maximum load of 20 kN, using both the F.E. calculated strains and the measured strains. Load/strain factors of 0.57, 0.59 and 0.52 we r e a p p l i e d to the k n o w n s e r v i c e h i s t o r y to represent finite element calculated strain and both the rosette and post yield strain gauge results. The fatigue life was found to be infinite in both cases. Clearly, the 2.3% and 9% strain difference between the computerised and measured strains has no effect on the fatigue life of the component under these conditions.

The m o d i f i c a t i o n of the radii a r o u n d the boss, as described in section 4.4.2, may have had a considerable influence upon the results, i.e. an increase of the radii around the boss may have reduced the amount of stress concentration at that area. To examine the effect of such an occurrence the F.E. calculated strain at the highest stressed node was increased by 10%. This gives strain

values of 1728 micro-strain. The fatigue life of the component was then predicted using the above strain and was again found to be infinite. Thus, it can be concluded

that in this case a 10% difference in finite element strains had no influence on the fatigue life of the component.For prediction of the post yield strain values at the critical location, the F.E. calculated equivalent stresses were used with both Neuber's rule and the energy approach, as described in chapter 4.5. The results are listed in table 4.5.

149

In order to judge the real life of the component it was decided to do incremental life evaluations in FATIMAS. This was carried out in load increments of 5 kN from 20 kN to 40 kN. Table 6.4 lists the predicted fatigue lives and figure 6.6 displays the graphical output of the data. The f a t i g u e lives b a s e d on the e n e r g y m e t h o d are g e n e r a l l y l a r g e r than those u s i n g Neuber.

For low loads the maximum predicted life is 1.63E7 cycles which was obtained from Neuber's method combined with maximum principal stress. The highest life was 2.4E9, cycles, obtained using the energy method and von Mises equivalence. This represents a spread factor of more than 147, but when expressed in logarithmic terms is a factor of 1.3.

At the upper load limit the minimum life is 7.5E3 cycles and again comes from the combination of maximum principal stress and Neuber's method. When using von Mises and the energy method the highest life of 4 . 0E4 r e p eats is obtained, which is a factor of 5.2 greater than the minimum life. Again when represented in logarithmic terms this is 1.18. Also included are results represented as blocks of service histories, shown in table 6.5.

Table 6.5 lists the predicted fatigue lives obtained using FATIMAS measured strain-time service history and those obtained using load calibrated m easured s t r a i n - t i m e service history based on F.E. calculated strain with both N e u b e r ' s rule and e n e r g y d e n s i t y m e t h o d f o r load decrements from 33 kN to 23.3 kN\ The former represents

150

the maximum 2734 micro-strain in the service history and the latter represents successive reduction in load history of 10% on the 33 kN load until the load was 70% of the initial value. This represented a maximum total strain of 1914 micro-strain in the strain-time service history. Tables 6.6 and 6.7 lists the predicted number of cycles and blocks of load-time service history to failure of the steering arm and figure 6.7 represents the graphical output of that data.

For load increments from 23.3 kN to 33 kN, the predicted fatigue lives obtained using maximum principal stress,

Tresca, von Mises and maximum principal strain methods were found to be non-conservative when compared to the predicted fatigue lives obtained using FATIMAS with the measured strain-time service history. The same is true of Neuber's estimated load-time service histories of Tresca and von Mises. The predicted lives based on maximum principal strain are conservative for a load ranging from 33 kN to 25 kN and below that range are non-conservative when compared to the predictions based on measured strain­time service history results. The predicitions based on maximum principal stress equivalence load-history are conservative in all cases when compared to m e a s u r e d strain-time service history results with FATIMAS.

6.7 Conclusions

i) The predicted fatigue lives based on energy density

method were found to be nonconservative when compared

151

with those obtained using Neuber's load-time service history.

ii) The predicted fatigue lives based on FATIMAS measured strain-time history are found to be conservative when compared with prediction based on both the energy density and Neuber's load-time service histories except for those obtained using maximum principal stress load-time service history.

iii) Of the two methods used the fatigue life predictions based on von Mises equivalent method and energy density were found to be highest-Those predicted using Neuber's load-time service history and maximum principal stress were found to be the lowest and most conservative.

152

DISPLAY

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153

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rain

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ice

Hist

ory.

Turning Point History

MaterialScaling FactorStress Concentration Factor, Kf

Damage Parameter

Plain Strain Correction Miners Constant Number of cycles used Fatigue Life

Table 6.1 Results of Analysis.

W B .DAT 41CR4V

1

1Smith-Topper-

Watson

Y144258 repeats of

history

154

FACTOR FATIGUE LIFE (REPEATS OF HISTORY)

0.7 78660.8 715

0.9 1571.0 58

Table 6.2 Strain Factor versusLife Analysis.

155

FACTOR FATIGUE LIFE (REPEATS OF HISTORY)

1 581.1 211.2 111.3 62

1.4 41.5 2.8

Table 6.3 Stress Concentration Factor K f Versus Life Analysis.

156

0.6 — i------- 1------- 1_______ i------- 12000 4000 6000 8000 10000

Life (repeats of history)

nCod« NSOFT V2.1

a) Strain Factor Versus Fatigue Life.

CROSS PLOT OF DflTfi « PLN2

1.3

0.950 60 7030 402010

Life (repeats of history)

nCode NSOFT V 2 .1 __________________________________ ;____________________________________________________________

b) Stress Concentration Factor, Kf Versus Fatigue Life.

Fig. 6.2. Fatigue Life Assessment.

' 157

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159

Fig. 6.4 Cycle Distribution For Washboard History.

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Fig. 6.5 Damage Distribution For Washboard History.

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166

CHAPTER 7

FATIGUE TESTING

7.1 Introduction

To verify the results obtained from the computerised fatigue life predictions, a number of experimental tests

were performed.

Testing of the steering arm was undertaken to determine the fatigue life of the component under "realistic" variable amplitude load histories. The number of cycles to failure obtained from the above test was compared with computerised results obtained from using FATIMAS software. Failure of the component was defined as when a visible

crack of approximately 3 mm was observed.

7.2 Test Equipment

Scanning Electron Microscope: A Philips S.E.M was used for examination of the fracture surface. The S.E.M provided a qualitative examination of surfaces, and magnifications of X80,000 were possible, maintaining an excellent depth of

focus.

7 . 3 Fatigue Testing

The Dartec 9500 computer controlled multiaxial testing machine described in section 5.2, was used for fatigue life evaluation of the steering arm.The strain history data file WB.DAT, shown in figure 7.1, was converted to a load history suitable for the Dartec

167

profile generator file WB.PG, shown in figure 7.2, using the 'Load1 program. The measured strain values were used to produce a load/strain calibration curve, shown in figures 5.4. Ideally the component should be cyclically stabilised prior to strain gauge measurement. However, this was not possible. This problem was o vercome by imposing a 10% reduction on the 36.5 kN load value o b t a i n e d from the m e a s u r e d m o n o t o n i c l o a d / s t r a i n calibration curve for the maximum strain value of 2734 M i c r o - s t r a i n obtained from the strain based service

history. The 33 kN load value was used to scale the strain based history to a load history for experimental fatigue life evaluation.

The WB.PG file was loaded and the actuator was set to run at a frequency of 2 Hertz.

It was required to modify the machine in order to apply the load in a way which resembled or simulated the actual service conditions. This was achieved by the attachment to

either end of the actuator of a swivel joint as shown in figure 5.1. These units provided +/-45 degrees of freedom in one direction and +/-5 degrees of freedom in the other, which represented the actual transmission of force from the steering rod to the steering arm.

7.3.1 Crack Detection Methods

Several methods were considered for measuring crack initiation, a brief operational procedure for each system is d e t a i l e d b e l o w : -

168

a) Crack Propagation Gauges:

These gauges were used for indicating the rate of crack propagation in the specimens, through micro-measurement of the cracks. The gauge consisted of a number of resistor s t r a n d s c o n n e c t e d in p a r a l l e l . Whe n b o n d e d to a structure, progression of the surface crack through the gauge pattern caused successive open-circuiting of the strands, resulting in an increase in total resistance. This produced stepped increases with successive open circuiting which was recorded on a chart recorder. To facilitate the use of crack propagation gauges the surface of the specimen was polished, which itself affects the fatigue life of a component. It is equally important tohave some knowledge of the point where the crack initiates and this limits the application of such gauges in 'real' components [78].

b) Direct Current Potential Difference Crack Monitoring System:

In this d.c. method a large direct current was applied along the length of the specimen and the potential drop due to the growing fatigue crack, monitored. However, due to the high current density requirements of the method it

can only be used for monitoring the growth of long cracks. Long current leads are necessary with this method causing

diffficulties with small specimens. There were further problems with vibrations which reduced the m a x i m u m frequency at which the fatigue tests could be carried out. Another disadvantage was the need to electrically insulate

169

the specimen from the testing machine. This limited the maximum load to which the specimen was subjected due to early failure of the insulating material [75].

c) A l t e r n a t i n g Current Potential Diffe r e n c e Crack Monitoring System:

In this method a constant a.c. current was applied along the length of a specimen and the potential difference due to the growing fatigue crack was monitored. The a.c. method had been developed to overcome the above mentioned problems. The method utilises a relatively low current density and is suitable for all test piece geometries. A

major advantage of the method is that it can be used at elevated temperatures and in hostile environments. However, the technique is relatively expensive to use. The m a j o r d i s a d v a n t a g e of the s y s t e m is the n e e d to electrically insulate the component from the testing machine [76, 77].

d) Dye Penetrant Method:

The dye penetrant method consists of a three stage process

using a cleaner, penetrant and a developer. In the cleaning stage the cleaner is used to clean the surface to be inspected, and then the penetrant is applied. This is left for at least 15 minutes until the penetration is completed. The excess penetrant is removed from the surface by the cleaner. In the last stage a thin film of developer is applied and left for at least 10 minutes prior to inspection for any defects. The disadvantage of

170

this method is that the crack length can not be accurately measured. However, the dye penetrant method was found to be the most acceptable method of crack detection and hence it was used [78].

7.3.2 Fatigue Crack Initiation Tests

Fatigue testing of the steering arm under v a r i a b l e amplitude loading to crack initiation was performed. A total of five components were tested at four different load levels. Two components were tested using the load calibrated measured strain-time service history for a 33 kN load. The steering arm failed at 84 and 97 blocks of the load history, or 37128 and 42874 cycles.

In o r d e r to v e r i f y the e x p e r i m e n t a l r e s u l t b e f o r e subsequent tests were conducted, a comparison was made between experimental and FATIMAS measured strain-time service history predicted fatigue life results. FATIMAS predicted Fatigue life of 58 (25636 cycles) blocks of the strain history was obtained. These results showed close agreement with the experimental results. Hence, the accuracy of data conversion was confirmed.

Ih order to assess the fatigue life of the steering arm at lower load increments the load calibrated service history was reduced by 10% over three successive tests until the

load was 70% of the initial value. Therefore, the measured strain history was scaled over the three r e m a i n d i n g e x p e r i m e n t a l tests. Thus, m a x i m u m l o a d

increments of 29.6, 26.5, and 23.3 kN were applied. The

171

results of the experimental tests and FATIMAS predictions are listed in tables 7.1 and 7.2 and shown in figures 7.3 and 7.4.

7.4 Visual Examination Of The Fracture Surface

Figure 7.5 shows the fracture surface of the component after testing to failure under a maximum 33 kN load. An examination of the fracture surface showed three distinct regions.

a) An area surrounding the initiation point marked, in which subsequent slow crack propagation occurred, reaching a point half way through the thickness. Overall, this area appeared to be flat.

This was due to repeated impact of the two surfaces under alternating loads. The radial marks at the c o r n e r s of the top s u r f a c e were c a u s e d by the progression of the crack into these areas.

b) The core of the component shows evidence of more

ductile failure, which was confirmed by Scanning Electron Microscope (SEM), shown in figures 7.9 to 7.11. The ductile fracture zone started at a crack len g t h of a p p r o x i m a t e l y 60% of the c o m p o n e n t thickness.

c) A final band of catastrophic crack p r o p a g a t i o n

consistent with over-load at a crack length of approximately 75% of the total component thickness.

172

7 . 5 Fractrocrraphv Investigation

The complete fracture surface, shown in figure 7.5 was then examined using a scanning electron microscope.

a) Figure 7.6 shows the surface immediately surroundingthe i n i t i a t i o n point. This s u r f a c e was m i c r o ­scopically flat with evidence of scuffing possibly due to repeated impact of the two crack surfaces during the first part of the test.

The fatigue crack evidently originated at the change in thickness, at which point the m a x i m u m stress concentration occurred as identified by finite element analysis, and shown in figure 4.7.

Figure 7.7 is typical of the slow crack propagation region. The s u r f a c e c o n t a i n s shell m a r k s p e r p e n d i c u l a r to the a p p l i e d s t r e s s and w e r e characteristic of slow fatigue crack growth.

Figure 7.8 shows the transition area between slow growth fatigue and ductile shear fracture. Secondarycracks on this surface are intergranular.

b) Figures 7.9 to 7.11 show an area of ductile shearfracture. There were mixed fracture modes in this area and d u c t i l e d i m p l i n g , t y p i c a l of d u c t i l e fracture was clearly visible. Also visible were areas where intergranular fracture had occurred. The spherical beads in the cavity roots are non-metallic

inlusions of manganese sulphide, as can be seen from

173

the spectra of inclusion, shown in figure 3.6, which serve to initiate ductile failure.

c) Figures 7.12 to 7.14 show the area of final brittle fracture. Two modes of fracture are clearly visible. The intergranular fracture mode predominates, but large regions of cleavage also were present.

7.6 Microstructure

As described in sections 3.4 and 3.5 the component was

austenised at 1200°C and oii quenched after forging. This treatment resulted in a 50% bainitic/martensitic micro­structure, with the proportion of marte n s i t e being

greater at the component surface.

Tempering was carried out at 600°C by the manufacturer. However, cooling conditions after tempering are not known, but it is thought likely that air cooling was used. This would have resulted in slow progress through the critical 450°C region and caused temper embrittlement [79, 80]. The presence of extensive intergranular c racking in the central and final crack zone would support this view.

7.7 Discussion

The predicted fatigue lives obtained using FATIMAS for the m e a s u r e d s t r a i n - t i m e h i s t o r y and F A T I M A S for load calibrated strain-time histories were compared with load controlled experimental results.

Of the five components, two were tested using the load calibrated strain history. The steering arm failed at 84

174

(37128) and 97 (42874 cycles) blocks of the load history, respectively. The FATIMAS measured strain-time history based fatigue life was 58 (25636 cycles) blocks of the washboard signal. Thus, the experimental results were

h i g h e r by fa c t o r s of 1.4 and 1.6 (29% and 39%)respectively, as shown in figures 7.3 and 7.4. During the durability assessment of the prototype truck on proving

grounds, the failure of the steering arm occurred after 120 circuits; this is quite close to both the FATIMAS strain history results of 58 repeats and p r o t o t y p e experimental results of 84 and 97 repeats of the washboard signal which suggests that only the washboard surface has caused the damage.

The strain history was reduced by 10% over the remaining three experimental tests to assess the effect on fatigue life of adjusting the magnitude of the washboard history. T hese w e r e then c o n v e r t e d to a load h i s t o r y for experimental fatigue life assessments. Experimental fatigue lives of 230 (101660 cycles), 874 (386308 cycles), and 4635 blocks (2075546 cycles) were obtained for load values of 29.8, 26.5, and 23.3 kN respectively, which compare well with FATIMAS experimental strain-time history predicted results of 158 (69836 cycles), 720 (318240cycles), and 7866 (347672 cycles) blocks of the strain histories.

For calibration loads of 29.8 and 26.5 kN the experimental results were higher by factors of 1.54 ( 34%) and 1.2

(17.6%) when compared to the FATIMAS results. For a

175

calibration load of 23.3 kN the FATIMAS result was higher than the experimental result by a factor of 1.7 (41%) as shown in figure 7.4.

Figure 7.4 displays a plot of the predicted fatigue lives based on cyclic load/strain calibrated strain-time history and FATIMAS measured strain service history versus the experimental data. Also shown is the 100% correlation line and factor of 3 scatter band. The predictions based

on N e u t e r ’s method and the energy density approach andFATIMAS strain-time service history results show good

correlation with the experimental results with 66% of the points falling within a factor 3 scatter.

The FATIMAS strain-time service history predicted fatigue lives fall below the 100% correlation line for load increments of 33 (2734 micro-strain), 29.8 (2461 micro­strain) and 26.5 (2187 micro-strain) kN, showing that the p r e d i c t i o n s are c o n s e r v a t i v e w h e n c o m p a r e d to the experimental results. For a 23.3 kN the predicted fatigue lives are non-conservative.and above the correlation line.

The a bove r e s u l t s c o n f i r m the p r e v i o u s l y d e r i v e d conclusion that Neuber's rule underestimates the fatigue

life of the component below the material yield point, thereafter, overestimates the life. The p r e d i c t e d fatigue lives based on the energy density method were

found to be n o n - c o n s e r v a t i v e and above the 100% correlation line in all cases. The predictions based on Tresca, von Mises and maximum principal strain load-time

176

service history calibrated washboard signal were found to be above and outside the scatter band, showing that the above equivalent methods grossly overestimated the fatigue life of the steering a r m , . The predictions based on maximum principal strain also have been overestimated but not to the same extent.

The fatigue life predictions of Neuber load-time service histories were found to be in close agreement with both the FATIMAS strain-time and experimental results. The

predictions based on maximum principal stress method were found to be the most conservative. Closest agreement is achieved with both Tresca and maximum principal strain methods.

177

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Fig. 7.5 The Fracture Surface Of The Component (x1-5)

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macroscopically flat with evidence of scuffing due to repeated impact of the two crack surfaces (x30).

186

Fig. 7.7. Crack propogation region. The surface contains shell marks perpendicular to the applied stress (x1000).

187

Fig. 7.8 Showing the transition area between slow crack growth fatigue and ductile shear failure (x1100).

188

Figure /.9 Showing an area of ductile shear failure. The spherical beads in the cavity roots are non-metallic inclusions of manganese (x5000).

189

Fig. 7.10 An Area of Ductile Fracture. Mixed Fracture Modes are clearly visible, ductile dimplin; typical of ductile fracture and inter-granular fracture (x2000).

190

Fig. 7.11 An area of ductile fracture, showing non- metallic inclusions of manganese sulphide, which serve to indicate ductile failure (x2100).

191

Fig. 7.12 Final brittle fracture. Two modes of fracture are visible. The intergranular fracture mode predominates, but there exists large regions of cleavage (x5000).

192

Fig. 7.13 Brittle fracture. Showing intergranular and cleavage fracture (x150).

193

Fig. 7.14 Brittle fracture region. Final catastrophic failure (x150).

CHAPTER 8INTEGRATED FE AND FATIGUE COMPUTATIONS

8.1 New Software Structure

As a r e s u l t of this i n v e s t i g a t i o n an i n t e g r a t e d CAD software package is being developed by nCode International Limited in conjunction with PAFEC, by which durability of

engineering components can be predicted in the conceptual design stage. The purpose written PAFEC/FATIMAS suite is called FALCON and was used ,to predict the fatigue life of the steering arm through a range of service h i s t o r i e s using the elastic finite element stress data. The FALCON

package requires a load-time service history which was provided for the steering arm as outlined in section 4.5. The F A L C O N p a c k a g e uses the e l a s t i c f i n i t e e l e m e n t equivalent stresses to convert the load-time service h i s t o r y to a strain s e r v i c e h istory, u s i n g N e u b e r 1 s method. This is then used in conjunction with the cyclic stress/strain curve to develop a local elastic/plastic s t r e s s - t i m e h i s t o r y w h i c h is u s e d for f a t i g u e life prediction. This takes account of the non-linear, load- strain relationship which was not included in the work d e s c r i b e d in s e ction 6. The F A L C O N p a c k a g e u s e s the following equivalent methods; principal stress, Tresca,

von Mises, and oxx . These are used in conjunction with the cyclic stress/strain data, Neuber's e q u a t i o n and rainflow counting for fatigue life prediction.

The flow c h a r t of fig u r e 8.1 shows the r e l a t i o n s h i p b e t w e e n F A L C O N and the FEA s y stem.

194

The procedure adopted in applying the FALCON package to fatigue life prediction of the steering arm component is as follows

1) A c t u a l l o a d i n g c o n d i t i o n s e x p e r i e n c e d by the component during service are simulated on the F.E. model.

2) Elastic finite element analysis is carried out.

3) The cyclic properties of the material are entered.

4) The washboard load history is entered.

5) The critical location is identified and the surface

finish strength reduction factor was entered.

6) Fatigue life prediction is carried out.

7) PIGS is used to display the results. The actual damage at each node surrounding the critical location was d i splayed. The life maps for 33 kN l o a d increments are shown in figures 8.2 to 8.5.

8.2 Steering Arm Fatigue Predictions

Fatigue life predictions of 80 blocks (3.5E4 cycles), 85

blocks (3.7E4 cycles), 113 (4.9E4 cycles) and 147 (6.5E4 cycles) of the load-time service history were obtained for maximum principal stress, axx, Tresca and von Mises, respectively for load value of 33 kN in the load history signal.

195

The predicted fatigue lives obtained using FATIMAS for m easured strain-time history and FATIMAS for FE load calibrated measured strain-time.histories were compared with load-time .service history results obtained using the FALCON package. The results are listed in tables 8.1 and8.2 and shown in figure 8.6.

The FATIMAS package used with measured strain-time history

gave a predicted fatigue life of 58 blocks (2.6E4 cycles). Fatigue life predictions of 63 blocks (2.8E4 cycles), 101blocks (4.5E4 cycles), 125 blocks (5.5E4 cycles) and 91blocks (4.0E4 cycles) of strain history derived from Neuber's method were obtained for maximum principal stress, Tresca, von Mises and maximum principal strain respectively under the 33 kN load. For the same load, predictions of 231 blocks (1.0E5 cycles), 338 blocks (1.5E5 cycles), 360 blocks (1.6E5 cycles) and 308 blocks (1.4E5 cycles) of the signal were obtained using the energy density approach, load c a l i b r a t e d s t r a i n - t i m e history. The F A L C O N p a c k a g e predicted fatigue lives of 80 blocks (3.5E4 cycles), 85 blocks (3.7E4 cycles), 113 blocks (4.9E4 cycles) and 147blocks (6.5E4 cycles) of washboard load- time servicehistory. As mentioned earlier, experimental tests gave lives of 84 and 97 blocks respectively. These results are summarised in Table 8.1 and 8.2.

The FATIMAS fatigue life predictions based on the measured strain-time service history are in close agreement with those obtained using the FALCON package. However, all of the predictions based on Neuber's equation were lower and all

196

based bn the energy density approach were higher than the FALCON results.The FATIMAS strain-time history predicted fatigue lives and the FALCON results are compared with the experimental data in figure 8.6 on which the 100% correlation line and factor of 3 scatter bands are shown. The predictions show a good correlation with experimental fatigue life data for a crack length of approximately 3mm. All data falls within a factor 3 scatter band when plotted. The FATIMAS, fatigue life predictions with both the strain-time service history and F.E. and Neuber's load calibrated washboard signal are in close agreement with those obtained using the F A L C O N p ackage. All data is w i t h i n a fact o r 3 of s c a t t e r .

However, all of the life predictions based on the energy density approach are non-conservative and much higher than the FALCON results. Best correlation was achieved using both the maximum principal strain and Tresca with Neuber's load-time histories.

8.3 Discussion

The reason for any lack of correlation between F A L C O N results and those obtained using Neuber's method are due to the following assumption:

A p p r o x i m a t e linear e x t r a p o l a t i o n (single p o i n t calibration) was used for calibration of the m e a s u r e d washboard strain-time service history for fatigue life predictions. Thus, this increased the accuracy of the fatigue life predicitions obtained using Neuber's method and decreases the correlation between the FALCON results and those obtained using the energy density approach.

197

8.4 Conclusions

The elastic/plastic strain values obtained using F.E. calculated equivalent stresses and both Neuber's equation and the energy density approach have been used successfully to convert a load history to a strain history suitable for fatigue life analysis. A comparison of these result s_ with the experimental data reveals that the load/strain fatigue life predictions as seen in figures 6.6 and 6.7 give good agreement, with 66% of the points falling within a factor of 3 scatter band. With the FATIMAS measured strain-time history and FATIMAS load-time service history with Neuber fatigue life predictions, all of the points are within a

factor 3 scatter band. The results confirm the accuracy of the procedures employed to obtain the e l a s t i c / p l a s t i c strains from finite element results using both the energy density and Neuber's rule. These specific relationships have been used to adjust the known meas u r e d w a s h b o a r d strain-time history for fatigue life assessment. The flow

chart shows the steps taken to achieve the results, see figure 8.7.

The FATIMAS package relies upon measured service history which is not available at the design stage (as shown in figure 8.7, (route 1). However, the F.E. i n t e g r a t e d technique can be used with a load history in the early design stage to assess the integrity and durability of engineering components at a CAD workstation. This enables the e n g i n e e r to d e s i g n a c o m p o n e n t and a p p l y f i n i t e e l e m e n t a n a l y s i s to stress the c o m p o n e n t u s i n g the

198

available nominal load history. The stress data can then be used to obtain elastic/plastic strains in conjunction with either Neuber's or the energy .method using a range of load increments,. This can then be used to create a service history which can be input into the FATIMAS software to assess the durability of the component, as shown in figure 8.7, (route 3).

199

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200

Steer tng Arn with Offset Loading

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Fatigue Life Controus for the Steering Arm (Tresca's Method).

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Fig. 8.4 Fatigue Life Contours for the Steering Arm (von Mises' method).

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CHAPTER 9DISCUSSION9.1 Introduction

The principal objective of the present work has been to identify the data requirements for the development of c o m p u t e r s o f t w a r e to e s t i m a t e the f a t i g u e life of engineering components at the conceptual design stage. In

particular, the programme has investigated ways of supplying appropriate data to existing computer packages which use the criticallocation' method of fatigue life assessment and pseudo-experimental data in the form of component strain histories. Typical of these types of software is the software suite FATIMAS, which hitherto

have tended to be used as development rather than design tools.

Finite element methods give stress fields which have been

u s e f u l in c o m p o n e n t design, however, f a t i g u e life prediction can be a reality if the finite element stress field can be translated into local strain histories for

input into fatigue life prediction software. Several alternative ways of achieving this objective have been investigated by using a real engineering component, namely a steering arm.

A three dimensional model of the steering arm was created and use d to select the r e l e v e n t s u r f a c e b o u n d a r y coordinates needed for the development of a finite element mesh. A three dimensional elastic finite element analysis of the steering arm was performed employing quadratic

209

isoparametric solid elements in order to identify the fatigue critical locations. The local elastic/plastic strains required for fatigue life estimation of the component were then calculated. Both the energy density and Neuber's method were used to predict strains necessary for incorporation into the critical location method.

To provide experimental comparison with the theoretical

analysis a number of strain gauges were installed around the critical location of an experimental component identified by the finite element analysis. Measured static

strain values were obtained for load increments of 10 kN up to a 70 kN load and c o m p a r e d to the c a l c u l a t e d e l a s t i c / p l a s t i c s t r a i n s o b t a i n e d u s i n g the a b o v e techniques, as shown in figure 5.4. An arbitrary 10% reduction in the measured strains was imposed to account for cycle-dependent softening of the component material. This was then used to plot an applied load/local strain calibration curve for conversion of the service strain history to a service load history suitable for fatigue testing of the steering arm.

Load control fatigue tests were performed on the steering arm using a Dartec computer controlled multi-axial servo- hydraulic fatigue testing machine with automated test control and data acquisition systems. A total of five c o m p o n e n t s wer e t e s t e d to c r a c k i n i t i a t i o n . The experimental results were compared to computer based fatigue life predictions obtained using the FATIMAS s o f t w a r e package.

210

The main objective of this section is to discuss the experimental and theoretical results. It is divided into two sections, computer based modelling and analysis, and theoretical and experimental fatigue life assessment.

9.2 Computer Based modelling and analysis

The elastic finite element results were compared with the measured strains in the elastic region. For a 20 kN load the F.E. calculated m a x imum principal strain at the highest stressed node (node 12) was 9% higher than the measured strain, listed in tables 4.2 and 5.2. Given the approximate nature of the finite element and the measured strains, also the simplifications in geometry, this can be considered to be a satisfactory correlation.

Since local strains are u s e d for f a t i g u e d a m a g e

evaluation, the first requirement for fatigue life estimation is to develop a technique for calculation of the plastic strain field. Current computer p r o g r a m s predict local strains from nominal stresses and strains using Neuber's method for both elastic and pl a s t i c conditions. Hence, it is important to c o m p a r e the estimated and measured strains for a range of load increments which provide both elastic and plastic local strains.

The multiaxial elastic F.E. calculated stresses around the critical location were reduced to equivalent stresses using maximum principal stress, von Mises, Tresca and maximum principal strain methods, listed in tables 4.1 to

211

4.3. The m a x i m u m v a l u e s f ound were then u s e d in conjunction with both Neuber's rule and the energy density approach as well as the monotonic uniaxial stress/strain curve to estimate the elastic/plastic strains. These were then compared to the measured strains in both ealstic and plastic ranges, listed in tables 5.2, and 5.3 and shown in figure 5.4.

Figure 5.5 displays the graphical representation of the same data, which shows that the estimated strains fall above the 100% correlation line using both methods. Both Neuber and the energy density calculations correlate well with the measured results throughout the elastic and plastic regions. Maximum differences of 15.5% was observed in the elastic range (10 kN load), and 20% was observed in the plastic region (70 kN load).

The experimental results confirm that Neuber's equation gives less accurate predictions than the energy density method when plastic yielding occurs. From the above discussion it is clear that the accuracy of the described m e t h o d s a p p e a r to be d e p e n d e n t upo n the e x t e n t of propagation of the plastic zone at the notch tip [37, 63]. It can be concluded that both Neuber’s rule and the energy density method can be used to estimate the elastic/plastic stress/strain values for any loading conditions, ahead of a notch if appropriate elastic stress field and the material stress/strain curves are known. While Neuber analysis is found to give a lower accuracy than the energy method, it is significant that all the predictions

212

are conservative when compared to the energy density method in the elastic and plastic region.

Having proved that the above techniques can be applied s u c c e s s f u l l y to o b t a i n the m o n o t o n i c n o t c h root elastic/plastic strains, attempts were made to estimate the cycle dependent elastic/plastic strain values. Table 4.5 lists the estimated strains and figure 4.10 displays the cyclic notch root load/strain calibration data. Good correlation exist between the measured and estimated strains based on both monotonic and cyclic stress/strain curves in the elastic•region. However, estimated strains in the plastic region are grossly overestimated when compared with the experimental and those obtained on the basis of the monotonic stress/strain curves. This can be explained with reference to figure 4.8 which shows that the onset of cyclic yielding for the component material occurs at approximately 20 kN load. Consequently, at this load the component material experienced some plastic deformation. The above results show that both Neuber's rule and the energy density method overestimate the local strains above the yield point. As the load increases the degree of. correlation decreases, which indicates that the accuracy of the results are dependent upon the extent of the plastic deformation at the notch root. This confirms the previous conclusion that Neuber's method grossly overestimates the plastic strain in the plastic region when compared to those obtained using the energy density method. The F.E. calculated stresses have been reduced to a single equivalent stress using maximum p r i n c i p a l

213

stress, von Mises, Tresca, and maximum principal strain methods. Both Neuber's rule and the energy density approach were used in conjunction with both monotonic and cyc l i c s t r e s s / s t r a i n c u r v e s to e s t i m a t e the local elastic/plastic strains. Applied load/local strain curves

are shown in figures 4.9 and 4.10. These are described by

the following relationship between local strain, e, and applied load, P:

P P 1/de = _ + (__) - 9.1Ci C2

Where Ci , C2 , and d are constants.Constants Ci , C 2 and d can be determined for the r e l a t i o n s h i p by u s i n g l i n e a r r e g r e s s i o n a n a l y s i s . Previously the development of the applied load/local strain curves has not been possible at the pre-prototype design stage. However, it is now possible to employ elastic F.E. analysis to identify the most crit i c a l location within a component for detailed investigation. Applied load/local strain curves are then developed and used to create a load service history or to modify the existing measured strain-time history. Further more the described technique avoids the time consuming and error- prone calculation of stress concentration factor, Kf .

214

9.3 Theoretical And Experimental Life EvaluationIn this section the results of life calculations for the steering arm are presented and discussed. The life prediction procedure based on a critical location approach as embodied in the FATIMAS software package was employed- with cyclic stress/strain data, geometric information and the measured strain history to predict the fatigue life of the component.The e x p e r i m e n t a l f a t i g u e lives o b t a i n e d f r o m load controlled tests carried out by converting the known washboard strain-time history to a load history were compared to FATIMAS predictions using the original washboard strain signal and those obtained using the developed load history with elastic FE equivalent methods and both the energy density and Neuber's m e thods to predict a strain history which was used in FATIMAS to give fatigue life. The results are listed in tables 7.1 and and 7.2 and shown in figures 7.3 and 7.4.The predictions show a good correlation with experimental data with 66% of the points falling within a factor of 3 scatter band. The predicted lives based on FATIMAS experimental strain-time history, FATIMAS load calibrated strain history and FALCON load-time service history are within a factor 3 scatter band when compared to the experimental lives. The following reasons are associated with the lack of correlation between the FALCON load-time service history and those obtained using the FATIMAS load calibrated strain-time history and the e x p e r i m e n t a l r e s u l t s .

215

Single point calibrations were used for conversion of the strain-time history to a load-time history. Consequently, lin e a r e x t r a p o l a t i o n was u s e d i n s t e a d of more sophisticated calibration method based on equation 9.1. Therefore, lower load reversals have been applied than the actual load reversals, which has lead to fatigue life p r e d i c t i o n s and e x p e r i m e n t a l r e s u l t s w h i c h are overestimated.

The FATIMAS strain based and FATIMAS load/local strain calibrated based results, appear to give conservative fatigue life estimates at short lives around 10E4 cycles, and non-conservative estimates at long lives around 10E6 cycles. Figure 7.3 shows a plot of load factor versus number of cycles to failure of the component which support this view [69, 83].

The f a t i g u e lives b a sed on N e u b e r ' s rule are m o r e conservative than both the FALCON results and those based on the energy approach. Therefore these results are more acceptable as a design tool.

Of the four methods (maximum principal stress, Tresca, von Mises and maximum principal strain), applied to predict the fatigue lives of the steering arm, the predictions based on Neuber's rule and both Tresca and m a x i m u m principal strain were found to be most suitable for life

216

e v a l u a t i o n a bove the y i e l d p o i n t of the c o m p o n e n t material. The fatigue life results based on Neuber's rule and the maximum principal stress theory were found to be overestimated. This technique is often used in life evaluation of brittle materials [64]. The lives based on the energy density approach and equivalent methods were found to be conservative and furthest away from the experimental results in both the elastic and plastic region.

D e s p i t e the a f o r m e n t l o n e d l i m i t a t i o n s , the l o cal stress/strain approach has been proved to be an effective method of fatigue life estimation and its present use in the early stages of design/development has proved an effective industrial tool.

The degree of correlation suggests that the local stress/ strain method can be used successfully to predict the fatigue life of engineering components under constant and variable load histories. To date this has r e q u i r e d e x t e n s i v e h i s t o r i c a l data on str a i n h i s t o r i e s for components similar to the one being d esigned or the

building and in service m easurement of prototypes. However, it is now possible to create a suitable load history for a specific engineering component using the

finite element analysis, equivalent stress reductions and Neuber's method to predict fatigue lives of engineering components without recourse to prototype building.

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CHAPTER 10

10. CONCLUSIONS AND SUGGESTIONS FOR FUTURE WORK

10.1 Computer Based Analysis

In the present investigations, two techniques have been employed for estimation of local elastic/plastic strain c o m p o n e n t s r e q u i r e d for input to the f a t i g u e life assessment package, FATIMAS.

a) The energy density approach.

b) Neuber's rule.

The multiaxial elastic F.E. calculated stress components at the c r i t i c a l l o c a t i o n w e r e r e d u c e d to a s i n g l e parameter using the maximum principal stress, von M i s e s 1, Tresca, and maximum principal strain methods. These were used in conjunction with both the monotonic and cyclic stress/strain curves and'both (a) and (b) to develop a number of applied load/local strain calibration curves which can be used to create a variable load-strain service

history.

In all cases the difference between the monotonic measured and the F.E. produced local strains were found to be less than 20% for all the cases considtfed. It can be considered that a good correlation exists between the measured and estimated strains despite the following inaccuracies arising from applying the F.E. package and affixing strain gauges.

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i) L o a d i n g and r e s t r a i n t of the c o m p o n e n t lacks precision.

ii) The complexity of the component geometry necessitates the employment of approximations in defining the

finite element skeleton.

iii) Homogeneous material properties are assumed for the steering arm medium.

iv) Difficulties arising from positioning the straingauges coincident with defined F.E. nodal positions.

v) Difficulties arising from positioning the straingauges coincident with the direction of the principalplane.

The techniques employed for estimation of the monotonic local strains were used for calculation of the local

strains under cyclic loading conditions. As a result a number of cyclic applied load/local strain calibration curves were developed.

The FATIMAS strain based history and FATIMAS load based history predicted and FALCON fatigue lives were compared with experimental results. It can be observed that 66% of the points were within a factor of 3 scatter band, respectively.

Although fatigue lives based on Neuber's estimated strains are conservative when compared to those based on the energy density method, a designer has increased confidence when using a technique that underestimates fatigue lives.

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As a result of this investigation an integrated CAD software package has been developed by nCode International Limited and PAFEC by which durability of engineering components can be predicted in the conceptual design stage. At the time of publication the FEA/FATIMAS package was iny development stage, however, a number of life maps for the steering arm have been produced in order to demonstrate the capabilities of the package.

10.2 Practical Applicability Of The Technique

Consideration of the computerised and experimental results suggest that the technique developed is suitable for quantatively predicting the fatigue life of engineering components in the early design stage to an acceptable levels of accuracy. To put t h e s e a c h i e v m e n t s in p e r s p e c t i v e , a c o n s i d e r a t i o n of the p r a c t i c a l applicability of the afforementioned techniques are discussed.

Implementation of such a technique would depend upon the availability o f : -

i) Knowledge of the cyclic stress/strain properties of the component material.

ii) Knowledge of the strength reduction factor, Kt.

iii) Detailed knowledge of the service loading to which the component will be subjected.

Ideally, a strength reduction factor, Kt, equal to unity may be used. The finite element analysis determines the

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highest stress within the component at a node within the defined mesh, however, it is very unlikley that the node coincides with the point of maximum stress within the structure. Furthermore the effects of surface finish are not considered within the analysis. Surface irregularities may act as a catalyst for localised stress concentration w h i c h may e x c e e d the m a x i m u m p r e d i c t e d stress. Consequently, a strength reduction factor, , greater than unity should be used.

The above t e c h n i q u e c a n be u s e d to p r e d i c t the stress/strain behaviour at the critical location if knowledge of the nominal load history is known, from which a constant or variable service history may be produced. Fatigue life predictions based on the critical location approach can be made for any combination of material and component geometry using a stipulated load history. Geometry, material and load history changes necessitated through redesign can be readily executed with confidence. The technique can also be used to reduce the weight of existing components while retaining the desired stiffness and service durability.

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10.4 Scope For Future Work

In its present form, the critical location approach is only capable of accurately estimating the fatigue life of engineering components to crack initiation, (defined as

when a crack length of approximately 3 mm is observed within a component). This may be good enough for the g r o u n d v e h i c l e i n d u s t r y and i n d e e d e d it has b e e n sucessfully used in the estimation of fatigue life. However, in situations where most of a component's life is spent in crack prorogation,' or for structures in which

defects are present-at the beginning of service, the propagation life is the total fatigue life. Consequently, crack initiation analysis becomes irrelevant. Therefore,

further research is required to enhance the software to model crack growth.

The use of polymeric materials inv ground vehicle industry

is becoming increasingly popular. The weight reduction,corrosion resistance and ease of manufacture offersgreater design flexibility than those associated withconventional materials. The use of plastic materials invehicle exterior and under the bonnet parts are wellestablished, and it is estimated that the consumption ofplastic materials will increase from 10% to about 20% of acar's weight within next 10 years [85, 86 ]. In.spite ofsuch rapid expansion, the fatigue behaviour of thepolymeric materials is not as advanced as that of metals.

vtVve.It is in this area that validation ofv critical location approach must be investigated. This can be achieved by

222

further research to obtain the cyclic p r o p e r t i e s of engineering plastics and then application of the data in the testing and evaluation of actual components.

The degree of biaxiality at the highest stressed node in the steering arm was found to be 9% which is relatively low. F u r t h e r i n v e s t i g a t i o n w o u l d be r e w a r d i n g by analysing components with higher orders of biaxiality to assess the capabilities of the FALCON package.

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