Available online at w.sciencedirect.com

ScienceDirect

JOURNAL OF IRON AND STEEL RESEARCH, INTERNATIONAL. 2011, 18(8): 42-45

A Methodology to Predict Fatigue Life of Cast Iron : Uniform Material Law for Cast Iron

Sinan Korkmaz [Applied Computing and Mechanics Laboratory, Swiss Federal Institute of Technology (EPFI,) , ENAC/IIC/IMAC, Lausanne 1015, Switzerland]

Abstract: Mechanical, physical and manufacturing properties of cast iron make it attractive for many fields of applica- tion, such as cranks and cylinder holds. As in design of all metals, fatigue life prediction is an intrinsic part of the design process of structural sections that are made of cast iron. A methodology to predict high-cycle fatigue life of cast iron is proposed. Stress amplitudestrain amplitude, strain amplitudenumber of loading cycles relationships of cast iron are investigated. Also, fatigue life prediction in terms of Smith, Watson and Topper parameter is carried out using the proposed method. Results indicate that the analytical outcomes of the proposed methodology are in good accordance with the experimental data for the two studied types of cast iron: EN-GJS400 and EN-GJSGOO. Key words: high-cycle fatigue; fatigue behavior; fatigue life prediction; cast iron

.--Strain amplitude; E-Young's modulus; K'-Cyclic strength coefficient; n'-Cyclic strain hardening exponent; a'i-Fatigue strength coefficient; 6-Fatigue strength exponent;

Fatigue analysis of materials and structures have been an essential consideration in design of me- chanical structures, including elevator shafts"] , tur- bine rotorsC2] , automotive component^[^-^' and civil structures, such as railroad bridgesE5]. Fatigue be- havior of metals has been also investigated by re- searchers from meta l l~ rgy[~-~ ' , automotive engi- neeringL8' , marine engineering['] , petroleum engi- neering"'] and roboticsL"'.

Fatigue is generally divided into two parts in terms of number of load cycles: high-cycle and low- cycle fatigue"". Behavior of a material is considered in high-cycle fatigue if plastic deformations are small enough and localized in the vicinity of the crack tip and the main part of the body is deformed elastical- ly. On the other hand, the behavior is considered within the field of low-cycle fatigue if cyclic loading is accompanied by elastoplastic deformations in the

Symbol List

e'f-Fatigue ductility coefficient; c-Fatigue ductility exponent; R,-Ultimate tensile strength; NE-Number of cycles at endurance limit; PswT-Smith, Watson and Topper damage parameter.

bulk of the body. A Wohlerc'3' published the first systematic fa-

tigue investigation in 1955. Wohler introduced the concept of fatigue curve, the diagram where a char- acteristic magnitude of cyclic stress is plotted against the cycle number until fatigue failure.

Investigations carried out on bridges, marine structures and power generation machines let S S Man~on[ '~ ] find out a local strain methodology, Method of Universal Slopes, to explain crack initia- tion with linear elastic fracture mechanics. This methodology was enhanced in Modified Universal Slopes Method"'' keeping the basic concept of fixed slopes for elastic and plastic strain life curves and changing values of the slopes.

Several studies are present in the literature ad- dressing relations between monotonic tensile proper- ties and uniaxial fatigue properties of engineering

Biography:Sinan Korkmaz(l983-), Male, Master; E-mail: sinan. korkmaz@epfl. chi Received Date: June 1 7 , 2010

Issue 8 A Methodology to Predict Fatigue Life of Cast Iron: Uniform Material Law for Cast Iron 43 - material~"~- '~1 . Among all methods, methodologies proposed by A Baumel and A Seeger (Uniform Ma- terial L a w ) , U Muralidharan and S S Manson (Modified Universal Slopes Method), and J H Song ( Modified Four-Point Correlation Method ) yield better outcome^^'^-'^^.

The uniform material law (UML)"41 is a con- venient method as it does not require the data of re- duction in area. Moreover, UML gives estimation of the endurance limit and the expected deviation be- tween estimated and experimentally determined curves"71. UML is based on different estimates for the aluminum and titanium alloys as well as unal- loyed and low-alloyed steels. S Kork~paz~ '* - '~~ ex- tended UML to high-strength steels.

High mechanical, physical and manufacturing quality of cast iron makes it attractive for many fields of application, such as cranks and cylinder holds[Zo-Z1l . Fatigue properties of cast iron were studied by a number of researchers. A N Damir et al[zzl investigated fatigue life of ductile and cast iron using model analysis. N Costa et al[231 proposed a method for the prediction of nodular cast iron fatigue limit. LI Chang-sheng et alCzal carried out numerical simulation of temperature field and thermal stress field of work roll during hot strip rolling. T Seifert and Riedelczs1 predicted thermomechanical fatigue life of cast iron in a mechanism-based manner. H Ger- mann et a1IZ6] proposed fatigue life prediction meth- ods to calculate Woehler curves for different proba- bilities of failure. However, no study addressing the application of UML to cast iron is available in the literature.

In this study, a methodology to predict high-cy- cle fatigue life of cast iron is proposed. The presen- ted methodology is built upon UML. The methodol- ogy is validated by comparing the estimations to ex- perimental results.

1 Uniform Material Law for Cast Iron

UML is given in Eqn. (l)['?'. (1)

Table 1 gives the parameters used in UML for high-strength steels['*l and uniform material law for cast iron (UMLCI).

In order to obtain a UML for cast iron, essential modifications are carried out. n' is set constant to 0. 1 instead of being a function of b and c. o'f is a func- tion of the ultimate tensile strength of the material. Therefore, it gets different values for different types of cast iron. E*' is also set to be constant, unlike in the

~ , = o ' f / E (~N)'+E'* (2N) '

Table 1 Uniform material law for high-strength steels and for cast iron

K'/MPa n'

af ' / MPa I

Ef

b

oE/MPa C

NE

(G

High-strength steel

0, '/ (Ef ') b / c R, - C l + ( G ) 0.58 - (G+O. 01 - Ig(of '/LTE) /6 R, * (0.32+$/6)

-0. 58

500 000

0 .5 * ( c o s [ x - (R,- 400)/22001+1)

Cast iron

LTf ' / (Ef ')nf 0. 1 1.34 * R,+208

0. 26

- Ig(a ' / w ) /6 0 .4 - R, -0. 7

1 000 000

~~

UML for high-strength steels. Instead of defining an extra function ($) in the

fatigue ductility coefficient and endurance stress cal- culation, a more straightforward approach is applied. The constants used in the calculation of essential pa- rameters are obtained using trial and error method.

2 Results

Comparison of Analytical and Experimental

The proposed UMLCI is applied for calculating stress amplitude ( MPa )-strain amplitude curves. The calculations are carried out for EN-GJS-400 and EN-GJS-GOO (Table 2 ) . Fig. 1 presents the stress amplitude-strain amplitude curves of EN-GJS-400.

Analytical results obtained by UMLCI are in good accordance with the experimental in terms of stress amplitude ( MPa)-strain amplitude relationship for EN-GJS-400 (Fig. 1).

Fig. 2 gives the stress amplitude-strain ampli- tude relationship for EN-GJS-600.

Results show that the stress amplitude values are greater for EN-GJS-GOO than they are for EN-GJS 400. Results also indicate that the analytical results obtained by UMLCI are in good accordance with the experimental results in terms of stress amplitude strain amplitude relationship.

Fig. 3 and Fig. 4 demonstrate the strain ampli- tude-number of loading cycle relationships for EN- GJS-400 and EN-GJS-GOO , respectively. Elastic strain amplitudes, plastic strain amplitudes and total strain amplitudes calculated analytically using UML- CI are given. Experimental provide a com- parison between analytical results and outcomes that are obtained by laboratory tests.

Predictions of UMLCI are close to the fatigue data obtained from the experiments in terms of strain amplitude-loading cycle relationship ( Fig. 3 and Fig. 4).

* 44 ' Journal of Iron and Steel Research, International Vol. 18

Table 2 Chemical compositions of EN-GJS400 and EN-GJS600 % C Si Mn Cr Mo c u Ni P S

EN-GJS400 3. 700 2.390 0.480 0.030 0.020

Issue 8 A Methodology to Predict Fatigue Life of Cast I ron: Uniform Material Law for Cas t I ron 45 -

3 Conclusions

This paper focuses on cyclic fatigue life prediction of cast iron without the usage of reduction in area data. A new methodology is obtained to modify UML. The proposed methodology, UMLCI, is applied to two types of cast iron: EN-GJS-400 and EN-GJS-600.

1 ) Using the UMLCI, stress amplitudestrain amplitude relationship, an important fatigue property, of cast iron is precisely predicted.

2) The deviation between the predictions of UMLCI and experimental data in terms of strain amplitude that corresponds to a given number of loading cycles for structural components made of cast iron is admis- sible. UMLCI yields precise results, especially for

3) Fatigue life prediction of cast iron in terms of Smith, Watson and Topper parameter is predicted with precision using UMLCI. Mean stress effect is taken into account using Smith, Watson and Topper parameter along with UMLCI.

4) UMLCI is designed to predict different types of cast irons since the methodology takes into ac- count changes in material properties, such as ulti- mate tensile strength.

EN-GJS-600.

T h e author would like to thank Professor Joachim W Bergmann f r o m Institute f o r Material Research and Testing , Bauhaus University (Germa- n y ) for he lp fu l discussion.

References:

111

C Z l

c31

c41

C51

C61

171

Goksenli A, Eryurek I B. Failure Analysis of an Elevator Drive Shaft [J]. Engineering Failure Analysis, 2009, 16(4): 1011. Suh Chang-min, Hwang Byung-won, Murakami Ri Ichi. Char- acteristics of Fatigue Crack Initiation and Fatigue Strength of Nitrided 1CrlMo-0. 25V Turbine Rotor Steels [J]. Journal of Mechanical Science and Technology, 2002, 16(8) : 1109. Vural M, Akkus A, Eryiirek B. Effect of Welding Nugget Di- ameter on the Fatigue Strength of the Resistance Spot Welded Joints of Different Steel Sheets [J]. Journal of Materials Pro- cessing Technology, 2006, 176(1/2/3) : 127. ZHANG Ying-jian, HUI Wei-jun, DONG Han. Hot Forging Simulation Analysis and Application of Microalloyed Steel Crankshaft [J]. Journal of Iron and Steel Research, Interna- tional, 2007, 14(Supplement l ) : 189. Caglayan B 0, Ozakgul K , Tezer 0. Fatigue Life Evaluation of a Through-Girder Steel Railway Bridge [J]. Engineering Fail- ure Analysis, 2009, 16(3): 765. Rasty J , Le X, Baydogan M, et al. Measurement of Residual Stresses in Nuclear-Grade Zircaloy-4(R) Tubes-Effect of Heat Treatment [J]. Experimental Mechanics, 2007, 47(2) : 185. ZHANG Mi-Ian, XING Shu-ming, XIN Qiao, et al. Abnormal Failure Analysis of H13 Punches in Steel Squeeze Casting Process [J]. Journal of Iron and Steel Research, International,

2008, 15(3): 47. Yum Y, Chu Y, Chu S, et al. Fatigue Analysis of Spot Welded Joints in Suspension Mounting Part [J]. Journal of Mechanical Science and Technology, 2003, 17(8): 1113. Cicek K, Celik M. Selection of Porous Materials in Marine Sys- tem Design: The Case of Heat Exchanger Aboard Ships [J]. Materials and Design, 2009, 30(10) : 4260. Akyildiz H K , Livatyali H. Effects of Machining Parameters on Fatigue Behavior of Machined Threaded Test Specimens [J]. Materials and Design, 2010, 31(2): 1015. Ji Won Yoon, Tae Won Park, Yim H J. Fatigue Life Predic- tion of a Cable Harness in an Industrial Robot Using Dynamic Simulation [ J]. Journal of Mechanical Science and Technolo- gy, 2007, 22(3): 484. ZHANG Zhan-ping, QI Yu-hong, Delagnes D, et al. Micro- structure Variation and Hardness Diminution During Low Cy- cle Fatigue of 55NiCrMoV7 Steel [J]. Journal of Iron and Steel Research, International, 2007, 14(6) : 68. Wohler A. Theory of Oblong Iron Bridge Beams With Mesh Panels and Sheet Metal Walls [J]. Zeitschrift fur Bauwesen, 1855(5): 121 (in German). Manson S S. A Complex Subject-Some Simple Approximations [J]. Experimental Mechanics, 1965(5) : 193. Muralidharan U , Manson S S. A Modified ,Universal Slopes Equation for Estimation of Fatigue Characteristics of Metals [J]. Journal of Engineering Materials and Technology, 1988, l lO(1): 55. Park J H , Song J H. Detailed Evaluation of Methods for Esti- mation of Fatigue Properties [J]. International Journal of Fa- tigue, 1995, 17(5): 365. Baumel A, Seeger T. Materials Data for Cyclic Loading [MI. Amsterdam: Elsevier Science Publishers, 1990. Korkmaz S. Uniform Material Law: Extension to Highstrength Steels: A Methodology to Predict Fatigue Life of Highstrength Steels [MI. Saarbrucken: VDM Verlag, 2010. Korkmaz S. Extension of the Uniform Material Law for High Strength Steels [D]. Weimar: Bauhaus University, 2008. ORourke R. Cast Iron: The Engineered Metal [J]. Advanced Materials and Processes, 2001, 159(1): 65. Dawson S, Schroeder T. Practical Applications for Compacted Graphite Iron [J]. Transactions of the American Foundry So- ciety, 2004, 112: 813. Damir A N, Elkhatib A, Nassef G. Prediction of Fatigue Life Using Modal Analysis for Grey and Ductile Cast Iron [J]. In- ternational Journal of Fatigue, 2007, 29(3): 499. Costa N, Machado N, Silva F S. A New Method for Predic- tion of Nodular Cast Iron Fatigue Limit [J]. International Journal of Fatigue, 2010, 32(7): 988. LI Chang-sheng, YU Hai-liang, DENG Guan-yu, et al. Nu- merical Simulation of Temperature Field and Thermal Stress Field of Work Roll During Hot Strip Rolling [J]. Journal of Iron and Steel Research, International, 2007, 14(5): 18. Seifert T, Maier G , Uihlein A, et al. Mechanism-Based Ther- momechanical Fatigue Life Prediction of Cast Iron Part 11: Comparison of Model Predictions With Experiments [J]. In- ternational Journal of Fatigue, 2010, 32(8): 1368. Germann H , Starke P , Kerscher E , et al. Fatigue Behaviour and Lifetime Calculation of the Cast Irons EN-GJL-250, EN- GJS600 and EN-GJV-400 [J]. Procedia Engineering, 2010, 2 (1) : 1087. Smith R N, Watson P , Topper T H. A Stress-Strain Function for the Fatigue of Metals [J]. Journal of Materials, 1970, 5 (4) : 767.