MECHANICS13.pdf

FEA Based Fatigue Life Assessment of an Automobile Lower Suspension Arm Using Various Strain-Life Models

1S. ABDULLAH, 1N.A. AL-ASADY, 1A. K. ARIFFIN, 2M.M. RAHMAN AND 1Z. M. NOPIAH

1Department of Mechanical and Materials Engineering, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor, Malaysia

2Department of Mechanical Engineering, Universiti Malaysia Pahang, 25000 Kuantan, Pahang, Malaysia

[email protected]

Abstract: - The recent emphasis on more suitable and reliable life predictions for fatigue-critical parts in ground vehicles so this paper deals with the problem of fatigue life assessment for automotive engineering component, especially for a lower control arm due to consider it as a vital component in the automobile suspension system. Finite element analysis (FEA) has been used to get the results for the first three models, while Fortran coding program has been used for the last. Experimental strain data has been collected using strain gauges to be used as input loading for the strain-life models. The results for three common strain-life models (Coffin Manson, Morrow, Smith-Watson-Topper (SWT) and the Effective strain damage (ESD) approach were discussed and compared. Finally, ESD can be considered as safer approach in design life for automobile lower suspension arm under variable amplitude loading. Key-Words: - Automobile lower suspension arm; life prediction; fatigue; finite element; strain life; Variable amplitude. 1 Introduction Fatigue analysis procedures for the design of modern structures rely on techniques, which have been developed over the last 100 years or so. Initially these techniques were relatively simple procedures, which compared measured constant amplitude stresses (from prototype tests) with material data from test specimens. These techniques have become progressively more sophisticated with the introduction of strain based techniques to deal with local plasticity effects. Nowadays, variable amplitude stress responses can be dealt with. It is very important to appreciate the issue of accuracy when performing fatigue life calculations with finite element (FE) models [1].

Most finite element analysis (FEA) based fatigue packages have three main life assessment methods, i.e. Stress-life, Strain-life and Crack-propagation. For the Strain-life method, three strain-life models, i.e. Coffin-Manson, Morrow and Smith-Watson-Topper (SWT), are available in most of the FE packages. The Morrow and SWT models consider the mean stress effect inside their calculation. In addition, the ESD model is also introduced for which it considers the cycle sequence effect in the calculation. However, the ESD model is not included as the post analysis of the FE packages,

because it has been used for research purposes not for commercial use. The present paper describes the fatigue life comparison for the automobile lower suspension arm under three surface road using four strain life models. The results show that the country road gives lower life (cause higher damage). For the fatigue strain life models, the ESD model can be considers as safer model in design life than the other three models. 2 Fatigue Strain-life Models Many practical problems in engineering are either extremely difficult or impossible to solve by conventional analytical methods. Such methods involve finding mathematical equation which define the required variables. For example, the distribution of stresses and strain in a solid component. One of the main attractions of finite element methods is the ease with which they can be applied to problems involving geometrically complicated systems [3]Fatigue life prediction represents one of the applications for FE. Among the plastic strain models, the Coffin-Manson, Morrow and SWT models are widely used. In this paper, the ESD has been used for comparing the results with the other three models. Each of these models is an empirical

Proceedings of the 4th WSEAS International Conference on APPLIED and THEORETICAL MECHANICS (MECHANICS '08)

ISSN: 1790-2769 81 ISBN: 978-960-474-046-8

relationship between cycles-to-failure, and analytically, numerically or experimentally determined plastic strain range per cycle. The first strain-life model is the Coffin-Manson relationship [2],

( ) ( ) cff

bf

fa N22 εΝ

Εσ

ε ′+′

= (1)

where E is the material modulus of elasticity, is a true strain amplitude, is the number of reversals

to failure,

aε

fN2

fσ ′ is a fatigue strength coefficient, b is a

fatigue strength exponent, fε ′ is a fatigue ductility coefficient and c is a fatigue ductility exponent.

Based on the proposal by Morrow (1965) [4], the relation of the total strain amplitude ( aε ) and the fatigue life in reversals to failure (2Nf ) can be expressed as

( ) ( )cff

bf

f

mfa 2Nε2N

σσ1

Eσ

ε ′+⎟⎟⎠

⎞⎜⎜⎝

⎛

′−

′= (2)

where mσ is the mean stress. Another strain-life mean stress correction model was suggested by Smith et al. [5], or often called the SWT parameter. This relationship was based on strain-life test data which was obtained at various mean stresses. Thus, the SWT expression is mathematically defined as

( ) ( ) ( ) cbfff

2bf

2famax 2NEεσ2NσEεσ +′′+′= (3)

where maxσ is the maximum tensile stress for the particular cycle. This equation is based on the assumption that for different combinations of strain amplitude, aε , and mean stress, maxσ , the product

amax εσ remains constant for a given life. A fatigue damage model for use with VA strain

loadings was developed by DuQuesnay et al. [6], knowing as the Effective Strain Damage (ESD). This model is based on the crack growth and crack crack closure mechanisms. It has been shown to work well for a wide range of materials, load spectra, component geometries, strain magnitudes and mean-strain effects [6-9]. Using this model, the fatigue damage can be analysed based on the assumption of a short crack growth, since the crack length at failure is usually less than a few millimeters. The ESD strain-life model is mathematically defined as

( )BfΝΑΕ Δε =∗ (4)

where E is the elastic modulus of the material,

is the net effective strain range for a closed hysteresis loop which is related to fatigue crack growth, A and B are material constants, and Nf is the number of cycles to failure.

∗εΔ

3 Finite Element Modelling 3.1 Geometrical Model A lower suspension arm is a vital component in the automobile suspension system. A geometric model of a lower suspension arm for a 2000 cc Sedan car was used for this study, which is subjected to a strain variable amplitude fatigue loading. Three-dimensional lower suspension arm model geometry is drawn using the CATIA software, as shown in Fig. 1. The FE-based durability analysis helps to eliminate unnecessary tests by allowing the engineer to check out the fatigue performance analytically and to perform the optimization which can shorten the time to the final results. The FE approach was used for modelling and simulating of the lower suspension component.

Fig. 1 Geometrical model of automotive lower suspension arm.

3.2 FE Model and Boundary Conditions The local strain, or crack initiation approach to fatigue life estimation requires accurate values of local elastic-plastic stresses and strains, especially at free surfaces. In principal, these can be obtained through non-linear FE analysis, but this approach is usually impractical for lengthy and complex load histories. For this reason elastic-plastic stresses and strains are commonly estimated using a combination of linear elastic FE analysis and a notch correction procedure (elastic-plastic correction) [10].

The auto tetrahedral meshing approach is a highly automated technique for meshing solid regions of the geometry. It crates a mesh of tetrahedral elements for any closed solid including boundary representation solid. Tetrahedral meshing produces high quality meshing for boundary representation solids model imported from the most CAD systems. The TET10 mesh can give more


ISSN: 1790-2769 82 ISBN: 978-960-474-046-8

accurate solution since the 10 nodes tetrahedral (TET10) element is used for the analysis with the adoption of a quadratic order interpolation function. There are three main parts in the lower suspension arm which their behaviour has been considered in the FE boundary conditions, ball joint, pivot 1 and pivot 2. The FE model of the lower suspension arm (Fig. 2) has boundary conditions as followed:

Fig. 2 FE model of automotive lower suspension

arm. Distributed load has been applied on the inner surface of pivot 1. Pivot 2 considers as a rigid section with a rotation around x-axis from the side of the vehicle body. In the same time, rigid has been considered on the ball joint with translations in x and y direction while rotation around x, y, and z-axis to represent the braking and cornering loads. There are no acceleration loads as inputs, due to collecting data during driving of the car at constant velocity. 3.3 Material Information The purpose of analysing the chemical composition of the steel sample is to enable its classification to be made. Based on the analysing data on Table 1, the steel can be classified as a medium carbon steel since SAE coded steel which carbon content ranges between 0.32-0.38%, manganese content ranges between 0.60-0.9% were identified to be medium carbon steel [11]. The SAE1045 steel represents the fabricated material for the 2000 cc Sedan lower suspension arm. The measured values have been getting using INCA Energy system. Three samples were cut from the lower suspension arm using a cutter. The samples were subsequently ground with successive SiC papers (grit 200-1200) and then polished with polishing cloth and Alomina solution. Table 1 Chemical composition of the steel Element C Mg Si V Cr Ni Mn Fe

Measured wt% 0.33 0.13 0.29 0.04 0.14 0.49 0.9 Bal.

3.4 Loading Information

The load history was obtained from the actual automotive lower suspension arm, which was driven over country road. The sampling frequency, fs for this case is 500 Hz. This fs value was chosen in order to have accurate data [12-13]. The data was measured using a fatigue data acquisition system called SoMat eDAQ (Fig. 3) when the car was driven at 25 km/h and the data was then recorded as strain time histories.

Fig 3 The setup of fatigue data acquisition SoMat eDAQ to be used for data collection.

Fig 4 shows the position of the fixing strain gauge location of the arm, which represents a critical area on the lower suspension arm. FEA has been used to get the exact position for the critical area. The strain load history which shown in Fig 5 has been collected during the driving of the car for three kinds of road, i.e. Highway, pave and country road because represent different kinds of surfaces can give variety in results, especially these surfaces represents common road surfaces.

Fig. 4 Strain gauge location on the lower suspension arm

4 Results and Discussion In general, four strain-life models have been used, including Coffin-Manson, Morrow, SWT, and ESD


ISSN: 1790-2769 83 ISBN: 978-960-474-046-8

for fatigue life prediction purposes for three kinds of road surfaces. The fatigue life prediction using these four models for the three kinds of road surfaces gave different results as shown in Table 2 as fatigue damage and in Table 3 as fatigue life. For the country road surface less life (higher damage) has been found while longer life (less damage) for highway has been got, moreover, pave road surface gave fatigue life between the other two roads. This is due to bump and main holes existing in the country road while smooth surface for highway road. The first three models have been applied using local strain values obtained directly from FEA at the failure location. The local elastic-plastic strains were obtained from FEA using a combination of elastic FEA and a Neuber-type stress correction. The strain-life methods were then implemented to predict fatigue life. Table 2 Fatigue damage using different strain-life models Road surface

CM Morrow SWT ESD

Highway 1.5E-6 1.8E-6 2.7E-6 1.4E-5 Pave 5.2E-6 6.1E-6 9.0E-6 1.6E-5 Country 7.3E-5 8.0E-5 1.0E-4 1.9E-4

Table 3 Fatigue life using different strain-life models

Road surfaces

CM [hrs]

Morrow [hrs]

SWT [hrs]

ESD [hrs]

Highway 49598 41976 28941 4013 Pave 2854 2455 1660 906 Country 1430 1311 1032 552

The ESD model gave less life than the other

models; this is due to its consideration the mean stress and cyclic sequence effects in fatigue life calculation [6-9, 14]. Longer life was for CM due to consider mean stress as zero and no cyclic sequence effects. For the results of the other two models (Morrow and SWT) are between the results of CM and ESD, this due to consider only the mean stress for fatigue life prediction because it suggested for constant amplitude only.

A study by Lynn and DuQuesnay [15] has developed computer software for the prediction of fatigue crack initiation based on ESD model. The results provide further credit to the applicability of both the software and the model as general tools for the prediction of fatigue crack initiation.

Another study by Abdullah [16] showed a better accuracy of the ESD model to predict the fatigue lives of VA loadings compared to Coffin–Manson, Morrow and SWT models. The average difference

of fatigue life between the Coffin–Manson, Morrow and SWT strain-life models to the respective experimental results is 358, 333 and 580%, respectively. Using the ESD model, the smallest difference was found to be of 17%.

Fig. 6 shows the contour plot of fatigue life for every element in the FE model. It also shows the ball-joint area near the tyre side as critical area of maximum damage.

Fig. 5 Strain time history plot of the strain

gauge for different road surfaces: (a) highway, (b) pave, (c) country road.


ISSN: 1790-2769 84 ISBN: 978-960-474-046-8

Fig. 6 The contour plot of lower suspension arm

fatigue life 4 Conclusions The FE modeling and analysis of the automotive lower suspension arm has been presented. The life prediction methods used in the ground vehicle industry mainly rely on crack nucleation approaches (i.e. stress-life and strain-life). Coffin-Manson model which consider zero mean stress, in addition to the two popular strain-life models (Morrow and SWT) which have been used to account for the mean stress effect, in addition to the ESD strain-life model which based on crack growth and crack closure mechanisms and it has been used to account for the cycles sequence effects. Different consideration of the used models to calculate fatigue life prediction, gave different results. As conclusion from the results, ESD model is safer in component life design. References: [1] N. Bishop, and F. Sherratt, Finite Element

Based Fatigue Calculations. The International Association for the Engineering Analysis Community Netherlands: NAFEMS Ltd, 2000.

[2] NE. Dowling, Mechanical Behaviour of Materials: Engineering Methods for Deformation, Fracture and Fatigue, 2nd ed., Prentice Hall, New Jersey, 1999.

[3] T.F. Roger, Finite Element Methods for Engineers, Imperical College Press, 1997.

[4] J. Morrow, Fatigue Design Handbook, Advances in Engineering, Society of Automotive Engineers, Warrendale, Pa., Vol.4, 1968, pp. 3-36.

[5] K.N., Smith, P. Watson and T. H.Topper, A stress-strain function for the fatigue of metals, Journal of Materials, Vol.4, No.5, 1970, pp. 767-778.

[6] D.L. DuQuesnay, M.A. Pompetzki, and T.H. Topper, Fatigue life predictions for variable amplitude strain histories, SAE transactions, Vol.5, No.102, 1993, pp. 455-465.

[7] D. L. DuQuesnay, T.H. Topper, M. A. Pompetzki and R. Jurcevic, The effective stress range as a fatigue damage parameter in the rainflow method, edited by Y. Murukami, Butterworth Heinemann, London, 1992, pp.132-141.

[8] D.L. DuQuesnay, T.H. Topper, M. T. Yu and M.A. Pompetzki, The effective strain range as a mean stress parameter, International Journal of Fatigue, Vol.1, No.14, 1992, pp. 45-50.

[9] D. L. DuQuesnay, Applications of overload data to fatigue analysis and testing, Application of Automation Technology in Fatigue and Fracture Testing and Analysis: Fourth Volume, ASTM STP 1411, edited by Braun, A.A., McKeighan, P.C., Nicolson, A. M. & Lohr, R. D., ASTM, West Conshohocken USA, 2002, pp. 165-180.

[10] P. Heyes, J. Dakin and C. StJohn, The assessment and use of linear static FE stress analyses for durability calculation, SAE technical paper, 951101, 1995.

[11] R.A. Lindberg, Processes and Materials of Manufacture, 2

nd ed. Allyn and Bacon, Boston,

MD, USA, 1977. [12] MA. Poelman and RP.Weir, Vehicle Fatigue

Induced by Road Surface Roughness, ASTM Digital Library. 1992.

[13] Oh C-S. Application of wavelet transform in fatigue history editing, International Journal of Fatigue, Vol.23, 2001, pp. 241-250.

[14] TH. Topper and TS. Lam, Effective strain- fatigue life data for variable amplitude loading. International Journal of Fatigue, Vol.1, No. 19, 1997, pp. 137–S43.

[15] A.K. Lynn and D.L. DuQuesnay, Computer simulation of variable amplitude fatigue crack initiation behaviour using a new strain-based cumulative damage model , International Journal of Fatigue, Vol.24, 2002, pp. 977-986.

[16] S. Abdullah, J.C. Choi, J.A. Giacomin and J.R. Yates, Bump extraction algorithm for variable


ISSN: 1790-2769 85 ISBN: 978-960-474-046-8

amplitude fatigue loading, International Journal of Fatigue, Vol.28, 2006, pp. 675-691.


ISSN: 1790-2769 86 ISBN: 978-960-474-046-8

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MECHANICS13.pdf