Fatigue Life Prediction Of Crankshaft Based On Strain Life Theories

Fatigue Life Prediction Of Crankshaft Based On Strain Life Theories

1Anant Prakash Agrawal and 2Dr. S. K. Srivastava

1M.Tech. Student, 2Associate Professor and Corresponding Author, Mechanical Engineering Department,

M.M.M. Engineering College, Gorakhpur-273 010 (U.P.) India

ABSTRACT

Fatigue analysis can be performed using one of the three basic methodologies such as stress-life theory, strain-life theory, and crack growth approach. These techniques are developed to determine the number of cycles to failure. Stress- life theory suitable when elastic stresses and strains are considered. However, for the components having nominal cyclic elastic stresses and plastic deformation, local strain-life theory is used for predicting the fatigue life. In the present work, fatigue behaviour of forged steel crankshaft, subjected to fully reversible cyclic loading, is analyzed using the strain-life theories. The analyses are aimed to identify the critical location through Finite Element Fatigue Analysis (FEFA) and, to predict the fatigue life of crankshaft. The modelling of crankshaft is carried out in parametric Pro/Engineer software whereas ANSYS workbench is used for the Finite Element Analysis (FEA). Maximum Von Mises stresses criterion is used for predicting the failure of crankshaft. Fillet area at crankpin is identified critical where stresses generated exceed the elastic limit. It is observed that Coffin-Manson strain-life theory is found to be conservative compared to Morrow and Smith-Watson-Topper (SWT) strain-life theories.

Keywords: Crankshaft, Fatigue life, Cyclic loading, FEM, Strain-life theories

1. Introduction

   Crankshaft is a large component having complex geometry that converts linear reciprocating displacement of the piston to a rotary motion. Since the crankshaft experiences a large number of load cycles during its service life, its fatigue

   performance and durability has to be considered in the design process. Design developments have always been an important issue in the crankshaft production industry, in order to manufacture a less expensive component with minimum weight, proper fatigue strength, higher fatigue life and satisfying other functional requirements.

   Chatterley et al. [2] compared the fatigue performance of crankshafts made from ductile iron, austempered ductile iron (ADI), and forged steel. The experiments show that when standard fillet rolling forces are used, ADI had significantly lower fatigue strength than the forged steel. Park et al. [8] showed that without any dimensional modifications, the fatigue life of a crankshaft could be improved significantly by applying various surface treatments such as fillet rolling and nitriding. Mostly, the failure occurs due to the crack initiation and a conservative approach is to denote the component as failed when a crack has initiated [5]. This simplification allows designers to use linear elastic stresses, obtained from multi- body dynamic finite element (FE) simulations, for the prediction of fatigue life.

   The crankshaft is subjected to fully reversible cyclic loading; consequently, exposed to fatigue damages. The fatigue life prediction is less accurate even under the controlled laboratory conditions. The numerical simulation is less expensive to perform; moreover, it provides insight to the failure mechanism. Rahman et al. [9] conducted FEFA of aluminium suspension arm subjected to variable amplitude loading conditions. They have identified the critical location and predicted the fatigue life using strain-life theory. The stress-life theory is found to have a better correlation at high cycle fatigue; however, the strain-life theory must be used if plastic overloads are observed, known as low cycle fatigue.

   Tevatia et al. [13] performed FEFA of plus section connecting rod for three different materials and predicted fatigue life based on Coffin-Manson, Morrow and Smith-Watson-Topper (SWT) strain- life theories. They concluded that Coffin-Manson strain-life theory gives conservative results.

   Morrow [7] and Smith et al. [12] studied the effect of mean stresses on fatigue behaviour of a component. Morrow [15] established a relationship between the mean stress and fatigue life

   2 as:

   Similar to the connecting rod, crankshaft is

   =

   2

   + 2

   (2)

   also a complex component subjected to fully reversible cyclic loading. In the present work, FEFA of crankshaft has been carried out under the fully reversible cyclic loading. Coffin-Manson [3, 6], Morrow [7] and Smith-Watson-Topper (SWT)

   [12] strain-life theories are used for prediction of the fatigue life of forged steel crankshaft. It is

   where, is the total strain amplitude, and

   the mean stress.

   Smith et al. [12] established another relationship, Smith-Watson-Topper (SWT) mean stress correction model, expressed as:

   = 2 2 2 + 2 + (3)

   observed that Coffin-Manson strain-life theory is

   found to be conservative for estimating the fatigue life as compared to Morrow and SWT strain-life theories; moreover, the optimized model of crankshaft possesses higher fatigue life.

   where, represents the maximum stress.

   Ramberg-Osgood [1] characterized the cyclic stress-strain behaviour of a component as:

   1

   = + (4)

2. Problem Formulation

   Fatigue analysis based on stress-life theory is well suited only when elastic stresses and strains are considered. Crankshaft may have nominal cyclic elastic stresses but stress concentrations in the crankshaft may result into local cyclic plastic deformation. The strain-life theory includes technique for converting the loading history, geometrical and material properties (monotonic and cyclic) as input parameters for predicting the fatigue life. This theory is preferred when effect of local plastic strains (due stress concentrations) is used as an additional fatigue parameter along with the elastic strain; and loading history is irregular and mean stress and load sequence effects are thought to be of importance. The strain-life theories can be used proactively for a component during early design stages. These theories are found to be the best for explanation of complex fatigue phenomenon in components like crankshafts for the estimation of fatigue strength.

   The fatigue resistance of metals can be characterized by its strain-life curve. Coffin [3] and Manson [6] have established a mathematical relationship between the total strain amplitude

   2 and the reversals to failure cycles 2

   as:

   where, is the total strain, the stress, the cyclic strength coefficient, and the cyclic strain hardening exponent.

3. Fatigue Life Estimation

   Figure 1 shows the conventional fatigue life estimation procedure in which geometry, material properties and mechanical loading are regarded as three input parameters. Initially, the geometry and loading are used together to produce a stress-time

   ( ) or strain-time ( ) history at critical location. Next, the material fatigue properties are introduced for estimating the fatigue life. The only material properties needed in the first step are the Young's modulus, the elastic-plastic stress-strain curve, etc., which are not true fatigue properties.

   In the present work, at first, the stress and strain at critical location are calculated. Next, finite element method (FEM) is used for converting reduced load-timehistory into the strain-time history, followed by the stress/strain calculations in the highly stressed (critical) area. Finally, three strain-life theories (Coffin-Manson, Morrow and SWT) are applied for the prediction of fatigue life.

   =

   2

   2

   + 2

   (1)

   where, 2 is the total strain amplitude, the fatigue strength coefficient, the fatigue ductility coefficient, the Youngs modulus of elasticity,

   2 the fatigue life, the fatigue strength exponent, and the fatigue ductile exponent.

   Figure 1: Conventional fatigue life estimation procedure [1]

4. Finite Element Fatigue Analysis

   The 3D model of crankshaft, termed original model, is generated in Pro/E software and FEFA is carried out on ANSYS workbench using 10-node tetrahedral SOLID 187 elements. Five design variables for the shape optimization of crankshaft model are: crankpin fillet radius ( ), crankpin oil hole diameter ( ) , crank web thickness ( ) , depth( ) and diameter( ) of drilled hole at the back of crankshaft. The original crankshaft model is analyzed by assuming the critical values of dimensions as = 2.38 mm, = 18.29 mm,

   = 20.32 mm, = 34.29 mm and = 8.64 mm. Seven critical locations on various fillet areas of the crankshaft are identified for the stress analysis. Figure 2 shows the Von Mises stresses distribution in different sectors of forged steel crankshaft in which maximum stresses are observed on crankpin fillet area.

   Figure 2: Von Mises stresses generated in various sectors of forged steel crankshaft (maximum stress point occurs near the crankpin fillet)

5. Results And Discussion

   Material properties play an important role in the interpretation of finite element results. The cyclic material properties are used for the calculation of the elastic/plastic stress-strain response and the rate at which fatigue damage accumulates during each cycle. The fatigue results are obtained for the forged steel material with monotonic and cyclic mechanical properties listed in Table 1.

   Figure 3 shows S-N curves obtained from the fatigue analysis of crankshaft. Stresses corresponding to the critical location are based on

   stress-life (S-N) theory as well as strain-life (e-N) theory. The maximum stresses at critical location are calculated by continuously increasing the force cycles up to 106. For = 20 cycles, the stresses at critical location (fatigue strength) are found to be

   24.77 MPa and 14.43 MPa based on stress-life theory and strain-life theory, respectively. As expected, the stresses at critical location are monotonically decreasing with increasing the number of force cycles. The crankshaft appears to have nominal cyclic elastic stresses but stress concentrations may result into local cyclic plastic deformation. Under these conditions, Coffin- Manson strain-life theory is used for estimating the fatigue life. The fatigue life (in seconds) at critical location is found to be conservative for the design; alternatively, strain-life theory estimates lower fatigue life.

   Table 1: Monotonic and Cyclic mechanical properties of forged steel [14]

   Monotonic Properties	Forged Steel
   Youngs Modulus (), GPa	221
   Yield Strength (), MPa	625
   Ultimate Tensile Strength ( ), MPa	827
   Strength Coefficient (), MPa	1316
   Strain Hardening Exponent ()	0.152
   Density, kg/m3	7833
   Poissons Ratio	0.30
   Fatigue Properties
   Fatigue Strength Coefficient ( ), MPa	1124
   Fatigue Strength Exponent ()	-0.079
   Fatigue Ductility Coefficient ( )	0.671
   Fatigue Ductility Exponent ()	-0.597
   Cyclic Yield Strength ( ) MPa	505
   Cyclic Strength Coefficient ( ), MPa	1159
   Cyclic Strain Hardening Exponent ( )	0.128

   The shape optimization of crankshaft has been carried out by successively varying the five critical design parameters and their optimized values are calculated as: crankpin fillet radius = 3.00 mm, crankpin oil hole diameter = 20.20 mm, crank web thickness = 18.10 mm, depth of drilled hole = 74.30 mm and diameter of drilled hole

   = 10.64 mm at the back of crankshaft. Figure 4 shows S-N curves based on Coffin-Manson, Morrow and Smith-Watson-Topper (SWT) strain- life theories corresponding to the optimized values of design parameters. For given force cycle, the maximum induced stresses at the critical location

   are found to be in the following order:

   < <

   . Thus, SWT strain-life theory exhibits higher fatigue strength compared to Morrow and Coffin-Manson strain-life theories but Coffin- Manson theory gives conservative results; hence safe for the design.

   50

   Stress Life Theory

   40 Strain Life Theory

   Forged Steel Crankshaft

   max

   30 Load = 1.142 MPa

   Mass = 3.80 kg

   20

   10

   0

   Table 2 presents the maximum stresses at critical/failure location and fatigue life based on the three strain-life theories for original and optimized forged steel crankshaft models. The critical location is elected as the point for fatigue failure. As far as fatigue life is concerned, the optimized model possesses higher fatigue life (in sec) irrespective of the strain-life theories. Moreover, for a given model, Coffin-Manson theory gives conservative results; consequently, estimates the lowest fatigue life, hence safe. Finally, it is concluded that the forged steel optimized shape crankshaft model is the best when both elastic and plastic strains are considered, i.e., Coffin-Manson theory is used for estimating the fatigue life.

   50

   Original Model

   40 Optimized Model

   Forged Steel Crankshaft

   max

   100 101 102 103 104 105 106 30

   Nf

   20

   Figure 3: S-N curves for crankshaft based on

   stress-life theory and strain life theory 10

   Coffin- Manson Load = 1.142 MPa Mass = 3.80 kg

   60

   Coffin-Manson

   50 Morrow

   SWT

   40 Forged Steel Crankshaft

   max

   Load = 1.142 MPa Mass = 3.80 kg

   30 Rf = 3.00 mm

   Do = 20.00 mm

   20 Wt = 18.10 mm

   Lh = 74.30 mm

   10 Dh = 10.64 mm

   0

   0

   100 101 102 103 104 105 106

   Nf

   Figure 5: S-N curves for original and optimized crankshaft models based on Coffin-Manson theory

   Table 2: Maximum stresses and fatigue life for original and optimized crankshaft

   100 101 102 103 104 105 106

   Nf

   Figure 4: S-N curves for optimized crankshaft model based on three different strain life theories

   Since Coffin-Manson strain-life theory is safe; hence, S-N curves based on Coffin-Manson are plotted (Figure 5) for the original and optimized crankshaft models. For = 20 force cycles, it is observed that maximum stresses at the critical location are (12.44) optimized < (14.27) original. Thus, the critical stresses ( ) generated for the optimized model are low compared to the original model.

   Crankshaft	Maximum stresses at critical location max (MPa) *	Fatigue life 106 (Sec)*
   		Coffin- Manson	Morrow	SWT
   Original model	32.453	15.34	16.21 /td>	17.70
   Optimized model	28.071	21.73	22.56	24.05

   * Mass = 3.80 kg (approximately constant), Load = 1.142 MPa (fully reversible cyclic)

6. Conclusions

   In the present work, FEFA of forged steel crankshaft are carried out using different strain-life theories. It is observed that crankpin fillet area is critical as far as maximum stresses generated are concerned. Coffin-Manson strain-life theory is

   found to be conservative for estimating the fatigue life as compared to Morrow and SWT theories.

7. References

[1]. Bishop, N., and Sherratt, F., 2000, Finite Element Based Fatigue Calculations, The Int. Association for the Engg. Analysis Community Netherlands, NAFEMS Ltd. [2]. Chatterley, T.C. and Murrell, P., 1998, ADI Crankshafts- An Appraisal of Their Production Potentials, SAE Technical Paper No. 980686, Society of Automotive Engineers.

[3]. Coffin, L.F., 1954, A Study Of The Effects of Cyclic Thermal Stresses on A Ductile Metal, Transactions of American Society for Testing and Materials, 76, pp. 931-950.

[4]. Hancq D.A., 2003, Fatigue Analysis Using ANSYS, ANSYS Inc., 22 P. http://www.ansys.com

[5]. Kyrre, S.A., Skallerud, B., Tveiten, W.T. and Holme, B., 2005, Fatigue Life Prediction of Machined Components Using Finite Element Analysis of Surface Topography, Int. J. of Fatigue, 27, pp. 1590- 1596.

[6]. Manson, S.S., 1953, Behavior of Materials Under Conditions of Thermal Stress, Heat Transfer Symposium, pp. 9-75.

[7]. Morrow, J., 1968, Fatigue Design Handbook- Advances in Engineering Warendale, PA, SAE, pp. 21- 29.

[8]. Park, H., Ko, Y. S., and Jung, S. C., 2001, Fatigue Life Analysis of Crankshaft at Various Surface Treatments, SAE Technical Paper No. 2001-01-3374, Society of Automotive Engineers.

Moreover, the optimized crankshaft model possesses higher fatigue life.

[9]. Rahman, M. M., Kadirgama, K., Noor, M.M., Rejab, M.R.M., Kesulai, S.A., 2009, Fatigue Life Prediction of Lower Suspension Arm Using Strain-Life, European J. of Scientific Research, 30(3), pp. 437-450.

[10]. Rahman, M.M., Ariffin, A.K., Abdullah, S. and Jamaludin, N., 2007, Finite Element Based Durability Assessment of A Free Piston Linear Engine Component, SDHM, 3 (1), pp. 1-13.

[11]. Rahman, M.M., Ariffin, A.K., Abdullah, S., Noor, M.M., Bakar, R.A. and Maleque, M.A. 2008 a, Finite Element Based Fatigue Life Prediction of Cylinder Head For Two-Stroke Linear Engine Using Stress-Life Approach, Journal of Applied Sciences, 8(19):3316- 3327

[12]. Smith, K.N., Watson, P. and Topper, T.H., 1970, A Stress-Strain Functions for the Fatigue on Materials,

J. of Materials. 5(4), pp. 767-78.

[13]. Tevatia, A., and Srivastava, S.K., 2011, Fatigue Life Prediction of Connecting Rod using Strain-Life Theories, Int. J. of Theoretical and App. Mechanics. [14]. Williams, J. and Fatemi, A., 2007, Fatigue

Performance of Forged Steel and Ductile Cast Iron Crankshafts, SAE Technical Paper No. 2007-01-1001, Society of Automotive Engineers.