Durability analysis of an automotive component in ......Durability analysis of an automotive component in consideration of inhomogeneous hardness† Hee-Jin Shim1,* and Jung-Kyu Kim2

Journal of Mechanical Science and Technology 25 (3) (2011) 621~629

www.springerlink.com/content/1738-494x DOI 10.1007/s12206-011-0126-4

Durability analysis of an automotive component in consideration

of inhomogeneous hardness† Hee-Jin Shim1,* and Jung-Kyu Kim2

1Power Engineering Research Institute, KEPCO E&C, Bundang-gu,Seongnam-si,Gyeoggi-do,463-870, Korea 2School of Mechanical Engineering, Hanyang University, Sungdong-gu, Seoul, 133-791, Korea

(Manuscript Received June 17, 2009; Revised April 30, 2010; Accepted December 1, 2010)

----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Abstract For the reliability of automotive components, it has to satisfy the dimension accuracy and the strength design requirements for part that

has the consistent strength distribution. Since it has the defect due to actual manufacturing process and inhomogeneity of material, the strength design requirement should be not satisfied. In this way, verification of analysis and prediction of fatigue life was very difficult from difference of the failure region. The cold forging products generally has heterogeneity of strength, hardening and fatigue resistance. Therefore, it’s important to understand the characteristics of material strength and fatigue of cold forging products considering heteroge-neous effect in order to do durability analysis. In this study, in order to propose the method of durability analysis with inhomogeneity of the material, the heterogeneous characteristics are confirmed by predicting the effective strain to perform the plastic deformation simula-tion influenced from the strength condition and microstructure of pulley at power transmission. Analysis and prediction of effective strain from cold forging is performed by software DEFROM for inhomogeneous characteristics. And the stress of the real operation in per-formed by MSC.NASTRAN. Also, through correlation about effective strain and hardness, the failure position and the life were esti-mated to predict the fatigue strength and the external applied stress.

Keywords: Cold forging; Fatigue life evaluation; Effective strain; Inhomogeneous properties ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- 1. Introduction

The mechanical component and system are mostly damaged in fatigue under the operating environments. Therefore, to ensure the safety and the integrity of the shaft axle and power transmission axis, it is very important to investigate methods of fatigue analysis and design under fatigue operating condi-tions. Mainly, durability analysis is based on finite element method. Assuming that mechanical properties at the element and node which had a relationship with division of the contin-uum are homogeneous, the analysis was accomplished. How-ever, to consider the effect of the inhomogeneous properties such as internal defect factor of the parts and local micro-scopic characteristics of material, thus it is necessary to do the study of the durability evaluation which considers the effect of inhomogeneous quality.

The previous research within the analysis of inhomogene-ous deformation in heterogeneous microstructure is usually focused on an investigation into micromechanical modelling

with statistical properties distributions. Microstructure features such as grain size, grain size distribution, and phase of volume friction have been investigated by Ghosh and Raj [1]. It is apparent that super plastic behavior cannot be properly charac-terized by considering only an average grain size to represent the material’s microstructural state. Torquate [2] and Satito [3] characterize grain size, including grain size distribution, and these can be defined to give the number of grains with a di-ameter for a given control region. A range of distribution functions has been considered for characterizing grain size.

Muszka K. et al. [4] noted the effect of grain size on the dy-namic mechanical properties of micro-alloyed steels. Al-though these studies complete a behavior analysis of material deformation using complete modeling, they are not focusing on components which are subject to inhomogeneous deforma-tion and, furthermore, they do not attempt to construct a dura-bility analysis and determine the accurate failure position with regard to inhomogeneous material properties.

This paper gives an outline of the methodology that has been used to analyze and predicate the fatigue life, together with a description of the most commonly used methods to improve the reliability of forged structures. And the present, the heterogeneous hardness distribution of a clutch pulley is

†This paper was recommended for publication in revised form by Associate EditorChongdu Cho

*Corresponding author. Tel.: +82 31 8021 6477, Fax.: +82 31 8021 6409 E-mail address: [email protected]

© KSME & Springer 2011

622 H.-J. Shim and J.-K. Kim / Journal of Mechanical Science and Technology 25 (3) (2011) 621~629

determined by a plastic deformation simulation and practical hardness tests. In addition, this study suggests that durability analysis can be used to study the prediction of both applied stress and fatigue strength at every node regarding the finite element analysis. To establish this methodology, a series of finite element analysis at cold forged structure was carried out while the material properties of the workpiece, such as effec-tive strain and hardening, were varied. Furthermore, the em-pirical equations were obtained with an effective strain-hardness-fatigue strength relationships for estimating the clutch pulley life based on failure position and fatigue life.

2. Theoretical analysis and experimental procedure

2.1 Materials and manufacturing process

The material of the pulley is S10C, which is manufactured in plastic process by the cold forging. The chemical composi-tion of S10C, which is low carbon steel, is given in Table 1. The mechanical properties for raw material and one in the cold forged material are shown in Table 2. The tensile test specimen was extracted from the pulley in the radial direction which notes the specimen direction on the component. Five tensile specimens were prepared in accordance with KS-1008 with each plastic process condition and were tested by using an MTS 810 System with a cross head speed of 2 mm/min at room temperature.

The prototype forging product was manufactured in order to verify not only predictions by the effective strain but also the fatigue strength. For cold forging, the knuckle joint press (Ha-noul Tech. Co.) was used with a die pressure of 1,216 ton. The die, the work piece for the manufacturing process, was as-sumed to be specified according to the requirements of the product. The extruded top die is used to flat punch and punched at a central hole such as [5] to have no interface be-tween the counter punch and the die insert. The die holder and punch material were heat-treated by SKH 43 and a shrunk fit SCM 4, respectively. To reduce the friction effect on the two contacting surfaces between the die and billet, lubrication was employed using a phosphate coating and bond lube, as well as a cold forging process at the room temperature. The manufac-turing process for cold forging was as follows; (1) shearing a board of raw material, (2) blanking and punching, (3) obtain-ing preliminary forming (named pre-deformed body) after forging at room temperature, (4) creation of a banana slot by piercing and punching, and finally (5) groove drawing and accurate cutting for the bearing insert. After austenitization of the pre-deformed body at 650 oC for 1 hour in an electric fur-nace, cooling conditions were supplied in an air-blast-cooled to room temperature. In this study, we assumed that the cut-ting effect is not able to significantly alter material properties during piercing for the banana slot, especially for some manu-facturing processes in which the precision cutting and post process are very short. However, this assumption does not hold for machining processes in which the heating rate may be

larger than 105 oC/s [6]. The critical region is the inner and outer bridge part which is 2.7 mm the distance from the dou-ble rib extrusion surface due to process cutting of the banana slot by piercing, as shown in Fig. 1 which contains a repre-sentation of the outward shape and scale up for the bridge part.

Table 1. Chemical composition (wt %).

C Mn P S Si Ni Cr

0.08 0.40 0.022 0.13 0.16 0.01 0.03

Table 2. Mechanical properties.

Material Yield strength (MPa)

Tensile strength (MPa)

Elongation (%)

Raw material 201 353 42

As cold forged 632 708 11

A-A sectionA-A section

A-A section

Inner bridge Outer bridge

2.7mm2.7mm

A-A section

Inner bridge Outer bridge

2.7mm2.7mm

Fig. 1. Schematic of the shape and position of the inner and outer bridge from double ribs.

Belt tensionBelt tension

FixedFixed

Belt tensionBelt tension

FixedFixed

(a) FE-model boundary conditions

T0T0

Pr (θ )

θ

2θ

2θ

T0T0

Pr (θ )

θ

2θ

2θ

(b) Forces acting on load distribution at the idle state Fig. 2. Finite element model and loading conditions of the pulley.

H.-J. Shim and J.-K. Kim / Journal of Mechanical Science and Technology 25 (3) (2011) 621~629 623

2.2 Finite element analysis

The applied stress distribution of the pulley was analyzed by the commercial package MSC.NASTRAN [7]. This model uses an 8-node brick element with 55,096 total elements. The boundary condition of the bearing part which adheres to the axis of the durability test machine was fixed. Fig. 2 (a) and (b) show the finite element model, boundary and loading condi-tions under compressive loading due to V-belt tension. A compressive load by unit angle was calculated using Eq. (1) from the V-belt.

2/sin2 0 θTPr = (1)

Here, 0T is the belt tension at the idle state. Based on the previous research [8, 9], it was assumed in this study that the friction force between V-belt and clutch pulley has a negligi-ble effect on the applied stress for durability analysis. The stress analysis for the clutch pulley was investigated to the critical region for the applied load.

The durability analysis can be performed with different fa-tigue strength owing to a difference in the plastic work process. Generally, in the metal fatigue analysis, each individual node (or element) of the same material is usually assumed to cumu-late equally to the fatigue damage that occurs in the compo-nent. Therefore, the durability analysis of commercial package simulation represents very little in this study, since the fatigue life distributions depend on the static stress distribution re-sponses due to the structural shape on the inelastic stress analysis. The procedure chart for predicting the fatigue strength at individual node through the rigid-plastic finite ele-ment analysis is shown in Fig. 3. Shown in this procedure, the suggested methodology was performed on durability analysis in consideration of the heterogeneous strength condition due to hardening. And, such a methodology was able to both fa-cilitate a prediction of fatigue strength variations and provide an evaluation of the approach to the probabilistic S-N.

Firstly, to evaluation of effective strain, a deformation analysis of cold forging and a simultaneous simulation of a clutch pulley were conducted by a CAE simulation software DEFORM [10]. The empirical relationship between hardness and effective strain for the S10C materials was determined to be the hardness test measurement and the verification. Fig. 4 shows a visualization of the forging simulation which is the initial and deformed work piece with a die by rigid-plastic FEM. The cylindrical hollow billets were prepared with a 50 mm inner diameter and a 110 mm outer diameter as described in previous work [11]. The forging process was conducted to sing a top die speed at 6mm/min and the element type was chosen by meshing the work piece in 810 plane elements. Assuming that the top and bottom die do not undergo plastic deformation and the elastic deformation has a negligible effect on the deformation of the work piece, their surfaces were de-fined as non-deformation by using rigid lines surrounded with their representative areas and thus the top and bottom die were not meshed. Only the work piece was meshed. Consequently,

the number of finite elements during the analysis was reduced and the required solution time was decreased.

In the FE model, there are only displacement boundaries and the axisymmetric condition applied on lines and nodes. As it is shown in Fig. 4, the left line had zero speed of the work piece walls representing the boundary condition for the mov-ing of flow deformation in the radial direction (x-direction). The surface between the top, bottom lines and the work piece was restrained from rotating and moving along the x-axis.

Deform Simulation(Rigid-Plastic Analysis)

Stress-Strain relationship(flow stress)

Effective Strain using Deform™Simulation

Hardness Distribution Conversion using Relation Effective and Hardness

Prediction of Fatigue Strength Distribution(Empirical Relationships)

Verification of Hardness TestEffective strain

Har

dnes

s

Verification of Fatigue TestNo. of cycles

Stre

ss

Prediction of Fatigue Strength Every Node

Deform Simulation(Rigid-Plastic Analysis)

Stress-Strain relationship(flow stress)

Effective Strain using Deform™Simulation

Hardness Distribution Conversion using Relation Effective and Hardness

Prediction of Fatigue Strength Distribution(Empirical Relationships)


Har

dnes

s


Har

dnes

s


Stre

ss


Stre

ss

Prediction of Fatigue Strength Every NodePrediction of Fatigue Strength Every Node

Fig. 3. Process to obtain fatigue strength using relationship of hardness and effective strain to predict hardness distribution by rigid-plastic simulation.

Top die

Bottom die

Billet(work piece)

Top die

Bottom die

Billet(work piece)

Symmetry

(a) Before forging

Top die

Bottom die

work piece

Top die

Bottom die

work piece

(b) After forging

Fig. 4. Visualization of the forging process with the work piece.


They were only allowed to move though the prescribed verti-cal displacement. The top die movement along the y-axis was controlled with a pilot node. The flow stress of S10C is as follows with the tensile test in order to the analysis of plastic deform:

218.038.677 εσ = (MPa) (2)

where σ and ε are effective stress and strain from the axial-tensile test. Eq. (2) is mostly used to represent relation-ship of plastic stress and strain. In practice, the friction coeffi-cient may depend on the type of the materials in contact. In this study, the friction constant was assumed to be 0.1 from the previous study [11]. 2.3 Relationship between effective strain and strength

As a measurement of material resistance for permanent de-formation, hardness is an important parameter. Generally, cold-formed parts are forged in a number of stages and at each stage the material undergoes additional permanent deforma-tion. The material during the process sometimes becomes so hard that further forming becomes impossible without fractur-ing the part. Because the measure of strength and a means of determining inhomogeneous deformability of the material are important quality criteria, it is more desirable to estimate the fatigue strength of a component for durability analysis without actually making the prototype. In order to establish a correla-tion between hardness and fatigue strength, we should primar-ily concern with the effective strain.

It is already known that the hardness number of a cold forged product is closely correlated with its effective strain and does not depend upon the forging process [12-14]. As it is shown in Fig. 5, they are the relationships between the effec-tive strain and the hardness for various materials as introduced by Sonmez [13] and Park [14] for low carbon steel and several materials. The relation between the hardness and the effective strain of AlSI 1010 steel from the FE-simulation according to Park [14] is as follows;

435.07.828.104HV ε+= (MPa). (3)

This equation is a successful prediction of the relation be-tween the effective strain and hardness for AISI 1010. How-ever, Eq. (3) relied on the studies of the hardness test on in-dentation procedure which means the work piece does not undergo a cold forging process. Thus, in this study the pro-posed equation was suggested by an interpolated hardness test value from the cold forging and then this relation was verified by comparing the predicted hardness distribution with the measured values. Furthermore, this relation is generalized to apply to cases where the material has undergone a permanent deformation through cold forging. Based on these results, the proposed methodology estimates the fatigue strength of an individual node (element) in order to predict of fatigue life and accurate failure position. The summarized relationship be-tween hardness and tensile strength can be regarded as the fatigue properties, which means that the hardness is related to strength. Such tensile and fatigue strengths are as follows;

3.29HV 47uσ = − (MPa) for HV≤445 (4) 4.02HV 374uσ = - (MPa) for HV > 445.

Here, uσ is tensile strength and Eq. (4) is recommended by Kloos-Velten [15] and in additional is reported by Song [16].

2.4 Prediction of fatigue strength and development of dura-

bility analysis

In this research, the main focus was to develop an efficient methodology for fatigue life improvement of cold forged component and durability estimation of inhomogeneous de-formation consideration. The methodology of development for an accurate durability analysis in consideration of heterogene-ous material characteristics is presented in Fig. 6. As it can be seen in Fig. 6, the component life is predicted in terms of work piece hardness. Once the hardness value is known in terms of effective strain, thus the tensile strength and fatigue properties can be calculated by effective strain results of software DEFORM simulation.

There are two main parameters for the durability analysis. One is the stress result from the applied stress on the compo-nent and the other is the fatigue properties or S-N curve in case of high cycle fatigue. The applied stress was investigated in elastic FEM and fatigue strength prediction was performed on rigid-plastic FEM via a relationship between effective strain – hardness and tensile strength – fatigue strength.

This methodology can result in a prediction of fatigue life and an accurate failure position from stress and strength pa-rameter for a part of the maximum applied load where the higher fatigue strength part is due to the actual plastic harden-ing. The fatigue strength prediction for the individual node is calculated from the relationship among Eqs. (3) and (4) by a rigid-plastic FEM and empirical fatigue equation. This ap-proach was taken because the fatigue strength was relative to

0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.00

100

200

300

400

500

Vic

kers

Har

dnes

s,HV

(MPa

)

Effective Strain, ε

1) Altan, T.(2005) 2) Chaudhri, M.M.(2000) 3) Lee, W.S.(1996) 4) Park, J.H.(2004)

1) Hv=102.8+84.9ε0.4

2) Hv=132ε0.1969

3) Hv=148+78.8ε0.66

4) Hv=104.8+82.7ε0.435

AISI 1010

Copper C010

SCR420H

Fig. 5. Comparison of relations of effective strain and hardness onseveral materials.


the tensile strength and could be attributed to a prediction from hardness data of material resistance parameter readily.

In this chapter we would like to present the empirical fa-tigue equation for the calculated fatigue strength as derived from the value of hardness and tensile strength. This method-

ology should note that the strength estimation has limited on accuracy for metal fatigue and is used in low or middle carbon steel and some of aluminium alloys because the experiment results of tensile strength and fatigue limit have great variation. The development methodology was determined based on an assumption that the service life of a component can be deter-mined by either the high-cycle fatigue failure or fatigue limit if lower than 3 × 106 cycles.

Several researchers have developed empirical relations to predict stress-life fatigue behavior using monotonic tensile properties. Some of these relations proved to be good ap-proximations for a variety of materials [17-19]. The fatigue limit can be expressed as a function of tensile strength in two point method by Shigley et al. [18], as follows;

uw σσ 504.0= (MPa) for 1460 ≤uσ (MPa)

(5) 700=wσ (MPa) for 1460 >uσ (MPa)

where wσ and uσ are the fatigue limit and tensile strength, respectively.

2.5 Verification of finite element analysis and fatigue testing

For verification of the FE model, the strain history was measured by the strain gage which boned the critical part with the rotation of the pulley. The strain gage was attached to po-sitions on the inner and outer bridge part. Fig. 7 shows the position of the strain gage for measurements. The hardness tests were performed on the forged pulley for the confirmation of heterogeneous material properties and for verifying the prediction of hardness via rigid-plastic simulation. Vickers, Brinell and Rockwell hardness are generally used as hardness numbers. Vickers hardness is primarily used considering the test material and individual error. Because the Vickers hard-

Improved Durability Analysis

Applied Stress Fatigue Properties

Stress distribution ;using elastic FEM(NASTRAN)

Critical Region and Stress obtain ijσ

Effective strain distribution ;Rigid-plastic FEM process simulation(DEFORM)

Calculation 1. Hardness from effective strain

Calculation 2. Tensile strength from hardness value

Calculation 3. Fatigue limits from tensile strengthS-N properties for every node

ijbpijij NAS =

ijσ ijS ≥

Fatigue life, Failure position

Improved Durability Analysis

Applied Stress Fatigue Properties

Stress distribution ;using elastic FEM(NASTRAN)

Critical Region and Stress obtain ijσ

Effective strain distribution ;Rigid-plastic FEM process simulation(DEFORM)

Calculation 1. Hardness from effective strain

Calculation 2. Tensile strength from hardness value

Calculation 3. Fatigue limits from tensile strengthS-N properties for every node

ijbpijij NAS =

ijσ ijS ≥ijσ ijS ≥ijσ ijS ≥

Fatigue life, Failure position


Har

dnes

s


Har

dnes

s


Har

dnes

s


Stre

ss


Stre

ss


Stre

ss

Fig. 6. Methodology of development for durability analysis with a consideration of inhomogeneous properties.

Fig. 7. Position of attached strain gage.

Outer type specimenInner type specimen

Outer type specimenInner type specimen

Fig. 8. Illustration of the specimen extracted fatigue test.


ness test uses a square-based diamond pyramid as the indenter, and the Microvickers hardness uses a pyramid Diamond Head indenter, the selection was made by considering the number of indentations and specimens size. The hardness was measured using a HMV-2000 (Shimazu Co.) micro-hardness tester [20]. Each measurement used 500gf of load and 10 seconds about holding time.

Meanwhile, verification of the prediction of fatigue strength at particle node (or element) becomes so difficult due to actual impossibility at very small regions (i.e. particle node) in this suggested methodology, thus fatigue testing was constructed by some positions near the inner and outer bridge region in order to verify the methodology. Fig. 8 shows the attached position of the inner and outer type fatigue specimen at 13,

22mm near the inner rib diameter. The geometry of the fatigue specimen is presented in Fig. 9 where the stress concentration (Kt) was 1.02. The fatigue tests were conducted by using an MTS model 810 servo-hydraulic testing machine, with the stresses imposed at a frequency of 5 Hz (which was directly correlated with the oscillating load). The fatigue test was con-ducted under T-C (tension to compression) sine wave load cycles with a stress ratio, R ( maxσ / minσ ) = -1. The stress am-plitude was revised to rotational bending stress (modified fac-tor = 0.85) [19] from the axial stress of the specimens because the applied load is significant and dominates rotation bending mode.

The component fatigue test at room temperature was con-ducted by a durability test machine (dead weight tester; Japan movement) considering the loading condition of the V-belt tension, and the test conditions was not revealed due to pri-vacy concerns.

3. Results and discussions

3.1 Stress analysis for investigation of critical part

Fig. 10 shows von-Mises stress distribution of the clutch pulley derived from a finite element analysis to examine the applied stress analysis of that pulley under service conditions. As it is shown in Fig. 10, the maximum von-Mises stress oc-curs at the inner bridge part.

On the other hand, the strain history measurement was per-formed by the analysis of the pulley rotation, since the posi-tion of the hole with the rotation was changed. The variation of the strain with rotation angle (θ ) is shown in Fig. 11. The solid line ( − ) and dashed line (--) denotes the strain history at the inner bridge and the outer bridge part, respectively. From viewing the amplitude strain of inner bridge part it was found that the inner bridge part was critical. Therefore, the theoreti-cal critical part for the applied stress analysis was evaluated as the inner bridge from Fig. 10 and Fig. 11.

3.2 Verification of finite element analysis and investigation

of inhomogeneous properties

As Fig. 12 indicates, the theoretical strain histories compare with the test results. The solid ( − ) and dashed line (--) de-notes the theoretical results of FEA and open (○) and solid mark (●) denotes the strain history of the test results, respec-tively.

Accordingly, it seemed quite probable that the failure posi-tion was the inner bridge. It was found that the load amplitude of the inner part was more than that of outer bridge part. How-ever, as Fig. 13 indicates the actual failure position did not correspond to the theoretical critical part. This is an important point in this paper as it demonstrated that the failure predic-tions will be in consideration of the inhomogeneous properties of a plastic working process.

The results of the hardness distribution in order to confirm of heterogeneous characteristics for a clutch pulley material

R 35

φ 6φ 3

64

32

32

Kt = 1.02

R 35

φ 6φ 3

64

32

32

Kt = 1.02

Fig. 9. Configuration of fatigue specimen (mm).

Fig. 10. Von-Mises stress contour of the elastic stress analysis.

0 100 200 300 400-1800

-1200

-600

0

600

1200

Computed stra in at inner part Computed stra in at outer part

Stra

in(x

10-6

ε)

Rotation angle,(degree) Fig. 11. Strain history due to rotation by FE analysis.


were as follows. Fig. 14 show the distribution of the Mi-crovickers hardness at the inner and outer bridge parts for a cold forging. Table 3 contains a summary of the mean and standard deviation. It is known that the cold forged process shows inhomogeneous distribution of hardness value and the hardness of the inner bridge part is more than that of the outer bridge part. Furthermore, it is very important to understand the preferential failures that occur at this position. Thus, the crack-ing phenomenon was mainly caused by the inhomogeneous behaviour of hardness and strength. The results of the simula-tion from the rigid-plastic analysis due to a transformation of

the plastic flow are shown in Fig. 15. The values of the defec-tive strain were 3.89 at the inner bridge part and 1.88 at the outer bridge part as a result of the rigid-plastic simulation. As it is shown in Fig. 15, the differences of effective strain distri-bution occurred because the inner part was incapable of fur-ther appreciable work hardening and they can be stronger due to the extrusion of the inner rib part, while the outer rib part was not affected. When a work hardening material is de-formed not uniformly, the flow stress of more deformed area was higher than one of the less deformed area. Therefore, the “more deformed area” (the inner rib part) is less likely to be deformed than the “less deformed area” (the outer rib part).

3.3 Prediction of fatigue strength and durability analysis

The life equations predicting the fatigue strength at every node by the rigid-plastic simulation with Eqs. (3)-(5) are as follows. The corresponding representative tensile strengths were 794MPa and 656MPa at the inner and outer bridge part from Eq. (4) related to the calculated hardness value by Eq. (3). By substituting Eq. (4) into Eq. (5), we may express the obtained fatigue properties (S-N curve) as follows by two point method according to Shigley et al. [18], which point is (0.9 uσ , 103) and ( ,wσ 106).

Inner bridge part (Prediction)

124.0.6.2229 −= pred

innera NS (6)

Outer bridge part (Prediction)

138.0.5.2210 −= pred

outera NS (7)

Here, .predN is the predicted life at the inner and outer bridge part.

In order to verify fatigue properties, fatigue tests of the in-

0 100 200 300 400-1800

-1200

-600

0

600

1200

Experimental strain at inner part Experimental strian at outer part Computed strain at inner part Computed strain at outer part

Stra

in(x

10-6

ε)

Rotation angle,(degree) Fig. 12. Comparison of measured and computed strain.

Fig. 13. Failure position with the plastic working process product.

0 10 20 30 40150

200

250

300

Mic

ro V

icke

rs h

ardn

ess,

Hv[

500g

]

Outer-bridgeInner-bridge

Number of times

Fig. 14. Hardness distribution of the inner and outer bridge.

Table 3. Summary of the mean and variation for hardness test.

Position Average (Hv) Standard deviation

Inner bridge 253.6 9.9

Outer bridge 213.9 12.0

1.883.98

outer bridge

3.98

3.14

2.78

2.42

2.06

1.70

1.34

0.98

0.26

Effective -StrainInner bridge

○□

1.883.98

outer bridge

3.98

3.14

2.78

2.42

2.06

1.70

1.34

0.98

0.26

Effective -StrainInner bridge

○□

Fig. 15. Distribution of the effective strain from rigid-plastic simula-tion for the cold-forged pulley.


ner and outer type specimens were performed and the pre-dicted S-N curves were compared with the test results. Fig. 16 shows a comparison between the experimental and predicted life with Eqs. (6) and (7). As it can see from the figure, the inner type specimen was significantly higher fatigue strength than the outer type specimen, and the tests results of the inner type specimen were overestimated. Nevertheless, the pre-dicted results at each position showed good agreement within a factor of 3 scatter bands considering the various sources of error. Based on the results, it was found out that applied stress at the critical part and the fatigue strength at each node should be considered simultaneously to propose the component life. This consideration was proposed of a durability analysis for the inhomogeneous behavior.

In these categories, the maximum stress at inner and outer bridge part was 258.3MPa and 209.8MPa, respectively, for the fatigue life calculation. By substituting these values and Eqs. (6) and (7) into the Basquin’s equation [18], we may obtain the fatigue lives of 71039.3 × and 71073.2 × cycles at inner and outer bridge part, respectively. These observations indi-cated that while there was relatively lower stress at the outer bridge part than at the inner bridge part, this position, never-theless, has lower fatigue strength due to the inhomogeneous behavior. The lower fatigue strength phenomenon, which was attributed to lower hardening, was clearly visible in the rigid-plastic simulation. Thus, for this reason the outer bridge may cause crack initiation in the clutch pulley. This methodology developed that a durability analysis for inhomogeneous de-formation can occur even under fatigue loading.

4. Conclusions

We performed a study on the development of durability analysis, to accurately predict fatigue life and crack initiation of a clutch pulley. The conclusions of the study are as follows:

This paper investigated the critical part of a clutch pulley via stress analysis to durability analysis and we suggested development method when there are inhomogeneous proper-

ties of structures. The critical part was evaluated as the inner bridge region. However, it was not validated as the failure position. Because the cold forged pulley showed inhomoge-neous hardness distribution and the hardness value of the inner bridge part is more than that of the outer bridge part. This phenomenon is mainly caused by the in homogeneously de-formed behavior during the procedure of plastic work.

In the study, the development methodology for predicting component life in the cold forging process, considering the heterogeneous hardening and inhomogeneous strength proper-ties, was proposed in terms of effective strain of the work piece.

We presented a calculated fatigue strength model to predict fatigue life for a cold forging component, which can be ob-tained through a simple hardness test, and effective strain through rigid-plastic simulation. The prediction of fatigue properties was compared with experimental data and the accu-racy of this prediction was satisfactory. Based on this relation of hardness and effective strain, this study predicted accurate failure life and position fatigue properties at each node (inner and outer bridge). The prediction results of the fatigue strength at each node through rigid-plastic simulation are as follows;

Inner bridge part (Prediction) 124.0

.6.2229 −= predinnera NS

Outer bridge part (Prediction) 138.0

.5.2210 −= predoutera NS

In addition, we can predict not only the variation of the fa-

tigue strength but also the probability S-N curve by differences of strength at each node. Thus, it was found that the applied stress at the critical part and the fatigue strength at each node should be considered simultaneously to determine the compo-nent life during the development process of durability analysis in the inhomogeneous behavior. The above results clearly show an improved performance in life and failure position predictions of the proposed methodology over the commercial durability solver as package software.

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[3] Y. Saito, The Monte Carlo simulation of microstructural evaluation in metal, Mater. Sci. Eng. A, 233 (1997) 114-124.

[4] K. Muszka, P. D. Hodgson and J. Majta, Study of the effect of grain size on the dynamic mechanical properties of micro-alloyed steels, Mater. Sci. Eng. A, 500 (2009) 25-33.

[5] D. K. Kim, S. Y. Kang, S. H. Lee and K. J. Lee, Analysis and prevention of cracking phenomenon occurring during cold forging of two AISI 1010 steel pulleys, Metall. & Mat. Trans. A, 301A (1999) 81-92.

102 103 104 105 106 107 108102

103

104

105

106

107

108

N Exp.=

N Pred./3

N Exp.=

N Pred.

Inner bridge part Outer bridge part

Pred

icte

d lif

e, N

Pred

.(Cyc

les)

Experimental life, ΝExp.(Cycles)

N Exp.=

3N Pred.

Fig. 16. Comparison of predicted and experimental fatigue.


[6] D. Umbrello, S. Rizzuti, J. C. Outeiro, R. Shivpuri, R. M’Saoubi, Hardness – based flow stress for numerical simu-lation of hard machining AISI H13 tool steel, J. Mater. Process. Tech., 199 (2008) 64-73.

[7] MSC. Software, MSC. Nastran users guide, USA, 2005. [8] H. J. Shim and J. K. Kim, Considering of fatigue life optimi-

zation of pulley in power steering system, Mater. Sci. Eng. A, 483-484 (2008) 452-455.

[9] H. J. Shim and J. K. Kim, Cause of failure and optimization of a V-belt pulley considering fatigue life uncertainty in automotive application, Eng. Fail. Anal., 16 (2009) 1955-1963.

[10] Deform 2D V. 9.0.1-User Manual, DeformTM, Scientific forming technologies corporation ed., Columbus, OH, USA (2006).

[11] D. J Kim and B. M. Kim, Application of neural network and FEM for metal forming processes, Int. J. Mach. Tool. Manu., 40 (2000) 991-925.

[12] H. K. Kim, S. M. Lee and T. Altan, Prediction of hardness distribution in cold backward extruded cups, J. Mater. Proc-ess. Tech., 59 (1996) 113-121.

[13] H. Tumer and F. O. Sonmez, Optimum shape design of die and perform for improved hardness distribution in cold forged parts, J. Mater. Process. Tech., 209 (3) (2009) 1538-1549.

[14] Y. Choi, J. H. Park, B. M. Kim, J. C. Choi and B. H. Min, Estimation of relationship between effective strain and hard-ness by rigid-plastic FEM, Met. Mater, 6 (2) (2000) 111-116.

[15] K. H. Kloos, E. Velten, Berechnung der dauerschwingfes-tigkeit von plasmanitrierten bauteilahnlichen proben untter berucksichtigung des härte-und eigenspannungs verlaufs, Konstrucktion, 36 (5) (1984) 181-188.

[16] J. H. Song and S. L. Kwang, Estimation method for strain-life fatigue properties from hardness, Int. J. Fatigue, 28 (2006) 386-400.

[17] M. L. Roessle and A. Fatemi, Strain-controlled fatigue properties of steels and some simple approximations, Int. J. Fatigue, 22 (2000) 495-511.

[18] J. E. Shigley, C. R. Mischke andR. G. Budynas, Mechani-cal Engineering Design, 7th Ed. MacGraw-Hill (2005).

[19] M. R. Mitchell, Fundamental of Modern Fatigue Analysis for Design, ASM Handbook Fatigue & Fracture, 19 (1996) 227-249.

[20] ASTM, Test Method for Microhardness of Materials, E348 (1989).

Hee-Jin Shim received the masters’ degree and Ph.D. degree from the De-partment of Mechanical Engineering, University of Hanyang, Korea, in 2005 and 2010, respectively. She is currently a senior researcher at KEPCO E&C. Dr. Shim’s research interests are in the ar-eas of fatigue, integrity evaluation,

welded joints and advanced materials. She studies these sub-jects through experimental and numerical means.

Jung-Kyu Kim received his Ph.D. de-gree from the University of Keio, Japan, In 1982. He is currently a full-professor in the Department of Mechanical Engi-neering in Hanyang University, Seoul South Korea. His principal research interests include the fatigue behavior of materials and components, the devel-

opment of experimental methods to evaluate and monitoring fatigue damage.

Documents

Durability analysis of an automotive component in ......Durability analysis of an automotive component in consideration of inhomogeneous hardness† Hee-Jin Shim1,* and Jung-Kyu Kim2