j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 9 ( 2 0 0 9 ) 1074–1084

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Die fatigue life improvement through the rationaldesign of metal-forming system

M.W. Fu ∗, J. Lu, W.L. ChanDepartment of Mechanical Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong

a r t i c l e i n f o

Article history:

Received 12 May 2007

Received in revised form

14 February 2008

Accepted 15 March 2008

Keywords:

Die fatigue life

S–N approach

a b s t r a c t

In metal-forming industries, die is an important tool for fabrication of metal-formed prod-

ucts. Die service life, which is defined as the maximum product number produced by die

before it fails, and die performance directly determine the quality of metal-formed prod-

uct and production cost. In cold forming process, die service life basically refers to the die

fatigue life. The die fatigue life is determined by the design of metal-formed product and

die, forming process configuration, die stress and the entire metal-forming system. In this

paper, a methodology for optimization of die fatigue life is developed via the rational design

of metal-forming system in such a way that the die stress is optimal and further the die

design in terms of its service life is the best. To realize this thought, the S–N approach is

employed for evaluation of die fatigue life. The die stress is first identified via the integrated

CAE simulation

Integrated product and process

design

simulation of billet plastic flow and the die deformation during the forming process. The die

stress is then optimized via the rational design of the combination of metal-formed prod-

uct, die and process configuration. The optimal die life is thus determined. Furthermore, a

framework for implementation of this methodology is developed and case studies are used

alida

Traditionally, die design is based more on heuristic know-

for verification and v

1. Introduction

Due to the increasing competition in global markets, the profitin metal-forming industries is pushed to the marginal or limitlevel. How to cut cost, improve productivity and enhance prod-uct quality decide whether the companies can keep theirleading edge and competitiveness in the severe competitivemarketplaces. Die is an important tool for deformation orfabrication of metal-formed products. Die performance andservice life, which is defined as the number of metal-formedparts produced by die before it fails, decide product quality,time-to-market and production cost. The optimal design ofdie service life has become an effective solution for addressing

the above-listed issues.

Die design and manufacturing are important steps inmetal-forming product development. Without suitable die,

∗ Corresponding author. Tel.: +852 2766 5527.E-mail address: mmmwfu@polyu.edu.hk (M.W. Fu).

0924-0136/$ – see front matter © 2008 Elsevier B.V. All rights reserved.doi:10.1016/j.jmatprotec.2008.03.016

tion of the developed methodology.

© 2008 Elsevier B.V. All rights reserved.

metal-forming processes are often crippled or rendered totallyinefficient. To have the die which has long service life, thedesign and manufacture of die must be well conducted. Thereare many factors which affect die service life (Lange et al., 1992;Fu et al., 2006; Tong et al., 2005; Fu et al., 2008). Fig. 1 showsthese factors from die design, die geometry and material, heattreatment condition, billet conditions and material, and fur-ther to manufacturing and tribological conditions between thedie and workpiece (Falk et al., 2001). Therefore, how to system-atical and integral design of die together with metal-formedproduct, forming process sequence and the detailed processconditions is a non-trivial issue.

how and experience acquired through trial-and-error thandeep scientific analysis and calculation. This kind of prod-uct development paradigm cannot ensure that the die service

j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h

F1

laloddmvt

vtda2iitdffrfoldlIeacam2vaGCfaF

which can be represented in Fig. 2. The service life of die isdefined as the number of these cycles. It is well known that dieis installed in a forming machine. In the one stroke of formingmachine, one or more parts can be produced by the die. The die

ig. 1 – The factors affecting die service life (Lange et al.,992).

ife is optimally designed as the interaction and interplaymong the above-mentioned affecting factors on die serviceife is difficult to quantitatively represent and determin basedn the traditional experiences and know-how. To have goodie performance and service life, the die should be optimallyesigned and precisely fabricated. On the other hand, dieaterials need to be well selected and heat-treated. In die ser-

ice stage, the working conditions and working processes needo be well determined.

To realize this goal, industries and academia have pro-ided a lot of efforts to conduct the extensive researches inhis area. Fu et al. (2006) has developed the simulation-basedie fatigue life assessment methodology based on stress-lifend strain-life (S–N) approaches (Tong et al., 2005; Fu et al.,008). The methodology provides good approaches for predict-ng die fatigue life. Falk et al. (2001) used different conceptsncluding local stress, local strain and local energy approacheso estimating die service life. As the approaches need toetermine the local stress and strain of the die during theorming process, the CAE simulation technology is employedor revealing the instantaneous stress and strain of die in theiresearch. Knoerr et al. (1994) adopted the fatigue techniquesor identifying the root-cause of fatigue failure and devel-ped a strain-based approach for estimation of die fatigue

ife. The approach used the elastic–plastic analysis model toetermine the maximum strain amplitude and further ana-

yze the fatigue life based on the damage analysis concept.n addition, Vassilopoulos used artificial neural network forstablishing the S–N curve of composite materials in suchway that only 40–50% of experimental data is needed for

onstruction of the S–N curve compared to the conventionalpproach. The expensive and time-consuming fatigue experi-ents can thus be significantly reduced (Vassilopolulos et al.,

007). Furthermore, many other effects have also been pro-ided in modeling of fatigue behaviors, failure mechanismnd probability of die (Pedersen, 2000; Srivastava et al., 2004;eiger and Falk, 2001; Arif et al., 2003; Bernhart et al., 1999;

osenza et al., 2004; Park and Colton, 2006). Some other are

ocused on investigation of the die stress in forming processnd the methods for die life improvement (Joun et al., 2002;u and Shang, 1995; Joun et al., 2002; Brucelle and Bernhart,

n o l o g y 2 0 9 ( 2 0 0 9 ) 1074–1084 1075

1999). All of these efforts are good exploration on die lifeassessment. Despite of the fact that there is no general wayto increase die service life, there are some tactics, which dohelp die service life improvement. How to identify and developthese “tactics” needs to systematically correlate the die ser-vice life with various influencing factors and mathematicallyrepresent the correlation to facilitate the optimal design of dieservice life.

In this paper, the notion of the metal-forming systemdesign is proposed for systematic consideration of the effectof many affecting factors and the whole forming system ondie fatigue service life. First of all, the detailed intent of metal-forming system is defined. The integrated simulation of thewhole forming system is presented. Through the rationaldesign of the affecting factors, the entire forming system andthe configuration of design scenarios for forming system, theinteraction and interplay of the detailed affecting factors ondie service life is systematically simulated and investigatedthrough the integrated simulation approach presented in thepaper. Upon the CAE simulation, the deformation load is deter-mined and the critical stage at which the deformation load isthe maximum is identified. The instantaneous maximum diestress at the critical stage in a service cycle is then revealedand identified. The service cycle here is defined as a periodicprocess for producing a part in the forming system. By employ-ing the S–N approach, the die service life is finally predicted insuch a way that the optimal design of the die service life canbe determined through the comparison of the predicted diefatigue life for different design scenarios. To implement thisthought, a framework is presented. The rationale, validity andthe robustness of the developed methodology are verified bycase studies.

2. Methodology

2.1. Die fatigue life assessment

Die is a tool used for forming of the deformed products. Whendie is used for forming of product, it undergoes cyclic stresses

Fig. 2 – Die service cycles and characteristic stresses.

1076 j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 9 ( 2 0 0 9 ) 1074–1084

Fig. 3 – S–N diagram.

is subjected to the cyclic loading in forming of the deformedparts, as shown in Fig. 2.

In the cyclic stress, there are four characteristic stresseswhich need to be extracted for the assessment of die servicelife based on S–N approach. These stresses are designated asthe maximum, minimum, mean and amplitude stresses. Theyare represented as �max, �min, �m, and �a, respectively. Amongthem, �max and �min refer to the maximum and minimumstresses, respectively. �m and �a, on the other hand, are themean stress and the stress amplitude, as shown in Fig. 2. Therelationship of these four stresses can be formulated as

�a = �max − �min

2(1)

�m = �max + �min

2(2)

To establish the relationship of die fatigue life with its stressstatus and the material property configuration of the die,the following Goodman equation (Bannantine et al., 1990) isemployed and represented as

�a

Se+ �m

Su= 1 (3)

The Goodman equation represents the relationship of diefatigue service life with �a, �m and the material properties,viz., endurance limit Se and ultimate strength Su. Based onthe equation, a diagram to represent the correlation of cyclicstress and fatigue cycle life, viz., S–N diagram, can be con-structed. From the S–N diagram, the die fatigue life can bedetermined based on the given amplitude and mean stresses.Fig. 3 illustrates the S–N diagram for a given mean stress.

In this research, the die material is M2. The S–N diagramof this material can be referred to reference (CRP, 1981), whichprovides the detailed curves for different mean stresses andamplitude stresses. Fig. 4 shows the S–N diagram of M2 and itprovides a basis for evaluation of die fatigue service life in thisresearch.

2.2. Metal-forming system

The metal-forming system consists of process, designed prod-uct, die, materials, preform (billet), equipment and the frictioncondition in-between the billet and die. The design of theentire forming system is to create the detailed content of these

Fig. 4 – S–N diagram of M2 (CRP, 1981).

components or configure the information needed. The detailsinclude

(1) Product design: Geometry, shape and features.(2) Die: Die structure, component geometry and fitting rela-

tionship.(3) Process: Process routing and operation sequence.(4) Equipment: Machine type, tonnage and working conditions.(5) Material and properties: Material selection and behavior

models.(6) Tribology: Friction between die and billet.(7) Billet: Billet geometry and shape.

In this research, the product design, die design and per-form design are considered as three design variables whichaffect the die service life. The process is cold forming andthe equipment is whatever which can perform the cold forg-ing process, viz., either hydraulic press or mechanical press.As the material is pre-defined, the properties are determinedalready. In addition, the friction condition between the die andbillet is also pre-selected. Regarding the perform shape, it isalso an important design variable. In this research, the billet isa cylinder and its geometry is determined based on the volumeneeded for fabrication of the designed products.

2.3. Integrated simulation of metal-forming system

The die service life is predicted by S–N approach. The die stressin forming process is identified via the integrated simulationof billet plastic flow and dies elastic deformation, which isassumed in this research. Therefore, the applicability of theintegrated FEM simulation is suitable for the design of coldforging process and die fatigue service life. The simulationof billet adopts a flow-type formulation, which can take dif-ferent forms but essentially is based on the consideration ofplastically flow of metal. The plastic flow behaviors can berepresented as the following function (Fu and Luo, 1992):

� =∫

V0

E(ε̇˜) dv −

∫SF

F˜

U˜dS +

∫V0

� ε̇iidV (4)

t e c h n o l o g y 2 0 9 ( 2 0 0 9 ) 1074–1084 1077

wiva

Wm

�

wnrt

∑

ENuo

Iif

nWfiacef

wa

iaed

tirdtc

j o u r n a l o f m a t e r i a l s p r o c e s s i n g

here � is the plastic potential, E(ε̇˜) is the work function, SF

s the surface on which traction is prescribed, F˜

is the tractionector, U

˜is the velocity vector, � is the Lagrangean multiplier,

nd V0 is the volume of the deforming body.The funtional in Eq. (4) is for the entire deforming body.

ith discretization of Eq. (4), the functional � can be approxi-ated by the following equation:

≈m∑

j=1

�j(u∼

j, �j) (5)

here � j is the function of the jth element, and u˜

j and �j are theodal velocities and Lagrangean multiplier of the jth element,espectively. According to the stational condition, it is foundhat the following equations exist

m

j=1

∂�j

∂u∼

j= 0 and

m∑j=1

∂�j

∂�j= 0 (6)

q. (6) is non-linear after discretization. To linearize it, theewton–Raphson approach or direct iteration method can besed. After linealization, the following linear equations can bebtained.

(7)

n Eq. (7), the sparseness of the stiffness matrix can be utilizedn solving the equation. The approach using this characteristicor solving Eq. (7) is the so-called sparce approach.

In Newton–Raphson approach, the initinal solution or initi-al value for all the nodal velocities needs to be pre-given.ith the initinal solution or pre-given Uo, the solution for the

rst loading step can be determined by iteration. In the iter-tion process, if the velocity and force norms meet certainriterion, the iteration of the specific loading step is consid-red as convergence. Taking the velocity as an instance, if theollowing criteron is met, the iteration is converged.

||�Un||||Un−1|| ≤ ı (8)

here ||�Un|| is the Euclidean vector norm for the nth iterationnd ı is a pre-defined small positive number, such as 10−5.

In the plastic FEM, Eq. (7) is used to determine the velocityncrement of the nth iteration in the deforming body or billet,nd in such a way that the velocity, strain rate, foming loading,ffective stress and strain, and the other state variables of theeforming body can be determined.

The instantaneous die stress state in forming process ishe focus in this paper. The above presented FEM approachs for simulation of the plastic flow of deforming body. To

eveal the die stress, the elastic FEM approach are used. Inie stress analysis, whether the stress can be accurately iden-ified depends on the accurate determination of the boundaryonditions of the die, which is in turn decided by the sim-

Fig. 5 – Integrated simulation of workpiece plastic flow anddie elastic deformation.

ulation of the deforming body. Fig. 5 illustrates an intergatedsimuation framework between the workpiece and die in whichthe billet deformination and die stress are simulated and ana-lyzed simultaneously. In each loading step, the state variablesof the billet are determined. They are then used to determinethe boundary conditions (BCS) including geometrical BCS andphysical BCS and the constraints for die stress analysis. Withthese input information, the instantaneous die stress can beefficiently revealed and explored, which provides the basis fordie fatigue life assessment.

2.4. Die fatigue life assessment

Fig. 6 shows the paradigm for die fatigue life prediction andassessment. For a design scenario of deformed part and form-ing system, the integrated simulation of workpiece plastic flowand die deformation is first conducted. Prior to the simula-tion, the modeling and representation of the whole formingsystem is conducted to generate the physical, mathematicaland numerical models for the CAE simulation system. Basi-cally, the physical model idealizes the deformation behaviorof the system and abstracts it to comply with certain physicaltheory with assumptions. The mathematical model specifiesthe mathematical equations such as the differential equationsin FEM analysis the physical model should follow. In currentoff-the-shelf and domain-specific CAE systems, the mathe-matical model is usually built in the systems. But users stillneed to specify some detailed data and information such as

boundary conditions and constraints. The numerical model,on the other hand, describes the elements types, mesh den-sity and solution parameters. The solution parameters furtherprovide detailed calculation tolerances, error bounds, and

1078 j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e

Fig. 6 – Die fatigue life assessment paradigm.

the iteration and convergence criteria in CAE simulation pro-cess.

Upon the completion of simulation, there are two sets ofdata which are critical for die fatigue life assessment. Oneis the deformation load and the other is the instantaneousdie stress. Since the deformation load varies in the deforma-tion cycle, the maximum deformation load corresponds to acritical fatigue stage at which the die fatigue failure has thegreatest possibility. In assessment of the die fatigue life, thedie stress at this critical fatigue stage is needed to be extracted.In this paper, the effective stress is used to determine thefatigue location in die. Based on this assumption, the maxi-mum and minimum effective stresses of die in one loadingcycle is retrieved and the amplitude and mean stresses isthen determined. The die fatigue life will then be determinedbased on S–N diagram. For different design scenarios, the cor-responding die fatigue life is determined and thus the bestdesign scenario can be identified via comparison of the diefatigue life.

3. Design of forming system and

simulation

To illustrate the above-proposed methodology for die fatiguelife optimization via rational design of forming system, a part

Fig. 7 – A cas

c h n o l o g y 2 0 9 ( 2 0 0 9 ) 1074–1084

as shown in Fig. 7 is used as a case study. The case will showhow the optimal die service life is identified via the rationaldesign of metal-forming system and the integration simula-tion of the forming system.

In Fig. 7(a), it shows a final product geometries and thisproduct can be formed by metal-forming process. To convertthe final product geometry to plastic-deformed part, a patch-up is needed for one operation of metal forming to producethis part. However, the different dimensions and locations ofthe patch-up constitute different part designs and formingsystems, which have different die service life and process per-formance. The focus of this paper is to investigate the bestdesign of die and forming system.

3.1. Design of metal-forming system

To fully explore the potential design alternatives for formingthe product, three factors are considered. The first one is thepatch-up dimension of the deformed part as the forming sys-tem cannot form a product with a through hole as shown inFig. 7. The patch-up is needed in the extrusion of a cylinderbillet to desired shape of the product. The second one is patch-up location and the third is punch geometry and shape. Theshape of the punch could be flat punch or bevel one. Basedon these three factors, the different design scenarios aboutthe deformed product, die and the cylinder billet volume andits dimensions can be figured out. Table 1 presents the 12design scenarios through the combination of the above differ-ent design variables. For the first design scenario as shown inTable 1, the billet is cylinder and its dimension is Ø37.6 × 14.7based on volume constancy of the billet and the deformedpart.

3.2. Integrated simulation of forming system

To reveal the die stress in the different design scenario, thesimultaneous simulation of billet plastic flow and the elasticdeformation of die are conducted. First of all, the designedmetal-forming system is modeled in a commercial CAD sys-tem and then converted into a data exchange format in such away that they can be imported into the CAE simulation system.

Regarding the material behavior of the forming system,

the punch material is M2 and is considered as a purelyelastic body during the forming process. The elastic moduleis 250,000 MPa and poison ratio � is 0.3. In this research,no temperature effect has been considered. For the billet

e study.

t e c h

m

�

w

j o u r n a l o f m a t e r i a l s p r o c e s s i n g

aterial, the following material relationship is employed

= 150ε0.1 + 547 (9)

here � is effective stress (MPa) and ε is effective strain.

Table 1 – Different design scenarios (dimension in mm)

n o l o g y 2 0 9 ( 2 0 0 9 ) 1074–1084 1079

In addition, the friction between the die and billet followsthe shear friction model, which is represented as

= mK (10)

1080 j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 9 ( 2 0 0 9 ) 1074–1084

Table 1 (Continued )

where m is the friction factor while K is the shear strength ofthe billet material. m is equal to 0.1 in this research.

3.3. Procedure for extraction of simulation results

The integrated simulations are conducted for the above 12design scenarios by using the material models in Section 3.2.Since the stress distribution of the die is not uniform, the

fatigue will initiate at the severe stress location, which is alsothe potential fatigue damage area. To determine this fatiguestress of die, the following procedure is adopted for extractionof the simulation results.

(1) Determination of the maximum deformation load: In the form-ing process, the deformation load varies. However, there isa maximum deformation load in each deformation cycle,

t e c h

(

j o u r n a l o f m a t e r i a l s p r o c e s s i n g

which determines the die service life. For the given designscenario, the geometry of punch is fixed. Therefore, thehigher the deformation load, the higher stress induced inthe punch. The maximum deformation load would corre-spond to the maximum stress in the punch. On the otherhand, the die service life is very sensitive to deforma-tion load. A subtle reduction of the die loading, which isequal to the deformation load, can increase the die ser-vice life up to 10-fold if the die loading is near to the fatiguelimit. Through simulation of billet plastic deformation, thechange of deformation load in the entire forming processis identified and further the deformation state of the max-imum deformation load is determined. The status of themaximum deformation will be used to determine the mostsevere die stress for fatigue life assessment.

2) Identification of the potential fatigue location: Under the max-

imum deformation load, the stress of the die will bethe most severe condition. Under this condition, the diewill have a non-uniform stress distribution. The effectivestress will be used as a criterion to determine the poten-

Fig. 8 – The deformed billet and th

Fig. 9 – The deformed billet and th

n o l o g y 2 0 9 ( 2 0 0 9 ) 1074–1084 1081

tial fatigue location. The potential location is located at theplace where the effective stress is maximum.

(3) Extraction of the maximum effective stress: From the moststress severe location, the maximum effective stressis identified. When the die is used for forming, theoriginal stress state is zero as it does not have anypre-stress condition (no shrinking fit condition in thiscase). On the other hand, the fatigue is more relatedto the mean stress and the amplitude stress based onthe Goodman’s equation, the mean stress and amplitudestress of the effective stress will be used for fatigue lifeassessment.

4. Result analysis and discussion

Fig. 8 shows the deformed billet and the deformation load incase I. In the figure, “Step 158” is the simulation loading step. Inthis research, each simulation-loading step is the 0.1-mm dis-placement. “Step 158” would mean that the stroke of punch is

e deformation load in case 1.

e deformation load in case 2.

1082 j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 9 ( 2 0 0 9 ) 1074–1084

Fig. 10 – Potential fatigue location in case 1.

tigu

of die.Tables 2 and 3 summarize the results for the 12 different

design scenarios. The simulation results include the deforma-tion load and the effective stress at the tracking point which

Fig. 11 – Potential fa

15.8 mm at this loading stage. Furthermore, from the figure, itcan be seen that the maximum deformation load is located atthe last deformation stage. From the simulation point of view,the simulation step is 158. The deformation load is 127 tons.Fig. 9 shows the simulation results of case II.

Based on the stage at which the deformation load is themaximum, the punch stress is investigated. It is found thatthe potential fatigue location is located at the radius corner inthe second shoulder of the punch when the deformation loadis the maximum. Defining a tracking point at point P1, theeffective stress at the point can be identified. Fig. 10 shows thepotential fatigue location in the punch, the defined trackingpoint and the effective stress distribution in the forming

processes in case I. Similarly, Fig. 11 shows the similar resultsin case II.

Fig. 12 shows the stress varies cyclically in the course of dieservice. To produce a product, the die undergoes a cyclic stress.

e location in case 2.

This cyclic stress is used to determine the potential fatigue life

Fig. 12 – The cyclic stress in forming process.

j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 9 ( 2 0 0 9 ) 1074–1084 1083

Table 2 – The simulation results for cases 1–6

Case 1 H6(bottom)

Case 2 H6(mid)

Case 3 H6(top)

Case 4 H4(bottom)

Case 5 H4(mid)

Case 6 H4(top)

Deformation load (ton) 127 128 130 122 134 131Effect stress at point P1 1770 1800 1630 1600 1810 1690�a (MPa) 885 900 815 800 905 845�m (MPa) 885 900 815 800 905 845Expected fatigue life 2750 2300 4200 4800 2280 3600

Table 3 – The simulation results for cases 7–12

Case 7 h6�10(bottom)

Case 8 h6�10(mid)

Case 9 h6�10(top)

Case 10 h4�10(bottom)

Case 11 h4�10(mid)

Case 12 h4�10(top)

Deformation load (Ton) 111 121 116 119 139 117Effect stress at point P1 1510 1590 1450 1620 1880 1620

77

90

isIruT

falhmtol

smTttmwtl

5

Dpcdsaitpds

r

�a (MPa) 755 795�m (MPa) 755 795Expected fatigue life 7800 4700

s located at the potential fatigue area. Mean and amplitudetresses are then derived and are also included in the table.n this research, the die is supposed to be an elastic body. Noesidual stress and pre-applied stress are considered in eval-ation of die life. �a is thus same as �m. This can be found inables 2 and 3.

Based on the S–N diagram as shown in Fig. 4, the expectedatigue life can be expected through the interpolation of thevailable curves in the figure and determine the die fatigueife. In Fig. 4, the vertical axis is amplitude stress �a and theorizontal axis is fatigue cycle, viz., fatigue life. For the givenean stress and amplitude stress, it needs to draw a horizon-

al line from vertical axis and interpolate it based on the curvesf specific �m. The final fatigue life is determined based on the

ine from the interpolated stress point in the 2D plane.From Tables 2 and 3, it can be found that the best design

cenario is case 9 where the expected die fatigue life is 9000. Iteans that the die can undergo 9000 cycles before it fails. From

able 1, it is found that the patch-up of 6 mm is located at theop of the smaller interior hole in the part. This would makehe metal flow in backward extrusion and forward extrusion

odes easily. In addition, the punch has a conic tip, whichould facilitate the deformation of metal. All of these lead to

he lowest stress in the punch and thus the punch has theongest service life.

. Conclusions

ie service life is affected by many factors related to die design,rocess determination and parameter configuration, materialonfiguration and the entire forming system. To optimize theie service life, not only the rational design of die is neces-ary, but the entire forming system needs to well designeds well. To investigate how the entire forming system design,ncluding product design and process determination affects

he die fatigue service life, a methodology is proposed in thisaper, which helps to determine the die service life via rationalesign of metal-forming system and CAE simulation. The casetudy shows the detailed procedure of the proposed method-

25 810 940 81025 810 940 81000 4500 1600 4500

ology and how the die fatigue life is assessed. For the givencase study, the optimal design scenario is identified. The bestdesign case has the conic tip of punch and the patch-up ison the top of the smaller interior hole. Furthermore, the effi-ciency and validity of the developed methodology is verified.This design digital paradigm would save design and manu-facturing lead-times of die and forming system design andsignificantly reduce the experimental tryout in real productdevelopment.

Acknowledgements

The authors would like to thank the Hong Kong PolytechnicUniversity for the research grant G-YF67 and BB90 to supportthis research.

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