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CAE enabled methodology for diefatigue life analysis and improvementK. K. Tong , M. S. Yong , M. W. Fu , T. Muramatsu , C. S. Goh & S.X. Zhanga Singapore Institute of Manufacturing Technology, 71 NanyangDrive, Singapore 638075b Singapore Institute of Manufacturing Technology, 71 NanyangDrive, Singapore 638075 E-mail:Published online: 22 Feb 2007.

To cite this article: K. K. Tong , M. S. Yong , M. W. Fu , T. Muramatsu , C. S. Goh & S. X. Zhang(2005): CAE enabled methodology for die fatigue life analysis and improvement, InternationalJournal of Production Research, 43:1, 131-146

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International Journal of Production Research,Vol. 43, No. 1, 1 January 2005, 131–146

CAE enabled methodology for die fatigue life analysis

and improvement

K. K. TONG, M. S. YONG, M. W. FU*, T. MURAMATSU,C. S. GOH and S. X. ZHANG

Singapore Institute of Manufacturing Technology, 71 Nanyang Drive, Singapore 638075

(Received October 2003)

Die performance and its service life are a non-trivial issue in metal-formingindustry due to three overriding issues in this industry cluster: productivity,cost and quality are mainly dependent on it. Many factors in die life cycle fromdesign and fabrication to downstream service all affect die performance and itsservice life. These factors could include die design and structure, material proper-ties, dies manufacturing and metal-forming processes, and die service conditions.The issue about how to develop an efficient and practical methodology for dielife assessment and improvement has not yet been fully addressed despite the factthat dies have been used in industry for many decades. In this paper, the metalfatigue theory and FEM technique are used as the basis for the developmentof a methodology for die fatigue life analysis and improvement. The stress–lifeor S-N approach is used for die fatigue analysis. To explore extensively and revealthe dynamic die stress state panorama during the forming loading cycle, a CAE-based approach is deployed for stress analysis. Based on the S-N approachand CAE analysis, a CAE-enabled methodology is then orchestrated and finallyimplemented in this research. Using an industrial part as a case study, thevalidity, robustness and efficiency of the developed methodology are verified.The methodology can provide a satisfactory solution for die life assessment andimprovement in metal-forming industry.

Keywords: Fatigue life analysis; CAE-enabled methodology; Die design

1. Introduction

Metal forming is a traditional and matured technology, but this industry is stillfacing new requirements from three overriding issues: productivity, cost and quality.The conventional trial-and-error approaches based on know-how and experiencesare tedious, time-consuming, error-prone and cannot provide satisfactory solutionsto address the above requirements. On the other hand, more and more metal-forming parts are becoming more complicated, miniaturized, net-shape, high qualityand manufactured with less operations. The die, which is a tool to produce metal-forming parts, has become one of the bottleneck issues in precision engineeringindustry. The performance and service life of a die directly relate to the competitive-ness of manufacturers in this industry cluster.

*Corresponding author. Email:mwfu@simtech.a-star.edu.sg

International Journal of Production Research ISSN 0020–7543 print/ISSN 1366–588X online # 2005 Taylor & Francis Ltd

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DOI: 10.1080/002075404123331281962

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In the context of die service, die life is a critical issue. Die life is usually definedas the number of parts produced by the die before it fails. In cold-forming processes,die life is even more crucial as the stress state of die is more severe than other formingprocesses and the die can only produce thousands of parts before it fails. If thedie and its structure are optimally designed, the determination of manufacturingprocesses and material selection are well conducted, the die could have longer life.Although there are many factors affecting die performance and its service life, dielife is mainly determined by the stress state no matter how the die design, materialproperties, manufacturing processes and working conditions are configured. Inpractical production, common die failure modes could be fatigue, wear and plasticdeformation or deflection (Lange et al. 1992, Li et al. 1998, Lee and Chen 2001, Arifet al. 2003).

Fatigue failure starts from fatigue crack initiation, propagation finally to notbeing able to produce quality products. In fatigue failure, brittle fatigue is themost common fatigue mode in cold forging die. It is caused by large cyclic stresstogether with high stress concentration. The concentrated and cyclic stress leadsto crack initiation, growth and propagation. Crack and fracture in a die body,with metal chipping off from the convex portion, especially the sharp corner ofa die, are some common types of die fatigue failure.

Wear is the gradual wearing out of the metal surfaces. The friction betweenthe billet and die land results in wear and surface tear. The accumulated wear canlead to die failure. In forming processes, the preheating of die and billet, high form-ing pressure in the die and the unbalance forces in between the die and billet can bringabout the deformation or deflection of the die. These deformations and deflectionscould also cause die failure. Among the three common die failure modes, about 46%of die failures is fatigue fracture, 26% is wear, 9% is deformation or deflection, andthe rest is the miscellaneous failure modes (Arif et al. 2003). It can be found that thefatigue fracture takes up a dominant percentage in die failure.

In this research, the focus is on the investigation of die fatigue failure. Die fatigueis a process that causes premature failure or damage of the die. Die fatigue fractureis usually caused by cyclic stress in the course of die service. Although dies have beenused in metal-forming industry to produce metal-formed parts for many decades,the research on die fatigue fracture is quite limited and there is very little publishedwork available in this area. The main reason is that the metal-forming process isvery complicated, difficult to control and predict as it could just take a few secondsto complete the forming of a part. Besides, parts and dies have complicatedthree-dimentional (3D) geometry and it is also very difficult, if not impossible, bytraditional solutions fully and more exactly to determine the dynamic stress distribu-tion in the die. Only with the birth and boom of numerical techniques can thedynamic die stress be determined and explored. With computer aided engineering(CAE) platforms, metal-forming process and the dynamic stress state can be simul-taneously simulated and analysed. On the other hand, the metal fatigue theory,which has existed for a few decades, can now be used in die fatigue prediction asthe dynamic stress can be revealed by the CAE approach. Although these technol-ogies have not been intensively explored in addressing the die life issue, there aresome existing efforts in this niche area. Arif et al. (2003) have conducted extensiveresearch on die failure modes based on many real die failure cases. They tried toestablish the relationships between die profile and die failure modes. Li et al. (1998)studied the die life for thermal fatigue crack and investigated the relationships of die

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life and the quenching and tempering temperatures for H13 and H21 die steels. Leeet al. (2001) explored four commonly used die materials and established the relation-ships between hardness and die fatigue life. They built up the relationship of fracturestrength with hardness and then predicted the die life based on the total plasticdeformation strain of the die. Since the strain-based approach is more suitable forlow-cycle fatigue failure, usually less than 1000, therefore, the approach is not ofmuch industrial relevance as most of the die life is more than 1000 cycles. Knoerret al. (1994) conducted research on the cause of fatigue failure in cold forging andpresented a fatigue analysis concept by using the strain-based approach. Geiger et al.(1992) tried to improve the fatigue resistance of cold forging dies based on numericalsimulation of forming process and computer aided design (CAD) of die shapedesign. In addition, some researchers put efforts on wear failure analysis and reduc-tion of die wears based on finite element method (FEM) simulation (Kim et al. 1997,Lee and Im 1999). Others also addressed the die life issue from processperspective (Laovok 1998, Sun et al. 2000). They investigated how to optimize per-form design, die parameters such as fillet radius and geometry to improve die stressand further increase die life. Fu and Shang (1995) investigated the forging die stressby the boundary element method (BEM) approach and adopted the double-reinfor-cement casings to improve die stress in forging process. All of these efforts are goodpioneering and exploratory work focused on improving die life.

Although the efforts have been provided in this area, in-depth research on dielife analysis and improvement has not yet been extensively conducted. There are a lotof issues that need to be addressed. In this research, the main focus is to developan efficient methodology for die fatigue life estimation and improvement. ACAE-enabled methodology is proposed by employing metal fatigue theory, FEMnumerical technique and CAD-related technology such as data exchange technologyand their combination thereto. Using industrial parts as a case study, the validity,robustness and efficiency of the proposed methodology are tested and verified. Themethodology had been proven to provide satisfactory solutions for die life predictionand improvement for the different configurations of die design, material properties,processes and service conditions.

2. Methodology

A CAE-enabled die fatigue life assessment and improvement methodology is pre-sented in this section based on the FEM approach, metal fatigue theory and CADdata exchange technology. The enabling technologies are also succinctly articulated.

2.1 FEM approach

The finite element technique, whose engineering birth and growth in the 1960s wasdue to the application of high-speed computers to structural analysis, has spread intoa variety of engineering and science disciplines in the last a few decades. The FEMapplications to large plastic-forming engineering can be traced back to the pioneerwork by Lee and Kobayashi (1973), which laid the foundation for the simulation oflarge plastic defomation. Since then, the plastic FEM approach has been widely usedin plastic-forming engineering for process determination and optimization, productquality assurance, and die design (Fu 1988, Kobayashi et al. 1989, Fu and Luo 1992,

133CAE enabled methodology for die fatigue life analysis and improvement

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1995). The basis of the plastic FEM is using the variational approach to formulatethe following functional and getting the velocity (for viscoplastic FEM) or dis-placement (for rigid-plastic FEM) solution when it has the minimum value at thestationary point:

� ¼

ZV0

Eð"Þ dv�

ZSf

FU dsþ

ZV0

�"ij dv, ð1Þ

where E(") is the work function, Sf is the surface on which the traction is prescribed,F is the traction vector, U is velocity, � is the Lagrangean multiplier and V0 is thevolume of the billet or deforming body.

The funtional in equation (1) is for the entire deforming body. With discretiza-tion of Eq (1), the functional � can be approximated by the following equation:

� �X

� jðU j , �jÞ ð2Þ

which is non-linear after discretization. To linearize it, the Newton–Raphonapproach or direct iteration method can be used. After linealization, the followinglinear equations can be obtained:

n–1 n–1

∆U

λnn

F ð3Þ

in which the sparseness of the stiffness matrix can be utilized in solving the equation.The approach using this characteristic for solving equation (3) is the so-called sparseapproach.

In the Newton–Raphon approach, the initinal solution or initinal value for allthe node velocities needs to be pre-given. With the initinal solution or pre-given Uo,the solution for the first loading step can be determined by iteration. In the iterationprocess, if the velocity and force norms meet a certain criterion, the iteration of thespecific loading step is considered as convergence. Taking the velocity as an instance,if the following criteron is met, the iteration is converged.

�Un

�� ��.kUn–1k � �, ð4Þ

where k�Unk is the Euclidean vector norm for the nth iteration and � is a predefinedsmall positive number, such as 10�5.

In plastic FEM, equation (3) is used to determine the velocity increment of thenth iteration in a deforming body or billet, and in such a way that the velocity, strainrate, foming loading, effective stress and strain, and the other state variables of thedeforming body can be determined.

The dynamic die stress state in the forming process is the focus in this paper.The above presented FEM approach is for simulation of the deforming body. Toreveal the die stress, the elastic FEM approach is used. In die stress analysis, whetherthe stress can be accurately identified depends on the accurate determination of theboundary conditions of the die, which is in turn decided by the simulation of thedeforming body. In this research, the coupled analysis concept is employed in whichthe billet deformination and die stress are simulated and analysed simultaneously.

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In each loading step, the state variables of the billet are determined. They are thenused to determine the boundary conditions and the constraints for die stress analysis.With these, the dynamic die stress can be efficiently revealed and explored. In die lifeassessment, the maximum and minimum principal stresses of the die in a loadingcycle are critical and must be determined. How to determine them will be discussedin the next section.

2.2 Die fatigue analysis

In metal fatigue analysis, there are two enabling approaches. One is stress–lifeapproach or S-N approach, the other is the strain-based approach (Bannantineet al. 1990). The S-N approach uses the minimum and maximum principal stressesin the loading cycle of a part to determine the part fatigue life, or cycles to failure.The approach has been used in industrial scenarios where the applied stress is pri-marily within the elastic range of the material and the resultant live, i.e. cycles tofailure is long. In general, the S-N approach should not be used to estimate thefatigue lives below 1000 cycles. In a low cycle scenario, the strain-based approachis more appropriate where the applied strains have a significant plastic component,which plays a big role in low-cycle fatigue failure.

In the S-N approach, the minimum and maximum principal stresses, which arerespectively designated as �max and �min in this paper, are used to analyse the metalfatigue failure. In fatigue analysis, stress variation amplitude in loading cycle isimportant. It is noted as the amplitude stress �a in the following

�a ¼ ð�max � �minÞ=2: ð5Þ

Besides, the mean stress is also used in S-N approach, which is defined as:

�m ¼ ð�max þ �minÞ=2: ð6Þ

These four stresses, i.e. the maximum and minimum principal stresses, and theamplitude and mean stresses, are termed as the characteristic stresses in thispaper. Figure 1 shows the variation of the maximum and minimum principal stressesat the fatigue area of the die in loading cycles. The amplitude and mean stressesare also illustrated. These four characteristic stresses periodically appear in eachloading cycle.

In the S-N approach, there are a few equations articulating the relationship of�a and �mean with the material properties, i.e. endurance limit Se and ultimate

sm

Stress

smax

smin

sa

One loading cycle

Figure 1. Terminology for stresses.

135CAE enabled methodology for die fatigue life analysis and improvement

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strength Su. In this research, the Goodman equation (Bannantine et al. 1990) is usedand it is represented in equation (7). Based on the Goodman equation, the Haighdiagram, which graphically illustrates the relationships of die fatigue life

�aSe

þ�mSu

¼ 1 ð7Þ

with die stress, can be constructed and shown in figure 2. In the Haigh diagram, thex-axis is mean stress while the y-axis is alternating stress or amplitude stress.To generate a Haigh diagram, there are two critical lines. One is the 106 line andthe other is the 103 line (the number represents the die fatigue life). The former can beconstructed by connecting the ultimate strength Su in the x-axis and the endurancelimit Se in the y-axis. The latter can be generated by connecting the ultimate strengthSu in the x-axis and the amplitude stress of 103 cycles in the y-axis. In the Haighdiagram, the Su point in the x-axis is the common intersection point for allthe fatigue life lines. Furthermore, the 106 line is usually considered as the infiniteline, while the 103 line is generally taken as the watershed line between low and highfatigues. For these different cycle fatigues, different analysis approaches, i.e. the S-Nand strain-based approaches, should be used, respectively.

Figure 3 is the Haigh diagram of M2. M2 is a typical high-speed tool steel andone of the popular tool steels in the metal-forging arena. The diagram is constructedbased on the experiment data and Goodman equation. In the diagram, three fatiguelife lines ranging from 103 to 105 are generated. For each die life line, it has a bandto represent the stress range for the die life. The band is also constructed based onthe experimental data. At the centre of the band, there is a mean line representing thehigh frequency zone for the die life.

2.3 Methodology framework

A CAE-enabled methodology for die life analysis and improvement is presented bythe framework shown in figure 4. From the framework, it can be found thatthe CAD models for process simulation and die stress analysis need to be createdforemost. These models could include those for workpiece, die and the related die

AmplitudeStress sa

Mean Stress smSu

103

106

105

Se

6.8×103

104

Figure 2. Haigh diagram.

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assembly components. The models are usually created in different CAD platformsand then converted into data exchange formats such as IGES, STL or STEP, etc.Upon the completion of data exchange, the CAD models can be imported into CAEplatforms for simulation. Besides, some compatibly native CAE formats can also

CAD platforms

CAD models

Neutral formats

IGESSTL STEP

Forming process

simulation

Die stress analysis

CAD model 1. Die geometry2. Workpiece geometry

Process parameters1. Tool movement. 2. Temperature.3. Friction condition.4. Interference.

Material Parameters1. Material models & its

properties (Elastic, Plastic, Elastic-plastic, porous)

2. Constitutional equations. 3. Temperature related data.

Simulation results1. Process state variables. 2. Die stress and

strain information.

Die life estimation

1. S-N approach2. Haigh diagram

Improvementsolution-3

Improvementsolution-2

Improvementsolution-1

CAE Platforms

Constraints & control

1. Boundary conditions.

2. Convergence criteria.

3. Loading step. 4. Iteration control.5. Re-meshing

criteria & control.

Model CAD

FEM Engine

Figure 4. Methodology framework.

M2-Haigh diagram

0

500

1000

1500

2000

2500

−2000 −1000 0 1000 2000 3000 4000 5000 6000

Mean stress (MPa)

Am

plit

ud

e st

ress

(M

Pa) 103

104

105

Figure 3. M2 Haigh diagram.

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be directly imported into CAE platforms from others. To conduct the deformationsimulation and die stress analysis, simulation constraints and process controlneed to be specified, which include the boundary condition of simulation models,convergence criteria, simulation loading step, iteration control of equation solving,and re-meshing criteria and control, etc. In addition, the process parameters, such astool movement, temperature, friction condition, and interference of tooling compo-nents such as shrink fit, need to be defined. From material parameters’ perspective,material models such as elastic, elastic-plastic, rigid-plastic, viscoplastic and porousmaterials should be specified. Furthermore, material properties, constitutional equa-tions and their detailed values, temperature-related material data are also needed tobe determined before simulation and analysis could be executed. Through formingprocess simulation, the forming loading, energies, stresses, strains, metal flow, etc.,can be obtained. Based on the above information, the boundary condition for diestress analysis can be determined via force interpolation.

In die stress analysis, the complete stress tensor should be determined.The maximum and minimum principal stresses �max and �min respectively in thecourse of forming loading cycle also need to be determined. The amplitude andmean stresses can further be calculated. Employing the S-N approach and Haighdiagram, the die life for this stress cycle could thus be estimated. Based on thesimulation results, improvement suggestions could be made to prolong die lifefrom different perspectives including die and billet geometry and preform design,process parameters, die components interference such as shrink fit, material selectionand material properties specifications. With the change of the configuration of diedesign, process specification and material properties, the die stress will also change.Based on these new configurations, new simulations and analyses can be conducted.The die stress states can further be revealed and the corresponding die life can beestimated. Once the satisfactory die life is reached, the corresponding configurationof the simulation conditions can be recommended for die life improvement.Practically, there are many factors affecting die life, searching for long die lifewould be an iteration process and the know-how and prior experiences are usefulin decision-making for the configuration of die service condition and die lifeimprovement.

From a numerical technique point of view, on the other hand, it is impossible forany numerical simulations to get the exact solutions. Nevertheless, these numericalsolutions for die life analysis and improvement are comparable and the feasible oroptimal solution can be obtained by comparing these solutions. In assessment of dielife improvement, this approach is employed for the optimal solution generation.

3. Solution generation procedure

In the implementation of the above proposed methodology to estimate die fatiguelife and generate the improvement approaches, there are three issues to be addressed:identification of potential fatigue failure locations in the die, determination of thedynamic die stress panorama in the loading cycles and estimation of die fatigue life.For each design, process and material configuration, it needs to go through thesethree steps to come out with the die fatigue life. The optimal solution could then begenerated by comparison of the die fatigue life for the different die configurations.

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3.1 Identification of potential fatigue areas

The most potential fatigue areas would be located at the place where the stress ismost severe. Stress severity could be represented by the magnitude and amplitudeof stress components of the die in loading cycles. Based on this argument, theeffective stress could be selected as a criterion to identifying the potential fatigueareas as it takes into consideration the magnitude and amplitude of the stress com-ponents. Therefore, the locations where the effective stress is greatest would be themost potential area of the fatigue failure.

To determine the effective stress, all the stress components or stress tensor shouldbe known. For current CAE platforms, they all have this function to determine allthe stress components and the corresponding effective stress.

3.2 Determination of pmax and pmin

�max and �min are the maximum and minimum principal stresses respectively whenforming the loading cycle. From a die fatigue perspective, the forming of a partconstitutes a complete fatigue loading cycle, which usually starts from zero loadingto the maximum loading at the end of the forming process. Effectively, �max is themaximum principal stress of the die at the final stage of the forming process, while�min is the minimum principal stress in the beginning of the forming loading cycle.To determine �min, it is necessary to consider the detailed scenario. If there is noshrink fit in die assembly, �min would be zero. For the cases with shrink fit, �min canbe determined based on the magnitude of shrink fit. The determination of �min needsto identify the complete stress tensor �ij first and then figure out three principalstresses, �1 , �2 and �3. The �3 will be �min, as designated in equation (5).

To determine the three principal stresses, the following equation is employedto get the solutions:

�3� I1�

2� I2 � � I3 ¼ 0, ð8Þ

where

I1 ¼ �x þ �y þ �z

I2 ¼ � ð�x�y þ �y�z þ �x�zÞ þ � 2xy þ � 2

yz þ � 2xz

I3 ¼ �x�y�z þ 2�xy�xz�yz � �x�2yz� �y�

2xz � �z�

2xy:

3.3 Die life assessment

In this research, die fatigue life is supposed to be dependent on the stress stateof the die. Once the stress variables are determined, die fatigue life could be assessed.Based on the amplitude and mean stresses, the predicted fatigue life can be figuredout on the basis of the die life calibration chart shown in figure 3. For each dieconfiguration in terms of design, process and material, there is a correspondingpredicted die life. The longer the die life, the better the configuration. The finalfeasible or optimal solution could be selected based on the predicted die life.

In a practical application, �a and �m are used to estimate the fatigue life of metalparts based on the Haigh diagram. In the metal-forming process, die is workingunder cyclic stress. �a and �m can be determined based on the minimumand maximum principal stresses. For the identified �a and �m, the die life can be

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determined by locating the values of �a and �m in the x-and y-axes of the Haighdiagram. As it may not exactly fall at the existing lines, the interpolation is neededto determine the die life based on the known die fatigue life lines generated fromactual experimental data.

4. Case study

To illustrate the proposed methodology, a case study of bevel gear forging is used totest and verify the procedure and its robustness. Figure 5 shows the die assemblyrelationship and die components, which need to be considered in forming processsimulation. Figure 5 shows the punch, billet, die insert, casing and ejection pin.To investigate die life at different stress scenarios, two different conditions are stu-died. In the first case, there is no shrink fit applied on the outside surface of the dieinsert. In the second case, 0.5% shrink fit is applied. Figure 6 shows the billet meshstate at different strokes. It shows that the workpiece is fully deformed at the strokeof 15.00mm.

Based on the proposed methodology and its procedure to predict die fatigue life,the potential fatigue initiation point in the die insert should be identified first accord-ing to the simulation. In these two cases, the workpiece deformation and thedynamic die stress are simulated simultaneously. The dynamic stress state of thedie insert can be investigated and identified at any deformation stage. As the effectivestress is used as the criterion to identify the potential fatigue area, the effective stressdistribution should be revealed based on the simulation results. Figure 7 shows theeffective stress distribution for the two cases. It shows that the maximum effectivestresses are all located at the teeth of the die insert, which shows that the mostpotential fatigue area appears in those areas. But where the fatigue crack couldfirst initiate would depend on the maximum principal stresses in the fatigue areas.Therefore, the maximum principal stress needs to be further identified.

Punch

Casing

Billet

Die insert Ejection pin

1˚30′

Figure 5. Die assembly.

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To determine the maximum principal stress, it is necessary to decide which stagein a loading cycle has the maximum principal stress. So the Z-direction loadings forthe two cases are thus investigated and shown in Figure 8(a) and (b). From thecurves, it can be seen that the loads and the curve shape are almost the same forthe two cases, as the forming process, billet material and the other conditions remainthe same. In addition, it can be seen that the maximum loading is located at the laststage of the loading cycle with 15.00mm stroke. The maximum principal stressshould be determined at the stage where the forming load is maximum.

Figure 8 shows the load cycle in a forming operation. Mapping the loading cycleinto a periodic loading map generates the cyclic forming loading cycle graph asshown in figure 9. It is this cyclic loading that causes the die fatigue failure.

Since the fatigue location and the variation of the forming loading are identified,the issue is how to reveal the maximum principal stresses: where to identify and whento get it in the loading cycle, has been addressed. Figure 10(a) and (b) show thevariation of the maximum principal stress for the two cases in a loading cycle,respectively. The characteristic stresses for case 1 are illustrated in figure 11, inwhich the periodical loading cycles of the characteristic stresses are extracted andmapped from figure 10(a).

Based on the loading cycle, the maximum and minimum principal stresses can beidentified. In these two cases, �max is 2184 and 1314 MPa, respectively. Since �min iszero in the first case, the amplitude and mean stresses are constantly read at 1092

(a) (b)

(c)

Figure 6. Billet mesh at different strokes: (a) 10mm, (b) 13mm and (c) 15mm.

141CAE enabled methodology for die fatigue life analysis and improvement

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MPa. Based on the Haigh diagram shown in figure 3, the predicted die life for case 1is 1000 cycles or parts.

In the second case, �min is not zero due to the shrink fit applied. The �min is� 420 MPa and �max is 1314 MPa. The amplitude and mean stresses are 867 and447 MPa, respectively. The predicted die life for case 2 is therefore 7000 cycles orparts.

(a)

(b)

Potential fatigueinitiation area

Potential fatigueinitiation area

Figure 7. Potential fatigue areas in the two cases: (a) effective stress distribution at15.00mm stroke (without shrink fit) and (b) effective stress distribution at 15.00mm stroke(with a 0.5% shrink fit).

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(a)

(b)

Figure 8. Z-loading in one forming cycle: (a) Z-loading variation in one cycle without shrinkfit and (b) Z-loading variation in one cycle with a 0.5% shrink fit.

Z-Loading

Cycles

Cycle-1 Cycle-2 Cycle-n

Figure 9. Forming loading cycles.

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(a)

(b)

Figure 10. Maximum principal stress in one loading cycle: (a) variation of the maximumprincipal stress in one cycle without shrink fit and (b) variation of the maximum principalstress in one cycle with a 0.5% shrink fit.

Cycles

Stress (MPa)

Cycle-1 Cycle-2

smax =2184

smean

smin = 0

sa

Figure 11. Characteristic stresses in loading cycles without shrink fit.

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It can be found from the predicted die life that the second configuration hasa longer fatigue life than the first case. This is because the shrink fit improves thestress state. As a result, the fatigue life of the die could be longer.

5. Conclusions

In this research, a CAE-enabled methodology is proposed for die fatigue life ana-lysis and improvement. The CAE technology is employed to reveal the dynamic diestress during the forming process while the metal fatigue theory is used to establishthe relationship of the die stress and its service life. To represent this relationship,a Goodman equation is deployed and the Haigh diagram for M2 die steel is con-structed. Two die configurations are simulated to test and validate the proposedmethodology, where the die stress state is explored and revealed. Once the identifiedpotential fatigue areas and the loading variation in the loading cycle are established,the stress panorama and the maximum and minimum principal stresses can beidentified. After the die life has been estimated, the optimum configuration fordesign, process and material can be established. The case studies have shown thevalidity and efficiency of the developed methodology and it can be used to assess dielife.

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