Fatigue Failure of Extrusion Dies: Effect of Process Parameters and Design Features on Die Life
Abstract
Analysis of die failure plays an important role in the prediction and prevention of die failure, and subsequently in improving economics of any metalforming process. Industrial experience has shown that fracture is the most common mode of failure in the case of hot aluminum extrusion dies. The purpose of the present work is to implement fatigue damage models in a Finite Element code for identification of critical process parameters and die design features in the case of fatigue being the dominating failure mode. For the maximum number of billets extruded by the die before fatigue crack initiation (fatigue life cycles in extrusion), Morrow’s stress and strainlife damage models are implemented for axisymmetric flat extrusion die. With the help of finite element software ABAQUS, extrusion process is simulated and dynamic stress and strain values were obtained by first identifying the potential fatigue location in the die. The evaluation of applicability of the damage models is done for specific hot extrusion die made of H13 steels with Al6063 as billet material. By considering temperature and strain rate as process parameters and bearing length and fillet radius of the die as geometric features, different simulation runs are performed to investigate the effect of process and design features on the useful die life. Morrow’s stress life model shows a good correspondence between computed and actual failure of dies. By establishing correlations of die life with process and design parameters under different conditions, it was shown that the present investigation is a useful guideline at die design and extrusion process stages.
Keywords
Fatigue analysis Extrusion die FE simulation Critical parametersIntroduction
So far, numerous studies have been performed for the improvement of tool fatigue life. Tong et al. [4] have used SN approach and finite element analysis for the estimation of forging die fatigue life and validated it by some industrial case studies. Fu et al. [1] employed both stress and strainbased fatigue analysis techniques to develop the relationship of die life with its various affecting factors. Falk et al. [5] used different approaches for estimation of time until crack initiation for closed cold forging die and calculated damage parameters yielding different estimates of tool life and compared with practical data. Falk et al. [6] showed that damage approaches like local stress, local energy, and volumebased lifetime approach could result in reasonable lifetime predictions. They claimed that the tool life estimation based on stress conditions should be calculated in terms of effective stress. Saroosh et al. [7] focused their research on high cycle fatigue life estimation based on material property of workpiece. Their calculation based on Morrow’s equation was proved to be more realistic compared to Basquin’s equation.
The purpose of the current study is to identify critical process parameters and die design features in fatigue life of axisymmetric extrusion die using Morrow’s stress and strainlife models. Finite Element code ABAQUS is used for determination of stress states at the critical locations of the die. The materials of die and billet investigated are H13 steel and Al6063, respectively. Considering temperatures and strain rate as process parameters and bearing length and fillet radius as die features, different simulation runs are performed by varying these parameters/features to investigate the effect on useful die life. The predictions are also compared with the industrial data.
Observations on Die Failures in Local Extrusion Industry
Fatigue Failure Approaches Employed
The following Morrow’s stress and strainlife equations are used for the prediction of fatigue life cycles of extrusion die.
Both these models are based on the use of damage parameters (i.e. \( \sigma_{\text{a}} \) and \( \varepsilon_{\text{a}} \)), which describe a mathematical relationship between maximum stress–strain conditions and the number of cycles to initiation of crack. These damage models are uniaxial and it is difficult to handle how process parameters and design changes will affect the multiaxial stress–strain state under loading. Successful implementation of these damage models requires the determination of existing load conditions in the potential fatigue location of the die, reliable fatigue data at required process conditions, and the accuracy and reliability of numerical values obtained from simulation [6].
Damage Parameters Used
The fundamental problem in reducing multiaxial loading conditions in the die to an equivalent uniaxial value is the choice of damage parameter used in the failure equations. The results gained from the numerical process simulation show that maximum principal stress takes small values compared to effective von Mises stress values in all case studies. Therefore, effective von Mises stress is used for the determination of damage parameter, \( \sigma_{\text{a}} \), in the case of stresslife equation. However, considering strainlife equation, the maximum principal strain is considered for calculating damage parameter, \( \varepsilon_{\text{a}} \), due to the reason that effective von Mises strain is not available as output variable in the simulation software. Since the initial stress and strain in the die is zero, the mean stress, stress amplitude, and strain amplitude is half of maximum values in all cases. Furthermore, the extrusion dies were deformed in elastic regime under extrusion pressure, elastic behavior of dies is analyzed and plastic strain values are neglected in life prediction [5]. Therefore, plastic terms are neglected in using strainlife equation (Eq 2).
Fatigue Data Used
Estimating die life using fatigue failure equations based on finite element results requires appropriate fatigue parameters. These parameters should describe the fatigue behavior of the die material. The accuracy of such material parameters is very important for accuracy of die life calculation. This information is not readily available in the literature. For die life estimation, an attempt is made to gather hightemperature properties data from different sources for H13 die steel and Al6063 billet. Some assumptions have also been made which may affect life estimation. Apart from other fatigue parameters, it has been found that value of modulus of elasticity, E, and fatigue strength coefficient, \( \sigma_{\text{f}}^{\prime} \), greatly affect die life estimation. The constant \( \sigma_{\text{f}}^{\prime} \) is often approximately equal to true fracture strength of material, which is usually a value larger than the ultimate tensile strength by amount 50 ksi (492 MPa) as reported by Dowling [8]. Since the value of \( \sigma_{\text{f}}^{\prime} \) for H13 steel at different temperatures was not available, it is extracted from the relationship of hardness and tensile properties at different temperatures available from work done by Wallace and Schwam [9]. H13 in the hardness ranges from 45 to 52 RC is excellent steel for extrusion dies. In current industrial practice in an aluminum extrusion plant, nitriding is commonly used to surface harden the extrusion dies. In the case of H13 hotwork tool steel, the hardness of the nitrided surface may reach to approximately 56–62 HRC. Therefore, tensile strength values are attained at 56 RC hardness at selected temperatures. Considering the fact that the plastic strain values are ignored and only elastic analysis is to be carried out for dies, the fatigue ductility coefficient, \( \varepsilon_{\text{f}}^{\prime} \), and fatigue ductility exponent, c, are not required. The same is also assumed by Falk et al. [5] in their work. It is noteworthy that the value of fatigue strength exponent, b, decreases with temperature. However, due to the nonavailability of b at different temperatures, a value of b equal to −0.0928 is used [8] in all case studies.
Methodology
The numerical simulation of extrusion process and dynamic die stress state during the process provides a systematic approach for simultaneous modeling of billet deformation behavior and die stress and strain distribution during the forming process. From the point of view of metalforming process, the flow behavior of billet material, which mainly depends upon working conditions like temperature and strain rate, greatly affects the die deformation response and hence the die stresses and strains. In addition, die material behavior also affects the flow properties of deforming billet. From the resulted stress and strains values, die fatigue life has been estimated for the given die design configuration, billet material, and other process parameters. Practically, there are many factors affecting the die life, searching for long die life would be an iterative process and the knowhow and prior experiences are useful in decision making for the configuration of die service condition and die life improvement. In this study, it was not possible to explore every factor affecting die life. To illustrate the proposed methodology, four variables are considered: process temperature, strain rate, die bearing length, and die fillet radius. In order to check the accuracy and validity of simulation results, a published work done by Lee and Im [10] is first considered and one of their results is reworked.

Identification of critical fatigue failure locations in the die during loading cycle.

Determination of stresses and strains in the die at critical locations.

Identification of critical process parameters and design features in the die based on estimated die life cycles using damage models.
Accuracy of Simulation
Finite Element Analysis
In fatigue life analysis of extrusion die, the die geometry and deformation simulation is the most important thing. Die geometry analysis determines and verifies the effects of the shape and geometry of die components such as die land, die angle, fillet corner radius, and extrusion ratio. Deformation analysis, on the other hand, reveals the stress and strain distribution in the die. The identified strain and stress provide the basic data and information for die life assessment. Simulation software ABAQUS is used for the determination of dynamic stresses and strains during extrusion process.
Simulation results and estimated die life cycles
Varying process parameter/die design feature  Max von Mises stress, σ_{max}, MPa  Max principal strain, ε_{max}  Number of billets extruded (life cycles, N _{f})  Other simulation conditions/die configurations  

Morrow’s stresslife approach  Morrow’s strainlife approach  
Temperature (T), °C  
300  1490  0.00424  1730  751300  Strain rate: 1 s^{−1} 
420  862  0.00273  2318011  307807041  Fillet radius: 2 mm 
540  620  0.00179  46042609  5.8e11  
Bearing length: 8 mm  
Extrusion ratio: 25  
Strain rate (έ), /s  
0.01  618  0.002057  17014874  2.49e10  Temperature: 420 °C 
1  862  0.00273  2318011  307807041  Fillet radius: 2 mm 
12  1262  0.003407  10641  78956201  Bearing length: 8 mm 
Extrusion ratio: 25  
Bearing length (L), mm  
6  812  0.00228  5124318  2.48e10  Temperature: 420 °C 
8  862  0.00273  2318011  3078077041  Strain rate: 1 s^{−1} 
10  999  0.00282  306399  1421095406  Fillet radius: 2 mm 
Extrusion ratio: 25  
Fillet radius (r), mm  
1  1515  0.008264  610  2379  Temperature: 420 °C 
2  862  0.00273  2318011  307807041  Strain rate: 1 s^{−1} 
3  694  0.002  39277174  1.44e11  Bearing length: 8 mm 
Extrusion ratio: 25 
Geometric Model
Mesh Model
In all cases, the die and billet are meshed while die container is assumed as rigid body. CAX4R (4node bilinear axisymmetric quadrilateral, reduced integration, hourglass control) elements are used for both die and billet material. Since deformation occurs in extrusion problems, especially in those that involve flat die geometries, is extreme; an arbitrary LagrangianEularian (ALE) adaptive meshing is used. A simple meshing technique has been developed as shown in Fig. 4. The mesh refinement is oriented such that the fine mesh along sides AB and DC will move up along the extruded walls as the billet is moved forward.
Solution Procedure, Boundary Conditions, and Contact Treatment
The process is assumed as quasistatic and solved using dynamic explicit with automatic time incrementation. Symmetric boundary conditions are applied on the centerline of the billet while the die is constrained in such a way that boundary conditions act as die backer. Surfacetosurface contact conditions are applied between billet–container and billet–die interfaces with coefficient of friction equal to 0.1.
Material Models
Material  Temperature, °C  

300  420  540  
H13  200 GPa  162 GPa  145 GPa 
Al6063  60 GPa  52 GPa  48 GPa 
Poisson’s ratio and density for H13 material at different temperatures used in simulation are taken from Wang [13].
Results and Discussion
Results Validation Against Industrial Die Failure Data
Effect of Process Parameters and Die Features
As can be observed from simulation results (Table 1), von Mises stress and maximum principal strain at potential fatigue regions in the die reduces with increasing extrusion temperature. This is likely due to the reduced flow stress and elastic modulus of the billet at higher temperature. As expected, these reduced stress and strain conditions at critical die location resulted in high life cycles prediction according to Eq 1 and 2, respectively. This is shown in Fig. 7(a). It must be noted that the temperature of the extrusion process is of vital importance, as it also determines other factors in addition to stress conditions in the die. These include maximum extrusion speed, hardness of the bearing surface of the die, friction conditions at the die billet interface, surface roughness of the extrudate, etc. The thickness of the nitride layer on the surface of the bearing area of the extrusion die decreases and gradually diminishes due to abrasion and decomposition at high extrusion temperature resulting in reduced die hardness. When the nitride layer disappears, the hardened bearing land of die is exposed, resulting in increased wearing rate due to increased affinity with aluminum. The wearing out of the bearing surface causes change in surface configuration and dimensional accuracy of the extruded product. Hence, it is not advisable to use temperature above the nitriding temperature.
The response of a billet to extrusion process can be influenced by the speed of deformation and hence strain rate which are proportional to each other. According to Saha [14], increasing the ram speed and hence strain rate produces increase in extrusion pressure. Billet flow stress behavior at different average strain rates is used as simulation inputs for strain rate effect on die life. Flow stress increases with increasing strain rate at any fixed temperature. As illustrated in Fig. 5, the flow stress increases with increasing strain rate from 0.01/s, to 1–12/s at 420 °C. This fact is also reflected in simulation results. von Mises stress and maximum principal strain values at critical fatigue locations increase with increasing strain rate as can be observed from Table 1. Due to highest stress and strain values at strain rate 12/s, predicted die life is lowest in both fatigue life concepts as shown in Fig 7(b).
von Mises stress and maximum principal strain values at potential fatigue locations slightly increase with increasing bearing length as given in Table 1. Such increase in stress/strain values also resulted in reduced die life cycles as shown in Fig. 8(a). It can be found that bearing length does not affect the life much. Friction at the die land is one of the controlling factors for retarding the metal flow and hence more stress and strains can be expected with longer land.
The influence of die fillet radius on die life is shown in Fig. 8(b). The minimum fillet radius for the die design is 1 mm. The results in Table 1 show that the optimal fillet radius is 3 mm where stress and strain values are the minimum. It can be observed that die fillet with 1 mm radius experienced highest stress and strain as compared to 2 and 3 mm radius. Such phenomenon can be attributed to higher resistance to flow in the case of small fillet radius. Figure 8(b) also indicates that the die life is increasing when the fillet radius is increasing. The trend shows that the stress and strains will continue to decrease (hence resulting in increasing of die life) when the fillet radius is increased. However, it is not practical to use fillet radius that is too large, where the final extrusion section may need more finishing operations or may not be accurate in final dimensions.
Concluding Remarks
The current investigation has shown that finite element simulation of extrusion process integrated with fatigue theory yield an efficient tool for the identification of critical process parameters and die design features in the case of fatigue being the dominating failure mode. It was found that Morrow’s stress based concept results in less number of die life cycles as compared to Morrow’s strainbased approach and it can be concluded that stressbased approach (highcycle fatigue) is more suitable to apply in the case of extrusion die life. It is also validated by real die failure data on extrusion dies. Die life was found increasing with increasing temperature and reducing with increasing strain rate. Such behavior is likely associated with billet flow stress, which reduces with temperature and increases with strain rate. Highflow stress results in high die stresses/strains and hence more susceptible to short life. Small die fillet radius severely reduces die life due to more resistance to flow at die entry. Bearing length was found to have small effect on die life. Long bearing length results in comparatively reduced life. With the help of case studies for each variable, the validity and efficiency of established fatigue failure approaches are verified and it can be very helpful for the identification of critical process parameters and design features in die fatigue life.
Notes
Acknowledgment
The authors acknowledge the support of King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia, for this work through project # SB080002.
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