PREDICTION OF FATIGUE LIFE OF COLD FORGING TOOLS BY FE SIMULATION AND COMPARISON OF APPLICABILITY OF DIFFERENT DAMAGE MODELS M. Meidert and C. Walter Thyssen/Krupp Presta AG Liechtenstein FL-9492 Eschen K. Pöhlandt Institut fü r Statik und Dynamik der Luft-und Raumfahrtkonstruktionen Universität Stuttgart Pfaffenwaldring 27 D-70569 Stuttgart Abstract Tools for cold forging mainly fail due to cyclic fatigue. Tool costs can reach a significant portion of production costs and therefore methods to improve tool life are of high interest. However, tools are still mainly designed and optimized by the trial and error method. The purpose of the work presented is to implement damage models in a FE code for determination of location of failure and prediction of tool life. Damage models implemented are the uni-axial models of Smith-Watson-Topper (SWT) and Bergmann and the multi-axial energy based model proposed by Hänsel. Tool material was ASP23 for which material data was available. The FE simulation of the tools is done non-linear with a material model proposed by Chaboche taking into account kinematic hardening and the Bauschinger effect. The evaluation of applicability of the damage models is done for specific cold forging tools made of PM steels. It is shown that the damage models of SWT and Bergmann give rather inaccurate results for multiaxial states of stress and strain. The energy based 815
816 6TH INTERNATIONAL TOOLING CONFERENCE model of Hänsel shows a good correspondence between computed and actual failure of tools. Location of failure is predicted correctly and prediction of tool life is acceptable. Keywords: Cold forging, low cycle fatigue, tool life, Finite Element Simulation INTRODUCTION Manufacturing costs for a cold forging part mainly consist of costs for material, forming machine and for tooling. The costs for the tools, dies and punches, are significantly high. The more complicated the geometry of the part and the tool is the higher the costs because manufacturing is more expensive and tool life is shorter. Today cold forging tools are designed by empiric principles. Loading by process loads onto the tool is often not exactly known and assumptions have to be made. Engineering tools like Finite Element simulation offer vast opportunities for improved process and tool layout. The main parameters which can be varied in tool design are the prestressing condition and tool material. The geometry of the cavity can seldom be altered because of given dimensions of the part to be formed. The parameters, stress and strain state in prestressing and loading condition and tool material highly affect the die life. Cold forging tools mainly fail by cracking due to low-cycle fatigue, seldom due to wear. In the work presented a software was established to calculate damage parameters and predict life time from results of non linear FEM die stress analysis. Uniaxial damage parameters considering mean stress (Smith-Watson- Topper and version) and multiaxial damage parameters (Hänsel and modified version) were investigated for their applicability for specific cases. Computed and practical results were compared. Tool material considered was ASP23 for which static and cyclic material was available from investigations carried out at Risœ National Laboratory. ESTIMATION OF DAMAGE The method applied in this work for estimation of fatigue life was the local concept. For the problems studied in this work uniaxial and multiaxial approaches were taken into account. The following damage models were implemented and evaluated:
Prediction of Fatigue Life of Cold Forging Tools by FE Simulation and Comparison...817 Smith-Watson-Topper (SWT) damage model. P SWT = (σ a + σ m ) ε a E (1) In the Smith-Watson-Topper model [1] the influence of cyclic mean stress is integrated. For purely elastic material the mean stress sensitivity is moderate and can be taken into account very well. However in case of highly strained material with higher mean stress sensitivity the SWT model will not lead to correct results. Bergmann damage model. P Berg = (σ a + a b σ m ) ε a E (2) Based on the difficulty described above Bergmann [2] proposed an improved damage model and introduced the correction factor a. The factor corrects the damage dependant on the mean stress state (tensile or compressive stress). Hänsel damage model. The damage models given above are restricted to one-dimensional problems. The influence of three dimensional stress states is described unprecisely. An energy based damage model taking into account the multi axial stress state and mean stress influence was postulated by Hänsel [3]. It is based on an approach which considers the energy brought in a material element during one cycle. The total work is defined as sum of elastic and plastic energy: W t = W e+ + W p (3) The elastic energy is defined as: W e+ = 1 ( ) σ 2 2 εe = 1 2 8 σ εe (4) The plastic energy is defined as: W p = (1 n ) (1 + n ) σ εp (5) The factor n considers the change of the area of the hysteresis loop during cyclic loading. For most metals the factor n is positive which means that a
818 6TH INTERNATIONAL TOOLING CONFERENCE Figure 1. Plastic and elastic deformation energy. strain hardening behavior exists. The elastic energy is influenced by mean stress. Mean stress causes a shift of the hysteresis loop. A positive mean stress results in an increase of elastic deformation energy area, a negative mean stress results in a decrease of elastic deformation energy area. The influence of mean stress is considered by an additional term W m. W m = 1 2 [ ] (σ m ε m ) C 2 (σ m ε m ) (6) In case of tensile mean stress W m is added to the elastic energy, in case of compressive mean stress W m is subtracted. With term (3) and (7) and W e++ = W e+ ± W m (7) C = 1 1 σm R m (8)
Prediction of Fatigue Life of Cold Forging Tools by FE Simulation and Comparison...819 Figure 2. Mean Stress influence. the total energy becomes: W t = 1 8 σ εe ± 1 2 [ ] (σ m ε m ) C 2 (σ m ε m ) + (1 n ) (1 + n ) σ ε p (9) Term (8) is valid for one dimensional stress states. Extended to three dimensional problems the term becomes: W eff = 1 8 σ ij ε e ij ± 1 2 [ ] (σ m,ij ε m,ij ) Cij 2 (σ m,ij ε m,ij ) + ( )1 ( )1 (1 n ) 3 (1 + n ) 2 σ 2 2 ij σ ij 3 εp ij 2 εp ij (10) Modified Hänsel damage model. It was shown that for high compressive mean stress the correction term for the mean stress sensitivity becomes so dominant that negative damage parameters are calculated. In addition to negative damage parameters a convergence of the curves for different stress amplitudes was observed.
820 6TH INTERNATIONAL TOOLING CONFERENCE Figure 3. Damage parameters W e++ over mean stress σ m. To correct this phenomenon a factor C was introduced which gives the equivalent amplitude of fully reversed cycles for cycles with negative or positive mean stress. The total energy is then W t = 1 8 σ2 E (1 n ) C2 + (1 + n ) σ εp (11) Extended to multiaxiality W eff = 1 8 σ ij 2 ( ) 1 (1 3 E C2 ij+ (1 + n ) 2 σ 2 2 ij σ ij )1 ( 3 εp ij 2 εp ij (12) Life time prediction: The stress cycle diagram was described in the low cycle regime (N N D ) by Manson, Coffin, Basquin and Morrow [4]. Elastic strain amplitude: ε e a = σ f E (2N)b (13)
Prediction of Fatigue Life of Cold Forging Tools by FE Simulation and Comparison...821 plastic strain amplitude: ε p a = ε f (2N) c (14) with total strain: ε a = ε e a + ε p a (15) the strain cycle diagram is: the stress cycle diagram is: ε a = σ f E (2N)b + ε f (2N) c (16) σ a = σ f (2N) b (17) Equation (16) and (17) put in damage model of Smith-Watson-Topper leads to P SWT = σ f (2N) b Equation (18) can be transformed to P SWT = ( ) σf E (2N)b + ε f (2N) c E (18) σ f 2 (2N) 2b + ε f σ f E (2N) b+c (19) The number of cycles 2N until failure can be determined by the Newton iteration method. Equation (16) and (17) put in damage model of Hänsel leads to elastic deformation energy. W e+ = 1 8 2 σ f (2N) b 2 σf E (2N)b (20) Equation (20) transformed is Plastic deformation energy is W p = W e+ = 1 2 σf 2 E (2N)2b (21) (1 n ) (1 + n ) σ f (2N) b 2 ε f (2N) c (22)
822 6TH INTERNATIONAL TOOLING CONFERENCE Equation (22) transformed is W p = 4 Total deformation energy is W t = 1 2 σf 2 E (2N)2b + 4 (1 n ) (1 + n ) σ f ε f (2N) b+c (23) (1 n ) (1 + n ) σ f ε f (2N) b+c (24) The number of cycles 2N until failure can also be determined by the Newton iteration method. SIMULATION PROCEDURE The simulations were carried out using the commercial Finite Element (FE) program systems DEFORM [5] und ANSYS [6] available at the Krupp- Presta company. The FE-program system DEFORM was utilized for simulation of the forming process. DEFORM includes a solver using an implicititerative procedure which is faster than an explicit one. Remeshing of heavily deformed meshes of the workpiece is possible. ANSYS was utilized for non-linear calculation of the tooling on which loads from the DEFORM simulation is applied. Also modeling of the components was carried out in ANSYS. Figure 4. Simulation Flowchart.
Prediction of Fatigue Life of Cold Forging Tools by FE Simulation and Comparison...823 Since cold forging tools often have complicated 3D shapes of the cavity and fatigue life estimation can not be done without finite element simulation, almost all the models studied in this work were 3D problems. For evaluation of the results axisymmetric specimens were included but they were also simulated by 3D models. Some auxiliary programs were written for coupling the program systems DEFORM and ANSYS. After the DEFORM simulation the nodal forces were mapped to the ANSYS model for each increment and a nonlinear static simulation was carried out. The results obtained this way were evaluated by means of a macro resp. C program for various damage parameters and finally given back to the ANSYS program for visualization by the postprocessor. MATERIAL DATA The utilized tool steel ASP23 was characterized by Brondsted and Skov- Hansen at Risœ national laboratory [7] by cyclic material testing and data was published. Material data is measured by strain controlled cyclic tensile experiments with mean strain and strain amplitude as parameter. Also step test were made. For the analytical description of the cyclic stress-strain curve the formula proposed by Ramsberg and Osgood [7] was applied: ε a = σ ( ) 1 a E + σa n K (25) The identification of cyclic material parameters b,c, ε f, σ f0, σ fm, σ, n and K was obtained by curve fitting procedures. ASP 23 exhibits no well-defined yield point but a continuous transition from elastic to plastic deformation. Therefore the material law proposed by Chaboche [9] was applied for simulation in ANSYS: RESULTS FATIGUE TEST SPECIMEN σ 2 k = C c γ c tanh(γ c ε p 2 ) (26) For evaluating the results, at first a fatigue test specimen was studied because of its almost uniaxial state of stress.
824 6TH INTERNATIONAL TOOLING CONFERENCE Figure 5. Stress-strain material response for tensile specimen (ASP23) After a large number of experiments the average life was about 4000 cycles but there was a large scatter from 500 to 10000 cycles. The tool life estimation according to Smith-Watson-Topper (axial component) was 140000 cycles. An explanation for this very high tool life prediction may be that only one component of damage is considered. Also the compressive mean stress reduces the damage parameter significantly. The damage parameter according to Bergmann is about 40 % higher than that according to SWT for all three directions, resulting into a life of about 600 parts. Both damage parameters defined for uniaxial load were inaccurate for the state of uniaxial stress. In the Hänsel damage parameter Fig. 8 the plastic contribution was only 1/3 of the entire deformation energy density; despite this, the plastic deformation energy determines damage in the range of low cycle fatigue. For the minimum life 2837 cycles were obtained. The modified damage parameter was lower, resulting in a minimum number of 6143 load cycles. These results do not allow a clear distinction between the Hänsel and the modified damage parameter.
Prediction of Fatigue Life of Cold Forging Tools by FE Simulation and Comparison...825 COLD FORGING DIE The forming process of a yoke is an example of a three dimensional state of stress. Figure 6. Tensile specimen. Figure 7. (SWT) Damage in axial direction Figure 8. Damage (Hänsel)
826 6TH INTERNATIONAL TOOLING CONFERENCE Figure 9. Cold forging part. Figure 10. Cold forging die with cracks (cut). Forming is carried out by combined forward extrusion and backward can extrusion. In the fillet radius cracks occur after an average of 50000 parts. In the damage calculation the SWT damage parameter became imaginary due to the high compressive mean stresses resulting from the prestress condition and no results could be obtained. The damage parameter according to Bergmann indicated the location of failure correctly for tangential and axial load but it predicted a fatigue life of more than 200000 cycles which was by far too high. Figure 11. Damage (Hänsel). Figure 12. Damage (modified Hänsel).
Prediction of Fatigue Life of Cold Forging Tools by FE Simulation and Comparison...827 Again the largest part of the Hänsel damage parameter is given by the elastic deformation energy density. This is in agreement with the observed fatigue life of about 50000 cycles which is in the range of high cycle fatigue. The life time calculation according to Hänsel gives a minimum of 7900 cycles at the lower position of the fillet radius and about 85000 cycles for the true position of failure. Compared with practical results this is rather inaccurate. The modified damage parameter, however, indicates the location of failure correctly and a life of about 34500 cycles is in good agreement with experiments. CONCLUSIONS Both the SWT and the Bergmann damage parameter gave rather inaccurate results for the examples studied. These uniaxial damage models seem not to be applicable for 3D problems with high compressive mean stress. The results obtained with the multiaxial damage parameters according to Hänsel were in good correlation with experimental results. In case of the extrusion die, the modified Hänsel damage parameter was even more accurate than the Hänsel parameter itself. However, this statement cannot be generalized before more examples have been studied. ACKNOWLEDGMENTS The presented work has been performed within the Fifth Framework Programme in the scope of G5RD-CT-1999-00067 project COLT, entitled Improvement of service Life and Reliability of Cold Forging Tools with Respect to Fatigue Damage due to Cyclic Plasticity. Technical support from the consortium and financial contribution from European Commission are gratefully acknowledged. REFERENCES [1] K. N. SMITH, P. WATSON and T. H. TOPPER, A stress-strain function for the fatigue of materials, J. of Materials 5 (1970), 767 775. [2] J. W. BERGMANN, Zur Betriebsfestigkeitsbemessung gekerbter Bauteile auf der Grundlage der 'örtlichen Beanspruchungen, Institut f'ür Stahlbau und Werkstoffmechanik, TH Darmstadt 1983.
828 6TH INTERNATIONAL TOOLING CONFERENCE [3] M. HÄNSEL, Beitrag zur Simulation der Oberflä chenerm'üdung von Umformwerkzeugen (On the simulation of surface fatigue of metal forming tools) Berlin, Springer-Verlag 1993. [4] Bä umel, A.: Experimentelle und numerische Untersuchung der Schwingfestigkeit randschichtverfestigter eigenspannungsbehafteter Bauteile, Institut f'ür Stahlbau und Werkstoffmechanik, Darmstadt 1991. [5] Scientific Forming Technologies Corporation (SFTC): DEFORM Users Manual 3D, Version 3.3, August 2001. [6] ANSYS 5.6 Theory Reference [7] P. BROENSTED and P. SKOV-HANSEN, Fatigue properties of high-strength materials used in cold forging tools, Int. J. Fatigue 20 (1998), 373 381. [8] S. SURESH, Fatigue of Materials, Cambridge University Press 1998. [9] J. LEMAITRE and J.-L. CHABOCHE, Mechanics of solid materials, Cambridge, Cambridge University Press 1990.