Modeling for the FE-Simulation of Warm Metal Forming Processes

Transcription

1 Modeling for the FE-Siulation of War Metal Foring Processes L. Tong, S. Stahel and P. Hora Institute of Virtual Manufacturing, Swiss Federal Institute of Technology, Zurich Abstract. Better forability, less foring force and satisfactory quality are the ost iportant characteristics of war foring processes. However, the aterial odels for either cold foring or hot foring cannot be directly adopted for the nuerical siulation of war foring processes. Suppleent and odification are necessary. Based on the Zener- Holloon forulation, additional ters are proposed in the presented work to describe the softening effect observed during war foring processes as well as the hardening effect. The nuerical siulation provides detailed inforation about the history and distribution of both deforation and teperature, the phase transforation can then also be evaluated, provided the experiental data are available. INTRODUCTION New types of high strength steel have been put into use in the autoobile industry in order to reduce the weight of the vehicles. Unfortunately, the aterials possess often insufficient forability under ordinary cold foring conditions. This disadvantage can be reedied by introducing war foring processes. However, the aterial properties in the teperature range of war foring exhibit rearkable differences fro that of cold or hot foring processes. First of all, the hardening behavior of the aterial is not only a function of and rate. It depends also strongly on the teperature. Recovery, re-crystallization and possible phase transforation ake the behavior ore coplex. Secondly, the teperature of war foring covers a large range. For exaple, the teperature decreases fro 9 o C at the beginning of a sheet foring process to only 4 o C in just a couple of seconds. The theral paraeters such as conductivity, heat flux and specific heat vary considerably according to the teperature. Besides, the lubrication condition is affected considerably by the teperature. It is very difficult to describe the tribological phenoenon. In order to describe the behaviors of the foring aterials in a wide range of teperature, any works have been published. Exaples are the odel proposed by Grosan: n + a2t σ = Cε exp( n1ε ) & ε exp( a1t ), the description according to Schotten: c 1T + c2 σ = c 4 & ε exp( c 3 T ) and the odel used in the progra Forge3: 1 T / ε 5T 7ε 3 8T σ = Aε T ε ε (1 + ε ) ε & ε & ε. Obviously the last one is not very easy to use because of the difficulty in deterining so any paraeters and the lack of physical explanation of each ter. The odel fro Zener and Holloon σ = A [exp( Q / RT ) & ε ] has been widely accepted to describe the viscous plasticity of aterial behavior at high teperatures. Based on the Zener-Holloon description, we proposed a odified for to calculate the yield stress in the war foring processes. Not only rate and teperature but also has been included in this description. The softening effect caused by the recovery and re-crystallization has been also considered in the forulation. The coparison with the experiental data shows the validity of this description. Coputation exaples 625

2 are also presented in this work. Since the nuerical siulation delivers the history as well as the distribution of both deforation and teperature, the possible phase transforation can also be evaluated provided that the experiental data are available. MATERIAL MODELING The yield behavior of the aterials is generally a function of, stain rate and teperature. The effect of teperature and rate is usually considered as negligible at roo teperature. In contrast, the function is doinated by these two variables at the high teperature in hot foring processes. In the teperature range for war foring processes, the influences of all variables have to be investigated systeatically, especially the influences of plastic. On the one hand, hardening effect exists; on the other hand, the softening effect appears due to the recovery and recrystallization. As suppleent to the Zener-Holloon description, we suggest the following for to evaluate the yield stress for the siulation of war etal foring processes: σ = Aexp( Q / RT ) & ε * 2 n {1 + α exp[ c( ε ε ) ]}[1 β exp( Nε )] The expression is coposed of 3 parts. The first one Aexp( Q / RT ) ε& is taken directly fro the Zener- Holloon odel. A slight odification is ade to separate the functions of teperature and rate. The paraeter Q used here equals *Q in the original Zener-Holloon odel. The second ter 2 {1 + α exp[ c( ε ε ) ]} describes the softening effect caused by either recovery or re-crystallization. The n third ter [1 β exp( Nε )] possesses the Hocket- Sherby type behavior and takes the hardening effect into account. The function satisfies the general requireent that it increases with higher rate and decreases with higher teperature, as shown in Figure 1. Figure 2 shows the influence of the plastic. The softening effect is described as well as the classical hardening effect.. Discussion and Coparison Although 9 paraeters are used in this forulation, it is by no eans a very coplex description because each paraeter has its own affect and is independent fro each other. For exaple, the coefficient α specifies the axiu peak value and ε defines approxiately the position of the peak value. For a aterial which doesn t exhibit softening effect, α can be siply set as zero. FIGURE 1. Yield stress as function of teperature and rate stress N/^ FIGURE 2. Yield stress as function of plastic T=1 C T= 9 C T = 8 C In order to deterine the paraeters in the function, any experients have to be perfored at different teperatures and using different rates. The least square ethod is widely used to handle the large ount of data to get the optiu cobination of the paraeters. Because the equations derived fro the least square ethod are generally nonlinear, iterations are necessary. However, the convergence of the procedure is often conditional. Experience shows that the better the initial values are set, the better the convergence is. With the expression proposed in this work, it is easy to estiate a set of reasonable initial values to start the iteration. Satisfactory convergence is achieved. 626

3 Figure 3 shows the coparisons of the calculated curves and the experient data of the steel 1Cr6. 7 different cobinations of teperature and rate are investigated. Figure 4 is the coparison using the teperature as variable. Obviously the accuracy is sufficient for the ai of nuerical siulation. stress (N/^2) rat e=.5/s rate = 5./s rate = 1./s FIGURE 5. Shift of the peak value with different rate To include this character, the paraeter α is set to be a function of teperature. It decreases with decreasing teperature. This easure leads to reasonable results as shown in Figure 6. FIGURE 3. Calculated curves and experient data kf [MPa] Versuch 1 Versuch 5 Versuch.2 Approx. 1 Approx. 5 Approx. stress N/^ T = 8 C T = 7 C T = 65 C T [ C] FIGURE 4. Coparison with the experient data Iproveent The behaviors of different alloys at high teperature are very coplicated. As pointed out by the researchers fro the industry, the s corresponding to the peak values of yield stresses for different rates are not a constant. They increase as the rate becoes higher because the recovery and re-crystallization possess the property of tie-lag. The iproveent is ipleented iediately since our forulation is very flexible. Instead of a constant value, the ε increases with increasing rate. The result is shown in Figure 5. Another well know phenoenon is that the recovery and re-crystallization take place only at higher teperatures. As the teperature decreases, they get weaker and weaker and cease at a certain teperature lever. FIGURE 6. Re-crystallization by different teperature However, it should be kept in ind that the Zener- Holloon odel uses actually only one paraeter Q to describe the influence of the teperature. It cannot be expected to cover very wide range of teperatures. Either soe ore coplicated forulations are needed, or we have to set a teperature liit under which the process is actually cold foring and the influence of the teperature is excluded. COMPUTATION EXAMPLES The odel can be applied for the siulation of sheet foring processes as well as for the siulation of bulk foring processes. Deep Drawing of thick Sheet The first exaple is siply the siulation of a deep drawing process. The data for steel 1Cr6 is used in the siulation. The sheet thickness t = 2.4 and the drawing ratio β = 2.2. In coparison with a 627

4 typical deep drawing process with β < 2, the risk of rupture exists. TABLE 1. The paraeters for steel 1Cr6 A Q α c ε β N n The aterial paraeters for the evaluation of yield stress are listed in Table 1. The initial teperature of the sheet is taken to be 9 o C. Figure 7 shows the siulation result when the teperature of all foring tools are kept as roo teperature T = 3 o C. Rupture appears in the wall and the process cannot be perfored successfully. In contrast, if the punch keeps cold but the drawing die and the holder are pre-heated to 55 o C, the process can be perfored successfully despite the large drawing ratio. Figure 8 shows the teperature distribution at the end of the foring process. The exaple deonstrated that war foring processes not only iprove the forability and reduce the foring force, but also provide ore possibilities to achieve better perforance of processes. A coplex foring part Figure 9 is the siulation of a coplex sheet foring part. The siulation showed that if the foring process is perfored within 9 seconds, the teperature of the foring parts can drop fro 9 o C to 45 o C if the tools teperatures are set as roo teperature. The distribution of the thickness is also shown in Figure 9 b. FIGURE 7. Rupture when using cold foring tools However, the siulation of war sheet foring processes is very coplicated because not only the aterial data are necessary but also the theral paraeters such as the heat flux to the foring tools and the convection coefficient etc. These paraeters are very difficult to obtain using siple experients. If these paraeters are not set properly, the distribution of teperature are also incorrect which in turn has strong influences on the echanical properties of the aterial. In this case, deviation fro the real process is inevitable. Soeties the foring processes are accopanied with phase transforations. The phase transforations are usually deterined by the distribution and history of teperature and deforation. Since the distribution and the developing of the teperature are evaluated in the siulation as well as the deforation, phase transforations can be calculated provided the TTT (Tie-Teperature-Transforation) diagra is available. Figure 1 shows a typical TTT diagra. In case the phase transforations appear, the yield stress is also a function of the states of icrostructure. However, it is beyond the range of this work and should be investigated in the future. FIGURE 8. Successful drawing using hot die and blank holder 628

5 task of FE-siulation is the prediction of possible failures in the processes. Since the concept of classic foring liit diagras (FLD) cannot be directly transplanted for the war foring processes, new easures are needed to perfor this task. a) Distribution of teperature FIGURE 1. A typical TTT diagra for steels ACKNOWLEDGMENTS The authors are grateful to Mr. L. Burkhardt for perforing the coparison shown in Figure 3. and the valuable discussions. REFERENCES b) Distribution of thickness FIGURE 9. Siulation of a real foring part DISCUSSIONS The odel proposed in this work can well describe the aterial behaviors in the war foring process. Even as any as 9 paraeters are used in the odel; it is not difficult to deterine the using enough experiental data. The odel can also be used to fit ore coplicated phenoenon with soe slight odifications. Coputational exaples verified the validity of this odel. However, in order to get sufficient accuracy, the experients ust be well designed to get correct aterial data. Furtherore the ost iportant 1. Zener C. and Holloon J. H., J., app. Phys , (1944) 2. Medina S. F. and Hernandez C. A., General Expression of the Zener-Holloon Paraeter as Function of the Cheical Coposition of low Alloy and Microalloyed Steels, Acta Mater. Vol. 44, No. 1 pp , (1996) 3. Pettersen T., et al., Metallurgical and Materials Transactions A: Physical Metallurgy and Materials Science. V. 34 n 12, p , (23) 4. F.J. Huphreys: Proc. ICOTOM, vol. 6 (1), pp , (1982) 5. Forge3 V6.1, Reference, General Data File page 9 (21) 6. Schotten, K., Matheatische Beschreibung der Fließkurve bei der Waruforung verschiedener Stähle, Dissertation Rheinisch-Westfälische Technische Hochschule Aachen, Shaker Verlag (2) 7. Spittel, M., Neubauer, S., Betrachtungen zur atheatischen Fliesskurvenbeschreibung, Neue Hütte 28 (1983), S Feurer U., Modell der Waruforungseigenschafen von Aluiniulegierungen, Project report, Institute of Foring Technology, ETH-Zurich, (1996) 629