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Characterization of yielding of sheet metal at elevated temperatures
Journal of Materials Processing Technology 191 (2007) 20–23
Characterization of yielding of sheet metal at elevated temperatures W. Hußn¨atter ∗ , M. Merklein, M. Geiger Chair of Manufacturing Technology (LFT), University of Erlangen-Nuremberg, 91058 Erlangen, Germany
Abstract In times of highest significance of process modeling and numerical simulation characterization of material properties is of special importance for components’ and tools’ dimensioning. Especially in fields of sheet metal forming the mechanical behavior of components highly differ according to real stress condition. In particular yield loci combine the information of beginning of yielding with biaxial stress conditions. Although these data are essential, they are unknown for many different sheet metals, mainly new materials used for light-weight constructions, e.g. aluminum and magnesium alloys. In this paper investigations done on a novel concept of experimental setup, which has been developed at the Chair of Manufacturing Technology (LFT) and which enables the determination of yield loci at elevated temperatures, are presented. The strategy for local heating is based on FE-calculations and verified afterwards. A 210 W-diode laser is used for the local heating of the specimens up to temperatures in the range of 300 ◦ C. During forming process a constant temperature is guaranteed by a closed-loop temperature-control (CLTC), the homogeneous distribution of temperature in the forming zone is realized using a special optical system. © 2007 Elsevier B.V. All rights reserved. Keywords: Materials’ characterization; Yield locus; Diode laser; FE-simulation
1. Introduction Numerical simulation by using finite element method is state of the art not only at scientific institutes, but also in industry. However, the quality of computational results is just as good as the abstract model, i.e. modeling of geometry, kinematics and of course material properties. Whereas, kinematics and geometry of all components can be described in a very definite way, especially the modeling of ambient conditions, e.g. radiation or contact behavior, and material characteristics is insecure. Depending on the specific theory which is used to describe the material behavior several variables, e.g. tensile strength, planar anisotropy, yield locus and others, can be taken into account for modeling sheet metal forming. In comparison with parameters that are determined in uniaxial experiments, e.g. uniaxial tensile test, yield loci can be calculated relating to different theories. Starting in 1948 Hill proposed a quadratic yield criterion [1] which can describe anisotropic material behavior by the usage of only three parameters. Later on different yield criteria of the Hosford family, e.g. Yld96, have been developed based on a generalized model [2], which is related to the crystallographic
∗
Corresponding author. E-mail addresses: [email protected] (W. Hußn¨atter), [email protected] (M. Merklein), [email protected] (M. Geiger). 0924-0136/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2007.03.038
structure of the material, i.e. face centered cubic (fcc) or body centered cubic (bcc). In the last years several modifications of this criterion have been published in order to fit with experimental data of different materials, special enhancements have been done for aluminum alloys by Barlat et al. [3]. According to its low formability at room temperature as a reason of its hexagonal crystal structure, magnesium alloys have to be formed and therefore also characterized at elevated temperatures in the range of 200–300 ◦ C [4]. Nevertheless, neither experimental yield loci, nor a yield criterion for this kind of material in particular at elevated temperatures are known until today. 2. Experimental setup In order to fulfill the requirements mentioned above a novel setup, which enables the characterization of material properties at elevated temperature, has been developed at LFT and has been applied for patent in 2003 [5]. Although this setup has been already introduced and explained in Refs. [6,7], the special feature of local heating is described within the following chapter due to its specific importance for this paper. The specimens are heated up to a range of 200–300 ◦ C by a 210 W-diode laser, type OTW-210-30-i of the company Optotools GmbH in Germany. Since heat accumulation in the center of the cruciform specimen must be avoided to obtain a homogenous heating of the forming zone a special optical system is used to generate a ring-shaped laser beam [7]. Both inner diameter di and outer diameter do of this ring can be variably defined according to the material properties of the specimen, e.g. absorption and thermal conduction. This is an important precondition for the localization of heating, since the specimen should
W. Hußn¨atter et al. / Journal of Materials Processing Technology 191 (2007) 20–23
21
Fig. 1. Results of a FE-simulation of temperature distribution on a 1.0 mm-sheet of AA6016 (left) and across the cross-sectional area (right) after 31.5 s heating by 210 W diode laser beam. reach maximum temperatures only in the forming zone. Additionally, changing the tested material, that means varying the thermal material properties a different setting of do and di is required due to guarantee comparable heating conditions. Thus, the used optical system enables the flexible heat treatment of various sheet metals. Furthermore, the diode laser is very comfortable, i.e. fast and straight for the control of laser power and therefore qualified for the closed-loop temperature-control (CLTC) during the forming process. Varying the power of the diode-current means a direct influence on the power output of the laser beam. Actual temperature on the specimen’s surface is measured by a pyrometer and builds the input for the online temperature-control realized with a PID-element to generate an adequate laser power. Since the sheet thickness t0 = 1.0 mm a constant temperature is guaranteed across the whole crosssection of the specimen (Fig. 1). In combination of these features the aim of homogenous temperature across the forming zone during the forming process is guaranteed.
3. Experimental results 3.1. Verification of suitability of local heating First of all, the homogenous distribution of temperature in the forming zone must be guaranteed. Therefore, different settings for di and do have been numerically investigated. Since the forming zone has a quadratic shape with a length of 30 mm
its diameter df ≈ 42.4 mm. According to this fact do = 45 mm was fixed and an optimum for di = 23.6 mm was identified based on FE-simulations using the software-tool Abaqus standard and these results have been also experimentally verified. As it is shown in Fig. 2 a homogenous temperature of about 300 ◦ C across the whole forming zone of an AA6016-specimen can be achieved using these settings. Furthermore, the influence of local heating by the diode laser on maximum reachable temperatures for the materials of main interest, i.e. the aluminum alloy AA6016 and AZ31, is examined. Thus, the different specimens are heated up varying the maximum amount of laser power PL without any control. Although this procedure is not practicable for real experiments, it shows the potentials of the diode laser source. Doing the experimental investigations for determining the forming behavior at elevated temperatures a closed-loop temperature-control is used (see Section 3.2) to reach the aimed temperature more quickly. Obviously it is possible to satisfy the whole range of relevant temperatures for both materials as it is illustrated in Fig. 3. Due to higher absorption of laser energy the magnesium alloy AZ31 is getting warmer than AA6016 for same laser power, e.g. PL = 150 W leads to Tmax = 248 ◦ C for AA6016 and Tmax = 311 ◦ C for AZ31.
Fig. 2. Distribution of temperature on a 1 mm-sheet of AA6016 calculated in FE-simulation (left) and measured with a thermal imaging camera (right).
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W. Hußn¨atter et al. / Journal of Materials Processing Technology 191 (2007) 20–23
Fig. 3. Temperature T in the forming zone (left) and maximum temperature Tmax against laser power PL for AA6016- and AZ31-sheet of 1.0 mm.
3.2. Closed-loop temperature-control Due to several disturbances during the forming process, e.g. variation of the distance from the specimen to the laser, contact between specimen and tools, and the enhanced heating process, i.e. faster achievement of estimated temperature, a CLTC is essential. Therefore, a pyrometer which is placed orthogonally above the specimen takes the temperature as an input-signal for the control. The principal difference of heating with and without CLTC is shown in Fig. 4. As it can be seen, ideal value of temperature T = 200 ◦ C is reached within 30 s using CLTC, whereas it approximately needs 80 s if the specimen is heated by constant laser power of 120 W without CLTC. Achieving this temperature-run with CLTC, PL rises up to its maximum value within a few seconds and this level is hold for a period of about 25 s. Afterwards the laser power linearly decreases to 170–180 W in a period of 10 s and remains at this standard for the further experiment. 3.3. Influence of temperature on the forming behavior The influence of temperature on the forming behavior is investigated by FE-calculations of the forming process with the
Fig. 4. Influence of CLTC on local heating of an AA6016-specimen.
LFT-setup and is shown as yield locus diagrams (YLD) in Fig. 5. The numerical model is divided into isothermal regions and assigned with material properties which have been determined in a uniaxial tensile test. The basic effect of temperature on the flow curves of both materials which have been investigated can be concluded as follows: the higher the temperature is, the lower the yield stress and the yield strength are. Expectedly, the impact of temperature on YLDs of AA6016 and AZ31 are significant. Reduced yield stresses with increasing
Fig. 5. FE-simulation of YLD of AA6016 (left) and AZ31 (right).
W. Hußn¨atter et al. / Journal of Materials Processing Technology 191 (2007) 20–23
temperature can be identified as well for the aluminum alloy as for the magnesium alloy by decreasing spread of the YLDs. It can also be seen, that the temperature-effect on AZ31 leads to a reduction of yield stresses in RD from 1556 N/mm2 for room temperature (20 ◦ C) to 33 N/mm2 at 300 ◦ C, i.e. 21% of the initial state. This behavior is much more pronounced than that on AA6016, where the heating causes a reduction to 40% of yield stress in RD, i.e. from 126 N/mm2 (20 ◦ C) to 50 N/mm2 (300 ◦ C). 4. Conclusions and outlook It has been shown that local heating of specimen up to more than 400 ◦ C for AZ31 and up to 300 ◦ C for AA6016 is possible with the LFT-setup using a diode laser source in combination with a special optical system for homogenous temperatures across the forming zone. In addition with the CLTC the heating process is fastened and it realizes constant temperature during the forming process although several disturbances may have influence. The effects of temperature on the forming behavior have been calculated with FE-simulations. For future work it is essential to enhance the CLTC for more effective and faster heating. Based on these results the real laser
23
power, which will vary with time, must be taken into account as input for optimization of thermo-mechanical FE-simulations. Completing, these calculations have to be experimentally verified. References [1] R. Hill, A theory of the yielding and plastic flow of anisotropic materials, in: Proceedings of the Royal Society of London A, London, 1948. [2] W.F. Hosford, On the crystallographic basis of yield criteria, Texture Microstruct. 26-7 (1996) 479–493. [3] F. Barlat, J.C. Brem, J.W. Yoon, K. Chung, R.E. Dicke, D.J. Lege, F. Pourboghrat, S.-H. Choi, E. Chu, Plane stress yield function for aluminum alloy sheets. Part 1: Theory, Int. J. Plasticity 19 (2003) 1297–1319. [4] T.K. Aune, et al., Magnesium alloys, in: Ullmann’s Encyclopedia of Industrial Chemistry, 2002. [5] M. Geiger, W. Hußn¨atter, M. Kerausch, M. Merklein, M. Pitz, Verfahren und Vorrichtung zur Durchf¨uhrung von Fließortkurven-Tiefungsversuchen an Blech-Probek¨orpern, German Patent Application DE 103 40 125.3 (2003). [6] M. Geiger, G. van der Heyd, M. Merklein, W. Hußn¨atter, Novel concept of experimental setup for characterisation of plastic yielding of sheet metal at elevated temperatures, in: Proceedings of the 11th International Conference on Sheet Metal, Erlangen, 2005, pp. 657–664. [7] W. Hußn¨atter, M. Geiger, Experimental setup for determination of yield loci—demands of accuracy, in: Proceedings of the Fourth JSTP Seminar on Precision Forging, Nara, 2006, pp. 215–218.
Characterization of yielding of sheet metal at elevated temperatures W. Hußn¨atter ∗ , M. Merklein, M. Geiger Chair of Manufacturing Technology (LFT), University of Erlangen-Nuremberg, 91058 Erlangen, Germany
Abstract In times of highest significance of process modeling and numerical simulation characterization of material properties is of special importance for components’ and tools’ dimensioning. Especially in fields of sheet metal forming the mechanical behavior of components highly differ according to real stress condition. In particular yield loci combine the information of beginning of yielding with biaxial stress conditions. Although these data are essential, they are unknown for many different sheet metals, mainly new materials used for light-weight constructions, e.g. aluminum and magnesium alloys. In this paper investigations done on a novel concept of experimental setup, which has been developed at the Chair of Manufacturing Technology (LFT) and which enables the determination of yield loci at elevated temperatures, are presented. The strategy for local heating is based on FE-calculations and verified afterwards. A 210 W-diode laser is used for the local heating of the specimens up to temperatures in the range of 300 ◦ C. During forming process a constant temperature is guaranteed by a closed-loop temperature-control (CLTC), the homogeneous distribution of temperature in the forming zone is realized using a special optical system. © 2007 Elsevier B.V. All rights reserved. Keywords: Materials’ characterization; Yield locus; Diode laser; FE-simulation
1. Introduction Numerical simulation by using finite element method is state of the art not only at scientific institutes, but also in industry. However, the quality of computational results is just as good as the abstract model, i.e. modeling of geometry, kinematics and of course material properties. Whereas, kinematics and geometry of all components can be described in a very definite way, especially the modeling of ambient conditions, e.g. radiation or contact behavior, and material characteristics is insecure. Depending on the specific theory which is used to describe the material behavior several variables, e.g. tensile strength, planar anisotropy, yield locus and others, can be taken into account for modeling sheet metal forming. In comparison with parameters that are determined in uniaxial experiments, e.g. uniaxial tensile test, yield loci can be calculated relating to different theories. Starting in 1948 Hill proposed a quadratic yield criterion [1] which can describe anisotropic material behavior by the usage of only three parameters. Later on different yield criteria of the Hosford family, e.g. Yld96, have been developed based on a generalized model [2], which is related to the crystallographic
∗
Corresponding author. E-mail addresses: [email protected] (W. Hußn¨atter), [email protected] (M. Merklein), [email protected] (M. Geiger). 0924-0136/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2007.03.038
structure of the material, i.e. face centered cubic (fcc) or body centered cubic (bcc). In the last years several modifications of this criterion have been published in order to fit with experimental data of different materials, special enhancements have been done for aluminum alloys by Barlat et al. [3]. According to its low formability at room temperature as a reason of its hexagonal crystal structure, magnesium alloys have to be formed and therefore also characterized at elevated temperatures in the range of 200–300 ◦ C [4]. Nevertheless, neither experimental yield loci, nor a yield criterion for this kind of material in particular at elevated temperatures are known until today. 2. Experimental setup In order to fulfill the requirements mentioned above a novel setup, which enables the characterization of material properties at elevated temperature, has been developed at LFT and has been applied for patent in 2003 [5]. Although this setup has been already introduced and explained in Refs. [6,7], the special feature of local heating is described within the following chapter due to its specific importance for this paper. The specimens are heated up to a range of 200–300 ◦ C by a 210 W-diode laser, type OTW-210-30-i of the company Optotools GmbH in Germany. Since heat accumulation in the center of the cruciform specimen must be avoided to obtain a homogenous heating of the forming zone a special optical system is used to generate a ring-shaped laser beam [7]. Both inner diameter di and outer diameter do of this ring can be variably defined according to the material properties of the specimen, e.g. absorption and thermal conduction. This is an important precondition for the localization of heating, since the specimen should
W. Hußn¨atter et al. / Journal of Materials Processing Technology 191 (2007) 20–23
21
Fig. 1. Results of a FE-simulation of temperature distribution on a 1.0 mm-sheet of AA6016 (left) and across the cross-sectional area (right) after 31.5 s heating by 210 W diode laser beam. reach maximum temperatures only in the forming zone. Additionally, changing the tested material, that means varying the thermal material properties a different setting of do and di is required due to guarantee comparable heating conditions. Thus, the used optical system enables the flexible heat treatment of various sheet metals. Furthermore, the diode laser is very comfortable, i.e. fast and straight for the control of laser power and therefore qualified for the closed-loop temperature-control (CLTC) during the forming process. Varying the power of the diode-current means a direct influence on the power output of the laser beam. Actual temperature on the specimen’s surface is measured by a pyrometer and builds the input for the online temperature-control realized with a PID-element to generate an adequate laser power. Since the sheet thickness t0 = 1.0 mm a constant temperature is guaranteed across the whole crosssection of the specimen (Fig. 1). In combination of these features the aim of homogenous temperature across the forming zone during the forming process is guaranteed.
3. Experimental results 3.1. Verification of suitability of local heating First of all, the homogenous distribution of temperature in the forming zone must be guaranteed. Therefore, different settings for di and do have been numerically investigated. Since the forming zone has a quadratic shape with a length of 30 mm
its diameter df ≈ 42.4 mm. According to this fact do = 45 mm was fixed and an optimum for di = 23.6 mm was identified based on FE-simulations using the software-tool Abaqus standard and these results have been also experimentally verified. As it is shown in Fig. 2 a homogenous temperature of about 300 ◦ C across the whole forming zone of an AA6016-specimen can be achieved using these settings. Furthermore, the influence of local heating by the diode laser on maximum reachable temperatures for the materials of main interest, i.e. the aluminum alloy AA6016 and AZ31, is examined. Thus, the different specimens are heated up varying the maximum amount of laser power PL without any control. Although this procedure is not practicable for real experiments, it shows the potentials of the diode laser source. Doing the experimental investigations for determining the forming behavior at elevated temperatures a closed-loop temperature-control is used (see Section 3.2) to reach the aimed temperature more quickly. Obviously it is possible to satisfy the whole range of relevant temperatures for both materials as it is illustrated in Fig. 3. Due to higher absorption of laser energy the magnesium alloy AZ31 is getting warmer than AA6016 for same laser power, e.g. PL = 150 W leads to Tmax = 248 ◦ C for AA6016 and Tmax = 311 ◦ C for AZ31.
Fig. 2. Distribution of temperature on a 1 mm-sheet of AA6016 calculated in FE-simulation (left) and measured with a thermal imaging camera (right).
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W. Hußn¨atter et al. / Journal of Materials Processing Technology 191 (2007) 20–23
Fig. 3. Temperature T in the forming zone (left) and maximum temperature Tmax against laser power PL for AA6016- and AZ31-sheet of 1.0 mm.
3.2. Closed-loop temperature-control Due to several disturbances during the forming process, e.g. variation of the distance from the specimen to the laser, contact between specimen and tools, and the enhanced heating process, i.e. faster achievement of estimated temperature, a CLTC is essential. Therefore, a pyrometer which is placed orthogonally above the specimen takes the temperature as an input-signal for the control. The principal difference of heating with and without CLTC is shown in Fig. 4. As it can be seen, ideal value of temperature T = 200 ◦ C is reached within 30 s using CLTC, whereas it approximately needs 80 s if the specimen is heated by constant laser power of 120 W without CLTC. Achieving this temperature-run with CLTC, PL rises up to its maximum value within a few seconds and this level is hold for a period of about 25 s. Afterwards the laser power linearly decreases to 170–180 W in a period of 10 s and remains at this standard for the further experiment. 3.3. Influence of temperature on the forming behavior The influence of temperature on the forming behavior is investigated by FE-calculations of the forming process with the
Fig. 4. Influence of CLTC on local heating of an AA6016-specimen.
LFT-setup and is shown as yield locus diagrams (YLD) in Fig. 5. The numerical model is divided into isothermal regions and assigned with material properties which have been determined in a uniaxial tensile test. The basic effect of temperature on the flow curves of both materials which have been investigated can be concluded as follows: the higher the temperature is, the lower the yield stress and the yield strength are. Expectedly, the impact of temperature on YLDs of AA6016 and AZ31 are significant. Reduced yield stresses with increasing
Fig. 5. FE-simulation of YLD of AA6016 (left) and AZ31 (right).
W. Hußn¨atter et al. / Journal of Materials Processing Technology 191 (2007) 20–23
temperature can be identified as well for the aluminum alloy as for the magnesium alloy by decreasing spread of the YLDs. It can also be seen, that the temperature-effect on AZ31 leads to a reduction of yield stresses in RD from 1556 N/mm2 for room temperature (20 ◦ C) to 33 N/mm2 at 300 ◦ C, i.e. 21% of the initial state. This behavior is much more pronounced than that on AA6016, where the heating causes a reduction to 40% of yield stress in RD, i.e. from 126 N/mm2 (20 ◦ C) to 50 N/mm2 (300 ◦ C). 4. Conclusions and outlook It has been shown that local heating of specimen up to more than 400 ◦ C for AZ31 and up to 300 ◦ C for AA6016 is possible with the LFT-setup using a diode laser source in combination with a special optical system for homogenous temperatures across the forming zone. In addition with the CLTC the heating process is fastened and it realizes constant temperature during the forming process although several disturbances may have influence. The effects of temperature on the forming behavior have been calculated with FE-simulations. For future work it is essential to enhance the CLTC for more effective and faster heating. Based on these results the real laser
23
power, which will vary with time, must be taken into account as input for optimization of thermo-mechanical FE-simulations. Completing, these calculations have to be experimentally verified. References [1] R. Hill, A theory of the yielding and plastic flow of anisotropic materials, in: Proceedings of the Royal Society of London A, London, 1948. [2] W.F. Hosford, On the crystallographic basis of yield criteria, Texture Microstruct. 26-7 (1996) 479–493. [3] F. Barlat, J.C. Brem, J.W. Yoon, K. Chung, R.E. Dicke, D.J. Lege, F. Pourboghrat, S.-H. Choi, E. Chu, Plane stress yield function for aluminum alloy sheets. Part 1: Theory, Int. J. Plasticity 19 (2003) 1297–1319. [4] T.K. Aune, et al., Magnesium alloys, in: Ullmann’s Encyclopedia of Industrial Chemistry, 2002. [5] M. Geiger, W. Hußn¨atter, M. Kerausch, M. Merklein, M. Pitz, Verfahren und Vorrichtung zur Durchf¨uhrung von Fließortkurven-Tiefungsversuchen an Blech-Probek¨orpern, German Patent Application DE 103 40 125.3 (2003). [6] M. Geiger, G. van der Heyd, M. Merklein, W. Hußn¨atter, Novel concept of experimental setup for characterisation of plastic yielding of sheet metal at elevated temperatures, in: Proceedings of the 11th International Conference on Sheet Metal, Erlangen, 2005, pp. 657–664. [7] W. Hußn¨atter, M. Geiger, Experimental setup for determination of yield loci—demands of accuracy, in: Proceedings of the Fourth JSTP Seminar on Precision Forging, Nara, 2006, pp. 215–218.