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Influencing factors of global and local deformation in hot compression
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Procedia Manufacturing 15 (2018) 381–387 Procedia Manufacturing 00 (2017) 000–000 www.elsevier.com/locate/procedia
17th International Conference on Metal Forming, Metal Forming 2018, 16-19 September 2018, 17th International Conference on MetalToyohashi, Forming, Metal Japan Forming 2018, 16-19 September 2018, Toyohashi, Japan
Influencing factors of global and local deformation in hot
Influencing factors ofInternational global and local deformation in hot Manufacturing Engineering Society Conference 2017, MESIC 2017, 28-30 June compression 2017, Vigo (Pontevedra), Spain compression Tian*, Siegfried Kleber, Silvia Schneller, Peter Markiewicz Costing Baohui models for Siegfried capacityKleber, optimization in Industry 4.0: Trade-off Baohui Tian*, Silvia Schneller, Peter Markiewicz Voestalpine Bohler Special Steel, Mariazeller Street 25, Kapfenberg, A-8605, Austria between used capacity andStreet operational efficiency Voestalpine Bohler Special Steel, Mariazeller 25, Kapfenberg, A-8605, Austria
A. Santanaa, P. Afonsoa,*, A. Zaninb, R. Wernkeb Abstract a University of Minho, 4800-058 Guimarães, Portugal Abstract b Unochapecó, 89809-000 Chapecó, SC, Brazil Hot compression of cylindrical specimens is carried out with Gleeble tests and simulated with the finite element method. Profiles Hot compression cylindrical carried out Gleeble tests andfriction simulated with the finite element method. Profiles of the specimens of and the local specimens strains are isevaluated at with different reductions, coefficients and temperature gradients. No of the specimens and the local strains evaluated at flow different reductions, friction coefficients temperaturedepends gradients. No correlations are identified between the are profiles and the stress - strain behaviors. Bulging of and the specimens on the correlations are identified between the profiles and the flow stress strain behaviors. Bulging of the specimens depends on the Abstract friction coefficient and temperature gradient. Variations in the effective strain at the center on the cross section correlate with friction and temperature Variations strain at the are center on the cross section correlate with and the bulging.coefficient The corresponding changesgradient. of the local straininonthe theeffective edge with bulging diminished by introducing frictions bulging. Thegradients. corresponding changes of the production local strain on the edge will with bulging are diminished by introducing frictions and temperature Under the concept of "Industry 4.0", processes be pushed to be increasingly interconnected, temperature gradients. information based on a real time basis and, necessarily, much more efficient. In this context, capacity optimization © 2018 The Authors. Published by of Elsevier B.V.maximization, contributing also for organization’s profitability and value. goes beyond the traditional aim capacity © 2018 2018 The The Authors. Published Elsevier B.V. © Authors. Published by by B.V. committee of the 17th International Conference on Metal Forming. Peer-review under responsibility of Elsevier the scientific Indeed, lean management and continuous improvement approaches suggest capacity optimization Peer-review under responsibility of the scientific committee of the 17th International Conference on Metal Forming. instead of Peer-review under responsibility of the scientific committee of the 17th International Conference on Metal Forming.
maximization. The study of capacity optimization and costing models is an important research topic that deserves Keywords: Profile; Strain; Friction; Temperature gradient; Compression; Deformation; Simulation; Finite element method contributions from both the practical and theoretical perspectives. ThisSimulation; paper presents and discusses a mathematical Keywords: Profile; Strain; Friction; Temperature gradient; Compression; Deformation; Finite element method model for capacity management based on different costing models (ABC and TDABC). A generic model has been developed and it was used to analyze idle capacity and to design strategies towards the maximization of organization’s 1. Introduction value. The trade-off capacity maximization vs operational efficiency is highlighted and it is shown that capacity 1. Introduction optimization might operational inefficiency. In industrial hot hide processing workpieces with different geometries are deformed following work schedules to final © 2017 The Authors. Published byworkpieces Elsevier B.V.with different geometries are deformed following work schedules to final In industrial hot processing sizes. The work schedules should on the one hand provide an optimal reduction at each pass to satisfy the efficiency Peer-review under schedules responsibility of the scientific of the Manufacturing Engineering Society International Conference sizes. The work should onecommittee hand provide optimal at each pass to satisfy the efficiency of productions. On the other hand,on thethe product should obtainanthe desiredreduction microstructures and mechanical properties. 2017. of productions. On the other hand, the product should obtain the desired microstructures and mechanical properties. Keywords: Cost Models; ABC; TDABC; Capacity Management; Idle Capacity; Operational Efficiency
1. Introduction
* Corresponding author. Tel.: +43-3862-203-7918; fax: +43-3862-203-7585. * E-mail Corresponding Tel.: +43-3862-203-7918; fax: +43-3862-203-7585. address:author. [email protected] The cost of idle capacity is a fundamental information for companies and their management of extreme importance E-mail address: [email protected]
in modern©production systems. In general, it isB.V. defined as unused capacity or production potential and can be measured 2351-9789 2018 The Authors. Published by Elsevier 2351-9789 2018 Authors. Published Elsevier B.V.hours of the Peer-review underThe responsibility of theby scientific committee 17th International on Metal Forming. in several©ways: tons of production, available manufacturing, etc.Conference The management of the idle capacity Peer-review under responsibility thefax: scientific committee * Paulo Afonso. Tel.: +351 253 510of 761; +351 253 604 741 of the 17th International Conference on Metal Forming. E-mail address: [email protected]
2351-9789 © 2017 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the scientific committee of the Manufacturing Engineering Society International Conference 2017. 2351-9789 © 2018 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the scientific committee of the 17th International Conference on Metal Forming. 10.1016/j.promfg.2018.07.233
Baohui Tian et al. / Procedia Manufacturing 15 (2018) 381–387 Author name / Procedia Manufacturing 00 (2018) 000–000
382 2
Lateral deformation of workpieces determines not only the profiles and eventually the reductions in following passes, but also filling of calibers. It is an important factor affecting the efficiency of hot processing such as rolling, forging etc. Corresponding to the global deformation, the parameters of local deformation such as the effective strain or stress are served as input in material models for recrystallization, damages and so on. Different lateral deformation means various local strains or stresses. Being the first prerequisite to use the material models, the lateral deformation as well as the geometry of workpieces should be determined with the minimal error. The lateral deformation in the conventional hot compression of a cylindrical specimen shows a barrel shaped profile, i.e., the bulging, due to the friction between workpieces and die. The bulging is increased with increasing friction coefficients, and can be evaluated with the diameter of cylinder [1, 2]. Previous investigations of hot compression and hot rolling showed a rather weak dependence of the lateral spread on the flow stress – strain behaviors of alloys [2-5]. In contrast to the results from the experiments [5-8], the lateral deformation in the industrial practices of hot rolling and forging is usually relevant to deformation temperatures and grades of alloys. An apparent difference in the hot deformation between the laboratory experiments and the industrial production lies in the size of workpieces. Normally, due to the small size of specimens temperature gradients are usually not considered in the hot deformation in laboratories. In contrast, inhomogeneous temperatures happen in most cases of actual manufactures. Quantitative investigations on the effect of temperature gradients on the lateral deformation are necessary in order to: 1) clarify the discrepancy concerning the geometry of workpieces between the laboratory experiments and industrial experiences; 2) define the applicability of laboratory results in industrial processes; 3) identify the key influencing factors of geometrical changes of workpieces in production controls and 4) establish the corresponding responses between the global and local deformation. In the present work, hot compression of cylindrical specimens is carried out and also simulated with the finite element (FE) method under various flow stress - strain behaviors, friction coefficients and temperature gradients, with the aim to identify the key factors influencing the bulging and the local deformation. 2. Method 2.1. Hot compression tests Hot compression tests were carried out employing Gleeble 1500™ simulator for the stainless steel A607, i.e., X5Cr18Ni10 from voestalpine Bohler Special Steel at 750 °C, 1050 °C and a strain rate of 0.1/s, 1/s. The specimens have a diameter of 10 mm and a height of 12 mm. The test at each deformation condition has been repeated twice. The profiles of the selected specimens have been digitally photographed and measured after deformation. The difference in the profiles with respect of the deformation temperature (T) and the strain rate is not significant so long the reduction is the same. 2.2. FE Simulations The compression tests were simulated with the finite element software DEFORM 2D™, version 10.2. The model used is a quarter one with the axial symmetry. In order to clarify the influence of the temperature gradient (Tg) on bulging, different diameters of specimens (125, 250 and 500 mm) with a fixed height – diameter ratio of 1.2 have been used in the simulation. These specimens are either set to have a constant deformation temperature, or air cooled from 1200 °C before compression to introduce the difference in temperatures between the center and the surface. This difference in the temperatures between the center (Tc) and the surface (Ts) on the radial-axial cross section of specimens is defined as the temperature gradient Tg, i.e., Tg = Tc - Ts. Ts is the average temperature at the surface. The flow stress – strain curves of the alloy A607 show a typical strain hardening and recrystallization behaviors within the ranges of temperatures and strain rates in the simulation. An example is as shown in Fig. 1. A modelled alloy is used to simplify the relationship between the deformation temperature and the flow stress. The flow stress () of the modelled alloy is assigned to be dependent only on the temperature (shown also in Fig. 1): � = 700 − 0.5�,
(1)
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Author name / Procedia Manufacturing 00 (2018) 000–000 Baohui Tian et al. / Procedia Manufacturing 15 (2018) 381–387
where T is the deformation temperature in °C. The reduction is defined as the decrease in the height of specimens as following: ∆�⁄�� =
�� ��� ��
,
(2)
where H0, H1 is the height of the specimen before and after compression, respectively. The global deformation in the hot compression is represented by the bulging. The bulging is evaluated as the maximal increase in the diameter of the specimen as following: ∆� =
(�� ��� )% ��
,
(3)
where D0 is the initial diameter of specimens before deformation; and D1 the maximal diameter after compression. For the local deformation two effective strains have engineering significances. One is the effective strain at the center on the cross section (c). c is meaningful either to closure of porosity or to avoidance of local melting. The other is the effective strain with a high value near the edge on the cross section (e). Together with a low local temperature e could be related to the crack initiation during hot deformation. The radial-axial cross section with the parameters Tc and Ts, D0 and D1, c and e is shown schematically in Fig. 2. The friction coefficient () between the specimen and die is defined as the shear type and varied from 0 to 0.5. The simulations are isothermal to exclude the influence of temperature changes during compression on the bulging. Most evaluations are carried out at the reduction of 0.5 at a constant strain rate of 1/s.
Fig. 1. Examples of flow stress – strain curves for A607 and modelled alloys at different temperatures and strain rate of 1/s.
3. Results and discussions The profiles of the specimens measured at different reductions are shown in Fig. 3a. The profile can be divided into four parts concerning its geometric center. The data of these four parts are put together in the first quadrant of the coordination system to simplify the comparison with the simulation. The scatter of the data indicates that the profiles are not exactly symmetric, especially at the large reduction such as H/H0 = 0.57. Fig. 3(b) shows an example of comparing the profiles between the measurements and simulations. The profile measured at room temperature has been converted to that at the deformation temperature. The measured profile is in general larger than the simulated one. This difference could be ascribed to the uncertainties in the tests, such as the friction conditions, the variations in the temperature during compression and so on. These factors are usually idealized in the simulation. The difference in the radius is less than 0.15 mm, or within 2% between the measurements and simulations.
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Fig. 2. Schematic illustrations for (a) radial-axial cross section for 2D simulations; (b) Tc, Ts and D0; (c) D1 and locations of c and e.
The simulated profile shows a minor dependence on the flow stress – strain characteristics relying on deformation temperatures, strain rates, microstructures, deformation history and so on. The profile is determined dominantly by the reduction at the approximate friction condition. Fig. 3(b) indicates undoubtedly that the influence of flow stress – strain behaviors on the bulging is negligible. It verifies clearly the previous reports about the insignificant influence of material flow stress on the barrel in hot compression [2, 3] and the lateral spread in hot rolling [5, 6].
Fig. 3. Profiles of specimens from Gleeble tests (a) and simulations with A607 and modelled alloys (b). T = 1050 °C at strain rate of 1/s for = 0.25.
Representative variations in the bulging and the effective strains with reductions are shown in Fig. 4. Both D and c, e increase nonlinearly with increasing H/H0. The variation in c is quite similar to that of D. The increase in e gets to be slow at the reduction near to 0.27, corresponding to the contact beginning between the element on the side under the surface of the specimen and the die. These changes in D and the effective strains are identical to different diameters of the specimens. No size effect is detectable at a constant height – diameter ratio in the hot compression simulation. Fig. 5 shows the influence of the friction coefficient () on the D at different temperature gradients. As the friction coefficient increases, D increases and even more at the high temperature gradient. However, D increases 5.8% at Tg = 0 °C, while merely 2.4% at Tg = 200 °C as the friction coefficient is changed from 0 to 0.5. The influence of friction on the bulging is more significant at the low temperature gradient.
Baohui Tian et al. / Procedia Manufacturing 15000–000 (2018) 381–387 Author name / Procedia Manufacturing 00 (2018)
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Fig. 4. Increases in bulging (a) and effective strains (b) with increasing reductions for D0 = 250 mm, T = 1100 °C and = 0.5.
Changes in c and e with the friction coefficient are shown in Fig. 6. c increases with increasing as well as the temperature gradient (Fig. 6(a)). The changes in e with are different concerning the temperature gradient. e changes little at Tg = 200 °C. It increases with increasing as <= 0.25 at Tg = 0 °C, and then changes little (Fig. 6(b)).
Fig. 5. Increases in D with increasing friction coefficient at different temperature gradients for H/H0 = 0.5.
Fig. 6. Changes in c (a) and e (b) with friction coefficient at different temperature gradients for H/H0 = 0.5.
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Baohui Tian et al. / Procedia Manufacturing 15 (2018) 381–387 Author name / Procedia Manufacturing 00 (2018) 000–000
The influence of the temperature gradient (Tg) on the D at different friction coefficients is shown in Fig. 7. D increases with increasing temperature gradients, but increases less at the large friction coefficient. D increases 6.0% at = 0, while merely 2.6% at = 0.5. The influence of temperature gradients on the bulging is reduced at the large friction coefficient. Changes in c and e with the temperature gradient are shown in Fig. 8. c increases with increasing Tg as well as the friction coefficient (Fig. 8(a)). The changes in e with Tg are different concerning the friction coefficient. e increases with increasing Tg at = 0, however, it decreases with Tg at = 0.5 (Fig. 8(b)). As indicated in Figs. 5 and 7, the factors affecting the bulging in hot compression can be identified as the friction coefficient and the temperature gradient. The influence of the temperature gradient on the bulging is comparable to that of the frictions. The effect of the temperature gradient on the lateral spread is caused by the difference in the flow stress between the center and the surface on the cross section of workpieces [9]. Tg is sensitive to numerous factors in industrial processing, for example, even with the same work schedule and product Tg can be varied due to fluctuations in dwell durations that cannot be exactly controlled. This is the reason why the lateral deformation in industrial practices are influenced by different deformation conditions and grades of alloys. The friction coefficient is not easy to be controlled in hot processing. As the effect of the friction can be replaced by that of the temperature gradient, an alternative to modify the lateral deformation is to change the stress ratio between the center and the surface on the cross section of workpieces by introducing different temperature gradients. Following is an example in the hot compression simulation to show how the bulging due to frictions can be avoided by introducing a predefined temperature gradient.
Fig. 7. Increases in D with increasing temperature gradient at different friction coefficients for H/H0 = 0.5.
In the conventional heating process especially the induction heating, the temperature at the surface of workpieces is higher than that in the center for a certain time, named as the negative temperature gradient in the context. A concave profile appears with the negative temperature gradient if the friction coefficient is small enough. With increasing the friction coefficient the shape of the specimen can be kept to be nearly cylindrical during compression, as shown in Fig. 9. Besides minimizing the friction coefficient, the combination between a given friction coefficient and a negative temperature gradient provides another possibility to get a cylindrical profile in hot compression. However, the effective strain on the cross section has an established distribution in contrast to a constant effective strain at = 0 and Tg = 0. The corresponding response between the global deformation, i.e., bulging, and the local deformation, i.e., c and e, can be established from the results in Figs. 4 to 8. Variations in c with the reduction, the friction coefficient and the temperature gradient correspond to those in D. Variations in e approximate those in D in case that the temperature gradient is zero (Fig. 6(b)) or the friction coefficient is zero (Fig. 8(b)), while, such a variation is diminished with introducing temperature gradients or frictions. The influence of the temperature gradient (or friction coefficient) on e is reduced or even vanished with increasing the friction coefficient (or temperature gradient).
Baohui Tian et al. / Procedia Manufacturing 15 (2018) 381–387 Author name / Procedia Manufacturing 00 (2018) 000–000
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Fig. 8. Changes in c (a) and e (b) with temperature gradient at different friction coefficients for H/H0 = 0.5.
(a)
(b)
Fig. 9. Distributions of temperature (a) and effective strain (b) on cross section of specimen for = 0.50 and H/H0 = 0.5.
4. Conclusion Regardless of the flow stress – strain characteristics of alloys, the budging of cylindrical specimens in hot compression depends on the friction coefficient and the temperature gradient. The dependence of the bulging on one of these two factors is reduced by enhancement of the other one. The correlated changes of the local deformation and the global geometry are manifested between the effective strain at the center of specimens and the bulging. Such correspondence is diminished with introducing the friction and the temperature gradient for the effective strain at the edge on the radial-axial cross section. References [1] R. Ebrahimi, A. Najafizadeh, A new method for evaluation of friction in bulk metal forming, Journal of Material Processing Technology, 135 (2004) 136–143. [2] C.S. Cetinarslan, Effect of aspect ratio on barreling contour and variation of total surface area during upsetting of cylindrical specimen, Materials & Design, 28 (2007) 1907–1913. [3] Y.P. Li, E. Onodera, A. Chiba, Evaluation of friction coefficient by simulation in bulk metal forming process, Metallurgical and Materials Transactions A, 41A (2010) 224–232. [4] P. Montmitonnet, P. Gratacos, R. Ducloux, Application of anisotropic viscoplastic behavior in 3D finite-element simulations of hot rolling, Journal of Material Processing Technology, 58 (1996) 201–211. [5] T. Sheppard, D.S. Wright, Parameters affecting lateral deformation in slabbing mills, Metals Technology, 8 (1981) 46–57. [6] J.H. Min, H.C. Kwon, Y. Lee, J.S. Woo, Y.T. Im, Analytical model for prediction of deformed shape in three-roll rolling process, Journal of Material Processing Technology, 140 (2003) 471–477. [7] L. Esteban, M.R. Elizalde, I. Ocana, Mechanical characterization and finite element modelling of lateral spread in rolling of low carbon steels, Journal of Material Processing Technology, 183 (2007) 390–398. [8] R. Riahifar, S. Serajzadeh, Three-dimensional model for hot rolling of aluminum alloys, Materials & Design, 28 (2007) 2366–2372. [9] B. Tian, S. Kleber, S. Zinner, P. Markiewicz, FE simulation of lateral deformation in hot rolling and its applications in industry, 10th International Rolling Conference, Graz, Austria, 2016.
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Procedia Manufacturing 15 (2018) 381–387 Procedia Manufacturing 00 (2017) 000–000 www.elsevier.com/locate/procedia
17th International Conference on Metal Forming, Metal Forming 2018, 16-19 September 2018, 17th International Conference on MetalToyohashi, Forming, Metal Japan Forming 2018, 16-19 September 2018, Toyohashi, Japan
Influencing factors of global and local deformation in hot
Influencing factors ofInternational global and local deformation in hot Manufacturing Engineering Society Conference 2017, MESIC 2017, 28-30 June compression 2017, Vigo (Pontevedra), Spain compression Tian*, Siegfried Kleber, Silvia Schneller, Peter Markiewicz Costing Baohui models for Siegfried capacityKleber, optimization in Industry 4.0: Trade-off Baohui Tian*, Silvia Schneller, Peter Markiewicz Voestalpine Bohler Special Steel, Mariazeller Street 25, Kapfenberg, A-8605, Austria between used capacity andStreet operational efficiency Voestalpine Bohler Special Steel, Mariazeller 25, Kapfenberg, A-8605, Austria
A. Santanaa, P. Afonsoa,*, A. Zaninb, R. Wernkeb Abstract a University of Minho, 4800-058 Guimarães, Portugal Abstract b Unochapecó, 89809-000 Chapecó, SC, Brazil Hot compression of cylindrical specimens is carried out with Gleeble tests and simulated with the finite element method. Profiles Hot compression cylindrical carried out Gleeble tests andfriction simulated with the finite element method. Profiles of the specimens of and the local specimens strains are isevaluated at with different reductions, coefficients and temperature gradients. No of the specimens and the local strains evaluated at flow different reductions, friction coefficients temperaturedepends gradients. No correlations are identified between the are profiles and the stress - strain behaviors. Bulging of and the specimens on the correlations are identified between the profiles and the flow stress strain behaviors. Bulging of the specimens depends on the Abstract friction coefficient and temperature gradient. Variations in the effective strain at the center on the cross section correlate with friction and temperature Variations strain at the are center on the cross section correlate with and the bulging.coefficient The corresponding changesgradient. of the local straininonthe theeffective edge with bulging diminished by introducing frictions bulging. Thegradients. corresponding changes of the production local strain on the edge will with bulging are diminished by introducing frictions and temperature Under the concept of "Industry 4.0", processes be pushed to be increasingly interconnected, temperature gradients. information based on a real time basis and, necessarily, much more efficient. In this context, capacity optimization © 2018 The Authors. Published by of Elsevier B.V.maximization, contributing also for organization’s profitability and value. goes beyond the traditional aim capacity © 2018 2018 The The Authors. Published Elsevier B.V. © Authors. Published by by B.V. committee of the 17th International Conference on Metal Forming. Peer-review under responsibility of Elsevier the scientific Indeed, lean management and continuous improvement approaches suggest capacity optimization Peer-review under responsibility of the scientific committee of the 17th International Conference on Metal Forming. instead of Peer-review under responsibility of the scientific committee of the 17th International Conference on Metal Forming.
maximization. The study of capacity optimization and costing models is an important research topic that deserves Keywords: Profile; Strain; Friction; Temperature gradient; Compression; Deformation; Simulation; Finite element method contributions from both the practical and theoretical perspectives. ThisSimulation; paper presents and discusses a mathematical Keywords: Profile; Strain; Friction; Temperature gradient; Compression; Deformation; Finite element method model for capacity management based on different costing models (ABC and TDABC). A generic model has been developed and it was used to analyze idle capacity and to design strategies towards the maximization of organization’s 1. Introduction value. The trade-off capacity maximization vs operational efficiency is highlighted and it is shown that capacity 1. Introduction optimization might operational inefficiency. In industrial hot hide processing workpieces with different geometries are deformed following work schedules to final © 2017 The Authors. Published byworkpieces Elsevier B.V.with different geometries are deformed following work schedules to final In industrial hot processing sizes. The work schedules should on the one hand provide an optimal reduction at each pass to satisfy the efficiency Peer-review under schedules responsibility of the scientific of the Manufacturing Engineering Society International Conference sizes. The work should onecommittee hand provide optimal at each pass to satisfy the efficiency of productions. On the other hand,on thethe product should obtainanthe desiredreduction microstructures and mechanical properties. 2017. of productions. On the other hand, the product should obtain the desired microstructures and mechanical properties. Keywords: Cost Models; ABC; TDABC; Capacity Management; Idle Capacity; Operational Efficiency
1. Introduction
* Corresponding author. Tel.: +43-3862-203-7918; fax: +43-3862-203-7585. * E-mail Corresponding Tel.: +43-3862-203-7918; fax: +43-3862-203-7585. address:author. [email protected] The cost of idle capacity is a fundamental information for companies and their management of extreme importance E-mail address: [email protected]
in modern©production systems. In general, it isB.V. defined as unused capacity or production potential and can be measured 2351-9789 2018 The Authors. Published by Elsevier 2351-9789 2018 Authors. Published Elsevier B.V.hours of the Peer-review underThe responsibility of theby scientific committee 17th International on Metal Forming. in several©ways: tons of production, available manufacturing, etc.Conference The management of the idle capacity Peer-review under responsibility thefax: scientific committee * Paulo Afonso. Tel.: +351 253 510of 761; +351 253 604 741 of the 17th International Conference on Metal Forming. E-mail address: [email protected]
2351-9789 © 2017 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the scientific committee of the Manufacturing Engineering Society International Conference 2017. 2351-9789 © 2018 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the scientific committee of the 17th International Conference on Metal Forming. 10.1016/j.promfg.2018.07.233
Baohui Tian et al. / Procedia Manufacturing 15 (2018) 381–387 Author name / Procedia Manufacturing 00 (2018) 000–000
382 2
Lateral deformation of workpieces determines not only the profiles and eventually the reductions in following passes, but also filling of calibers. It is an important factor affecting the efficiency of hot processing such as rolling, forging etc. Corresponding to the global deformation, the parameters of local deformation such as the effective strain or stress are served as input in material models for recrystallization, damages and so on. Different lateral deformation means various local strains or stresses. Being the first prerequisite to use the material models, the lateral deformation as well as the geometry of workpieces should be determined with the minimal error. The lateral deformation in the conventional hot compression of a cylindrical specimen shows a barrel shaped profile, i.e., the bulging, due to the friction between workpieces and die. The bulging is increased with increasing friction coefficients, and can be evaluated with the diameter of cylinder [1, 2]. Previous investigations of hot compression and hot rolling showed a rather weak dependence of the lateral spread on the flow stress – strain behaviors of alloys [2-5]. In contrast to the results from the experiments [5-8], the lateral deformation in the industrial practices of hot rolling and forging is usually relevant to deformation temperatures and grades of alloys. An apparent difference in the hot deformation between the laboratory experiments and the industrial production lies in the size of workpieces. Normally, due to the small size of specimens temperature gradients are usually not considered in the hot deformation in laboratories. In contrast, inhomogeneous temperatures happen in most cases of actual manufactures. Quantitative investigations on the effect of temperature gradients on the lateral deformation are necessary in order to: 1) clarify the discrepancy concerning the geometry of workpieces between the laboratory experiments and industrial experiences; 2) define the applicability of laboratory results in industrial processes; 3) identify the key influencing factors of geometrical changes of workpieces in production controls and 4) establish the corresponding responses between the global and local deformation. In the present work, hot compression of cylindrical specimens is carried out and also simulated with the finite element (FE) method under various flow stress - strain behaviors, friction coefficients and temperature gradients, with the aim to identify the key factors influencing the bulging and the local deformation. 2. Method 2.1. Hot compression tests Hot compression tests were carried out employing Gleeble 1500™ simulator for the stainless steel A607, i.e., X5Cr18Ni10 from voestalpine Bohler Special Steel at 750 °C, 1050 °C and a strain rate of 0.1/s, 1/s. The specimens have a diameter of 10 mm and a height of 12 mm. The test at each deformation condition has been repeated twice. The profiles of the selected specimens have been digitally photographed and measured after deformation. The difference in the profiles with respect of the deformation temperature (T) and the strain rate is not significant so long the reduction is the same. 2.2. FE Simulations The compression tests were simulated with the finite element software DEFORM 2D™, version 10.2. The model used is a quarter one with the axial symmetry. In order to clarify the influence of the temperature gradient (Tg) on bulging, different diameters of specimens (125, 250 and 500 mm) with a fixed height – diameter ratio of 1.2 have been used in the simulation. These specimens are either set to have a constant deformation temperature, or air cooled from 1200 °C before compression to introduce the difference in temperatures between the center and the surface. This difference in the temperatures between the center (Tc) and the surface (Ts) on the radial-axial cross section of specimens is defined as the temperature gradient Tg, i.e., Tg = Tc - Ts. Ts is the average temperature at the surface. The flow stress – strain curves of the alloy A607 show a typical strain hardening and recrystallization behaviors within the ranges of temperatures and strain rates in the simulation. An example is as shown in Fig. 1. A modelled alloy is used to simplify the relationship between the deformation temperature and the flow stress. The flow stress () of the modelled alloy is assigned to be dependent only on the temperature (shown also in Fig. 1): � = 700 − 0.5�,
(1)
3 383
Author name / Procedia Manufacturing 00 (2018) 000–000 Baohui Tian et al. / Procedia Manufacturing 15 (2018) 381–387
where T is the deformation temperature in °C. The reduction is defined as the decrease in the height of specimens as following: ∆�⁄�� =
�� ��� ��
,
(2)
where H0, H1 is the height of the specimen before and after compression, respectively. The global deformation in the hot compression is represented by the bulging. The bulging is evaluated as the maximal increase in the diameter of the specimen as following: ∆� =
(�� ��� )% ��
,
(3)
where D0 is the initial diameter of specimens before deformation; and D1 the maximal diameter after compression. For the local deformation two effective strains have engineering significances. One is the effective strain at the center on the cross section (c). c is meaningful either to closure of porosity or to avoidance of local melting. The other is the effective strain with a high value near the edge on the cross section (e). Together with a low local temperature e could be related to the crack initiation during hot deformation. The radial-axial cross section with the parameters Tc and Ts, D0 and D1, c and e is shown schematically in Fig. 2. The friction coefficient () between the specimen and die is defined as the shear type and varied from 0 to 0.5. The simulations are isothermal to exclude the influence of temperature changes during compression on the bulging. Most evaluations are carried out at the reduction of 0.5 at a constant strain rate of 1/s.
Fig. 1. Examples of flow stress – strain curves for A607 and modelled alloys at different temperatures and strain rate of 1/s.
3. Results and discussions The profiles of the specimens measured at different reductions are shown in Fig. 3a. The profile can be divided into four parts concerning its geometric center. The data of these four parts are put together in the first quadrant of the coordination system to simplify the comparison with the simulation. The scatter of the data indicates that the profiles are not exactly symmetric, especially at the large reduction such as H/H0 = 0.57. Fig. 3(b) shows an example of comparing the profiles between the measurements and simulations. The profile measured at room temperature has been converted to that at the deformation temperature. The measured profile is in general larger than the simulated one. This difference could be ascribed to the uncertainties in the tests, such as the friction conditions, the variations in the temperature during compression and so on. These factors are usually idealized in the simulation. The difference in the radius is less than 0.15 mm, or within 2% between the measurements and simulations.
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Author name / Procedia Manufacturing 00 (2018) 000–000 Baohui Tian et al. / Procedia Manufacturing 15 (2018) 381–387
Fig. 2. Schematic illustrations for (a) radial-axial cross section for 2D simulations; (b) Tc, Ts and D0; (c) D1 and locations of c and e.
The simulated profile shows a minor dependence on the flow stress – strain characteristics relying on deformation temperatures, strain rates, microstructures, deformation history and so on. The profile is determined dominantly by the reduction at the approximate friction condition. Fig. 3(b) indicates undoubtedly that the influence of flow stress – strain behaviors on the bulging is negligible. It verifies clearly the previous reports about the insignificant influence of material flow stress on the barrel in hot compression [2, 3] and the lateral spread in hot rolling [5, 6].
Fig. 3. Profiles of specimens from Gleeble tests (a) and simulations with A607 and modelled alloys (b). T = 1050 °C at strain rate of 1/s for = 0.25.
Representative variations in the bulging and the effective strains with reductions are shown in Fig. 4. Both D and c, e increase nonlinearly with increasing H/H0. The variation in c is quite similar to that of D. The increase in e gets to be slow at the reduction near to 0.27, corresponding to the contact beginning between the element on the side under the surface of the specimen and the die. These changes in D and the effective strains are identical to different diameters of the specimens. No size effect is detectable at a constant height – diameter ratio in the hot compression simulation. Fig. 5 shows the influence of the friction coefficient () on the D at different temperature gradients. As the friction coefficient increases, D increases and even more at the high temperature gradient. However, D increases 5.8% at Tg = 0 °C, while merely 2.4% at Tg = 200 °C as the friction coefficient is changed from 0 to 0.5. The influence of friction on the bulging is more significant at the low temperature gradient.
Baohui Tian et al. / Procedia Manufacturing 15000–000 (2018) 381–387 Author name / Procedia Manufacturing 00 (2018)
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Fig. 4. Increases in bulging (a) and effective strains (b) with increasing reductions for D0 = 250 mm, T = 1100 °C and = 0.5.
Changes in c and e with the friction coefficient are shown in Fig. 6. c increases with increasing as well as the temperature gradient (Fig. 6(a)). The changes in e with are different concerning the temperature gradient. e changes little at Tg = 200 °C. It increases with increasing as <= 0.25 at Tg = 0 °C, and then changes little (Fig. 6(b)).
Fig. 5. Increases in D with increasing friction coefficient at different temperature gradients for H/H0 = 0.5.
Fig. 6. Changes in c (a) and e (b) with friction coefficient at different temperature gradients for H/H0 = 0.5.
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Baohui Tian et al. / Procedia Manufacturing 15 (2018) 381–387 Author name / Procedia Manufacturing 00 (2018) 000–000
The influence of the temperature gradient (Tg) on the D at different friction coefficients is shown in Fig. 7. D increases with increasing temperature gradients, but increases less at the large friction coefficient. D increases 6.0% at = 0, while merely 2.6% at = 0.5. The influence of temperature gradients on the bulging is reduced at the large friction coefficient. Changes in c and e with the temperature gradient are shown in Fig. 8. c increases with increasing Tg as well as the friction coefficient (Fig. 8(a)). The changes in e with Tg are different concerning the friction coefficient. e increases with increasing Tg at = 0, however, it decreases with Tg at = 0.5 (Fig. 8(b)). As indicated in Figs. 5 and 7, the factors affecting the bulging in hot compression can be identified as the friction coefficient and the temperature gradient. The influence of the temperature gradient on the bulging is comparable to that of the frictions. The effect of the temperature gradient on the lateral spread is caused by the difference in the flow stress between the center and the surface on the cross section of workpieces [9]. Tg is sensitive to numerous factors in industrial processing, for example, even with the same work schedule and product Tg can be varied due to fluctuations in dwell durations that cannot be exactly controlled. This is the reason why the lateral deformation in industrial practices are influenced by different deformation conditions and grades of alloys. The friction coefficient is not easy to be controlled in hot processing. As the effect of the friction can be replaced by that of the temperature gradient, an alternative to modify the lateral deformation is to change the stress ratio between the center and the surface on the cross section of workpieces by introducing different temperature gradients. Following is an example in the hot compression simulation to show how the bulging due to frictions can be avoided by introducing a predefined temperature gradient.
Fig. 7. Increases in D with increasing temperature gradient at different friction coefficients for H/H0 = 0.5.
In the conventional heating process especially the induction heating, the temperature at the surface of workpieces is higher than that in the center for a certain time, named as the negative temperature gradient in the context. A concave profile appears with the negative temperature gradient if the friction coefficient is small enough. With increasing the friction coefficient the shape of the specimen can be kept to be nearly cylindrical during compression, as shown in Fig. 9. Besides minimizing the friction coefficient, the combination between a given friction coefficient and a negative temperature gradient provides another possibility to get a cylindrical profile in hot compression. However, the effective strain on the cross section has an established distribution in contrast to a constant effective strain at = 0 and Tg = 0. The corresponding response between the global deformation, i.e., bulging, and the local deformation, i.e., c and e, can be established from the results in Figs. 4 to 8. Variations in c with the reduction, the friction coefficient and the temperature gradient correspond to those in D. Variations in e approximate those in D in case that the temperature gradient is zero (Fig. 6(b)) or the friction coefficient is zero (Fig. 8(b)), while, such a variation is diminished with introducing temperature gradients or frictions. The influence of the temperature gradient (or friction coefficient) on e is reduced or even vanished with increasing the friction coefficient (or temperature gradient).
Baohui Tian et al. / Procedia Manufacturing 15 (2018) 381–387 Author name / Procedia Manufacturing 00 (2018) 000–000
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Fig. 8. Changes in c (a) and e (b) with temperature gradient at different friction coefficients for H/H0 = 0.5.
(a)
(b)
Fig. 9. Distributions of temperature (a) and effective strain (b) on cross section of specimen for = 0.50 and H/H0 = 0.5.
4. Conclusion Regardless of the flow stress – strain characteristics of alloys, the budging of cylindrical specimens in hot compression depends on the friction coefficient and the temperature gradient. The dependence of the bulging on one of these two factors is reduced by enhancement of the other one. The correlated changes of the local deformation and the global geometry are manifested between the effective strain at the center of specimens and the bulging. Such correspondence is diminished with introducing the friction and the temperature gradient for the effective strain at the edge on the radial-axial cross section. References [1] R. Ebrahimi, A. Najafizadeh, A new method for evaluation of friction in bulk metal forming, Journal of Material Processing Technology, 135 (2004) 136–143. [2] C.S. Cetinarslan, Effect of aspect ratio on barreling contour and variation of total surface area during upsetting of cylindrical specimen, Materials & Design, 28 (2007) 1907–1913. [3] Y.P. Li, E. Onodera, A. Chiba, Evaluation of friction coefficient by simulation in bulk metal forming process, Metallurgical and Materials Transactions A, 41A (2010) 224–232. [4] P. Montmitonnet, P. Gratacos, R. Ducloux, Application of anisotropic viscoplastic behavior in 3D finite-element simulations of hot rolling, Journal of Material Processing Technology, 58 (1996) 201–211. [5] T. Sheppard, D.S. Wright, Parameters affecting lateral deformation in slabbing mills, Metals Technology, 8 (1981) 46–57. [6] J.H. Min, H.C. Kwon, Y. Lee, J.S. Woo, Y.T. Im, Analytical model for prediction of deformed shape in three-roll rolling process, Journal of Material Processing Technology, 140 (2003) 471–477. [7] L. Esteban, M.R. Elizalde, I. Ocana, Mechanical characterization and finite element modelling of lateral spread in rolling of low carbon steels, Journal of Material Processing Technology, 183 (2007) 390–398. [8] R. Riahifar, S. Serajzadeh, Three-dimensional model for hot rolling of aluminum alloys, Materials & Design, 28 (2007) 2366–2372. [9] B. Tian, S. Kleber, S. Zinner, P. Markiewicz, FE simulation of lateral deformation in hot rolling and its applications in industry, 10th International Rolling Conference, Graz, Austria, 2016.