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An approach to process limitations in hydroforming of X-joints as based on formability evaluation
Journal of Materials Processing Technology 177 (2006) 663–667
An approach to process limitations in hydroforming of X-joints as based on formability evaluation A. Kocanda ∗ , H. Sadlowska Institute of Materials Processing, Warsaw University of Technology, 85 Narbutta Street, 02-524 Warsaw, Poland
Abstract Experimental results of copper X-joint hydroforming have been compared with the results of FEA simulations. An influence of loading history and properties of deformed tubular material on process feasibility has been presented. The method of forming limit curve (FLC) prediction was utilised in order to determine the onset of strain localization and bursting failure. Prediction of failure based on the FLC commonly used for sheet metal forming has given a considerable underestimation of hydroforming limit for X-joints. Hence, the modified FLCm has been suggested that could be used in hydroforming process planning. © 2006 Elsevier B.V. All rights reserved. Keywords: Hydroforming; X-joint; Fracture; Forming limit; FEA simulation
1. Introduction
2. Hydroforming of X-joints
There has been an accelerating growth in production of hydroformed parts in recent years. Regarding process features and various blanks, hydroforming (HF) could be classified into sheet HF and tube HF [1,2]. Extensive research and development works have led to the economic mass production of high-quality lightweight components, especially from tubular materials [2]. Advantages of the HF include simplification of complex assemblies, weight savings, elimination of superfluous joints and parts, and so on. About 90% of the applications have been automotive parts, e.g. exhaust system parts, front and rear axles, engine cradles or structural body components. Another big number of hydroformed components – joints and fittings – could be found in the area of sanitary and piping constructions. Some of them have been hydroformed for quite a long time but their forming still causes problems. Wide spreading of the HF has been limited by a kind of secrecy on knowledge bases and the lack of specific material specifications for incoming shapes and tubes. Hence, new component applications cause many problems that usually must be solved individually. In this paper, the HF process feasibility of X-joint is discussed. Experimental results of X-joint hydroforming have been compared with the results of extensive FEA simulations in order to find a method of failure prediction.
Experimental tests on HF of X-joints have been performed in order to find the influence of various loading paths on failure modes. Tubular blanks were used to make the X-joints. The outer diameter of initial tubes made of copper was 22 mm and the wall thickness was 1 mm. A straight tube blank of 120 mm in the length was placed and restrained in the die that determined the final shape of the component. The tube was sealed at the ends by the axial punches, Fig. 1. The velocity of the left and right axial feeds was kept constant during axial punch displacement s. The axial feeding force P was a result of deformation resistance of a tube blank. During the HF stage, the internal pressure p was changing according to specified internal pressure versus punch displacement curve. Material properties were determined by tensile tests of flattened sub-size samples taken from tubes in the longitudinal direction. By this method, the amount of effects induced by the tube making processes was taken into account. The work hardening law was, σ = 428ε0.063 (MPa). It should be noticed that the work hardening exponent was very low. The combinations of axial feeding displacement and various internal pressure curves gave different loading paths. Higher increase of pressure in the initial stage of forming resulted in premature bursting of the bulged branch whereas lower initial pressure did not protect the tube against wrinkling. Some examples of the loading paths are shown in Fig. 2. As a result of excessive internal pressure during final stage of branch forming, the bursting failure
∗
Corresponding author. Tel.: +48 22 8499437; fax: +48 22 8499797. E-mail address: [email protected] (A. Kocanda).
0924-0136/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2006.04.069
664
A. Kocanda, H. Sadlowska / Journal of Materials Processing Technology 177 (2006) 663–667
and sidewall fractures. Buckling and wrinkling could be overcome by an appropriate combination of axial feeding force and inner pressure or even by deformation in the final calibration stage. However, necking, followed by bursting and sidewall fractures are irrecoverable, which means that some criteria should be used for avoiding these failures. In this paper a criterion based on the forming limit curve (FLC) is employed. 3.2. Prediction of forming limit curve
Fig. 1. Outline of the final stage of X-joint hydroforming.
Keeler and Backofen introduced forming limit curve for studying failures in biaxially stretched sheets [3]. The FLC indicates combinations of the major-minor strains at the onset of critical necking leading to failure for various strain paths. Keeler found that material properties had great influence on the strain distribution in biaxial stretching of sheet metal [4]. For example, when the material work-hardening exponent n is high, the strain distribution will be relatively homogeneous. On the other hand materials having lower n values develop sharp strain gradients and the strain concentration in a very small region leads to premature failure. The FLCs have been used mainly in the area of sheet metal forming in order to check the forming severity for each point on the sheet. The intensive development of computer simulation has found the FLC being the primary method to determine when a sheet metal is going to fail. It has become possible to track part severity throughout the all stages of the part forming processes. Assuming that hydroforming is a specific case of sheet metal forming with bursting failure, there have been various applications of the FLCs in the analysis of hydroforming processes as well [5]. Forming limits are influenced by several factors. However, the minimum value of the predicted FLC, the major strain, is usually characterized by n value [6]. As all curves have approximately the same shape for single alloys that do not show any phase transformation during the deformation process, then it is possible to predict the required conventional FLC. Some practical method of finding the FLC, Fig. 3, is based on plastic instablity criteria of Hill [7] and Swift [8] with taking into account n-value and strain ratio ρ = εminor /εmajor . Local necking (Hill) takes place for ρ < 0 and diffuse necking (Swift) for ρ > 0.
Fig. 2. Influence of loading path on X-joint HF results; (a) bursting of branch at the final stage of HF, (b) X-joint without failure.
occurred, Fig. 2(a). On the other hand, the X-joint without any failure could be obtained by finding “optimal” process parameters, Fig. 2(b). 3. Application of forming limit diagram 3.1. Process limitations Process limitations in HF of X-joints are related mainly with forming limits such as buckling, wrinkling, necking, bursting
Fig. 3. Predicted (broken line) and experimental (solid gray line) FLCs.
A. Kocanda, H. Sadlowska / Journal of Materials Processing Technology 177 (2006) 663–667
This method is included in the software MSC Marc & Mentat [9] and has been applied by the present authors to analyze X-joint hydroforming. Critical strains shown on the FLC are not only the limits of useful deformation but are also the points below which safety margins are calculated. The experimental forming limit curve is characterized by FLC0 , Fig. 3, which is calculated as a function of n value and thickness [6,9]. This value increases with the increase of strain hardening exponent n. The important problem with the experimentally or analytically determined FLC is that it is valid only for linear loading path or for its own unique loading paths. In complex stampings or hydroformed parts, the strain paths vary throughout the multi-stage forming operations. In such cases, the ratio of strain increaments is changing as well as directions of the increaments. Then some other method is required to have good assessment of marginal safety of forming process. One definition of marginal safety zone is a band below the FLC with a bandwith of ten percent of strain [6,9]. This safety zone should accommodate all irregularities of the FLC related with the non-linear loading path. However, what should be the bandwith of safety zone for X-joint hydroforming to utilize the FLC and to determine the maximum amount of strain a tube can withstand before failure? An attempt to answer this question will be presented in the following sections.
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constant during hydroforming process as it was in the experiment. The model of material was determined experimentally (see Chapter 2). The tube was modelled by 3D Solid elements. An elastic Coulomb friction law defined the contact between tube and tools and the coefficient of friction was 0.1. This value was successfully applied in previous work for T-joints [10] and tubes [11]. Also, the results of numerical modeling were verified by comparing the geometry of calculated and experimentally obtained X-joints, Figs. 4 and 5, for the same process parameters.
4. Numerical simulation of HF process FEA simulations of HF of X-joints were conducted with MSC Marc software. The die and punches were modeled as rigid bodies and were not meshed. The velocity of punch displacement was kept
Fig. 4. Comparison of X-joint shape with wrinkles; (a) experiment, (b) FEA.
Fig. 5. Comparison of thickness distribution in the transverse (a) and longitudinal (b) cross sections of X-joint.
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A. Kocanda, H. Sadlowska / Journal of Materials Processing Technology 177 (2006) 663–667
Fig. 6. Deformation paths (indicated by lines with circles) for nodes at the pole of branch. The cases (a) and (b) obtained for different internal pressure curves shown in Fig. 2.
Fig. 4 shows the X-joint with wrinkles that were formed because of too small inner pressure whereas Fig. 5 shows thickness distribution for final geometry of X-joint without any failure. Due to the good agreement of the results, it was assumed that the numerical model was quite accurate for the purpose of hydroforming process analysis. 5. Proposal of modified forming limit diagram The method of forming limit curve prediction was involved in order to determine the onset of strain localization and bursting failure. The results of calculations for X-joint hydroforming were compared with the results of experiments with different loading paths. Predicted forming limit curves, the same as in Fig. 3, are shown in Fig. 6 by grey lines. Minimum major strain is indicated by FLC0 value. As for the case of X-joints with bursting failures, FLC0 curves were shifted up to the modified position indicated by the minimum value of major strain FLCm and shown as black curves. The modified position of the FLCm represents critical combinations of strains found by the experimental tests. Fig. 6(a) shows the deformation path up to the occurrence of bursting failure whereas the deformation path in Fig. 6(b) ends considerably below the modified FLCm . In this second case no failure was noticed in the experiment (see Fig. 2(b)). The comparison of experimental and numerical results shows that prediction of failure based on the FLC0 commonly used for sheet metal forming gives very conservative evaluation of hydroforming limit for X-joints. It means that the safety margin is much higher than usually assumed for sheet metal forming. Hence the modified FLCm shows more accurate reference limits that could be used in process designing procedure. It has already been successfully applied in finding
the best process parameters for making X-joints without failures. 6. Conclusions (1) Experimental results of copper X-joint hydroforming have been compared to the results of FEA simulations. The numerical model proved to be a very useful tool to analyse variations in the overall geometry of hydroformed X-joints. (2) An influence of loading history and properties of deformed tubular material on process feasibility has been discussed. The method of forming limit curve (FLC) prediction was involved in order to determine the onset of strain localization and bursting failure. Prediction of failure based on the FLC commonly used for sheet metal forming has given a considerable underestimation of hydroforming limit for Xjoints. (3) A modified forming limit curve FLCm has been suggested that could be used in more accurate hydroforming process planning. References [1] L.H. Lang, Z.R. Wang, D.C. Kang, S.J. Yuan, S.H. Zhang, J. Danckert, K.B. Nielsen, Hydroforming highlights: sheet hydroforming and tube hydroforming, J. Mater. Process. Technol. 151 (2004) 165–177. [2] Ch. Hartl, Research and advances in fundamentals and industrial applications of hydroforming, J. Mater. Process. Technol. 167 (2005) 383– 392. [3] S.P. Keeler, W.A. Backofen, Plastic instability and fracture in sheets stretched over rigid punches, Trans. ASM 56 (1963) 25–48. [4] S.P. Keeler, Determination of forming limits in automotive stampings, Society of Automitive Engineers, Technical paper No. 650535, 1965.
A. Kocanda, H. Sadlowska / Journal of Materials Processing Technology 177 (2006) 663–667 [5] H. Sadlowska, A. Kocanda, Discussion of failure criteria used in finite element analysis of hydroforming, in: Proceedings International Conference on Net-shape sheet metal forming Poznan, 2005, pp. 195–207. [6] S.P. Keeler, Enhanced forming limit diagram—project team technology report, Auto/Steel Partnership, Southfield, MI 2002. Available at http://www.a-sp.org/.
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[7] R. Hill, On discontinuous plastic states, with special reference to localized necking in thin sheets, J. Mech. Phys. Solids 1 (1952) 19–30. [8] H.W. Swift, Plastic instability under plane stress, J. Mech. Phys. Solids 1 (1952) 1–18. [9] MSC Marc & Mentat 2004 Theory Manual, 2004.
An approach to process limitations in hydroforming of X-joints as based on formability evaluation A. Kocanda ∗ , H. Sadlowska Institute of Materials Processing, Warsaw University of Technology, 85 Narbutta Street, 02-524 Warsaw, Poland
Abstract Experimental results of copper X-joint hydroforming have been compared with the results of FEA simulations. An influence of loading history and properties of deformed tubular material on process feasibility has been presented. The method of forming limit curve (FLC) prediction was utilised in order to determine the onset of strain localization and bursting failure. Prediction of failure based on the FLC commonly used for sheet metal forming has given a considerable underestimation of hydroforming limit for X-joints. Hence, the modified FLCm has been suggested that could be used in hydroforming process planning. © 2006 Elsevier B.V. All rights reserved. Keywords: Hydroforming; X-joint; Fracture; Forming limit; FEA simulation
1. Introduction
2. Hydroforming of X-joints
There has been an accelerating growth in production of hydroformed parts in recent years. Regarding process features and various blanks, hydroforming (HF) could be classified into sheet HF and tube HF [1,2]. Extensive research and development works have led to the economic mass production of high-quality lightweight components, especially from tubular materials [2]. Advantages of the HF include simplification of complex assemblies, weight savings, elimination of superfluous joints and parts, and so on. About 90% of the applications have been automotive parts, e.g. exhaust system parts, front and rear axles, engine cradles or structural body components. Another big number of hydroformed components – joints and fittings – could be found in the area of sanitary and piping constructions. Some of them have been hydroformed for quite a long time but their forming still causes problems. Wide spreading of the HF has been limited by a kind of secrecy on knowledge bases and the lack of specific material specifications for incoming shapes and tubes. Hence, new component applications cause many problems that usually must be solved individually. In this paper, the HF process feasibility of X-joint is discussed. Experimental results of X-joint hydroforming have been compared with the results of extensive FEA simulations in order to find a method of failure prediction.
Experimental tests on HF of X-joints have been performed in order to find the influence of various loading paths on failure modes. Tubular blanks were used to make the X-joints. The outer diameter of initial tubes made of copper was 22 mm and the wall thickness was 1 mm. A straight tube blank of 120 mm in the length was placed and restrained in the die that determined the final shape of the component. The tube was sealed at the ends by the axial punches, Fig. 1. The velocity of the left and right axial feeds was kept constant during axial punch displacement s. The axial feeding force P was a result of deformation resistance of a tube blank. During the HF stage, the internal pressure p was changing according to specified internal pressure versus punch displacement curve. Material properties were determined by tensile tests of flattened sub-size samples taken from tubes in the longitudinal direction. By this method, the amount of effects induced by the tube making processes was taken into account. The work hardening law was, σ = 428ε0.063 (MPa). It should be noticed that the work hardening exponent was very low. The combinations of axial feeding displacement and various internal pressure curves gave different loading paths. Higher increase of pressure in the initial stage of forming resulted in premature bursting of the bulged branch whereas lower initial pressure did not protect the tube against wrinkling. Some examples of the loading paths are shown in Fig. 2. As a result of excessive internal pressure during final stage of branch forming, the bursting failure
∗
Corresponding author. Tel.: +48 22 8499437; fax: +48 22 8499797. E-mail address: [email protected] (A. Kocanda).
0924-0136/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2006.04.069
664
A. Kocanda, H. Sadlowska / Journal of Materials Processing Technology 177 (2006) 663–667
and sidewall fractures. Buckling and wrinkling could be overcome by an appropriate combination of axial feeding force and inner pressure or even by deformation in the final calibration stage. However, necking, followed by bursting and sidewall fractures are irrecoverable, which means that some criteria should be used for avoiding these failures. In this paper a criterion based on the forming limit curve (FLC) is employed. 3.2. Prediction of forming limit curve
Fig. 1. Outline of the final stage of X-joint hydroforming.
Keeler and Backofen introduced forming limit curve for studying failures in biaxially stretched sheets [3]. The FLC indicates combinations of the major-minor strains at the onset of critical necking leading to failure for various strain paths. Keeler found that material properties had great influence on the strain distribution in biaxial stretching of sheet metal [4]. For example, when the material work-hardening exponent n is high, the strain distribution will be relatively homogeneous. On the other hand materials having lower n values develop sharp strain gradients and the strain concentration in a very small region leads to premature failure. The FLCs have been used mainly in the area of sheet metal forming in order to check the forming severity for each point on the sheet. The intensive development of computer simulation has found the FLC being the primary method to determine when a sheet metal is going to fail. It has become possible to track part severity throughout the all stages of the part forming processes. Assuming that hydroforming is a specific case of sheet metal forming with bursting failure, there have been various applications of the FLCs in the analysis of hydroforming processes as well [5]. Forming limits are influenced by several factors. However, the minimum value of the predicted FLC, the major strain, is usually characterized by n value [6]. As all curves have approximately the same shape for single alloys that do not show any phase transformation during the deformation process, then it is possible to predict the required conventional FLC. Some practical method of finding the FLC, Fig. 3, is based on plastic instablity criteria of Hill [7] and Swift [8] with taking into account n-value and strain ratio ρ = εminor /εmajor . Local necking (Hill) takes place for ρ < 0 and diffuse necking (Swift) for ρ > 0.
Fig. 2. Influence of loading path on X-joint HF results; (a) bursting of branch at the final stage of HF, (b) X-joint without failure.
occurred, Fig. 2(a). On the other hand, the X-joint without any failure could be obtained by finding “optimal” process parameters, Fig. 2(b). 3. Application of forming limit diagram 3.1. Process limitations Process limitations in HF of X-joints are related mainly with forming limits such as buckling, wrinkling, necking, bursting
Fig. 3. Predicted (broken line) and experimental (solid gray line) FLCs.
A. Kocanda, H. Sadlowska / Journal of Materials Processing Technology 177 (2006) 663–667
This method is included in the software MSC Marc & Mentat [9] and has been applied by the present authors to analyze X-joint hydroforming. Critical strains shown on the FLC are not only the limits of useful deformation but are also the points below which safety margins are calculated. The experimental forming limit curve is characterized by FLC0 , Fig. 3, which is calculated as a function of n value and thickness [6,9]. This value increases with the increase of strain hardening exponent n. The important problem with the experimentally or analytically determined FLC is that it is valid only for linear loading path or for its own unique loading paths. In complex stampings or hydroformed parts, the strain paths vary throughout the multi-stage forming operations. In such cases, the ratio of strain increaments is changing as well as directions of the increaments. Then some other method is required to have good assessment of marginal safety of forming process. One definition of marginal safety zone is a band below the FLC with a bandwith of ten percent of strain [6,9]. This safety zone should accommodate all irregularities of the FLC related with the non-linear loading path. However, what should be the bandwith of safety zone for X-joint hydroforming to utilize the FLC and to determine the maximum amount of strain a tube can withstand before failure? An attempt to answer this question will be presented in the following sections.
665
constant during hydroforming process as it was in the experiment. The model of material was determined experimentally (see Chapter 2). The tube was modelled by 3D Solid elements. An elastic Coulomb friction law defined the contact between tube and tools and the coefficient of friction was 0.1. This value was successfully applied in previous work for T-joints [10] and tubes [11]. Also, the results of numerical modeling were verified by comparing the geometry of calculated and experimentally obtained X-joints, Figs. 4 and 5, for the same process parameters.
4. Numerical simulation of HF process FEA simulations of HF of X-joints were conducted with MSC Marc software. The die and punches were modeled as rigid bodies and were not meshed. The velocity of punch displacement was kept
Fig. 4. Comparison of X-joint shape with wrinkles; (a) experiment, (b) FEA.
Fig. 5. Comparison of thickness distribution in the transverse (a) and longitudinal (b) cross sections of X-joint.
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A. Kocanda, H. Sadlowska / Journal of Materials Processing Technology 177 (2006) 663–667
Fig. 6. Deformation paths (indicated by lines with circles) for nodes at the pole of branch. The cases (a) and (b) obtained for different internal pressure curves shown in Fig. 2.
Fig. 4 shows the X-joint with wrinkles that were formed because of too small inner pressure whereas Fig. 5 shows thickness distribution for final geometry of X-joint without any failure. Due to the good agreement of the results, it was assumed that the numerical model was quite accurate for the purpose of hydroforming process analysis. 5. Proposal of modified forming limit diagram The method of forming limit curve prediction was involved in order to determine the onset of strain localization and bursting failure. The results of calculations for X-joint hydroforming were compared with the results of experiments with different loading paths. Predicted forming limit curves, the same as in Fig. 3, are shown in Fig. 6 by grey lines. Minimum major strain is indicated by FLC0 value. As for the case of X-joints with bursting failures, FLC0 curves were shifted up to the modified position indicated by the minimum value of major strain FLCm and shown as black curves. The modified position of the FLCm represents critical combinations of strains found by the experimental tests. Fig. 6(a) shows the deformation path up to the occurrence of bursting failure whereas the deformation path in Fig. 6(b) ends considerably below the modified FLCm . In this second case no failure was noticed in the experiment (see Fig. 2(b)). The comparison of experimental and numerical results shows that prediction of failure based on the FLC0 commonly used for sheet metal forming gives very conservative evaluation of hydroforming limit for X-joints. It means that the safety margin is much higher than usually assumed for sheet metal forming. Hence the modified FLCm shows more accurate reference limits that could be used in process designing procedure. It has already been successfully applied in finding
the best process parameters for making X-joints without failures. 6. Conclusions (1) Experimental results of copper X-joint hydroforming have been compared to the results of FEA simulations. The numerical model proved to be a very useful tool to analyse variations in the overall geometry of hydroformed X-joints. (2) An influence of loading history and properties of deformed tubular material on process feasibility has been discussed. The method of forming limit curve (FLC) prediction was involved in order to determine the onset of strain localization and bursting failure. Prediction of failure based on the FLC commonly used for sheet metal forming has given a considerable underestimation of hydroforming limit for Xjoints. (3) A modified forming limit curve FLCm has been suggested that could be used in more accurate hydroforming process planning. References [1] L.H. Lang, Z.R. Wang, D.C. Kang, S.J. Yuan, S.H. Zhang, J. Danckert, K.B. Nielsen, Hydroforming highlights: sheet hydroforming and tube hydroforming, J. Mater. Process. Technol. 151 (2004) 165–177. [2] Ch. Hartl, Research and advances in fundamentals and industrial applications of hydroforming, J. Mater. Process. Technol. 167 (2005) 383– 392. [3] S.P. Keeler, W.A. Backofen, Plastic instability and fracture in sheets stretched over rigid punches, Trans. ASM 56 (1963) 25–48. [4] S.P. Keeler, Determination of forming limits in automotive stampings, Society of Automitive Engineers, Technical paper No. 650535, 1965.
A. Kocanda, H. Sadlowska / Journal of Materials Processing Technology 177 (2006) 663–667 [5] H. Sadlowska, A. Kocanda, Discussion of failure criteria used in finite element analysis of hydroforming, in: Proceedings International Conference on Net-shape sheet metal forming Poznan, 2005, pp. 195–207. [6] S.P. Keeler, Enhanced forming limit diagram—project team technology report, Auto/Steel Partnership, Southfield, MI 2002. Available at http://www.a-sp.org/.
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[7] R. Hill, On discontinuous plastic states, with special reference to localized necking in thin sheets, J. Mech. Phys. Solids 1 (1952) 19–30. [8] H.W. Swift, Plastic instability under plane stress, J. Mech. Phys. Solids 1 (1952) 1–18. [9] MSC Marc & Mentat 2004 Theory Manual, 2004.