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Material property changes associated with laser forming of mild steel components
Journal of Materials Processing Technology 118 (2001) 40±44
Material property changes associated with laser forming of mild steel components Gareth Thomson*, Mark Pridham Department of Mechanical Engineering, University of Dundee, Dundee, Scotland DD1 4HN, UK
Abstract Laser forming is a technique developed over the last 5 years or so which allows the forming and bending of metallic components without the need for hard tooling. This makes it a potentially useful prototyping and limited production technique. The laser forming method makes use of the laser's ability to heat very localised regions of material very quickly. The large temperature gradients set up within the material create internal stresses, which result in permanent deformation. A variety of sharp folds and curved surfaces can be generated by this technique. Work carried out on this technique both by ourselves and others has tended to concentrate on developing control systems and mathematical models in order to gain an insight into the mechanics of the technique. An area neglected so far, however, is how the rapid and repeated heating and cooling cycles associated with laser bending alter material properties. If components produced by this technique are to be used in practice it is vital that any weaknesses (or bene®ts) imparted by the technique are identi®ed. This paper gives a brief introduction on the general principles and applications of the laser forming technique. An analysis of the effects of the technique on the material properties of mild steel is then presented and this is followed by a discussion on how, in practice, components formed using the thermally based laser forming technique are likely to function in comparison to more conventionally produced parts. # 2001 Elsevier Science B.V. All rights reserved. Keywords: Laser; Forming; Properties
1. Introduction Laser forming is a relatively novel technique which uses energy from a high powered CO2 laser to set up con¯icting thermal stresses in metallic material [1,2]. These thermal stresses create permanent localised deformation in the material. On a single pass by the laser the specimen will de¯ect by around 28 depending on a number of process parameters including the plate thickness and the tracking speed of the laser over the material. By repeated application of the laser beam and careful manipulation of the beam's path, both sharp folds and curvatures may be generated. A fuller discussion on the mechanics of the technique may be found elsewhere [3±12]. Fig. 1 shows an example of the sort of part which can be produced by this technique. The technique is useful in that, in combination with laser cutting, complex geometries can be produced without the cost and long lead times associated with hard tooling. This offers possibilities in the production of prototype and limited run parts. *
Corresponding author. Tel.: 44-1382-344908; fax: 44-1382-345509. E-mail address: [email protected] (G. Thomson).
Work to date has tended to examine the process from the basis of gaining an understanding of the relationship between process parameters and the resulting degree of deformation, and this has been examined from both an experimental and theoretical basis. Control systems have also been produced to allow speci®c geometries to be produced in a repeatable manner [13±15]. An area neglected so far, however, is the effect on the microstructure and material properties of the folded material by the rapid heating and cooling cycles of the laser forming process. A part produced by laser forming should have stiffness and strength characteristics as good as parts produced more conventionally for the new approach to be useful in producing functional prototypes. This paper examines this issue for laser-formed mild steel parts. 2. Simple tensile test Tests were carried out on mild steel plate of approximately 0.05 wt.% C content with a nominal thickness of 1 mm. This material was chosen, since it is readily available, lends itself to laser forming and is typical of the type of sheet used in conventional metal forming work.
0924-0136/01/$ ± see front matter # 2001 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 4 - 0 1 3 6 ( 0 1 ) 0 0 8 5 9 - 7
G. Thomson, M. Pridham / Journal of Materials Processing Technology 118 (2001) 40±44
41
Fig. 1. Typical laser-formed part.
It was decided to perform both microscopic analysis and tensile tests on specimens which had been subjected to varying degrees of laser forming. Two types of tensile tests were performed. The ®rst set involved conventional dog-bone specimens with a working breadth of 10 mm and gauge length of 40 mm as shown in Fig. 2. These specimens were formed with 10 single pass laser tracks 1 mm apart. A number of specimens were produced in this way with the tracking speed of the laser varied between specimens. A problem encountered with this technique was that the degree of forming had to be limited to ensure that the specimens stayed ¯at enough to be properly gripped in the tensile testing jaws to ensure a valid test was obtained. Control specimens were produced from the same sheet with the same dog-bone geometry. Two forms of control were used. The ®rst were ¯at specimens, while other control specimens were curved using conventional rollers to give curvatures, similar to those experienced by the laserformed specimens. It can be seen from Fig. 3 that as the traverse velocity drops, in other words as the laser energy input increases, the effective yield point for the specimens rises and some drop in
ductility is also noticeable. This will induce a higher degree of laser forming per pass. The mechanically curved, control specimens did not show signi®cantly different properties from their undeformed equivalents suggesting that the degree of work hardening is limited due to the modest degree of deformation in these parts. This suggests that the changes in the material properties experienced by the laser-formed specimen are due to unique aspects of this process rather than simply the deformation of the material. These relationships can also be seen in Fig. 4, which shows load displacement graphs for a range of the test specimens. It can also be seen that a change of behaviour also occurs at the elastic±plastic transition region as the degree of laser forming increases. The control specimen shows a small amount of discontinuous yielding as it is stretched beyond its elastic limit. Specimens with a high traverse velocity, in other words those subjected to limited laser energy, show a much reduced level of this behaviour. However, as the traverse speed is brought down and the degree of laser exposure is increased, the transition again experiences discontinuous yielding, which is even more marked than in the unformed plate.
Fig. 2. Laser-formed tensile specimen.
42
G. Thomson, M. Pridham / Journal of Materials Processing Technology 118 (2001) 40±44
Fig. 3. Yield stress and deflection at break for specimens with increasing degrees of laser forming.
The discontinuous yielding of the control specimen is typical of mild steel in this condition. This effect, known as ``strain ageing'', is associated with the diffusion of carbon atoms to the sites of edge dislocations, where they can be accommodated with an overall lowering of the strain energy of the crystal. To subsequently move the dislocation and thereby initiate plastic deformation, the overall strain energy must be raised to separate the dislocation and the carbon atom. A larger stress than normal is required to do this and thus the dislocation is effectively ``pinned'' by the carbon atoms. Once moved from its original site, the dislocation is free to move and deformation proceeds in the usual way with associated work hardening. The effects of strain ageing disappear if the material is deformed by an increment greater than the strain associated with discontinuous yielding after its ®nal temper. This condition is temporary, however, as the carbon atoms will, in time, diffuse back to the dislocation sites as it is energetically favourable for them to do so. Clearly, the diffusion rate will increase with temperature. It is possible that the specimens deformed by the faster laser traverse rates (i.e. lower energy inputs) are being effectively deformed this small amount as bending takes
place and the temperature rise in the material as a whole is not high enough to drastically increase the carbon diffusion rate and hence restore signi®cant discontinuous yielding. Those specimens which are deformed at the lower traverse speeds (i.e. high energy inputs), however, see an appreciable temperature rise and hence a much increased diffusion rate. Thus, the effects of deformation by bending may be swamped by the diffusion of carbon atoms back to the dislocation sites leading to a markedly increased degree of discontinuous yielding. 3. Straightening test It was felt important that some measure of the force required to straighten a laser-formed specimen should be performed. A supporting bracket produced by laser forming must not have been so weakened by the bending process that it fails by either unfolding or fracturing when a working load is applied. A test piece, as shown in Fig. 5, was devised to test this property. Each specimen features four folds. The multiple folds will amplify the difference between the laser-formed
Fig. 4. Load versus deflection relationships for control, lightly laser-formed and heavily laser-formed tensile test specimens.
G. Thomson, M. Pridham / Journal of Materials Processing Technology 118 (2001) 40±44
Fig. 5. Specimen used in ``straightening test''.
test parts and conventionally bent control specimens. This design also ensures that the ends to be pulled on, during the unfolding operation are coplanar. It should be noted that in addition to the obvious geometry changes between the ®rst and second tests, the straightening test experiences multiple passes of the laser beam over each fold line until the 908 fold is achieved and also that this fold line lies perpendicular rather than parallel to the axis of tensile pull. Fig. 6 shows typical results of the straightening test. In the case of both the control and laser-formed samples, as the load is applied the folds ®rst straighten out before undergoing conventional tensile elastic extension and yielding. The curves produced by both the laser-formed and conventionally produced specimens are very similar, with respect to the load while straightening, and ultimate load. It can be seen that the laser-formed specimens generally exhibit a slightly shallower load/displacement gradient Ð an effective reduction in modulus. This is probably due to some slight thinning of the fold line caused by the repeated action of the laser which vapourises a thin layer of the surface of the material on each pass. This thinning was not apparent on the simple tensile tests, since only single passes were used and so any reduction in cross-section would be negligible. This thinning of section would also show other effects. In these tests, the ultimate tensile load is essentially unchanged between the control and laser-formed specimens. It is likely, however, that the thinning of the specimen, which would
43
reduce the ultimate load is offset by an increase in the basic strength of the laser-formed sections as seen in the simple tensile test. It is not obvious from the single samples of each type shown in Fig. 6 that the break point for both conventionally produced and laser-formed parts is unpredictable. Some parts, e.g., failed suddenly just before or after the yield point as was the case with the particular conventionally formed example shown in Fig. 6. This is due to the folding processes damaging the specimens slightly, so creating stress raisers at the edge of the test pieces. In the case of the laser-formed parts, those which failed suddenly could be seen to have some burn through at their edges where the laser energy had been unable to dissipate. This effect could be eliminated by close process control. 4. Microstructural observation A number of the specimens and control parts used in the simple tensile test were examined microscopically. Fig. 7 shows a typical microstructure of the material used in this work. This is a cross-section through the control
Fig. 7. Microstructure of steel control specimen.
Fig. 6. Straightening test results for conventionally formed and laser-formed specimens.
44
G. Thomson, M. Pridham / Journal of Materials Processing Technology 118 (2001) 40±44
detail the apparent increase in the amount of strain ageing present in mild steel specimens subjected to high degrees of laser forming. The existing work should also be carried forward to other laser formable materials, in particular steel. Other tests will also be used to investigate the effect of laser forming on corrosion rates and fatigue resistance. At present, however, the results of the current work show that laser forming is a technique which can be used to produce sheet metal components without fear of compromising structural integrity. References Fig. 8. Microstructure of laser-formed specimen.
specimen and shows a basically ferritic structure with only a tiny amount of pearlite as would be expected with the very low carbon content of the steel used. This structure is also representative of the formed samples in regions away from the laser affected surface. Fig. 8 shows the region around a laser track in a formed specimen. As can clearly be seen, the structure in the proximity of the forming track is altered, possibly by partial melting. The effect on the structure is localised and appears to extend to a depth of no more than approximately 0.2 mm, which corresponds in this case to one-®fth of the total thickness. Further work is necessary to establish the exact nature of these changes and hence evaluate their speci®c effect on the material. 5. Conclusion The work presented here shows that laser-formed parts are likely to perform at least as well as conventionally produced equivalents. In general laser forming increases the yield strength of the material locally to the formed sections. This increase in strength may not be able to be utilised, since the bulk of the material will not have been altered by the laser process, but most signi®cantly laser forming does not weaken structures. The slight loss of ductility would mean that a laser-formed part may not be suitable for large amounts of subsequent manual forming. This is not felt to be a problem, since laser forming is likely to be used as the sole forming operation or as a ®ne adjustment technique after conventional bending. Further work will, however, need to be carried out. In particular, tests will be carried out to investigate in more
[1] J.A. Vaccari, The Promise of Laser Forming, American Machinist, June 1993, pp. 36±38. [2] H. Frackiewicz, Laser metal forming technology, in: Proceedings of the Fabtech International'93, Chicago, 1993, pp. 733±747. [3] F. Vollertsen, Mechanisms and models for laser forming, in: Proceedings of the Laser Assisted Net Shape Engineering'94, Erlangen, 1994, pp. 345±360. [4] F. Vollertsen, I. Komel, R. Kals, The laser bending of steel foils for microparts by the buckling mechanism Ð a model, Modell. Simul. Mater. Sci. Eng. 3 (1995) 107±119. [5] M. Geiger, Synergy of laser material processing and metal forming, Ann. CIRP 43 (2) (1994) 563±570. [6] M. Geiger, F. Vollertsen, The mechanism of laser forming, Ann. CIRP 42 (1) (1993) 301±304. [7] H. Arnet, F. Vollertsen, Extending laser bending for the generation of convex shapes, J. Eng. Manuf. 209 (1995) 433±441. [8] F. Vollertsen, M. Rodle, Model for the temperature gradient mechanism of laser bending, in: Proceedings of the Laser Assisted Net Shape Engineering'94, Erlangen, October 1994, pp. 371±378. [9] A. Sprenger, F. Vollertsen, W.M. Steen, K. Watkins, Influence of strain hardening on laser bending, in: Proceedings of the Laser Assisted Net Shape Engineering'94, Erlangen, October 1994, pp. 361±370. [10] F. Vollertsen, S. Holzer, 3D-thermomechanical simulation of laser forming, in: Proceedings of the NUMIFORM 95 on Simulation of Materials Processing: Theory, Methods and Applications, New York, 1995, pp. 785±791. [11] N. Alberti, L. Fratini, F. Micari, Numerical simulation of the laser bending process by a coupled thermomechanical analysis, in: Proceedings of the Laser Assisted Net Shape Engineering'94, Erlangen, October 1994, pp. 327±336. [12] L. Fratini, F. Micari, The influence of the technological and geometrical parameters in the laser bending process, in: Proceedings of the International Symposium for ElectroMachining, Lausanne, Switzerland, 1995, pp. 827±836. [13] G. Thomson, M. Pridham, Prototype and part manufacture using laser forming with feedback control, IMC-14, Trinity College Dublin, September 1997, pp. 753±761. [14] G. Thomson, M. Pridham, A feedback control system for laser forming, Mechatronics 7 (5) (1997) 429±441. [15] G. Thomson, M. Pridham, Controlled laser forming for rapid prototyping, Rapid Prototyping J. 3 (4) (1997) 137±143.
Material property changes associated with laser forming of mild steel components Gareth Thomson*, Mark Pridham Department of Mechanical Engineering, University of Dundee, Dundee, Scotland DD1 4HN, UK
Abstract Laser forming is a technique developed over the last 5 years or so which allows the forming and bending of metallic components without the need for hard tooling. This makes it a potentially useful prototyping and limited production technique. The laser forming method makes use of the laser's ability to heat very localised regions of material very quickly. The large temperature gradients set up within the material create internal stresses, which result in permanent deformation. A variety of sharp folds and curved surfaces can be generated by this technique. Work carried out on this technique both by ourselves and others has tended to concentrate on developing control systems and mathematical models in order to gain an insight into the mechanics of the technique. An area neglected so far, however, is how the rapid and repeated heating and cooling cycles associated with laser bending alter material properties. If components produced by this technique are to be used in practice it is vital that any weaknesses (or bene®ts) imparted by the technique are identi®ed. This paper gives a brief introduction on the general principles and applications of the laser forming technique. An analysis of the effects of the technique on the material properties of mild steel is then presented and this is followed by a discussion on how, in practice, components formed using the thermally based laser forming technique are likely to function in comparison to more conventionally produced parts. # 2001 Elsevier Science B.V. All rights reserved. Keywords: Laser; Forming; Properties
1. Introduction Laser forming is a relatively novel technique which uses energy from a high powered CO2 laser to set up con¯icting thermal stresses in metallic material [1,2]. These thermal stresses create permanent localised deformation in the material. On a single pass by the laser the specimen will de¯ect by around 28 depending on a number of process parameters including the plate thickness and the tracking speed of the laser over the material. By repeated application of the laser beam and careful manipulation of the beam's path, both sharp folds and curvatures may be generated. A fuller discussion on the mechanics of the technique may be found elsewhere [3±12]. Fig. 1 shows an example of the sort of part which can be produced by this technique. The technique is useful in that, in combination with laser cutting, complex geometries can be produced without the cost and long lead times associated with hard tooling. This offers possibilities in the production of prototype and limited run parts. *
Corresponding author. Tel.: 44-1382-344908; fax: 44-1382-345509. E-mail address: [email protected] (G. Thomson).
Work to date has tended to examine the process from the basis of gaining an understanding of the relationship between process parameters and the resulting degree of deformation, and this has been examined from both an experimental and theoretical basis. Control systems have also been produced to allow speci®c geometries to be produced in a repeatable manner [13±15]. An area neglected so far, however, is the effect on the microstructure and material properties of the folded material by the rapid heating and cooling cycles of the laser forming process. A part produced by laser forming should have stiffness and strength characteristics as good as parts produced more conventionally for the new approach to be useful in producing functional prototypes. This paper examines this issue for laser-formed mild steel parts. 2. Simple tensile test Tests were carried out on mild steel plate of approximately 0.05 wt.% C content with a nominal thickness of 1 mm. This material was chosen, since it is readily available, lends itself to laser forming and is typical of the type of sheet used in conventional metal forming work.
0924-0136/01/$ ± see front matter # 2001 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 4 - 0 1 3 6 ( 0 1 ) 0 0 8 5 9 - 7
G. Thomson, M. Pridham / Journal of Materials Processing Technology 118 (2001) 40±44
41
Fig. 1. Typical laser-formed part.
It was decided to perform both microscopic analysis and tensile tests on specimens which had been subjected to varying degrees of laser forming. Two types of tensile tests were performed. The ®rst set involved conventional dog-bone specimens with a working breadth of 10 mm and gauge length of 40 mm as shown in Fig. 2. These specimens were formed with 10 single pass laser tracks 1 mm apart. A number of specimens were produced in this way with the tracking speed of the laser varied between specimens. A problem encountered with this technique was that the degree of forming had to be limited to ensure that the specimens stayed ¯at enough to be properly gripped in the tensile testing jaws to ensure a valid test was obtained. Control specimens were produced from the same sheet with the same dog-bone geometry. Two forms of control were used. The ®rst were ¯at specimens, while other control specimens were curved using conventional rollers to give curvatures, similar to those experienced by the laserformed specimens. It can be seen from Fig. 3 that as the traverse velocity drops, in other words as the laser energy input increases, the effective yield point for the specimens rises and some drop in
ductility is also noticeable. This will induce a higher degree of laser forming per pass. The mechanically curved, control specimens did not show signi®cantly different properties from their undeformed equivalents suggesting that the degree of work hardening is limited due to the modest degree of deformation in these parts. This suggests that the changes in the material properties experienced by the laser-formed specimen are due to unique aspects of this process rather than simply the deformation of the material. These relationships can also be seen in Fig. 4, which shows load displacement graphs for a range of the test specimens. It can also be seen that a change of behaviour also occurs at the elastic±plastic transition region as the degree of laser forming increases. The control specimen shows a small amount of discontinuous yielding as it is stretched beyond its elastic limit. Specimens with a high traverse velocity, in other words those subjected to limited laser energy, show a much reduced level of this behaviour. However, as the traverse speed is brought down and the degree of laser exposure is increased, the transition again experiences discontinuous yielding, which is even more marked than in the unformed plate.
Fig. 2. Laser-formed tensile specimen.
42
G. Thomson, M. Pridham / Journal of Materials Processing Technology 118 (2001) 40±44
Fig. 3. Yield stress and deflection at break for specimens with increasing degrees of laser forming.
The discontinuous yielding of the control specimen is typical of mild steel in this condition. This effect, known as ``strain ageing'', is associated with the diffusion of carbon atoms to the sites of edge dislocations, where they can be accommodated with an overall lowering of the strain energy of the crystal. To subsequently move the dislocation and thereby initiate plastic deformation, the overall strain energy must be raised to separate the dislocation and the carbon atom. A larger stress than normal is required to do this and thus the dislocation is effectively ``pinned'' by the carbon atoms. Once moved from its original site, the dislocation is free to move and deformation proceeds in the usual way with associated work hardening. The effects of strain ageing disappear if the material is deformed by an increment greater than the strain associated with discontinuous yielding after its ®nal temper. This condition is temporary, however, as the carbon atoms will, in time, diffuse back to the dislocation sites as it is energetically favourable for them to do so. Clearly, the diffusion rate will increase with temperature. It is possible that the specimens deformed by the faster laser traverse rates (i.e. lower energy inputs) are being effectively deformed this small amount as bending takes
place and the temperature rise in the material as a whole is not high enough to drastically increase the carbon diffusion rate and hence restore signi®cant discontinuous yielding. Those specimens which are deformed at the lower traverse speeds (i.e. high energy inputs), however, see an appreciable temperature rise and hence a much increased diffusion rate. Thus, the effects of deformation by bending may be swamped by the diffusion of carbon atoms back to the dislocation sites leading to a markedly increased degree of discontinuous yielding. 3. Straightening test It was felt important that some measure of the force required to straighten a laser-formed specimen should be performed. A supporting bracket produced by laser forming must not have been so weakened by the bending process that it fails by either unfolding or fracturing when a working load is applied. A test piece, as shown in Fig. 5, was devised to test this property. Each specimen features four folds. The multiple folds will amplify the difference between the laser-formed
Fig. 4. Load versus deflection relationships for control, lightly laser-formed and heavily laser-formed tensile test specimens.
G. Thomson, M. Pridham / Journal of Materials Processing Technology 118 (2001) 40±44
Fig. 5. Specimen used in ``straightening test''.
test parts and conventionally bent control specimens. This design also ensures that the ends to be pulled on, during the unfolding operation are coplanar. It should be noted that in addition to the obvious geometry changes between the ®rst and second tests, the straightening test experiences multiple passes of the laser beam over each fold line until the 908 fold is achieved and also that this fold line lies perpendicular rather than parallel to the axis of tensile pull. Fig. 6 shows typical results of the straightening test. In the case of both the control and laser-formed samples, as the load is applied the folds ®rst straighten out before undergoing conventional tensile elastic extension and yielding. The curves produced by both the laser-formed and conventionally produced specimens are very similar, with respect to the load while straightening, and ultimate load. It can be seen that the laser-formed specimens generally exhibit a slightly shallower load/displacement gradient Ð an effective reduction in modulus. This is probably due to some slight thinning of the fold line caused by the repeated action of the laser which vapourises a thin layer of the surface of the material on each pass. This thinning was not apparent on the simple tensile tests, since only single passes were used and so any reduction in cross-section would be negligible. This thinning of section would also show other effects. In these tests, the ultimate tensile load is essentially unchanged between the control and laser-formed specimens. It is likely, however, that the thinning of the specimen, which would
43
reduce the ultimate load is offset by an increase in the basic strength of the laser-formed sections as seen in the simple tensile test. It is not obvious from the single samples of each type shown in Fig. 6 that the break point for both conventionally produced and laser-formed parts is unpredictable. Some parts, e.g., failed suddenly just before or after the yield point as was the case with the particular conventionally formed example shown in Fig. 6. This is due to the folding processes damaging the specimens slightly, so creating stress raisers at the edge of the test pieces. In the case of the laser-formed parts, those which failed suddenly could be seen to have some burn through at their edges where the laser energy had been unable to dissipate. This effect could be eliminated by close process control. 4. Microstructural observation A number of the specimens and control parts used in the simple tensile test were examined microscopically. Fig. 7 shows a typical microstructure of the material used in this work. This is a cross-section through the control
Fig. 7. Microstructure of steel control specimen.
Fig. 6. Straightening test results for conventionally formed and laser-formed specimens.
44
G. Thomson, M. Pridham / Journal of Materials Processing Technology 118 (2001) 40±44
detail the apparent increase in the amount of strain ageing present in mild steel specimens subjected to high degrees of laser forming. The existing work should also be carried forward to other laser formable materials, in particular steel. Other tests will also be used to investigate the effect of laser forming on corrosion rates and fatigue resistance. At present, however, the results of the current work show that laser forming is a technique which can be used to produce sheet metal components without fear of compromising structural integrity. References Fig. 8. Microstructure of laser-formed specimen.
specimen and shows a basically ferritic structure with only a tiny amount of pearlite as would be expected with the very low carbon content of the steel used. This structure is also representative of the formed samples in regions away from the laser affected surface. Fig. 8 shows the region around a laser track in a formed specimen. As can clearly be seen, the structure in the proximity of the forming track is altered, possibly by partial melting. The effect on the structure is localised and appears to extend to a depth of no more than approximately 0.2 mm, which corresponds in this case to one-®fth of the total thickness. Further work is necessary to establish the exact nature of these changes and hence evaluate their speci®c effect on the material. 5. Conclusion The work presented here shows that laser-formed parts are likely to perform at least as well as conventionally produced equivalents. In general laser forming increases the yield strength of the material locally to the formed sections. This increase in strength may not be able to be utilised, since the bulk of the material will not have been altered by the laser process, but most signi®cantly laser forming does not weaken structures. The slight loss of ductility would mean that a laser-formed part may not be suitable for large amounts of subsequent manual forming. This is not felt to be a problem, since laser forming is likely to be used as the sole forming operation or as a ®ne adjustment technique after conventional bending. Further work will, however, need to be carried out. In particular, tests will be carried out to investigate in more
[1] J.A. Vaccari, The Promise of Laser Forming, American Machinist, June 1993, pp. 36±38. [2] H. Frackiewicz, Laser metal forming technology, in: Proceedings of the Fabtech International'93, Chicago, 1993, pp. 733±747. [3] F. Vollertsen, Mechanisms and models for laser forming, in: Proceedings of the Laser Assisted Net Shape Engineering'94, Erlangen, 1994, pp. 345±360. [4] F. Vollertsen, I. Komel, R. Kals, The laser bending of steel foils for microparts by the buckling mechanism Ð a model, Modell. Simul. Mater. Sci. Eng. 3 (1995) 107±119. [5] M. Geiger, Synergy of laser material processing and metal forming, Ann. CIRP 43 (2) (1994) 563±570. [6] M. Geiger, F. Vollertsen, The mechanism of laser forming, Ann. CIRP 42 (1) (1993) 301±304. [7] H. Arnet, F. Vollertsen, Extending laser bending for the generation of convex shapes, J. Eng. Manuf. 209 (1995) 433±441. [8] F. Vollertsen, M. Rodle, Model for the temperature gradient mechanism of laser bending, in: Proceedings of the Laser Assisted Net Shape Engineering'94, Erlangen, October 1994, pp. 371±378. [9] A. Sprenger, F. Vollertsen, W.M. Steen, K. Watkins, Influence of strain hardening on laser bending, in: Proceedings of the Laser Assisted Net Shape Engineering'94, Erlangen, October 1994, pp. 361±370. [10] F. Vollertsen, S. Holzer, 3D-thermomechanical simulation of laser forming, in: Proceedings of the NUMIFORM 95 on Simulation of Materials Processing: Theory, Methods and Applications, New York, 1995, pp. 785±791. [11] N. Alberti, L. Fratini, F. Micari, Numerical simulation of the laser bending process by a coupled thermomechanical analysis, in: Proceedings of the Laser Assisted Net Shape Engineering'94, Erlangen, October 1994, pp. 327±336. [12] L. Fratini, F. Micari, The influence of the technological and geometrical parameters in the laser bending process, in: Proceedings of the International Symposium for ElectroMachining, Lausanne, Switzerland, 1995, pp. 827±836. [13] G. Thomson, M. Pridham, Prototype and part manufacture using laser forming with feedback control, IMC-14, Trinity College Dublin, September 1997, pp. 753±761. [14] G. Thomson, M. Pridham, A feedback control system for laser forming, Mechatronics 7 (5) (1997) 429±441. [15] G. Thomson, M. Pridham, Controlled laser forming for rapid prototyping, Rapid Prototyping J. 3 (4) (1997) 137±143.