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A study on the laser forming of near-alpha and metastable beta titanium alloy sheets
Journal of Materials Processing Technology 108 (2001) 376±383
A study on the laser forming of near-alpha and metastable beta titanium alloy sheets M. Marya*, G.R. Edwards Center for Welding, Joining and Coatings Research, The G.S. Ansell Department of Metallurgical and Materials Engineering, Colorado School of Mines, Golden, CO 80401-1887, USA Accepted 12 September 2000
Abstract Laser forming has been identi®ed as a technique suitable for producing sheet metal products and for making on-site repairs. One application is the repair of titanium turbines for military airplanes, which consists of shaping distorted blades back to their original shape without removing them. This paper essentially analyzes the effects of consecutive scans at known beam parameters, and to a practical standpoint, it can help to select adequate forming conditions. Two titanium alloys were chosen: a near-alpha alloy, Ti±6Al±2Sn±4Zr±2Mo, and a metastable beta alloy, Ti±15V±3Cr±3Al±3Sn. Empirical equations for predicting bending and section thickening were derived so that series of experimental points could be reduced into two parameters. Effects of repeated scans on bending angle and thickening were ®rst investigated. Second, these two geometric changes were correlated and the two materials compared. The reduced bending often observed after a few scans was related to the initial thickening. Alloy Ti±6Al±2Sn±4Zr±2Mo was found to bend more in the early stage of forming, but it also thickened more than alloy Ti±15V±3Cr±3Al±3Sn. It was concluded that gradual thickening reduced subsequent bendability. The greater initial bending in alloy Ti±6Al±2Sn±4Zr±2Mo was due to a lower yield temperature and a higher thermal expansion coef®cient. Because lesser thickening occurred in Ti±15V±3Cr±3Al±3Sn, a better formability was found after many scans. It is also proposed that buckling could cause bending to decrease. As a result of this work, process parameters can be chosen to create the largest bending angles and minimize the number of scans. # 2001 Elsevier Science B.V. All rights reserved. Keywords: Laser forming; Bending; Buckling; Sheet metal; Titanium alloys; Modeling
1. Introduction Laser forming (bending) has been recognized for its potential to become a ¯exible manufacturing process. The process has its origin in the bending of heavy plates by ¯ame heating, a process that has been empirically tailored for many years in the shipyards to bend ship hull structural plates. Unlike ¯ame heating, laser beams are highly controllable in size and power. Laser forming has since emerged as a new shaping technique that offers both excellent reproducibility and low manufacturing time. The idea of using lasers for forming was ®rst proposed by Kitamura [1] in the joint MIT and HPL Committee of the Japan Welding Engineering Society dating from 1981. Steel plates, 22-mm thick, were repeatedly bent with a 15-kW CO2 laser. Since then, laser forming has been the object of considerable attention. Most articles available today are dedicated to the computer modeling of laser forming, and * Corresponding author. E-mail address: [email protected] (M. Marya).
underestimate the microstructural contribution to forming. It is thus not surprising that ®nite element models (FEM) have sometimes limited success in reproducing laser forming of sheet metals [2±7]. Despite large simpli®cations in their FEM model, Ueda et al. [4±7] published a set of four technical papers giving considerable insight into the practicalities of the process for shaping ship hulls. Recently, Zhong and Shichum [8] analyzed the process exclusively from the perspective of heat ¯ow, also using an FEM code. Marya and Edwards [9,10], also recognizing the role played by the heat ¯ow, related process parameters, temperature distributions and bending angles through a set of analytical heat ¯ow equations. This approach helped to identify the thermal conditions that maximize the bending angle, but could not be used to predict bending angles with accuracy. Although several practical and fundamental aspects are now better understood, other important characteristics of laser forming still have not been much addressed. For instance, it is for practical reasons of utmost importance to understand the effects of consecutive scans on both the material and its subsequent response to forming. Industrial
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M. Marya, G.R. Edwards / Journal of Materials Processing Technology 108 (2001) 376±383
design often requires bending angles far greater than those produced with a single scan, which rarely exceed a few degrees. The effects of consecutive scans have sometimes been overlooked because linear relations between bending angle and number of scans were often observed [11]. Sprenger et al. [12] showed that bending gradually decreased after consecutive scans, partially as a result of strain hardening. The current paper not only discusses the effects of repeated scans, but also compares the forming of two titanium alloys used in the aerospace industry. Laser forming has recently received attention from the military because of its potential for repairing on-site turbine blades in airplanes, thus saving considerable time and expense. Near-alpha titanium alloy Ti±6Al±2Sn±4Zr±2Mo was laser formed and compared to a metastable beta alloy, Ti±15V±3Cr± 3Al±3Sn. This last alloy was selected for this study because it does not undergo signi®cant phase changes under offequilibrium conditions, as during laser bending thermal cycles. Unless aged later, the high temperature bodycubic-centered crystal structure of beta titanium is fully retained at room temperature. Unlike metastable beta alloys, near-alpha titanium alloys are mostly composed of the low temperature hexagonal closed-packed alpha titanium. During cooling from the high temperature beta structure, they can experience diffusion-controlled as well as displacive phase transformations leading to a wide variety of products. The peak temperature and the cooling rate are the two factors that most directly govern solid-state phase transformations. Although phase transformations might have a noticeable effect, forming is ®rst in¯uenced by the process conditions, as discussed in the ®rst portion of this article.
377
Fig. 1. Analogy between laser forming mechanisms and yielding processes produced with simple mechanical loads.
2. Laser forming mechanisms
sional heat ¯ow [9,10], is really at the origin of bending. It dominates most situations and explains why the process is simply, but logically, termed laser bending. The absence of this temperature gradient is a condition established by a twodimensional heat ¯ow; this condition can give rise to either upsetting or buckling. Laser forming is not only a function of the heat ¯ow, but also of the material properties. Interactions between these inherent characteristics of the material can be found in the thermoelastic stress, de®ned as the product of Young's modulus, the linear thermal expansion coef®cient and the temperature change from ambient. Thermoelastic stress is a useful quantity for evaluating the ability to form materials by lasers. Fig. 2 depicts, within a wide range of temperatures, how this thermoelastic stress compares to the yield strength [15] for both alloy Ti±6Al±2Sn±4Zr±2Mo and alloy Ti± 15V±3Cr±3Al±3Sn. Permanent deformation is induced when thermal stresses exceed, in a combined state of stress, the ¯ow stress of the material. Assuming that they can be
Although the temperature generated by a moving heat source is non-uniform in space, laser forming can be considered as a two-dimensional process because the angular changes predominantly occur in planes perpendicular to the scanning direction. In this two-dimensional space, rectangular components of force or stress can be considered to explain the shape change, as illustrated in Fig. 1. It is seen with a two-dimensional element that bending originates from stresses normal to the neutral axis, but shape change can also result from the action of stresses parallel to the neutral axis. Two other mechanisms, differentiated by the magnitude of the stresses involved, are then possible; they are upsetting and buckling. In laser forming of sheets, it is possible that the three mechanisms, bending, upsetting and buckling, develop at the same time, but to various extents. The temperature gradient, and associated stress gradient established through the sheet thickness, is undoubtedly the most important factor. The so-called temperature gradient mechanism [13,14], which has been associated with the three-dimen-
Fig. 2. Yield strength and thermoelastic stress as a function of temperature for Ti±6Al±2Sn±4Zr±2Mo and Ti±15V±3Cr±3Al±3Sn (both initially annealed) [15].
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replaced by an equivalent thermal stress that does not differ much from a calculated thermoelastic stress, yielding is predicted to develop when the temperature exceeds approximately one third of the melting temperature. This simple calculation also suggests that laser forming of alloy Ti±6Al± 2Sn±4Zr±2Mo is easier because the yield temperature, de®ned at the intersection of two lines, is less for the near-alpha alloy (see shaded circles in Fig. 2). Heat ¯ow and material properties are important laser forming variables. Their interactions give rise to various degrees of yielding. Based upon Fig. 1, yielding can be described as shortening in some directions and thickening in others, because the constancy of volume is preserved. Measurements of thickening, which can be de®ned as a percent increase in thickness with respect to the original value, are therefore a subject of considerable interest. Thickening is expected to provide additional information regarding the mechanism of laser bending; the absence of thickening should suggest buckling. 3. Experimental procedure Laser bending experiments were conducted with a 1.2 kW Nd:YAG laser, as schematically illustrated in Fig. 3. Samples consisted of 80 mm-long, 38 mm-wide and 0.6 mmthick specimens, sheared from two initially annealed sheets. One was made of the near-alpha alloy, Ti±6Al±2Sn±4Zr± 2Mo, and the other of the metastable beta alloy, Ti±15V± 3Cr±3Al±3Sn. Specimens were placed into a transparent chamber, which was ®lled with an inert gas (argon) to prevent the material from oxidizing during forming. A narrow opening at the top allowed the beam to directly irradiate the sample while maintaining the inert shielding. The parameters of the traversing beam were varied signi®cantly. Focused (0.6 mm-diameter) and less focused beams
Fig. 3. Schematic of the experimental set-up for laser bending.
(as large as 3.3 mm-diameter) with variable powers (from 150 to 850 W) were used. For most experiments, the scan speed was held constant, but when increases in heat input were required, reduced travel speeds were employed. Comparisons of the two materials were, however, made only at a constant scan speed of 38 mm sÿ1. The maximum number of consecutive scans was set to 20; the focus of the study was ®rst on the early angular changes during a laser forming operation. The bending angle and thickness changes were simply measured using optical cross-section macrographs. 4. Experimental results Fig. 4 depicts the bending angle measured as a function of number of scans and beam power, for the two materials. At ®rst glance, the bending angle appeared to be simply proportional to the number of scans. However, closer examination reveals that bending angle gradually decreased with each additional scan. This observation is particularly true for the near-alpha alloy, processed with beam powers of 200 and 250 W. The resulting heat ¯ow produced the largest bending angles. Note that the bending rate, de®ned as the rate at which the bending angle changed after consecutive scans, decreased more rapidly when large bending angles were initially produced. This observation held only for the nearalpha alloy; similar observations were less evident for the beta titanium alloy. Fig. 5 clearly demonstrates that section thickening also increased with the number of scans. The rate at which thickening developed also decreased with the number of scans. Unlike bending angle, thickening continued to increase with the beam power. Though bending angle and thickening varied differently with beam power, Figs. 4 and 5
Fig. 4. Effect of consecutive scans on the bending angle.
M. Marya, G.R. Edwards / Journal of Materials Processing Technology 108 (2001) 376±383
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least-squares minimization criterion: a GjN0 N 1=b
Fig. 5. Effect of consecutive scans on the thickening.
showed that they have similar variations with the number of scans. This suggests that bending angle and thickening could be used to predict the variation in the other value for a given number of scan, provided that the beam parameters are kept constant.
(1)
where a is the bending angle in degrees, GjN0 the average initial bending rate in degrees, N the number of scans, and b a dampening constant because it causes the bending angle to progressively decrease. With Eq. (1), bending at known process conditions can be represented by only two parameters. The constant GjN0 denotes a ``statistically derived'' value of the initial bending angle, while b quanti®es all the subsequent bending, gathered into an unique parameter. Although Eq. (1) is a simple representation based on empiricism, some physical meaning can be attached to it. The socalled dampening constant measures that rate at which the bending angle decreases with the number of scans. For large bending angles, parameters that would create low dampening constants and high initial bending angles are hence necessary. Both constants, GjN0 and b, are a function of both the material properties and the heat ¯ow conditions. They can be evaluated by means of logarithmic plots (Figs. 6 and 7), once Eq. (1) is rewritten as 1 ln a ln GjN0 ln N b
(2)
6. Discussion 6.1. Effect of alloying
5. Mathematical representation In sheet metal working, empirical expressions relating stress, strain, strain-rate and temperature have been developed to quantify the plastic behavior of materials. These expressions can later be applied to model forming. However, the fact that laser bending occurs in conditions far from thermal equilibrium makes the use of these analytical relations impossible. Different relationships are consequently needed. Expressions that would predict, at known lasing parameters, the bending angle after a given number of scans are of primary interest. These expressions can aid understanding and provide quantitative comparisons of data obtained with relatively good accuracy. A function relating bending angle to number of scans must satisfy several conditions. First, the bending rate must attain its maximum after the ®rst scan, then gradually decrease as the cumulative bending angle tends toward its ®nal value. The value of this maximum angle is unknown, but certainly not greater than 908, because beam and scan-line would then no longer be in contact. Although the point where bending angle eventually levels off remains uninvestigated, analytical expressions can still be developed. Restrictions of the model within a limited number of scans must hence be speci®ed. Since the current intent was to model the early angular changes; i.e. up to 20 scans, the following representation was selected based upon a
Figs. 6 and 7 clearly demonstrate that Eq. (1) closely ®ts the experimental data. The largest bending angles are those shown adjacent to the shaded region. For the near-alpha alloy, maximum bending is obviously produced by beam powers between 200 and 250 W. The following equation then applies: ajAlpha 4:3N 1=1:25
(3)
Fig. 6. Logarithmic plot depicting the effects of number of scans and beam power on bending angle (near-alpha alloy).
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Fig. 7. Logarithmic plot depicting the effects of number of scans and beam power on bending angle (metastable beta alloy).
For the metastable beta alloy, the relation that holds is for signi®cantly greater beam powers, approximately 450 W. The equation between bending angle and number of scans is then the following: ajBeta 3:3N 1=1:08
(4)
In Eqs. (3) and (4), GjN0 and b are estimated to be within 10 and 3% accuracy, respectively. The optimal beam power for the metastable beta alloy is approximately 2.3 times higher than that for the near-alpha alloy. A comparison of the two plots of Fig. 5 revealed that higher powers are required to bend the metastable beta alloy. Because both materials still possess similar thermal properties [16] despite their microstructures, differences in either beam absorptivity or mechanical properties, or both, remain as the only possible explanations. It is already known that the near-alpha alloy deforms more than the beta titanium alloy, and that its yield temperature is lower and its thermal expansion is greater. Also, the fact that the highest bending angles were produced at only 70 W in excess of the threshold power for bending (130 W) for the near-alpha alloy, but after more than 200 W for the metastable beta alloy, demonstrates that the metastable beta alloy is more dif®cult to deform. These results indirectly con®rm that the yield temperature of the metastable beta alloy was higher than that for the near-alpha alloy. A large variance in beam absorptivity between the two materials is also probable. Under ambient light, alloy Ti± 15V±3Cr±3Al±3Sn was more re¯ective than alloy Ti±6Al± 2Sn±4Zr±2Mo. Because these alloys probably have different beam absorptivities, they must be compared when their bending angles are at a maximum. Eqs. (3) and (4), which then apply, highlight two important features. The near-alpha alloy initially responds better to laser bending than the metastable beta alloy. In fact, it is expected to initially bend 1.3 (4:3 3:3) times more than the beta alloy. On the other hand, the metastable beta alloy becomes more formable after multiple scans because of its smaller dampening constant (1:25 1:08 or approximately 1.2 times smaller). Eqs. (3) and (4) thus predict that the metastable beta alloy, Ti±15V±3Cr±3Al±3Sn, eventually generates larger
bending angles. Proof of this prediction is shown in Figs. 4 and 5, when identical numbers of scans are considered. Below approximately 5 scans, the bending angles were indeed greater in the near-alpha alloy, but became smaller than with the Ti±15V±3Cr±3Al±3Sn alloy when additional scans were performed. Near 20 scans, bending angles produced with the metastable beta alloy were by far greater. Because of the similarity in the variations of bending angle and thickening with consecutive scans, an expression similar to Eq. (1) was employed to model thickening. Excellent correlations were also found. With conditions identical to that for Eqs. (3) and (4), Eq. (5) (200±250 W) and Eq. (6) (450 W) were derived. ejAlpha 9:8N 1=2:8
(5)
ejBeta 7:3N 1=2:0
(6)
Coef®cients in Eqs. (5) and (6) are within the same accuracy of those found for the bending angle (10% on initial thickening and 2% on dampening constant). Their values also provide considerable insight into the phenomenology. The initial thickening of the near-alpha alloy is noticeably larger than in the metastable beta alloy (approximately 9:8 7:3 1:35 times larger). The rate at which thickening increased in the near-alpha alloy was also larger than in the metastable beta alloy (approximately 2:8 2:0 1:4 times larger). The fact that both bending angle and thickening, as well as the rates at which both increase with number of scans, remain 1.2±1.4 times greater in the near-alpha alloy is probably not coincidental. These results demonstrate that the forming response of the near-alpha alloy is roughly 1.2± 1.4 times higher. To explain why the near-alpha alloy constantly responded about 1.4 times more readily than the metastable beta alloy, the average thermal expansion of both materials alloys were considered. The average thermal expansion of both materials have been measured and published elsewhere [9,10±15]. Mean values in the range 400±10008C are given in Fig. 2. Results clearly show that alloy Ti±6Al±2Sn±4Zr±2Mo dilates, on an average, 1.5 times more than alloy Ti±15V±3Cr±3Al±3Sn. 6.2. Relationship between bending angle and thickening Data shown earlier suggest that bending angle and thickening are related. These characteristics can now be compared with the aid of the formalism introduced in the preceding part. Fig. 8 depicts the variations with the beam power of both the initial bending rate and the dampening constant, as found in Eq. (1). Fig. 9 introduces similar coef®cients, but applied to thickening. On the two graphs, the shaded region designates the locus of the largest angles, and thus provides conditions to maximize bending. It is seen from Fig. 8 that the bending angles created by several scans remain largest when the initial bending rate is already maximized. This was consistently observed on both
M. Marya, G.R. Edwards / Journal of Materials Processing Technology 108 (2001) 376±383
Fig. 8. Bending angle coef®cients as a function of the beam power.
Fig. 9. Thickening coef®cients as a function of the beam power.
materials. The consecutive bending rate, indirectly depicted by the dampening constant, plays comparatively a minor role. For the near-alpha alloy, consecutive bending rate varies exactly like the initial bending rate, but it remains approximately constant for the metastable beta alloy. Data on the near-alpha alloy thus suggest that large initial bending creates large subsequent dampening, and hence reduces bending. However, because the change in dampening constant is small, it is the initial bending rate rather than the dampening constant that controls the magnitude of bending (at least up to 20 scans). In other words, the thickening resulting from the ®rst scans is clearly a major factor in reducing subsequent bending angles.
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Other data have shown that bending angle could decrease even though thickening was absent. In Table 1, beam conditions which produced largest bending angles at different beam diameters are given for the near-alpha alloy. These few data show that thickening ®rst increased with beam diameter, but eventually decreased with larger beams; i.e. when the heat ¯ow became essentially two-dimensional. When thickening did not occur, other explanations for the decreasing bending after consecutive scans must prevail. In the absence of thickening, there are several possible explanations for the reduced bendability observed after repeated scans. Local strengthening within the heat affected region or in its vicinity could rationalize more dif®cult forming. However, the constancy in the microstructure, which was observed by optical microscopy, indicated that no new phases were formed during bending of the near-alpha alloy, probably because forming then occurred at temperatures too low. Strain hardening could also explain the decreasing bending rate. However, tensile tests showed that strain hardening of the near-alpha alloy was insigni®cant at ordinary strain rates. Lack of strain hardening were also indirectly con®rmed by microhardness measurements, performed between scans. A more rational explanation for decreased bending rate in the absence of thickening is a gradual decrease in beam absorptivity with an increase in bending angle. However, the role of beam absorptivity was not experimentally con®rmed. When surface melting was maintained in between scans to approximate conditions of constant beam absorptivity, the bending rate still was found to decrease with repeated scans. Other explanations for a decreasing bending rate in the absence of thickening are needed. Although large beams do not generate noticeable thickening, they signi®cantly reduce the thermal gradient through the thickness. As a result, the forming mechanism can be altered. With the 3.3 mm beam, buckling probably became more important, especially at higher powers where the strength of the material was even more reduced. Because the beam power in this study could not be raised signi®cantly above 860 W, the beam speed was gradually reduced down to 4.3 mm sÿ1, with conditions chosen so that the sample surface temperature remained approximately constant. Experiments were thus conducted with process conditions providing the onset of melting. Fig. 9 depicts the results of these experiments, as well as those obtained with a 3.3 mm beam of 500 W which created largest bending angles.
Table 1 Effect of beam diameter on bending characteristics of the near-alpha alloy after 6 scans [10] Beam diameter (mm)
Optimized beam power for forming (W)
Bending angle at/near optimized conditions (degree)
Thickening (%)
0.60 1.15 1.62 2.46 3.28
130 200 240 320 500
14.0 min 18:5 0:5 21:0 0:5 17:5 1:0 20:0 2:5
14.50.5 16.70.5 17.80.5 11.01.0 5.02.5
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the bending component resulting from the small temperature gradient. 7. Conclusions
Fig. 10. Angle as a function of number of scans at various heat inputs (near-alpha alloy only).
Fig. 10 shows that the bending angles produced just below surface melting lie under those obtained with the optimized bending angle conditions. These data prove that increasing the temperature to its highest limit did not promote larger angles, as already depicted in Fig. 4. However, comparisons of data obtained at nearly constant surface temperature (melting) allowed a study of the temperature gradients and yielded widths. These two characteristics had been previously found to be important quantities [10]. At the lowest speed (4.3 mm sÿ1), the thermal gradient through the sheet thickness was smallest while the yielded width was largest. Although large bending angles were initially produced, they became slight only after a few scans. With further scans, however, bending again started to increase until it reached its ®nal value at approximately 21.58. The shape change thus developed during two consecutive and distinct stages. The initial angles developed under these parameters were larger than with any other conditions near melting, although the temperature gradient through the thickness had never been so small. Clearly, this bending did not result from a response to the temperature gradient mechanism. The second increase in bending angle, occurring after 5 scans, was distinct. The distortion no longer resembled a v-shape, but an omega-shaped loop left at the centerline of the scan. Once this buckle was fully formed, no further distortion was possible. These observations of buckling were schematically represented in Fig. 1. Indirect observation of buckling can be made from the plots of the bending angle against the number of scans, which exhibit an in¯ection. This in¯ection is characteristic of buckling. From Fig. 10, one can consequently conclude that buckling also developed at higher speed (12.7 mm sÿ1), but to a lesser extent. At 38 mm sÿ1, buckling may have occurred but could not be detected with certainty. Under the conditions for maximized bending with the 3.3 mm beam (beam power reduced 1.7 times), the contribution from buckling in the shaping is in fact unknown. Nonetheless it is speculated that that there was a buckling component that assisted forming. Its effect was comparatively much lower than
This investigation was primarily intended to investigate the important effect of consecutive scans on the laser bending of two different titanium alloys. Analysis was facilitated by introducing a formalism that was applied to both bending and thickening. Bending rate was shown to decrease as the number of scans increased, often as a result of thickening. The bending of the near-alpha alloy, Ti±6Al± 2Sn±4Zr±2Mo, exceeded that of the metastable beta alloy, Ti±15V±3Cr±3Al±3Sn, when laser scans were limited to numbers less than 5. These results were attributed to the yield temperature and the thermal expansion coef®cient. Both these parameters have been discussed in a previous article [10]. Large bending response requires that yield temperature and thermal expansion coef®cient be large, criteria best satis®ed with the near-alpha alloy, Ti±6Al± 2Sn±4Zr±2Mo. When the selected process conditions create a limited thermal gradient through the sample thickness, buckling can be encountered. The plot of bending angle versus number of scans then exhibits in¯ections that reveal the presence of buckling. Buckling is thought to be a contributing factor regarding the decrease in bending rate observed as a function of consecutive scans. Empirical equations developed here were found useful to quantify the changes in geometry with the number of scans. It is evident that they apply to bending but not to buckling. Although these equations were used for comparing bending angle with thickening for the two titanium alloys, they could also assist in determining adequate process parameters. Together with a procedure to select parameters for maximizing the initial bending angle [10], these empirical equations can be used to predict the total number of scans required in a laser forming operation. Acknowledgements The authors would like to acknowledge the ®nancial support of the Advanced Research Projects Agency, US. Department of Defense under Contract No. F33615-95-C5503 and the American Welding Society for managing this project. References [1] N. Kitamura, Technical Report of Joint Project on Materials Processing by High Power Laser, JWES-TP-8302, March 1983, pp. 359±371. [2] N. Alberti, L. Fratini, F. Micari, Numerical simulation of the laser bending process by a coupled thermal mechanical analysis, Proc. CIRP Semin. 24 (3) (1995) 197±202.
M. Marya, G.R. Edwards / Journal of Materials Processing Technology 108 (2001) 376±383 [3] S. Holzer, H. Arnet, M. Geiger, Physical and numerical modeling of the buckling mechanism, Proc. CIRP Semin. 24 (3) (1995) 229± 233. [4] Y. Ueda, H. Murakawa, A.M. Rashwan, Y. Okumoto, R. Kamichika, Development of computer aided process planning for plate bending by line heating (Report I), relation between the ®nal form of plate and the inherent strain, Trans. JWRI 20 (2) (1991) 129±139. [5] Y. Ueda, H. Murakawa, A.M. Rashwan, Y. Okumoto, R. Kamichika, Development of computer aided process planning for plate bending by line heating (Report II), practice for plate bending in shipyard viewed of aspect of inherent strain, Trans. JWRI 21 (1) (1992) 123± 133. [6] Y. Ueda, H. Murakawa, A.M. Rashwan, I. Neki, R. Kamichika, M. Ishiyama, J.I. Ogawa, Development of computer aided process planning for plate bending by line heating (Report III), relation between heating condition and deformation, Trans. JWRI 22 (1) (1993) 145±155. [7] Y. Ueda, H. Murakawa, A.M. Rashwan, R. Kamichika, M. Ishiyama, J.I. Ogawa, Development of computer aided process planning for plate bending by line heating (Report IV), relation between the ®nal form of plate and the inherent strain, Trans. JWRI 22 (2) (1993) 305± 313. [8] J. Zhong, W. Shichun, FEM simulation of the temperature ®eld
[9] [10] [11] [12] [13] [14] [15] [16]
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during the laser forming of sheet metal, J. Mater. Process. Technol. 85 (1±3) (1998) 89±95. M. Marya, G.R. Edwards, The Laser Forming of Titanium Alloys, Proceed. Trends in Welding Research, Callaway Gardens Resort, Pine Mountain, GA, 1998, pp. 982±987. M. Marya, G.R. Edwards, Heat ¯ow analysis for the optimization of the laser forming of Ti-6242, J. Eng. Mater. Technol., submitted for publication. M. Kutsuna, R. Kuno, J. Nakamura, Study on laser plate bending of stainless steels and aluminum alloys, in: Proceedings of TIWC'98, Taipei, 1998. A. Sprenger, F. Vollertsen, W.M. Steen, K. Watkins, In¯uence of strain hardening on laser bending, Manuf. Syst. 24 (3) (1995) 215± 221. F. Vollertsen, M. RoÈdle, Model for the temperature gradient mechanism of laser bending, Manuf. Syst. 24 (3) (1995) 220±224. J. Magee, K.G. Watkins, W.M. Steen, Advances in laser forming, J. Laser Appl. 10 (6) (1998) 235±246. M. Marya, M.S. Thesis, Colorado School of Mines, Golden, CO, 1999. Y.S. Touloukian, P.E. Ciley, S.C. Saxena, Thermophysical Properties of Matter, The TPRC Data Series, IPI/Plenum Press, New York, 1970.
A study on the laser forming of near-alpha and metastable beta titanium alloy sheets M. Marya*, G.R. Edwards Center for Welding, Joining and Coatings Research, The G.S. Ansell Department of Metallurgical and Materials Engineering, Colorado School of Mines, Golden, CO 80401-1887, USA Accepted 12 September 2000
Abstract Laser forming has been identi®ed as a technique suitable for producing sheet metal products and for making on-site repairs. One application is the repair of titanium turbines for military airplanes, which consists of shaping distorted blades back to their original shape without removing them. This paper essentially analyzes the effects of consecutive scans at known beam parameters, and to a practical standpoint, it can help to select adequate forming conditions. Two titanium alloys were chosen: a near-alpha alloy, Ti±6Al±2Sn±4Zr±2Mo, and a metastable beta alloy, Ti±15V±3Cr±3Al±3Sn. Empirical equations for predicting bending and section thickening were derived so that series of experimental points could be reduced into two parameters. Effects of repeated scans on bending angle and thickening were ®rst investigated. Second, these two geometric changes were correlated and the two materials compared. The reduced bending often observed after a few scans was related to the initial thickening. Alloy Ti±6Al±2Sn±4Zr±2Mo was found to bend more in the early stage of forming, but it also thickened more than alloy Ti±15V±3Cr±3Al±3Sn. It was concluded that gradual thickening reduced subsequent bendability. The greater initial bending in alloy Ti±6Al±2Sn±4Zr±2Mo was due to a lower yield temperature and a higher thermal expansion coef®cient. Because lesser thickening occurred in Ti±15V±3Cr±3Al±3Sn, a better formability was found after many scans. It is also proposed that buckling could cause bending to decrease. As a result of this work, process parameters can be chosen to create the largest bending angles and minimize the number of scans. # 2001 Elsevier Science B.V. All rights reserved. Keywords: Laser forming; Bending; Buckling; Sheet metal; Titanium alloys; Modeling
1. Introduction Laser forming (bending) has been recognized for its potential to become a ¯exible manufacturing process. The process has its origin in the bending of heavy plates by ¯ame heating, a process that has been empirically tailored for many years in the shipyards to bend ship hull structural plates. Unlike ¯ame heating, laser beams are highly controllable in size and power. Laser forming has since emerged as a new shaping technique that offers both excellent reproducibility and low manufacturing time. The idea of using lasers for forming was ®rst proposed by Kitamura [1] in the joint MIT and HPL Committee of the Japan Welding Engineering Society dating from 1981. Steel plates, 22-mm thick, were repeatedly bent with a 15-kW CO2 laser. Since then, laser forming has been the object of considerable attention. Most articles available today are dedicated to the computer modeling of laser forming, and * Corresponding author. E-mail address: [email protected] (M. Marya).
underestimate the microstructural contribution to forming. It is thus not surprising that ®nite element models (FEM) have sometimes limited success in reproducing laser forming of sheet metals [2±7]. Despite large simpli®cations in their FEM model, Ueda et al. [4±7] published a set of four technical papers giving considerable insight into the practicalities of the process for shaping ship hulls. Recently, Zhong and Shichum [8] analyzed the process exclusively from the perspective of heat ¯ow, also using an FEM code. Marya and Edwards [9,10], also recognizing the role played by the heat ¯ow, related process parameters, temperature distributions and bending angles through a set of analytical heat ¯ow equations. This approach helped to identify the thermal conditions that maximize the bending angle, but could not be used to predict bending angles with accuracy. Although several practical and fundamental aspects are now better understood, other important characteristics of laser forming still have not been much addressed. For instance, it is for practical reasons of utmost importance to understand the effects of consecutive scans on both the material and its subsequent response to forming. Industrial
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 0 ) 0 0 8 3 1 - 1
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design often requires bending angles far greater than those produced with a single scan, which rarely exceed a few degrees. The effects of consecutive scans have sometimes been overlooked because linear relations between bending angle and number of scans were often observed [11]. Sprenger et al. [12] showed that bending gradually decreased after consecutive scans, partially as a result of strain hardening. The current paper not only discusses the effects of repeated scans, but also compares the forming of two titanium alloys used in the aerospace industry. Laser forming has recently received attention from the military because of its potential for repairing on-site turbine blades in airplanes, thus saving considerable time and expense. Near-alpha titanium alloy Ti±6Al±2Sn±4Zr±2Mo was laser formed and compared to a metastable beta alloy, Ti±15V±3Cr± 3Al±3Sn. This last alloy was selected for this study because it does not undergo signi®cant phase changes under offequilibrium conditions, as during laser bending thermal cycles. Unless aged later, the high temperature bodycubic-centered crystal structure of beta titanium is fully retained at room temperature. Unlike metastable beta alloys, near-alpha titanium alloys are mostly composed of the low temperature hexagonal closed-packed alpha titanium. During cooling from the high temperature beta structure, they can experience diffusion-controlled as well as displacive phase transformations leading to a wide variety of products. The peak temperature and the cooling rate are the two factors that most directly govern solid-state phase transformations. Although phase transformations might have a noticeable effect, forming is ®rst in¯uenced by the process conditions, as discussed in the ®rst portion of this article.
377
Fig. 1. Analogy between laser forming mechanisms and yielding processes produced with simple mechanical loads.
2. Laser forming mechanisms
sional heat ¯ow [9,10], is really at the origin of bending. It dominates most situations and explains why the process is simply, but logically, termed laser bending. The absence of this temperature gradient is a condition established by a twodimensional heat ¯ow; this condition can give rise to either upsetting or buckling. Laser forming is not only a function of the heat ¯ow, but also of the material properties. Interactions between these inherent characteristics of the material can be found in the thermoelastic stress, de®ned as the product of Young's modulus, the linear thermal expansion coef®cient and the temperature change from ambient. Thermoelastic stress is a useful quantity for evaluating the ability to form materials by lasers. Fig. 2 depicts, within a wide range of temperatures, how this thermoelastic stress compares to the yield strength [15] for both alloy Ti±6Al±2Sn±4Zr±2Mo and alloy Ti± 15V±3Cr±3Al±3Sn. Permanent deformation is induced when thermal stresses exceed, in a combined state of stress, the ¯ow stress of the material. Assuming that they can be
Although the temperature generated by a moving heat source is non-uniform in space, laser forming can be considered as a two-dimensional process because the angular changes predominantly occur in planes perpendicular to the scanning direction. In this two-dimensional space, rectangular components of force or stress can be considered to explain the shape change, as illustrated in Fig. 1. It is seen with a two-dimensional element that bending originates from stresses normal to the neutral axis, but shape change can also result from the action of stresses parallel to the neutral axis. Two other mechanisms, differentiated by the magnitude of the stresses involved, are then possible; they are upsetting and buckling. In laser forming of sheets, it is possible that the three mechanisms, bending, upsetting and buckling, develop at the same time, but to various extents. The temperature gradient, and associated stress gradient established through the sheet thickness, is undoubtedly the most important factor. The so-called temperature gradient mechanism [13,14], which has been associated with the three-dimen-
Fig. 2. Yield strength and thermoelastic stress as a function of temperature for Ti±6Al±2Sn±4Zr±2Mo and Ti±15V±3Cr±3Al±3Sn (both initially annealed) [15].
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replaced by an equivalent thermal stress that does not differ much from a calculated thermoelastic stress, yielding is predicted to develop when the temperature exceeds approximately one third of the melting temperature. This simple calculation also suggests that laser forming of alloy Ti±6Al± 2Sn±4Zr±2Mo is easier because the yield temperature, de®ned at the intersection of two lines, is less for the near-alpha alloy (see shaded circles in Fig. 2). Heat ¯ow and material properties are important laser forming variables. Their interactions give rise to various degrees of yielding. Based upon Fig. 1, yielding can be described as shortening in some directions and thickening in others, because the constancy of volume is preserved. Measurements of thickening, which can be de®ned as a percent increase in thickness with respect to the original value, are therefore a subject of considerable interest. Thickening is expected to provide additional information regarding the mechanism of laser bending; the absence of thickening should suggest buckling. 3. Experimental procedure Laser bending experiments were conducted with a 1.2 kW Nd:YAG laser, as schematically illustrated in Fig. 3. Samples consisted of 80 mm-long, 38 mm-wide and 0.6 mmthick specimens, sheared from two initially annealed sheets. One was made of the near-alpha alloy, Ti±6Al±2Sn±4Zr± 2Mo, and the other of the metastable beta alloy, Ti±15V± 3Cr±3Al±3Sn. Specimens were placed into a transparent chamber, which was ®lled with an inert gas (argon) to prevent the material from oxidizing during forming. A narrow opening at the top allowed the beam to directly irradiate the sample while maintaining the inert shielding. The parameters of the traversing beam were varied signi®cantly. Focused (0.6 mm-diameter) and less focused beams
Fig. 3. Schematic of the experimental set-up for laser bending.
(as large as 3.3 mm-diameter) with variable powers (from 150 to 850 W) were used. For most experiments, the scan speed was held constant, but when increases in heat input were required, reduced travel speeds were employed. Comparisons of the two materials were, however, made only at a constant scan speed of 38 mm sÿ1. The maximum number of consecutive scans was set to 20; the focus of the study was ®rst on the early angular changes during a laser forming operation. The bending angle and thickness changes were simply measured using optical cross-section macrographs. 4. Experimental results Fig. 4 depicts the bending angle measured as a function of number of scans and beam power, for the two materials. At ®rst glance, the bending angle appeared to be simply proportional to the number of scans. However, closer examination reveals that bending angle gradually decreased with each additional scan. This observation is particularly true for the near-alpha alloy, processed with beam powers of 200 and 250 W. The resulting heat ¯ow produced the largest bending angles. Note that the bending rate, de®ned as the rate at which the bending angle changed after consecutive scans, decreased more rapidly when large bending angles were initially produced. This observation held only for the nearalpha alloy; similar observations were less evident for the beta titanium alloy. Fig. 5 clearly demonstrates that section thickening also increased with the number of scans. The rate at which thickening developed also decreased with the number of scans. Unlike bending angle, thickening continued to increase with the beam power. Though bending angle and thickening varied differently with beam power, Figs. 4 and 5
Fig. 4. Effect of consecutive scans on the bending angle.
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least-squares minimization criterion: a GjN0 N 1=b
Fig. 5. Effect of consecutive scans on the thickening.
showed that they have similar variations with the number of scans. This suggests that bending angle and thickening could be used to predict the variation in the other value for a given number of scan, provided that the beam parameters are kept constant.
(1)
where a is the bending angle in degrees, GjN0 the average initial bending rate in degrees, N the number of scans, and b a dampening constant because it causes the bending angle to progressively decrease. With Eq. (1), bending at known process conditions can be represented by only two parameters. The constant GjN0 denotes a ``statistically derived'' value of the initial bending angle, while b quanti®es all the subsequent bending, gathered into an unique parameter. Although Eq. (1) is a simple representation based on empiricism, some physical meaning can be attached to it. The socalled dampening constant measures that rate at which the bending angle decreases with the number of scans. For large bending angles, parameters that would create low dampening constants and high initial bending angles are hence necessary. Both constants, GjN0 and b, are a function of both the material properties and the heat ¯ow conditions. They can be evaluated by means of logarithmic plots (Figs. 6 and 7), once Eq. (1) is rewritten as 1 ln a ln GjN0 ln N b
(2)
6. Discussion 6.1. Effect of alloying
5. Mathematical representation In sheet metal working, empirical expressions relating stress, strain, strain-rate and temperature have been developed to quantify the plastic behavior of materials. These expressions can later be applied to model forming. However, the fact that laser bending occurs in conditions far from thermal equilibrium makes the use of these analytical relations impossible. Different relationships are consequently needed. Expressions that would predict, at known lasing parameters, the bending angle after a given number of scans are of primary interest. These expressions can aid understanding and provide quantitative comparisons of data obtained with relatively good accuracy. A function relating bending angle to number of scans must satisfy several conditions. First, the bending rate must attain its maximum after the ®rst scan, then gradually decrease as the cumulative bending angle tends toward its ®nal value. The value of this maximum angle is unknown, but certainly not greater than 908, because beam and scan-line would then no longer be in contact. Although the point where bending angle eventually levels off remains uninvestigated, analytical expressions can still be developed. Restrictions of the model within a limited number of scans must hence be speci®ed. Since the current intent was to model the early angular changes; i.e. up to 20 scans, the following representation was selected based upon a
Figs. 6 and 7 clearly demonstrate that Eq. (1) closely ®ts the experimental data. The largest bending angles are those shown adjacent to the shaded region. For the near-alpha alloy, maximum bending is obviously produced by beam powers between 200 and 250 W. The following equation then applies: ajAlpha 4:3N 1=1:25
(3)
Fig. 6. Logarithmic plot depicting the effects of number of scans and beam power on bending angle (near-alpha alloy).
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Fig. 7. Logarithmic plot depicting the effects of number of scans and beam power on bending angle (metastable beta alloy).
For the metastable beta alloy, the relation that holds is for signi®cantly greater beam powers, approximately 450 W. The equation between bending angle and number of scans is then the following: ajBeta 3:3N 1=1:08
(4)
In Eqs. (3) and (4), GjN0 and b are estimated to be within 10 and 3% accuracy, respectively. The optimal beam power for the metastable beta alloy is approximately 2.3 times higher than that for the near-alpha alloy. A comparison of the two plots of Fig. 5 revealed that higher powers are required to bend the metastable beta alloy. Because both materials still possess similar thermal properties [16] despite their microstructures, differences in either beam absorptivity or mechanical properties, or both, remain as the only possible explanations. It is already known that the near-alpha alloy deforms more than the beta titanium alloy, and that its yield temperature is lower and its thermal expansion is greater. Also, the fact that the highest bending angles were produced at only 70 W in excess of the threshold power for bending (130 W) for the near-alpha alloy, but after more than 200 W for the metastable beta alloy, demonstrates that the metastable beta alloy is more dif®cult to deform. These results indirectly con®rm that the yield temperature of the metastable beta alloy was higher than that for the near-alpha alloy. A large variance in beam absorptivity between the two materials is also probable. Under ambient light, alloy Ti± 15V±3Cr±3Al±3Sn was more re¯ective than alloy Ti±6Al± 2Sn±4Zr±2Mo. Because these alloys probably have different beam absorptivities, they must be compared when their bending angles are at a maximum. Eqs. (3) and (4), which then apply, highlight two important features. The near-alpha alloy initially responds better to laser bending than the metastable beta alloy. In fact, it is expected to initially bend 1.3 (4:3 3:3) times more than the beta alloy. On the other hand, the metastable beta alloy becomes more formable after multiple scans because of its smaller dampening constant (1:25 1:08 or approximately 1.2 times smaller). Eqs. (3) and (4) thus predict that the metastable beta alloy, Ti±15V±3Cr±3Al±3Sn, eventually generates larger
bending angles. Proof of this prediction is shown in Figs. 4 and 5, when identical numbers of scans are considered. Below approximately 5 scans, the bending angles were indeed greater in the near-alpha alloy, but became smaller than with the Ti±15V±3Cr±3Al±3Sn alloy when additional scans were performed. Near 20 scans, bending angles produced with the metastable beta alloy were by far greater. Because of the similarity in the variations of bending angle and thickening with consecutive scans, an expression similar to Eq. (1) was employed to model thickening. Excellent correlations were also found. With conditions identical to that for Eqs. (3) and (4), Eq. (5) (200±250 W) and Eq. (6) (450 W) were derived. ejAlpha 9:8N 1=2:8
(5)
ejBeta 7:3N 1=2:0
(6)
Coef®cients in Eqs. (5) and (6) are within the same accuracy of those found for the bending angle (10% on initial thickening and 2% on dampening constant). Their values also provide considerable insight into the phenomenology. The initial thickening of the near-alpha alloy is noticeably larger than in the metastable beta alloy (approximately 9:8 7:3 1:35 times larger). The rate at which thickening increased in the near-alpha alloy was also larger than in the metastable beta alloy (approximately 2:8 2:0 1:4 times larger). The fact that both bending angle and thickening, as well as the rates at which both increase with number of scans, remain 1.2±1.4 times greater in the near-alpha alloy is probably not coincidental. These results demonstrate that the forming response of the near-alpha alloy is roughly 1.2± 1.4 times higher. To explain why the near-alpha alloy constantly responded about 1.4 times more readily than the metastable beta alloy, the average thermal expansion of both materials alloys were considered. The average thermal expansion of both materials have been measured and published elsewhere [9,10±15]. Mean values in the range 400±10008C are given in Fig. 2. Results clearly show that alloy Ti±6Al±2Sn±4Zr±2Mo dilates, on an average, 1.5 times more than alloy Ti±15V±3Cr±3Al±3Sn. 6.2. Relationship between bending angle and thickening Data shown earlier suggest that bending angle and thickening are related. These characteristics can now be compared with the aid of the formalism introduced in the preceding part. Fig. 8 depicts the variations with the beam power of both the initial bending rate and the dampening constant, as found in Eq. (1). Fig. 9 introduces similar coef®cients, but applied to thickening. On the two graphs, the shaded region designates the locus of the largest angles, and thus provides conditions to maximize bending. It is seen from Fig. 8 that the bending angles created by several scans remain largest when the initial bending rate is already maximized. This was consistently observed on both
M. Marya, G.R. Edwards / Journal of Materials Processing Technology 108 (2001) 376±383
Fig. 8. Bending angle coef®cients as a function of the beam power.
Fig. 9. Thickening coef®cients as a function of the beam power.
materials. The consecutive bending rate, indirectly depicted by the dampening constant, plays comparatively a minor role. For the near-alpha alloy, consecutive bending rate varies exactly like the initial bending rate, but it remains approximately constant for the metastable beta alloy. Data on the near-alpha alloy thus suggest that large initial bending creates large subsequent dampening, and hence reduces bending. However, because the change in dampening constant is small, it is the initial bending rate rather than the dampening constant that controls the magnitude of bending (at least up to 20 scans). In other words, the thickening resulting from the ®rst scans is clearly a major factor in reducing subsequent bending angles.
381
Other data have shown that bending angle could decrease even though thickening was absent. In Table 1, beam conditions which produced largest bending angles at different beam diameters are given for the near-alpha alloy. These few data show that thickening ®rst increased with beam diameter, but eventually decreased with larger beams; i.e. when the heat ¯ow became essentially two-dimensional. When thickening did not occur, other explanations for the decreasing bending after consecutive scans must prevail. In the absence of thickening, there are several possible explanations for the reduced bendability observed after repeated scans. Local strengthening within the heat affected region or in its vicinity could rationalize more dif®cult forming. However, the constancy in the microstructure, which was observed by optical microscopy, indicated that no new phases were formed during bending of the near-alpha alloy, probably because forming then occurred at temperatures too low. Strain hardening could also explain the decreasing bending rate. However, tensile tests showed that strain hardening of the near-alpha alloy was insigni®cant at ordinary strain rates. Lack of strain hardening were also indirectly con®rmed by microhardness measurements, performed between scans. A more rational explanation for decreased bending rate in the absence of thickening is a gradual decrease in beam absorptivity with an increase in bending angle. However, the role of beam absorptivity was not experimentally con®rmed. When surface melting was maintained in between scans to approximate conditions of constant beam absorptivity, the bending rate still was found to decrease with repeated scans. Other explanations for a decreasing bending rate in the absence of thickening are needed. Although large beams do not generate noticeable thickening, they signi®cantly reduce the thermal gradient through the thickness. As a result, the forming mechanism can be altered. With the 3.3 mm beam, buckling probably became more important, especially at higher powers where the strength of the material was even more reduced. Because the beam power in this study could not be raised signi®cantly above 860 W, the beam speed was gradually reduced down to 4.3 mm sÿ1, with conditions chosen so that the sample surface temperature remained approximately constant. Experiments were thus conducted with process conditions providing the onset of melting. Fig. 9 depicts the results of these experiments, as well as those obtained with a 3.3 mm beam of 500 W which created largest bending angles.
Table 1 Effect of beam diameter on bending characteristics of the near-alpha alloy after 6 scans [10] Beam diameter (mm)
Optimized beam power for forming (W)
Bending angle at/near optimized conditions (degree)
Thickening (%)
0.60 1.15 1.62 2.46 3.28
130 200 240 320 500
14.0 min 18:5 0:5 21:0 0:5 17:5 1:0 20:0 2:5
14.50.5 16.70.5 17.80.5 11.01.0 5.02.5
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the bending component resulting from the small temperature gradient. 7. Conclusions
Fig. 10. Angle as a function of number of scans at various heat inputs (near-alpha alloy only).
Fig. 10 shows that the bending angles produced just below surface melting lie under those obtained with the optimized bending angle conditions. These data prove that increasing the temperature to its highest limit did not promote larger angles, as already depicted in Fig. 4. However, comparisons of data obtained at nearly constant surface temperature (melting) allowed a study of the temperature gradients and yielded widths. These two characteristics had been previously found to be important quantities [10]. At the lowest speed (4.3 mm sÿ1), the thermal gradient through the sheet thickness was smallest while the yielded width was largest. Although large bending angles were initially produced, they became slight only after a few scans. With further scans, however, bending again started to increase until it reached its ®nal value at approximately 21.58. The shape change thus developed during two consecutive and distinct stages. The initial angles developed under these parameters were larger than with any other conditions near melting, although the temperature gradient through the thickness had never been so small. Clearly, this bending did not result from a response to the temperature gradient mechanism. The second increase in bending angle, occurring after 5 scans, was distinct. The distortion no longer resembled a v-shape, but an omega-shaped loop left at the centerline of the scan. Once this buckle was fully formed, no further distortion was possible. These observations of buckling were schematically represented in Fig. 1. Indirect observation of buckling can be made from the plots of the bending angle against the number of scans, which exhibit an in¯ection. This in¯ection is characteristic of buckling. From Fig. 10, one can consequently conclude that buckling also developed at higher speed (12.7 mm sÿ1), but to a lesser extent. At 38 mm sÿ1, buckling may have occurred but could not be detected with certainty. Under the conditions for maximized bending with the 3.3 mm beam (beam power reduced 1.7 times), the contribution from buckling in the shaping is in fact unknown. Nonetheless it is speculated that that there was a buckling component that assisted forming. Its effect was comparatively much lower than
This investigation was primarily intended to investigate the important effect of consecutive scans on the laser bending of two different titanium alloys. Analysis was facilitated by introducing a formalism that was applied to both bending and thickening. Bending rate was shown to decrease as the number of scans increased, often as a result of thickening. The bending of the near-alpha alloy, Ti±6Al± 2Sn±4Zr±2Mo, exceeded that of the metastable beta alloy, Ti±15V±3Cr±3Al±3Sn, when laser scans were limited to numbers less than 5. These results were attributed to the yield temperature and the thermal expansion coef®cient. Both these parameters have been discussed in a previous article [10]. Large bending response requires that yield temperature and thermal expansion coef®cient be large, criteria best satis®ed with the near-alpha alloy, Ti±6Al± 2Sn±4Zr±2Mo. When the selected process conditions create a limited thermal gradient through the sample thickness, buckling can be encountered. The plot of bending angle versus number of scans then exhibits in¯ections that reveal the presence of buckling. Buckling is thought to be a contributing factor regarding the decrease in bending rate observed as a function of consecutive scans. Empirical equations developed here were found useful to quantify the changes in geometry with the number of scans. It is evident that they apply to bending but not to buckling. Although these equations were used for comparing bending angle with thickening for the two titanium alloys, they could also assist in determining adequate process parameters. Together with a procedure to select parameters for maximizing the initial bending angle [10], these empirical equations can be used to predict the total number of scans required in a laser forming operation. Acknowledgements The authors would like to acknowledge the ®nancial support of the Advanced Research Projects Agency, US. Department of Defense under Contract No. F33615-95-C5503 and the American Welding Society for managing this project. References [1] N. Kitamura, Technical Report of Joint Project on Materials Processing by High Power Laser, JWES-TP-8302, March 1983, pp. 359±371. [2] N. Alberti, L. Fratini, F. Micari, Numerical simulation of the laser bending process by a coupled thermal mechanical analysis, Proc. CIRP Semin. 24 (3) (1995) 197±202.
M. Marya, G.R. Edwards / Journal of Materials Processing Technology 108 (2001) 376±383 [3] S. Holzer, H. Arnet, M. Geiger, Physical and numerical modeling of the buckling mechanism, Proc. CIRP Semin. 24 (3) (1995) 229± 233. [4] Y. Ueda, H. Murakawa, A.M. Rashwan, Y. Okumoto, R. Kamichika, Development of computer aided process planning for plate bending by line heating (Report I), relation between the ®nal form of plate and the inherent strain, Trans. JWRI 20 (2) (1991) 129±139. [5] Y. Ueda, H. Murakawa, A.M. Rashwan, Y. Okumoto, R. Kamichika, Development of computer aided process planning for plate bending by line heating (Report II), practice for plate bending in shipyard viewed of aspect of inherent strain, Trans. JWRI 21 (1) (1992) 123± 133. [6] Y. Ueda, H. Murakawa, A.M. Rashwan, I. Neki, R. Kamichika, M. Ishiyama, J.I. Ogawa, Development of computer aided process planning for plate bending by line heating (Report III), relation between heating condition and deformation, Trans. JWRI 22 (1) (1993) 145±155. [7] Y. Ueda, H. Murakawa, A.M. Rashwan, R. Kamichika, M. Ishiyama, J.I. Ogawa, Development of computer aided process planning for plate bending by line heating (Report IV), relation between the ®nal form of plate and the inherent strain, Trans. JWRI 22 (2) (1993) 305± 313. [8] J. Zhong, W. Shichun, FEM simulation of the temperature ®eld
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