 Advances in Technology Innovation , vol. 1, no. 1, 2016, pp. 01 - 06 1 Copyright © TAETI The Effect of the Curvature-Rate on the Response of Local Sharp-Notched SUS304 Stainless Steel Tubes under Cyclic Bending Kuo-Long Lee 1 , Shih-Bin Chien 2 , and Wen-Fung Pan 3,* 1 Department of Innovative Design and Entrepreneurship Management, Far East University , Tainan, Taiwan. 2,3 Department of Engineering Science, National Cheng Kung University, Tainan, Taiwan . Received 20 January 2016; received in revised form 24 March 2016; accept ed 28 March 2016 Abstract In this study, the response of local sharp-notched SUS304 stainless steel tubes with diffe rent notch depths of 0.2, 0.4, 0.6, 0.8 and 1.0 mm subjected to cyclic bending at different curvature-rates of 0.0035, 0.035 and 0.35 m -1 s -1 were e xpe rimentally investigated. The tube bending machine and curvature-ovalization measure ment apparatus, which was designed by Pan et a l. [1], we re used for conducting the curvature-controlled cyclic bending. For a constant curvature-rate, the mo ment-curvature curve revealed that the cyclic hardening and became a steady loop after a few bending cycles; the notch depth had almost no influence on the curves. Moreover, the ovalizat ion-curvature curve increased in an increasing and ratcheting manner with the nu mber of bending cycles. La rge notch depths resulted in larger ovalization of the tube cross -section. In addition, for a constant notch depth, higher curvature-rates led to larger cyclic hardening and faster increasing of ovalization. Keywor ds : local sharp notch, SUS304 stainless s teel tubes, notch depth, curvature-rate, cyclic bending, moment, curvature, ovalization 1. Introduction It is we ll known that the bending of c ircula r tubes results in the ovalization (change in the outer dia meter div ided by the origina l outer dia meter) of the tube cross -section. This ovalization increases slowly during reverse bending and continuous cyclic b ending and, in turn, results in the deterioration of the circular tube, which buckles when the ovalization reaches some critica l value. The circu lar tube is severely damaged during buckling and cannot bear the load, which ultimate ly results in obstruction and leakage of the materia l being transported. As such, a complete understanding of the response of the circular tube to cyclic bending is essential for industrial applications. In 1998, Pan et al. [1] designed and set up a new measure ment apparatus. It was used with the cyclic bending machine to study various kinds of tubes under diffe rent cyclic bending conditions. For instance, Pan and Her [2] investigated the response and stability of 304 stainless steel tubes that were subjected to cyclic bending with diffe rent curvature-rates, Lee et al. [3] studied the influence of the Do/t ratio on the response and stability of c ircula r tubes that were subjected to symmetrical cyc lic bending, Lee et al. [4] e xperimentally e xp lored the effect of the Do/t ratio and curvature-rate on the response and stability of circula r tubes subjected to cyclic bending, and Chang and Pan [5] discussed the buckling life estimat ion of c ircu lar tubes subjected to cyclic bending. Expe rimental investigations have shown that some engineering materials, such as 304 stainless steel, 316 stainless steel and high-strength titanium a lloy, change mechanica l properties (yield strength, hardening, ductility … etc.) under different strain-rates or stress -rates. Therefore, once a tube wh ich is fabricat ed by afore mentioned materials is manipulated under cyclic bending at diffe rent curvature-rates, the response and collapse of tubes for each * Corresponding aut hor, Email: z7808034@email.ncku.edu.tw Advances in Technology Innovation, vol. 1, no. 1, 2016, pp. 01 - 06 2 Copyright © TAETI curvature-rate are expected to be generated diffe rently. Pan and his co-worke rs have investigated the influence of curvature-rate on the response and collapse of SUS304 stainless steel tubes (Pan and Her [2]), titaniu m a lloy tubes (Lee and Pan [6]) and 316L stainless steel tubes (Chang et al. [7]) subjected to cyclic bending. However, a ll of their investigations considered tubes with a smooth surface. If a tube with a notch is considered, the response should be different from a tube with a smooth surface. In this study, the response for local sharp- notched SUS304 stainless steel tubes subjected to cyclic bending at different curvature-rates is discussed. A four-point bending mach ine (Sha w and Kyria kides [8], Lee et a l. [3]) was used to conduct the cyclic bending test. A curvature- ovalization measurement apparatus (COMA) designed and reported previously by Pan et al. [1] was used to control and measure the curvature. For local sharp-notched tubes, five different notch depths, 0.2, 0.4, 0.6, 0.8 and 1.0 mm, we re considered in this study. In addition, three diffe rent curvature-rates, 0.0035, 0.035 and 0.35 m -1 s -1 , were controlled. The magnitude of the bending mo ment was measured by two load cells mounted in the bending device, and the magnitudes of the curvature and ovalization of the tube cross -section were measured by COMA. 2. Experiment Local s harp-notched SUS304 stainless steel tubes with five diffe rent notch depths were subjected to cyclic bending at three different curvature-rates by using a tube- bending device and a curvature-ovalization measurement apparatus in this study. Detailed descriptions of the device, apparatus, materia ls, specimens and test procedures are given as follows . 2.1. Bending Device Fig. 1 shows a picture of the bending device. It is designed as a four-point bending machine, capable of apply ing bending and reverse bending. The device consists of two rotating sprockets resting on two support beams. Heavy chains run around the sprockets and are connected to two hydraulic cylinders and load cells forming a c losed loop. Each tube is tested and fitted with solid rod e xtension. The contact between the tube and the rollers is free to move along axia l direct ion during bending. The load transfer to the test specimen is in the form of a couple formed by concentrated loads fro m two of the rollers. Once e ither the top or bottom cylinder is contracted, the sprockets are rotated, and pure bending of the test specimen is achieved. Reverse bending can be achieved by reversing the direction of the flow in the hydraulic c ircuit. Detailed description of the bending device can be found in Shaw and Kyriakides [8] and Lee et al. [3]. Fig. 1 A picture of the bending device Fig. 2 A picture of the COMA 2.2. Curvature-Ovalization Measurement Apparatus (COMA) The COMA, shown in Fig. 2, is an instrument used to measure the tube curvature and ovalizat ion of a tube cross -section. It is a lightwe ight instrument, wh ich is mounted close to the tube mid-span. There a re three inclinometers in the COMA. T wo inclinometers are fixed on two holders, which a re denoted side-inclinometers . These holders are fixed on the circular tube before the test begins. From the fixed distance between the two side- inclinometers and the angle change detected by the two side-inclino meters, the tube curvature can be derived. In addition, a magnetic detector Advances in Technology Innovation , vol. 1, no. 1, 2016, pp. 01 - 06 3 Copyright © TAETI in the middle part of the COMA is used to measure the change of the outside dia meter. A more detailed description of the bending device and the COMA is given in Pan et al. [1]. 2.3. Material and Specimens The circu lar tubes used in this study were made of SUS304 stainless steel. The tubes’ chemical co mposition is Cr (18.36%), Ni (8.43%), Mn (1.81%), Si (0.39% ), …., and a few other trace elements, with the re mainder being Fe. The ultimate stress, 0.2% strain offset the yield stress and the percent elongation are 626 MPa, 296 MPa and 35%, respectively. The ra w smooth SUS 304 stainless steel tube had an outside diameter Do of 36.6 mm and wa ll- thickness t of 1.5 mm. The raw tubes were mach ined on the outside surface to obtain the desired local notch depth a of 0.2, 0.4, 0.6, 0.8 and 1.0 mm. Fig. 3 shows a schematic dra wing of the local sharp-notched tube. According to the drill of the machine, the corresponding surface dia meters b were 0.6, 1.2, 1.8, 2.4 and 3.0 mm, respectively. Fig. 3 A schematic drawing of the local sharp- notched tube 2.4. Test Procedure The test involved a curvature-controlled cyclic bending. The controlled -curvature ranges were fro m  0.015 to  0.45 m -1 and three diffe rent curvature-rates of the cyclic bending test were 0.0035, 0.035 and 0.35 m -1 s -1 . The magnitude of the bending mo ment was measured by two load cells mounted in the bending device. The magnitudes of the curvature and ovalizat ion of the tube cross -section were measured by the COMA. 3. Results and Discussion Fig. 4 shows a typical set of experimentally determined mo ment (M) - curvature () curve for local sharp-notched SUS304 stainless steel tubes , with notch depth of a = 0.2 mm, subjected to cyclic bending under the curvature-rate of 0.0035 m -1 s -1 . The tubes were cycled between  =  0.3 m -1 . However, the tube exh ibits cyclic hardening and becomes stable after a few cycles. Since the notch is small and local, the notch depth has almost no influence on the M- curve. Therefore, the M- curves for different values of a are not shown in this paper. Fig. 4 Experimentally determined mo ment (M) - curvature () curve for local sharp- notched SUS304 stainless steel tube, with notch depth of a = 0.2 mm, subjected to cyclic bending under the curvature-rate o f 0.035 m -1 s -1 Figs. 5(a)-(b) present experimentally determined mo ment (M) - curvature () curve for local sharp-notched SUS304 stainless steel tubes , with notch depth of a = 0.2 mm, subjected to cyclic bending under the curvature-rate of 0.0035 and 0.35 m -1 s -1 , respectively. It is evident that the M- curves shown in Figs. 4, 5(a) and 5(b) are very simila r. Ho wever, higher curvature-rates lead to higher magnitude of the ma ximu m mo ment at the ma ximu m curvature. The ma ximu m mo ments of 303, 316 and 325 N-m correspond to the curvature-rates of 0.0035, 0.035 and 0.35 m -1 s -1 , respectively. The highest and lowest curvature-rates have 100 times diffe rence. But, the ma ximu m mo ment only increases 7.3%. Due to simila r phenomenon, the e xperiment results of the M- response for loca l sharp-notched SUS304 stainless steel tubes with a = 0.4, 0.6, 0.8 and 1.0 mm under cyclic bending at the curvature-rates of 0.0035, 0.035 and 0.35 m -1 s -1 are omitted in this paper. Advances in Technology Innovation, vol. 1, no. 1, 2016, pp. 01 - 06 4 Copyright © TAETI (a) (b) Fig. 5 Experimentally determined mo ment (M) - curvature () curve for local sharp- notched SUS304 stainless steel tubes , with notch depth of a = 0.2 mm, subjected to cyclic bending under the curvature- rates o f (a) 0.0035 and (b) 0.35 m -1 s -1 Figs . 6(a)-(e) depict the e xperimentally determined ovalizat ion of the tube cross -section (ΔDo/Do) versus the applied curvature () for local sharp-notched SUS304 stainless steel tubes , with notch depths a of 0.2, 0.4, 0.6, 0.8 and 1.0 mm, respectively, subjected to cyclic bending at the curvature-rate of 0.035 m -1 s -1 . The ovalization is defined as ΔDo/Do where Do is the outside diameter and ΔDo is the change in the outside diameter. It can be seen that the ovalization increases in a ratcheting manner with the number of bending cycles. Higher a of the notch tube leads to a more severe unsymmetrica l trend of the ΔDo/Do- curve. In addition, higher a of the notch tube causes greater ovalizat ion of the tube cross -section. The ma ximu m ovalizations of 0.0023, 0.0025, 0.0026, 0.0027 and 0.0028 fo r the curvature of -0.3 m -1 at the 6 th cycle correspond to notch depths a of 0.2, 0.4, 0.6, 0.8 and 1.0 mm, respectively. (a) (b) (c) Fig. 6 Experimentally determined ovalization of the tube cross -section (ΔDo/Do) versus the applied curvature () for local sharp- notched SUS304 stainless steel tubes , with notch depths of a = (a) 0.2, (b) 0.4, (c) 0.6, (d) 0.8 and (e) 1.0 mm, subjected to cyclic bending under the curvature- rate of 0.035 m -1 s -1 (continued) Advances in Technology Innovation , vol. 1, no. 1, 2016, pp. 01 - 06 5 Copyright © TAETI (d) (e) Fig. 6 Experimentally determined ovalization of the tube cross -section (ΔDo/Do) versus the applied curvature () for local sharp- notched SUS304 stainless steel tubes , with notch depths of a = (a) 0.2, (b) 0.4, (c) 0.6, (d) 0.8 and (e) 1.0 mm, subjected to cyclic bending under the curvature- rate of 0.035 m -1 s -1 Figs . 7(a)-(b) depict the e xperimentally determined ovalizat ion of the tube’s cross -section (ΔDo/Do) versus the applied curvature () for local sharp-notched SUS304 stainless steel tubes , with notch depth of a = 0.2 mm, subjected to cyclic bending under the curvature-rates of 0.035 and 0.35 m -1 s -1 , respectively. It can be noted that a higher degree of ovalizat ion can be noticed under higher curvature-rates. The ma ximu m ovalizations of 0.0018, 0.0023 and 0.0028 for the curvature of -0.3 m -1 at the 6 th cycle correspond to the curvature-rates of 0.0035, 0.035 and 0.35 m -1 s -1 , respectively. The highest and lowest curvature-rates have 100 t imes diffe rence. But, the ma ximu m mo ment increases 55.6 %. It is concluded that the curvature-rate has a strong influence on the ΔDo/Do- curve. Again, due to similar results, the e xperimental results of the ΔDo/Do- response for loca l sharp-notched SUS304 stainless steel tubes with notch depths of 0.4, 0.6, 0.8 and 1.0 mm under the curvature-rates of 0.0035 and 0.35 m -1 s -1 are omitted in this paper. (a) (b) Fig. 7 Experimentally determined ovalization of the tube cross -section (ΔDo/Do) versus the applied curvature () for loca l sharp-notched SUS304 stainless steel tubes , with notch depths of a = 0.2 mm, subjected to cyclic bending under the curvature-rate of (a) 0.0035 and (b) 0.35 m -1 s -1 4. Conclusions The response of local sharp-notched SUS304 stainless steel tubes with d ifferent notch depths subjected to cyclic bending at different curvature-rates was experimentally inves tigated in this study. Based on the e xperimental results, the following important conclusions can be drawn: Advances in Technology Innovation, vol. 1, no. 1, 2016, pp. 01 - 06 6 Copyright © TAETI (1) It is found from the M- curves that the local sharp-notched SUS304 stainless steel tubes with any notch depth at any curvature-rate exh ibits cyclical hardening and gradually steady after a few cycles under symmetrica l curvature-controlled cyclic bending. (2) It can be seen that a higher curvature-rate leads to a higher magnitude of the mo ment. In addition, the curvature-rate has a slight influence on the M- curves (Figs. (4), 5(a ) and 5(b)). (3) It is observed from the ΔDo/Do- curves that the ovalization of the tube cross -section increases in an unsymmetrical and ratcheting manner with the nu mber of cycles. Higher a leads to more severe unsymmetrica l trend of the ΔDo/Do- curve. (4) It can be seen that a higher curvature-rate leads to a greater ovalization of the tube cross -section. In addition, the curvature-rate has a strong influence on the ΔDo/Do- curves (Figs. 6(a), 7(a) and 7(b)). Acknowledgement The support of the National Sc ience Council (Taiwan), under Grant NSC 102-2221- E-006-037 is gratefully acknowledged. References [1] W. F. Pan, T . R. Wang, and C. M. Hsu, “A curvature- ovalization measurement apparatus for circula r tubes under cyclic bending,” Experimental Mechanics , vol. 38, no. 2, pp. 99-102, 1998. [2] W. F. Pan and Y. S. Her, “ Viscoplastic collapse of thin- wa lled tubes under cyclic bending,” Journal of Engineering Materials and Technology, vol. 120, no. 4, pp. 287-290, 1998. [3] K. L. Lee, W. F. Pan, and J. N. Kuo, “The influence of the diameter -to-thickness ratio on the stability of c ircular tubes under cyclic bending,” International Journal of Solids and Structures , vol. 38, no. 14, pp. 2401-2413, 2001. [4] K. L. Lee, W. F. Pan, and C. M . Hsu, “Expe rimental and theoretical evaluations of the effect between dia meter-to- thic kness ratio and curvature-rate on the stability of circula r tubes under cyclic bending,” JSM E International Journal, Series A, vol. 47, no. 2, pp. 212-222, 2004. [5] K. H. Chang and W. F. Pan, “Buckling life estimation of c ircula r tubes under cyclic bending,” International Journal of Solids and Structures , vol. 46, no. 2, pp. 254-270, 2009. [6] K. L. Lee and W. F. Pan, “ Viscoplastic collapse of titanium a lloy tubes under cyclic bending,” Structural Eng ineering and Mechanics, vol. 11, no. 3, pp. 315-324, 2001. [7] K. L. Lee, C. M. Hsu, S. R. Sheu, and W. F. Pan, “ Viscoplastic response and collapse of 316L stainless steel tubes under cyclic bending,” Steel and Composite Structures, vol. 5, no. 5, pp. 359-374, 2005. [8] P. K. Shaw and S. Kyria kides, “Inelastic analysis of thin-wa lled tubes under cyclic bending,” International Journal of Solids and Structures , vol. 21, no. 11, pp. 1073-1110, 1985.