A device and method for testing the dynamic tensile properties of a metal film
By using an improved Hopkinson tie rod device with low wave impedance aluminum alloy flat rods and adhesive bonding, the problem of weak signal in the dynamic performance testing of micron-thick metal thin films was solved, and accurate dynamic tensile performance measurement was achieved.
Patent Information
- Application Number
- CN202310037569.4
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2023-01-09
- Publication Date
- 2026-02-24
- Estimated Expiration
- 2043-01-09
AI Technical Summary
Existing dynamic tensile testing devices and methods are difficult to accurately measure the dynamic performance of micron-thick metal films. The generalized wave impedance mismatch between the traditional Hopkinson bar and the metal film results in a weak transmission signal. Existing improvement schemes, such as using hollow bars, polymer bars, and semiconductor strain gauges, have signal noise or error problems.
An extended incident flat rod and an extended transmission flat rod with extremely small cross-sectional area are used. The material is aluminum alloy with low wave impedance. The metal thin film specimen is connected by threaded connection and adhesive bonding. The stress-strain curve is calculated using the one-wave method to ensure that the signal propagation does not cause significant dispersion.
It enables precise testing of the dynamic tensile properties of micron-thick metal films, reduces connection errors, improves the amplitude of transmission signals, and ensures the accuracy of test results.
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Figure CN116086997B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of dynamic tensile testing technology for metal films, and more particularly to a testing device and method for the dynamic tensile properties of metal films. Background Technology
[0002] Metallic thin films are widely used in various devices and structures due to their superior performance and unique functionality. However, during their use, they inevitably experience impacts and collisions from external objects. This high-strain-rate dynamic load can cause plastic deformation or even failure of the metallic thin film. Accurately obtaining the dynamic properties of metallic thin films is crucial for their safe application. Because metallic thin films are extremely thin, traditional dynamic testing devices and methods (mainly split Hopkinson bars) are insufficient for accurately testing their dynamic properties. Therefore, developing a precise testing device and method for the dynamic tensile properties of micron-thick metallic thin films is of great significance for the engineering design and application of metallic thin films.
[0003] The most widely used technique for testing the high strain rate performance of materials and structures is the split Hopkinson bar technique. The basic principle of the Hopkinson bar is the stress wave theory. In the stress wave theory, the generalized wave impedance Z is defined as Z = ρCA, where ρ is the material density, C is the material wave velocity, and A is the cross-sectional area. Due to the extremely thin thickness of metal films, which can be as thin as 1 micrometer, the generalized wave impedance of the traditional split Hopkinson bar is extremely mismatched with that of the metal film sample. This results in a very weak signal detected by the strain gauge on the transmission bar, and the generated noise signal may even completely drown out the transmission signal. To address the problem of the weak transmission signal, selecting a bar system with low generalized impedance to match the low generalized impedance specimen is one of the important directions for solving this problem. In reference 1: Chen W, Zhang B, Forrestal M JA split Hopkinson bar technique for low-impedance materials[J]. Experimental Mechanics, 1999, 39(2): 81-85, a hollow transmission bar is proposed. The hollow structure can reduce the cross-sectional area to reduce the generalized wave impedance of the transmission bar. However, it is difficult to connect the metal thin film to the hollow bar structure in a simple way, and the complex stress on the end face of the hollow bar system itself does not satisfy the assumption of one-dimensional wave. The resulting error makes it impossible to use the already weak transmission signal to calculate the stress of the metal thin film. In reference 2: Wang LL, Labibes K, Azari Z, et al. A generalization of split hopkinson bar technique to using viscoelastic bars[J]. International Journal of Impact Engineering, 1994, 15(5): 669-686, it was proposed to replace the traditional Hopkinson metal bar with a polymer bar. The polymer bar has a lower elastic modulus, which can improve the amplitude of the transmission signal. However, on the one hand, the polymer material has poor thermal conductivity. The current flowing through the surface of the bar will generate heat, and the temperature rise will affect the strain gauge, resulting in measurement errors. On the other hand, the polymer material is a viscoelastic material. Viscoelasticity will cause the stress wave to produce a dispersion effect during propagation. Although the test results can be corrected by a dispersion correction model, the correction model itself will inevitably introduce errors. The influence of these two factors makes the signal obtained by the polymer bar inaccurate as well.Reference 3: Liu J, Wang Z, Hu S. The SHPB experiment technology for low wave impedance porous materials[J]. Journal of Experimental Mechanics, 1998, 13(2): 218-223, proposes using semiconductor strain gauges instead of traditional metal resistance strain gauges to measure the transmission signal through low impedance materials, which can increase the signal amplitude by nearly two orders of magnitude. However, semiconductor strain gauges are greatly affected by the environment during use, the sensitivity coefficient is nonlinear, and the temperature stability is poor, which seriously affects the accuracy of experimental results. Reference 4: Lin Y, Lu F, Lu L. The application of quartz transducer technique in SHPB[J]. Chinese Journal of High Pressure Physics, 2005, 19(4): 299, proposes using a high-sensitivity quartz piezoelectric sensor to detect weak transmission signals in the Hopkinson bar test. Experiments show that this technique can increase the signal amplitude by nearly three orders of magnitude. However, the piezoelectric sensor cannot be used in the Hopkinson bar test due to the influence of the connection form.
[0004] In summary, although various solutions have been proposed in domestic and international research to address the problem of weak transmission signals in the dynamic performance testing of low impedance materials, existing solutions are not applicable to the accurate testing of the dynamic tensile properties of micron-thick metal films. Summary of the Invention
[0005] To address the shortcomings and deficiencies of existing technologies, a testing device and method for the dynamic tensile properties of metal thin films are provided. This method effectively solves the technical problem that the generalized wave impedance of micron-thick metal thin films is too low, and the transmission signal in traditional split Hopkinson bars is too weak to be accurately measured.
[0006] A testing device and method for the dynamic tensile properties of a metal film, provided to achieve the purpose of this invention, includes a test bench. On the test bench, an energy transfer rod 2, a transfer flange 3, an impact tube 4, an air cannon 5, an incident rod 6, an extended incident flat rod 7, and an extended transmission flat rod 10 are arranged coaxially in sequence. The incident rod 6 and the extended incident flat rod 7 are tightly connected by threads. An energy absorber 1 is provided on the outer side of the energy transfer rod 2. The impact tube 4 is installed inside the air cannon 5. The transfer flange 3 is installed at the end of the incident rod 6. Strain gauges 8 are provided on both the extended incident flat rod 7 and the extended transmission flat rod 10. The extended incident flat rod 7 and the extended transmission flat rod 10 are coplanar. Specimen bonding grooves are opened on the inner ends of both the extended incident flat rod 7 and the extended transmission flat rod 10. Metal film specimens 9 are bonded to the two specimen bonding grooves by adhesive.
[0007] As a further improvement to the above scheme, the energy transfer rod 2, the impact tube 4, and the incident rod 6 are made of 18Ni maraging steel. Its elastic modulus is 190 GPa, and its density is 8 g / cm³. 3 The yield strength is above 1.8 GPa.
[0008] As a further improvement to the above scheme, the extended incident flat rod 7 and the extended transmission flat rod 10 are manufactured by staged cold rolling of 6061-T651 aluminum alloy with excellent machinability. The elastic modulus remains unchanged at 69 GPa after rolling, and the density remains unchanged at 2.7 g / cm³. 3 Its yield strength is significantly improved. Specifically, the initial blank cross-section is a 10mm × 10mm square. The aluminum alloy blank used for rolling the extended incident flat bar 7 is 1514mm long, with a rolling length of 1500mm. The aluminum alloy blank used for rolling the extended transmission flat bar 10 is 1200mm long. After full rolling and multiple rolling stages, the thickness of the flat bars is 1mm. After rolling, the width and longitudinal extensions after rolling are removed by wire cutting. After removing the extensions, the lengths of the extended incident flat bar 7 and the extended transmission flat bar 10 are 1500mm and 1200mm respectively, and the width is 14mm. The extended incident flat bar 7 conforms to the one-dimensional stress wave assumption, and the stress wave will not disperse significantly during propagation, such as... Figure 5 As shown.
[0009] As a further improvement to the above scheme, the unrolled portion of the extended incident flat rod 7 is 14mm, and 12mm of it is machined with M8 threads. A 12mm deep M8 threaded hole is opened at one end of the incident rod 6.
[0010] As a further improvement to the above scheme, the gauge length of the metal thin film specimen 9 is 8mm and the width is 6mm.
[0011] As a further improvement to the above scheme, the specimen bonding groove is manufactured by wire cutting, and the thickness of the specimen bonding groove is 0.2 mm. The specimen bonding section of the metal film specimen 9 is coated with adhesive and bonded to the specimen bonding groove of the extended incident flat rod 7 and the extended transmission flat rod 10. This connection method can effectively avoid the test error introduced by the connection method.
[0012] As a further improvement to the above scheme, both the extended incident flat rod 7 and the extended transmission flat rod 10 are thin rods with small cross-sectional areas and are made of aluminum alloy material with low wave impedance. This reduces the generalized wave impedance of the rods, significantly improves the amplitude of the transmitted signal, and enables accurate testing of the dynamic tensile mechanical properties of micron-thick metal films.
[0013] A method for testing the dynamic tensile properties of a metal thin film using the apparatus described in claim 1, comprising the following steps:
[0014] Step 1: Adjust the impact tube 4, incident rod 6, extended incident flat rod 7 and extended transmission flat rod 10 to make them coaxial. Connect the extended incident flat rod 7 and incident rod 6 by thread. Adjust the extended transmission flat rod 10 and extended incident flat rod 7 to make them coplanar.
[0015] Step 2: The metal thin film specimen 9 is glued to the specimen bonding groove between the extended incident flat rod 7 and the extended transmission flat rod 10.
[0016] Step 3: Adjust the air pressure of the air cannon 5, and launch the impact tube 4 to impact the transmission flange 3, generating a tensile stress wave in the incident rod 6. This tensile stress wave is transmitted to the extended incident flat rod 7 at the thread between the extended incident flat rod 7 and the incident rod 6. The tensile stress wave transmitted to the extended incident flat rod 7 continues to be transmitted to the metal thin film specimen 9. Part of the stress wave is reflected in the extended incident flat rod 7 to form a reflected wave. The strain gauge 8 on the extended incident flat rod 7 records the reflected wave signal ε. R Another portion of the stress wave is transmitted through the metal thin film specimen 9 along the extended transmission flat rod 10, and the transmitted wave signal ε is recorded by the strain gauge 8 on the extended transmission flat rod 10. T The stress-strain curve of the metal thin film specimen 9, which is also the stress-strain curve in this tensile deformation, was obtained by calculating the one-wave method.
[0017] As a further improvement to the above scheme, the one-wave method calculation in step 3 is specifically calculated using the following formula:
[0018]
[0019]
[0020]
[0021] In equations (1)-(3), ε S Let σ be the strain of the specimen during this tensile process. S This refers to the stress during the tensile process. Let C0 be the strain rate during the tensile process, C0 be the longitudinal wave velocity of the extended incident bar, L be the length of the specimen, E be the elastic modulus of the extended incident bar, and A be the cross-sectional area of the extended incident bar. S This represents the cross-sectional area of the specimen.
[0022] As a further improvement to the above scheme, the extended incident flat bar 7 and the extended transmission flat bar 10 are specifically manufactured by the following method: during rolling, a rolling roll with a radius of 4.5 mm is used, the single roll pressing amount is set to be equal to the rolling roll radius of 4.5 mm, the total pressing amount is 9 mm, and three rolling passes are performed. After each pass, an annealing process with an annealing temperature of 300°C is applied for 1 hour.
[0023] The beneficial effects of this invention are:
[0024] Compared with the prior art, the present invention has the following beneficial effects:
[0025] (1) In view of the problem that the generalized wave impedance of metal thin film is too low and the transmission signal of dynamic test is weak, the present invention proposes an improved split Hopkinson rod device with an extended incident flat rod and an extended transmission flat rod having an extremely small cross-sectional area.
[0026] (2) The extended incident flat bar and the extended transmission flat bar in this invention are made of aluminum alloy material with low wave impedance, which is rolled in stages. The thickness of the rolled extended flat bar is only 1 mm, and its elastic modulus and density remain unchanged, but its yield strength is significantly improved. The extremely thin extended incident flat bar and the extended transmission flat bar greatly improve the amplitude of the transmission signal, which can realize the accurate testing of the dynamic tensile mechanical properties of micron-thick metal films.
[0027] (3) In this invention, the extended incident flat rod and the incident rod are connected by threads, which makes disassembly simple and facilitates repeated testing. Furthermore, the extended incident flat rod and the extended transmission flat rod have simple structures and can be achieved using existing rolling and wire cutting technologies.
[0028] (4) The metal thin film specimen is glued to the specimen bonding groove of the extended incident flat rod and the extended transmission flat rod. This connection method can effectively avoid the test error introduced by the connection method. Attached Figure Description
[0029] The specific embodiments of the present invention will be further described in detail below with reference to the accompanying drawings, wherein:
[0030] Figure 1 This is a schematic diagram of the structure of the present invention;
[0031] Figure 2 for Figure 1 Partial sectional view at point A in the middle;
[0032] Figure 3 for Figure 1 Enlarged view of a section at point B in the middle;
[0033] Figure 4 This is a schematic diagram of the specimen of the present invention;
[0034] Figure 5 The stress wave propagation signal is shown at different cross-sections (0.4m, 0.8m, and 1.2m from the reflecting end) on the extended incident flat rod.
[0035] In the figure: 1-Energy absorber, 2-Energy transfer rod, 3-Transfer flange, 4-Impact tube, 5-Gas cannon, 6-Incident rod, 7-Extended incident flat rod, 8-Strain gauge, 9-Metal thin film specimen, 10-Extended transmission flat rod, 11-Incident rod threaded hole, 12-Extended incident flat rod thread, 13-Extended incident flat rod specimen bonding groove, 14-Extended transmission flat rod specimen bonding groove, 15-Specimen bonding section. Detailed Implementation
[0036] like Figure 1 As shown, the present invention provides a testing device and method for the dynamic tensile properties of metal films, comprising a test bench on which an energy transfer rod 2, a transfer flange 3, an impact tube 4, an air cannon 5, an incident rod 6, an extended incident flat rod 7, and an extended transmission flat rod 10 are coaxially arranged in sequence. The extended incident flat rod 7 and the extended transmission flat rod 10 are both thin rods with small cross-sectional areas and are made of aluminum alloy material with low wave impedance. This reduces the generalized wave impedance of the rods, significantly increasing the amplitude of the transmitted signal, and enabling accurate testing of the dynamic tensile mechanical properties of micron-thick metal films. The incident rod 6 and the extended incident flat rod 7 are tightly connected by threads (i.e., Figure 2The incident rod 6 has a threaded hole 11 and an extended incident flat rod threaded 12. The unrolled portion of the extended incident flat rod 7 is 14mm, with 12mm of it being machined into an M8 thread. A 12mm deep M8 threaded hole is formed at one end of the incident rod 6. An energy absorber 1 is installed on the outside of the energy transfer rod 2. The impact tube 4 is installed inside the air cannon 5. The transmission flange 3 is installed at the end of the incident rod 6. Strain gauges 8 are provided on both the extended incident flat rod 7 and the extended transmission flat rod 10. The extended incident flat rod 7 and the extended transmission flat rod 10 are coplanar. Specimen bonding grooves are formed on the inner ends of both the extended incident flat rod 7 and the extended transmission flat rod 10. Metal film specimens 9 are bonded to the two specimen bonding grooves by adhesive. The specimen bonding grooves are machined by wire cutting, and the thickness of the specimen bonding grooves is 0.2mm. The specimen bonding section 15 of the metal thin film specimen 9 is coated with adhesive and bonded to the specimen bonding grooves of the extended incident flat rod 7 and the extended transmission flat rod 10 (i.e., within the specimen bonding grooves 13 and 14 of the extended incident flat rod and the extended transmission flat rod, respectively). This connection method can effectively avoid test errors introduced by the connection method. The gauge length of the metal thin film specimen 9 is 8 mm long and 6 mm wide.
[0037] Specifically, the energy transfer rod 2, the impact tube 4, and the incident rod 6 are made of 18Ni maraging steel. Its elastic modulus is 190 GPa, and its density is 8 g / cm³. 3 The yield strength is above 1.8 GPa.
[0038] Further improvements include the generation of the extended incident flat bar 7 and the extended transmission flat bar 10 through staged cold rolling of 6061-T651 aluminum alloy, which exhibits excellent machinability. Specifically, the extended incident flat bar 7 and the extended transmission flat bar 10 are manufactured using the following method: rolling is performed using 4.5mm radius rolls, with the single-roll pressing amount equal to the roll radius of 4.5mm, resulting in a total pressing amount of 9mm. Three rolling passes are performed, followed by an annealing process at 300℃ for 1 hour after each pass. The elastic modulus remains unchanged at 69GPa, and the density remains unchanged at 2.7g / cm³. 3 Its yield strength is significantly improved. Specifically, the initial blank cross-section is a 10mm × 10mm square. The aluminum alloy blank used for rolling the extended incident flat bar 7 is 1514mm long, with a rolling length of 1500mm. The aluminum alloy blank used for rolling the extended transmission flat bar 10 is 1200mm long. After full rolling and multiple rolling stages, the thickness of the flat bars is 1mm. After rolling, the width and longitudinal extensions after rolling are removed by wire cutting. After removing the extensions, the lengths of the extended incident flat bar 7 and the extended transmission flat bar 10 are 1500mm and 1200mm respectively, and the width is 14mm. The extended incident flat bar 7 conforms to the one-dimensional stress wave assumption, and the stress wave will not disperse significantly during propagation, such as... Figure 5As shown. The extended incident flat rod 7 conforms to the one-dimensional stress wave assumption, and the stress wave will not significantly disperse during propagation, as... Figure 5 As shown.
[0039] A method for testing the dynamic tensile properties of a metal thin film using the apparatus described in claim 1, comprising the following steps:
[0040] Step 1: Adjust the impact tube 4, incident rod 6, extended incident flat rod 7 and extended transmission flat rod 10 to make them coaxial. Connect the extended incident flat rod 7 and incident rod 6 by thread. Adjust the extended transmission flat rod 10 and extended incident flat rod 7 to make them coplanar.
[0041] Step 2: The metal thin film specimen 9 is glued to the specimen bonding groove between the extended incident flat rod 7 and the extended transmission flat rod 10.
[0042] Step 3: Adjust the air pressure of the air cannon 5, and launch the impact tube 4 to impact the transmission flange 3, generating a tensile stress wave in the incident rod 6. This tensile stress wave is transmitted to the extended incident flat rod 7 at the thread between the extended incident flat rod 7 and the incident rod 6. The tensile stress wave transmitted to the extended incident flat rod 7 continues to be transmitted to the metal thin film specimen 9. Part of the stress wave is reflected in the extended incident flat rod 7 to form a reflected wave. The strain gauge 8 on the extended incident flat rod 7 records the reflected wave signal ε. R Another portion of the stress wave is transmitted through the metal thin film specimen 9 along the extended transmission flat rod 10, and the transmitted wave signal ε is recorded by the strain gauge 8 on the extended transmission flat rod 10. T The stress-strain curve of the metal thin film specimen 9, i.e., the stress-strain curve during this tensile deformation, was obtained by calculation using the one-wave method. Specifically, it was calculated using the following formula:
[0043]
[0044]
[0045]
[0046] In equations (1)-(3), ε S Let σ be the strain of the specimen during this tensile process. S This refers to the stress during the tensile process. Let C0 be the strain rate during the tensile process, C0 be the longitudinal wave velocity of the extended incident bar, L be the length of the specimen, E be the elastic modulus of the extended incident bar, and A be the cross-sectional area of the extended incident bar. S This represents the cross-sectional area of the specimen.
[0047] The above embodiments are not limited to the technical solutions of the embodiments themselves, and the embodiments can be combined with each other to form new embodiments. The above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the scope of the technical solutions of the present invention.
Claims
1. A testing device for the dynamic tensile properties of metal films, characterized in that: The test bench includes an energy transfer rod (2), a transfer flange (3), an impact tube (4), an air cannon (5), an incident rod (6), an extended incident flat rod (7), and an extended transmission flat rod (10) arranged coaxially on the test bench. The incident rod (6) and the extended incident flat rod (7) are tightly connected by threads. An energy absorber (1) is provided on the outside of the energy transfer rod (2). The impact tube (4) is installed inside the air cannon (5). The transfer flange (3) is installed at the end of the incident rod (6). The extended incident flat rod (7) and the extended transmission flat rod (10) are connected coaxially on the test bench. Strain gauges (8) are provided on the incident flat rod (10). The extended incident flat rod (7) and the extended transmission flat rod (10) are coplanar. The inner ends of the extended incident flat rod (7) and the extended transmission flat rod (10) are provided with specimen bonding grooves. Metal film specimens (9) are bonded to the two specimen bonding grooves by adhesive. The extended incident flat rod (7) and the extended transmission flat rod (10) are both thin rods with small cross-sectional areas. The material of the extended incident flat rod (7) and the extended transmission flat rod (10) is set to aluminum alloy with a wave impedance lower than that of the incident rod (6).
2. The testing device for the dynamic tensile properties of a metal film according to claim 1, characterized in that: The energy transfer rod (2), impact tube (4) and incident rod (6) are made of 18Ni maraging steel.
3. The testing device for the dynamic tensile properties of a metal film according to claim 1, characterized in that: The extended incident flat bar (7) and the extended transmission flat bar (10) are made by staged cold rolling of 6061-T651 aluminum alloy with excellent processing performance.
4. The testing device for the dynamic tensile properties of a metal film according to claim 1, characterized in that: The unrolled portion of the extended incident flat rod (7) is 14mm, and 12mm of it is machined into an M8 thread. A 12mm deep M8 threaded hole is opened at one end of the incident rod (6).
5. The testing device for the dynamic tensile properties of a metal film according to claim 1, characterized in that: The gauge length of the metal thin film specimen (9) is 8 mm and the width is 6 mm.
6. The testing device for the dynamic tensile properties of a metal film according to claim 1, characterized in that: The bonding groove of the specimen is manufactured by wire cutting, and the thickness of the bonding groove is 0.2 mm.
7. A method for testing the dynamic tensile properties of metal films using the apparatus described in claim 1, characterized in that: The steps include the following: Step 1: Adjust the impact tube (4), incident rod (6), extended incident flat rod (7) and extended transmission flat rod (10) to make them coaxial. Connect the extended incident flat rod (7) and incident rod (6) by thread. Adjust the extended transmission flat rod (10) and extended incident flat rod (7) to make them coplanar. Step 2: The metal thin film specimen (9) is glued to the specimen bonding groove between the extended incident flat rod (7) and the extended transmission flat rod (10) by means of adhesive. Step 3: Adjust the air pressure of the air gun (5), launch the impact tube (4) to impact the transmission flange (3), and generate a tensile stress wave in the incident rod (6). This tensile stress wave is transmitted to the extended incident flat rod (7) at the thread of the incident rod (6). The tensile stress wave transmitted to the extended incident flat rod (7) continues to be transmitted to the metal thin film specimen (9). Part of the stress wave is reflected in the extended incident flat rod (7) to form a reflected wave. The strain gauge (8) on the extended incident flat rod (7) records the signal of the reflected wave. Another portion of the stress wave is transmitted through the metal thin film specimen (9) along the extended transmission flat rod (10), and the transmitted wave signal is recorded by the strain gauge (8) on the extended transmission flat rod (10). The stress-strain curve of the metal thin film specimen (9) was obtained by one-wave method, which is also the stress-strain curve in this tensile deformation.
8. The method for testing the dynamic tensile properties of metal films according to claim 7, characterized in that: The one-wave method calculation in step 3 is specifically calculated using the following formula: ; In equations (1)-(3), The strain of the specimen during this tensile process is represented by the following: This refers to the stress during the tensile process. Let be the strain rate during this stretching process. To extend the longitudinal wave velocity of the incident flat rod, The length of the specimen. To extend the elastic modulus of the incident flat rod, To extend the cross-sectional area of the incident flat rod, This represents the cross-sectional area of the specimen.
9. The method for testing the dynamic tensile properties of metal films according to claim 8, characterized in that: The extended incident flat bar (7) and the extended transmission flat bar (10) are specifically manufactured by the following method: during rolling, a rolling roll with a radius of 4.5 mm is used, the single roll pressure is set to be equal to the rolling roll radius of 4.5 mm, the total pressure is 9 mm, and three rolling passes are performed. After each pass, an annealing process with an annealing temperature of 300℃ is applied for 1 hour.
Citation Information
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