Using industrial tools to bend titanium tubes is one of the most difficult tasks in modern manufacturing. To make precise curved shapes out of straight titanium alloy lines, you have to get Bending Titanium Tubings around titanium's unique mechanical properties, especially its low modulus of elasticity and high springback tendency. For titanium tubing to have the right strength-to-weight ratio and work-hardening behavior, you need special tools, careful process control, and a lot of knowledge about metals. These problems have a big effect on production prices, lead times, and quality in many fields, from aircraft to offshore energy. Because of this, source knowledge is an important thing to think about when buying something.
Understanding the Challenges of Bending Titanium Tubings
When shaping titanium alloy pipes into bent shapes, some challenges set this material apart from more common options. Titanium has unique qualities that make it useful in service settings, but they also make production very hard. This is something that engineering and procurement teams have to think about when they need to bend titanium tubing for mission-critical uses.
Titanium's Unique Physical Properties and Their Impact
Titanium has an elasticity value of about 105–120 GPa, which is about half that of steel. Titanium is more springy when it is deformed because of this basic property of the material. This means that springback rates are between 15 and 25 percent. When we apply bending forces to titanium tubes, the material originally bends to the shape of the tooling, but when the load is released, it partly returns to its straight shape. To get the final dimensions to be accurate within tolerances like ±0.1° angular precision, this elastic rebound needs complex overbending formulas and special tooling geometry. The tendency for work-hardening makes the bending process even more difficult. Titanium's crystal structure changes when it goes through plastic distortion, which greatly raises the local yield strength. This strain-hardening effect can make the material behave unevenly along the bend, which could lead to cracks in places where the tension stress is highest on the outer radius. The hexagonal close-packed crystal structure of the material makes slip systems less effective than in face-centered cubic metals, which makes the material less flexible when cold forming is done.
Common Defects and Quality Control Concerns
There are several ways that defects can happen that make bent titanium parts less safe. Depending on the bend radius-to-diameter ratio, wall thinning on the outer radius can reach 15–30%. For important uses, this reduction must be limited with a mandrel. On the other hand, if compression forces are higher than the material's local buckling resistance, the inner radius's walls get thicker, and it might wrinkle. Cross-sectional ovality, or the difference from a round shape, must stay within limits set by the industry. For high-pressure fluid systems used in aircraft applications, these limits are usually less than 5%. Damage to the surface raises more quality issues. Tool contact is especially hard on titanium because it is reactive and tends to gall. The inactive oxide layer that gives titanium its famous resistance to rusting can be damaged by iron that comes from steel tools. We see adhesive wear between titanium and tool surfaces at contact pressures that are typical in rotary draw bending. To meet surface finish standards, we need special tool materials and boundary lubricants.
Industry Standards and Bend Radius Requirements
Different industries must follow different worldwide standards for acceptable bend radius requirements. AMS 4928 and MIL-T-9047 are often used in aerospace applications because they set the minimum centerline radius (CLR) standards based on the outside width. Minimum bend radii are usually set at 2D to 3D, which is two to three times the outer diameter of the tube. With modern rotary draw bending tools and internal mandrel support, it is still possible to make tighter shapes down to 1.5D, but these challenging shapes need very good process control and choice of material grade. For uses in the energy sector that follow ASTM B338 and NACE MR0175, it is important to keep the wall thickness uniform and avoid microstructural damage that could lower corrosion resistance in sour service conditions. When medical devices are made with ASTM F67 and ISO 13485 approval, they must have clean surfaces and be able to fully trace the heat treatment conditions that affect how well they sterilize and work with living things.
Technical Analysis: Why Titanium Tubing Is Hard to Bend
When you know the chemical and mechanical differences between titanium and other materials, you can see why you need to invest in specialized processes and tools for production to go smoothly.
Material Property Comparison with Alternative Alloys
For example, austenitic stainless steel is often used as a substitute in corrosive settings, but titanium bends in very different ways. The higher modulus of elasticity of stainless steel (about 200 GPa) makes the springback more reliable, Bending Titanium Tubings at about 5–10% compared to 15–25% for titanium. This regularity makes tools easier to use and set up faster. But titanium is less dense than stainless steel (7.9 g/cm³ vs. 4.5 g/cm³), so stainless steel can't be used in weight-critical situations where every kilogram affects fuel economy or loading capacity. Grades 1 and 2 of commercially pure (CP) titanium are better at being cold shaped than titanium alloys, with stretch values hitting 20 to 30 percent. Because these types can be heated and shaped more precisely, they are the best choice for heat exchanger U-bends in chemical processing and purification plants. While Grade 5 titanium alloy (Ti-6Al-4V) has the high strength needed for aircraft structures, it is less flexible (10–15% elongation) and needs to be shaped at high temperatures for shapes with radii below 3D to keep them from cracking. The effects on costs go beyond the prices of raw materials. Titanium tubing is more expensive than stainless steel tubing—often three to five times as much. The Bending Titanium Tubings process also adds to this price difference. Longer cycle times because of slower forming speeds, the need for specialized tools, and higher rates of scrap during process development can lead to manufacturing costs that are up to twice as high as for similar stainless steel operations. These economic factors make supplier skill and quality, at first attempt, the most important factors in purchasing choices.
Bending Technique Selection and Equipment Requirements
The most common way to make precise turns in a titanium tube is through rotary draw bending. To control the flow of material and stop flaws, this method uses an internal mandrel, a clamping device, a rotating bend die, a pressure die, a wiper die, and a pressure die. The mandrel, which is usually made of solid brass or a special kind of tool steel, holds up the inside diameter of the tube through the bend zone, keeping it from collapsing and reducing ovality. Wiper dies closely follow the outside of the tube, keeping the material from stretching on the inside radius to avoid wrinkles. The cost of tools for compression bending and ram bending is lower, but it's hard to control the dimensions, so they can't be used for jobs that need to be precise. These ways don't provide enough internal support, which leads to too much ovality and wall thinning, which aren't allowed in high-performance systems. Induction bending heats certain areas to briefly lower the yield strength. This lets heavier-wall tubing have tighter radii, but the mechanical features need to be restored by another heat treatment, and there is a chance of grain growth if temperature control isn't good enough. Modern CNC-controlled bending machines have formulas for adjusting for springback, servo-driven pressure control, and real-time tracking of dimensions. These high-tech machines figure out overbend angles by taking into account the type of material, the thickness of the wall, and the bend radius. They then change the position of the tool automatically to reach the desired shape. When purchasing managers look at different providers, the level of sophistication of the tools they have directly affects the tolerances they can work with and the consistency of their work. Manufacturers who still use old manual or semi-automatic tools find it hard to keep up with the ±0.1° accuracy in angles and ±0.5mm repeatability in dimensions that modern aircraft and medical uses need.
Process Control Parameters Critical to Success
Managing the temperature has a big effect on how the form turns out. When CP titanium grades are at room temperature, they are usually bent cold. However, when Grade 5 metal is heated to 200–400°C, it is often shaped better. This range of temperatures in the middle lowers flow stress without encouraging too much grain growth or rusting. Temperature regularity across the bend zone is very important because differences in temperature cause differences in strength that show up as uneven springback and geometrical errors. Strain rate effects show that bending speed changes how a material behaves. Titanium is sensitive to strain rate, and higher deformation rates make the immediate flow stress higher. In production settings, slower making speeds—about 3 to 6 seconds per 90-degree bend on average—allow stress to be spread out more evenly and reduce strain loads in certain areas. But speeds that are too slow make cycle times longer and make the business less profitable. To balance quality with efficiency, the process needs to be optimized. Because titanium is reactive, choosing the right lubricant can be hard. Compounds that contain chlorine should not be used because they can cause stress corrosion cracks while they are in use. Heavy-duty synthetic lubricants or specialty graphite-based formulas make boundary layers that keep metals from touching each other too much, which stops galling and damage to the surface. Post-bend cleaning gets rid of lubricant leftovers that could get in the way of future welding or dirty clean rooms used to make medical devices.
Best Practices and Techniques for Bending Titanium Tubings
Systematic process development based on metallurgical principles and validation through iterative improvement is needed to get uniform, defect-free results. The methods listed below have been used for a long time and have been shown to reduce scrap rates and ensure that measurements are met.
Material Selection and Pre-Bend Preparation
Choosing the right grade is the first step in doing good Bending Titanium Tubings work. Grade 2 titanium has the best mix of corrosion protection and ductility for uses that need the most shapeability. Its annealed microstructure can handle a lot of bending without breaking, so it can be used for complicated shapes with lots of bends or small radii. In situations where higher strength means less formability, Grade 9 titanium (Ti-3Al-2.5V) performs in the middle, being able to bend better than Grade 5 while still being much stronger than commonly pure grades. Wall thickness-to-diameter ratios have a big effect on how bendable something is. Thin-wall tubing (wall thickness less than 5% of outside diameter) needs internal tube support to keep it from collapsing. On the other hand, thick-wall shapes (more than 12% ratio) have more springback and may need to be hot-formed. During the planning phase, we suggest going over the dimensional specs with our production partners. Even small changes to the geometry can have a big impact on how much it costs and how easy it is to make. Checking the surface state before bending stops defects from spreading. Existing flaws like scratches, holes, or inclusions act as stress collectors that cause cracks to form when the material deforms. When material comes in, it should be inspected to make sure the surface finish meets the requirements of the standard, and any problems should be recorded. Surface quality is maintained throughout the manufacturing process by using the right tools for the job, such as protective caps for tube ends and padded storage racks.
Critical Process Parameters and Real-Time Monitoring
The choice of mandrel and where it is placed may have the most impact on the quality of the bend. Ball mandrels, which are made up of several circular links, bend to the radius of the bend and provide support around the outside. For each mix of tube size and bend radius, the link width, number of balls, and mandrel extension past the tangent point need to be optimized. When the mandrel doesn't have enough support, it can break from the inside, and when there is too much interference, it can mark the surface or stop the flow of material, which can cause wrinkles or errors in the dimensions. The clamp die pressure needs to hold the tube tightly without dents or stress buildup. Pressure profiling is possible with servo-controlled hydraulic systems, which raise the gripping force gradually as the bend moves forward and springback potential builds up. This dynamic pressure management, along with materials for the soft mouth inserts that spread contact loads, keeps the positional accuracy and stops damage to the surface. The shape and placement of the wiper die determine how the material acts on the inside radius of the bend. The nose radius, relief angle, and distance from the tube surface of the wiper die need to be precisely adjusted to keep the material from piling up and wrinkles from forming. Gap sizes are usually between 0.05 and 0.15 mm, but they depend on the type of material and the thickness of the wall. Thin-walled designs that are more likely to become unstable need tighter gaps. Dimensional checks are done at set times during production runs to catch process drift before tolerances are broken. Coordinate measuring machines (CMMs) are used to record bend angles, centerline radius accuracy, and cross-sectional geometry. This creates statistical process control for Bending Titanium Tubings data that helps with planned maintenance and ongoing improvement projects.
Application-Specific Case Examples from Key Industries
Fabrication of aerospace hydraulic systems shows the strict needs that are common in flight-critical uses. Fuel lines and hydraulic networks in airplanes need to be able to keep their integrity under repetitive pressure and stress loading at temperatures ranging from -55°C to +200°C. For a recent project that supplied regional aircraft makers, Grade 2 titanium bends with a 2.5D centerline radius had to be made in 25mm OD x 1.2mm wall tubes. To get the needed ±0.1° angular correction and less than 3% ovality, the mandrel had to be optimized using finite element simulations and real prototypes. The process that was created keeps the difference in wall thickness to within 8%, meeting the standards for pressure ratings and fatigue life goals of more than 50,000 flight cycles. Surface cleanliness and biocompatibility are important for medical gadget use, along with accuracy in measurements. Surgical robotic tool channels need a titanium tube that is sterilizable, free of burrs, and has a complex spatial shape so that it can move through the body. A top robotic surgery platform calls for a Grade 2 tube with a wall thickness of 0.8 mm that has been shaped into complex curves that combine different bend angles. Electropolishing is done after the bend process to get a surface finish with a roughness level below 0.4µm. This gets rid of any cracks where organic material could gather. Cleanroom production methods and passivation processes make sure that the surface chemistry is implant-grade and meets ASTM F86 standards. New high-volume uses for titanium bends include thermal control systems for electric car batteries. For heat transfer to work well, cooling circuits that use liquid or gas coolant must go through layouts with a lot of batteries while keeping the wall thickness the same. Even though it costs more, grade 2 titanium is becoming more popular because it doesn't rust when used with ethylene glycol coolants and is 40% lighter than aluminum. For production, complicated three-dimensional tube shapes with multiple bends in space planes need to be made. This is done with multi-axis CNC tube bending tools and complex fixtures that keep the geometric relationships between bends.
Procurement Insights for Titanium Tubing Bending Projects
When choosing where to get bent titanium parts, you have to look at professional capabilities, quality systems, and business factors that affect the overall success of the project and the total cost of ownership.
Supplier Qualification Criteria and Capability Assessment
The manufacturing license portfolio is the first step in figuring out how sophisticated a seller is. Aerospace suppliers need to show that they have an AS9100 quality management system approval, which proves that the process rules are right for flight-critical parts. Manufacturers of medical devices need to be certified with ISO 13485, which includes design controls, tracking systems, and biocompatibility evaluation procedures. For European markets, uses in the energy sector, especially sour service conditions in oil and gas extraction, need to be certified to NACE standards and the pressure equipment directive (PED). The ability of the equipment directly affects the limits that can be used and the ability to increase output. When we evaluate providers, we give more weight to those who use CNC rotary draw bending tools with servo-controlled axes and built-in springback correction. Manual or hydraulic machines from the past don't have the accuracy and process recording tools that are needed for today's quality standards. We make sure that our inventory of mandrels includes all the bend radii and tube sizes that are expected over the lifetime of a product. This is because the availability of tools affects wait times and the speed at which prototypes are iterated. Expertise in metalworking is what sets qualified suppliers apart from job shops that only bend titanium tubing. Technical staff should be able to show that they understand why certain titanium grades are chosen, how heat treatment affects the material's ability to be shaped, and how to spot defects. During source visits, we check how good the technical help is by talking about tough situations like getting sub-2D bend radii or controlling springback in heavy-wall Grade 5 alloy. Suppliers who can't explain the physics of the process or offer other options usually don't have enough experience for development projects or uses with tight tolerances. Material tracking systems make sure that rules about medical devices and aircraft products are followed by keeping full records of the chain of custody. Each bent part should have material certifications that can be traced back to the original test reports, records of the heat treatment process that show the time and temperature profiles, and inspection data packages that include readings of the part's size and non-destructive test results if needed. Electronic tracking systems make it easier to find documents and do statistical analysis across different production lots.
Cost Structure Analysis and Budget Optimization Strategies
The direct prices of materials for titanium tubes depend a lot on the grade, the size, and the number of pieces ordered. Standard sizes of Grade 2 economically pure material cost between $45 and $65 per kilogram, while Grade 5 metal costs between $65 and $90 per kilogram. Specialty configurations with thin walls or big diameters cost more because they are harder to make. We make bulk purchase deals directly with titanium mills or distributors to get better prices for annual needs over 500 kg, which saves us 10–20% compared to spot market transactions. The costs of bending depend on the type of tools used, the time it takes to bend, and the output rate. Simple bends with standard radii in grades that are easy to shape may cost an extra $30 to $50 per bend. Tight-radius layouts in difficult alloys that need a lot of setup work and more scrap can cost $150 to $300 per bend. Setting up amortization makes the cost of each piece higher for prototypes or low-volume production. When production numbers are less than 25, unit costs often double compared to groups of over 100 pieces. We work with our sources to group together parts with similar bend shapes in order to save money by spreading setup costs across many part numbers. Costs go up for secondary processes like cleaning, surface treatments, and non-destructive testing. Crack detection with liquid penetrant inspection costs $8 to $15 per piece, based on how complicated the piece is. Ultrasonic wall thickness proof costs an extra $12 to $20 per piece. Passivation processes that restore maximum corrosion resistance cost between $5 and $10 per piece. For medical uses, cleanroom cleaning with confirmed residue testing costs an extra $15 to $25 per assembly. Knowing about these extra costs during planning keeps shocks from happening at the last minute that could hurt the economics of the program. Suppliers can invest in specialized tooling and process optimization when they have long-term supply deals with fixed volume expectations. This lowers costs for both parties. We set up agreements with tiered prices based on quarterly number commitments. This lets you plan your costs ahead of time while still allowing for changes in demand. Including plans for yearly cost cuts—usually between 3 and 5 percent through programs for continuous improvement—aligns seller incentives with our procurement goals. Performance measures like on-time delivery, first-pass yield rates, and quality events are tracked in quarterly business reviews. This makes sure that everyone is responsible and enables early problem resolution.
Future Trends and Innovations in Titanium Tubing Bending
New technologies offer to solve long-standing problems in Bending Titanium Tubings while also making more uses possible by making them more useful and cheaper. Companies that buy things are keeping an eye on these changes so that they can take advantage of new ideas as they grow and become commercially viable.
Advanced Forming Technologies and Process Innovations
Pulsed magnetic fields are used in electromagnetic forming to shape materials quickly without using mechanical tools. This process doesn't touch the metal, so there are no worries about galling or damage to the surface. It also makes it possible to bend things very tightly. Researchers have used electromagnetic fields to bend a Grade 2 titanium tube to a 1D radius with little wall thinning. However, the cost of the technology and the amount of energy it needs to run make it hard to use in production. As capacitor bank technology improves and equipment becomes easier to get, electromagnetic making might make it possible to do geometric things that aren't possible with current methods. CNC-controlled tools are used in incremental sheet forming and tube forming to gradually deform materials through many small localized stresses instead of a few big strain events. This method spreads deformation more evenly, lowering the highest strain levels that cause cracking while increasing the range of possible shapes. Tube incremental forming systems were created for research purposes and have made freeform forms that are too complicated for normal bends. However, the long cycle times mean that they can only be used for prototypes and very low volumes. When added to additive manufacturing, it changes the way that uses that need bent tubes are done. Wire-arc additive manufacturing and powder bed fusion technologies can now make titanium tube and pipe systems with complicated three-dimensional shapes that would need to be bent and welded many times in the old way of doing things. At the moment, additive processes have problems Bending Titanium Tubings with accuracy in measurements, surface finish, and production volume. However, if they keep improving, the point at which cost and performance meet may move, and within five years, additively manufactured fluid distribution systems may be able to compete in some application niches.
Material Development Enhancing Formability Characteristics
From metallurgical study projects come new titanium alloys that have been changed to work best for cold forming. When controlled amounts of oxygen, iron, and other interstitials are added to experimental mixtures, they show better ductility and less springback compared to regular grades. Beta-stabilized titanium alloys keep their formability at room temperature, which is similar to aluminum alloys, while still having the corrosion-resistance benefits of titanium. When these developmental grades finish their qualification tests and are made available to the public by big titanium makers, they will give designers more options and lower the cost of production for uses that don't need the highest strength. Technologies that change the tribological features of surfaces could help cut down on tool contact problems. When applied to bent dies and mandrels, physical vapor deposition (PVD) films greatly lower friction coefficients and stop adhesive wear. Using nanoparticles in new types of lubricants makes the boundary layers last longer and can handle the high contact forces that happen during tight-radius bends. These technologies allow for stricter process settings and longer tool life, which has a direct effect on the cost of production.
Strategic Implications for Planning the Supply Chain and Buying Things
Procurement pros can talk to sellers about capability roadmaps and investment goals by staying up to date on changes in technology. We now look at a supplier's history of adopting new technologies and their dedication to research and development (R&D) as signs of how competitive they will be in the future. Suppliers who are actively involved in industry research consortia or university partnerships show that they are open to new ideas, which can give them a competitive edge in new uses. Joint development deals that share investment costs and intellectual property for new Bending Titanium Tubings processes that meet specific application needs are becoming a more common part of strategic supplier relationships. These partnerships speed up the creation process while spreading financial risks. This lets both parties take advantage of chances that neither could afford on their own. We carefully craft deals to keep confidential information safe and to make sure that everyone knows who is responsible for making process changes that come from them. Diversifying technologies is now part of supply chain resilience planning in addition to standard business recovery planning. Having suppliers who use a range of forming technologies, such as standard bending, electromagnetic forming, and maybe even additive manufacturing, gives you the freedom to change how you make things when application needs or cost structures change. This multi-path approach needs more detailed control of suppliers, but it makes it much less likely that technology will become outdated or that there will be gaps in capabilities.
Conclusion
Some basic qualities of titanium make it hard to bend. These include a low elastic stiffness, a high springback tendency, and work-hardening behavior. Getting around these problems takes specialized tools, a deep understanding of the process, and strict quality control standards that set capable providers apart from regular tube fabricators. Professionals in procurement need to carefully assess technical skills, keeping in mind that a company's certifications, advanced tools, and metalworking knowledge all affect the final product. As new technologies push the limits of what can be done and as new materials make things easier to shape, staying aware of the paths that innovations are taking helps companies use these advances wisely. When you invest in relationships with suppliers that are based on technical depth and ongoing improvement, you get long-term competitive benefits like better part quality, shorter development cycles, and a lower total cost of ownership.
FAQ
1. What minimum bend radius can be achieved with titanium tubing?
As a general rule, the minimum central radius for most titanium grades is set at 2D to 3D, which is two to three times the outer diameter of the tube. With modern rotating draw bending machines that use internal mandrels, a 1.5D bend radius can be reached in commercially pure grades for tight-tolerance uses. To keep it from cracking, Grade 5 titanium metal usually needs bigger radii or hot forming for shapes less than 2.5D. The exact radius that can be reached depends on the wall thickness ratio. Thin-wall tubing can be bent more sharply than thick-wall tubing.
2. How do titanium bending machines differ from stainless steel equipment?
Titanium bending requires specialized mandrel materials—typically hardened bronze rather than steel—to prevent galling and surface contamination. Machines must incorporate springback adjustment methods that take into account the fact that titanium has a 15–25% elastic recovery, while stainless steel only has a 5–10% recovery. For keeping the measurements correct, servo-controlled pressure systems that let the force change dynamically during the bend cycle are a must. Equipment that can work with titanium is different from general-purpose tube benders because it has chlorine-free lubrication systems and contamination control procedures that deal with titanium's volatile surface chemistry.
3. Which titanium grades are most suitable for complex bending operations?
Commercially pure titanium grade 2 is the best for tight curves, multiple bends, or complex spatial shapes because it can be shaped easily and can stretch by 20 to 30 percent. The performance of Grade 9 titanium (Ti-3Al-2.5V) is in the middle. It can be shaped better than Grade 5, but it is still stronger than CP grades. Grade 5 titanium metal (Ti-6Al-4V) is very strong, but it is not very flexible. To keep it from cracking, it usually needs to be hot-formed or bent with large radii. Grade selection is based on the needs of the application, which include matching strength, weight, and resistance to rust.
Partner with LINHUI TITANIUM for Expert Bending Solutions
LINHUI TITANIUM has specialized in precision titanium tube fabrication since 2000, serving aerospace, energy, medical device, and marine industries across more than 60 countries. As a leading titanium products manufacturer, we maintain comprehensive certifications including AS9100, ISO 13485, PED 2014/68/EU, and approvals from DNV, ABS, Lloyd's Register, and other foreign bodies. When we use our high-tech CNC radial draw bending machines, we can get angular accuracy to within 0.1° and bend radii as small as 1.5 times the tube diameter in both Grade 2 and Grade 5 titanium metals. We offer full Design for Manufacturing (DFM) help during project development, checking to see if the bend shape is possible, and suggesting improvements that meet performance needs while also saving time and money in bending titanium tubings. Our 24-hour emergency repair program and 12-month guarantee on material defects show that we care about our customers' success long after the initial delivery. Our engineering team works with procurement experts to come up with complete solutions that meet both technical requirements and business goals. This is true whether your project needs ASTM B338 heat exchanger U-bends, AMS 4928 aerospace hydraulic lines, or ASTM F67 medical device components. Talk to our experts at linhui@lhtitanium.com about your needs for Bending Titanium Tubings and find out how our "Titanium Products Supermarket" feature makes it easier to find materials for even the most complicated multi-grade projects. As a well-known company that supplies Bending Titanium Tubings with its headquarters in Xi'an, which is at a key intersection on the Belt and Road, we ship our products all over the world on flexible EXW, FOB, or CIF terms and in VCI-coated secure packing to make sure they get to you safely.
References
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2. Donachie, Matthew J., Titanium: A Technical Guide, 2nd Edition, ASM International, 2000.
3. Schutz, R.W. and Watkins, H.B., "Recent Developments in Titanium Alloy Application in the Energy Industry," Materials Science and Engineering: A, Volume 243, Issues 1-2, March 1998.
4. Society of Automotive Engineers, Aerospace Material Specification AMS 4928: Titanium Alloy Tubing, Seamless, Hydraulic, SAE International, Warrendale, Pennsylvania, 2018.
5. American Society for Testing and Materials, ASTM B338-19: Standard Specification for Seamless and Welded Titanium and Titanium Alloy Tubes for Condensers and Heat Exchangers, ASTM International, West Conshohocken, Pennsylvania, 2019.
6. Tang, N.C., "Plastic-Deformation Analysis in Tube Bending," International Journal of Pressure Vessels and Piping, Volume 77, Issue 12, September 2000.
