Joining tubes to tubesheets and steam drums by mechanically expanding them to create an artificial shrink fit between the tubes and surrounding tubesheet or drum material has been a successful process since the 19th century. In this process, after the tube is inserted into the tubesheet or drum holes, the tube is first enlarged until it contacts the hole surfaces. Enlargement continues with the initial tube distortion elastic and further distortion plastic. After contact with the hole surface, the outside of the tube presses against the inside of the hole and distorts the surrounding metal. The distortion of the surrounding metal may be fully elastic or plastic near the tube and elastic farther out.
Upon release of expanding force, the tube and surrounding metal recover. Recovery is elastic but not to the original dimensions. If the tube and surrounding metal have substantially identical properties, after relaxation, there will be a residual stress field with zero magnitude at the tube I.D. and increasing magnitude to a maximum at some radius in the tube-hole structure, diminishing to zero magnitude farther out. The residual stress at the interface between the tube and hole is the equilibrium stress between the parts equal to an interfacial pressure. If the tubesheet or drum has twice the yield stress of the tubes, distortion of the tubesheet or drum remains elastic throughout the process. If the tubes have a yield stress higher than the tubesheet or drum, the position of maximum residual stress shifts depending upon the tube diameter and thickness. The equilibrium stress at the interface of tube and hole surfaces is lower than for constructions of equal tube-tubesheet or drum yield stresses or in which the tube or drum yield stress is higher that of the tube yield stress.
The axial shear strength of the expanded joint is approximately equal to the product of the tube-hole contact area, the interfacial pressure and the coefficient of static friction for the metal pair.
Although, most expanded joints have historically been made by roller expanding, most investigations of tube expanding have used the concept of uniformly applied pressure inside a capsulated length of tubing in contact with the tubesheet or drum. This simplifies the analysis by eliminating a many variables that define the roller expanding process.
How to Visualize Tube Expanding
The simplest way to visualize tube expanding is to picture an infinite number of infinitesimally thin cylinders in contact with each other. Here it is necessary to define the limits of elastic stress and plastic stress. The stress regime in the tubes will be elastic until the pressure inside the tubes reaches the elastic limit as shown in equation (1) and will be plastic beyond the elastic limit up to the plastic limit shown in equation (2).
(1)
(2)Any attempt to apply pressure greater than the plastic limit will be unsuccessful and will result only in extruding the tube end.
Roller Expanding
Now consider that when a rolling tool is inserted into the tube, there is a line of contact between each pin and the hole surface. Thrusting the mandrel into the tube applies greater pressure under each pin than the elastic limit pressure and quickly reaches the plastic limit pressure. Further application of the pin pressure causes the interior cylinders to extrude while applying pressure to adjacent cylinders. As the pressure on adjacent cylinders reaches the plastic limit they begin to extrude. There is a continuum of the pressure regime to the outer cylinders of the tube-tubesheet structure which may be at or less than the plastic limit and where there is no further extrusion. The extrusion is accompanied by tube wall thinning and strain hardening of the tubes. The strain hardening of the tubes prevents relaxation of residual stress during operation of the tubular.
In the 1940s several investigators examined whether the amount of tube extrusion or the degree of wall thinning (expressed as percent apparent wall reduction) would provide suitable parameters for determining the success of the roller expanding process. Because of measurement problems it was determined that percent wall reduction was more suitable and it is widely used as the controlling parameter for achieving joint strength and tightness suitable for the service of the boiler or heat exchanger.
Readers should be aware that although rolling tool manufacturers publish recommended percent wall reductions for various tube-tubesheet metal combinations and tube diameters and wall thicknesses, there is substantially no published literature that relates percent wall reduction to joint shear load strength or tightness. Depending upon the metal pair characteristics, tube diameter and thicknesses, expanding tool manufacturers’ recommended percent wall reduction vary from 5% to 12%.
Most heat exchanger and boiler manufacturers either have informally correlated percent wall reduction with making joints tight enough to be acceptable during hydrostatic testing or have tested mockup specimens of tube-tubesheet combinations that represent production equipment to establish suitable percent wall reduction for roller expanding.
In the roller expanding process, shear load strength equal to the tube cross-sectional area times its yield stress is usually achieved in approximately 2-inches of rolled depth. If it is desired to seal the whole depth of thick tubesheets, rolling has to be done in steps (step rolling) and consideration has to be given to the effects of progressive VS regressive rolling (rolling from the outer tubesheet face toward the inner face or rolling from the inner face toward the outer face.
Uniform Pressure Expanding
There are two types of uniform pressure expanding in widespread use in tubular equipment manufacture: (1) applying pressure directly into the tube end with water encapsulated between two seals in a pressure chamber, and (2) exploding an explosive charge contained in a plastic cushioning cylinder inserted into the tube.
In neither process is the pressure or intensity of the charge so high that it causes the inner cylinders to extrude, i.e the pressure or force applied is never greater than the plastic limit pressure or force. Rather than extruding the tubes become slightly shortened because of the Poisson effect as the elastic limit is reached and further shortened because of maintaining the metal volume as plastic deformation takes place. The degree of wall thinning expressed as percent wall reduction is considerably less that for roller expanding and is the result of the combination of Poisson effect and volume maintenance.
Although purchasers, not thoroughly familiar with either hydroexpanding or explosive expanding sometimes demand percent wall reduction in the same order of magnitude as are achieved in roller expanding, the typical limit for these processes is about 3%. Excessive pressure or excessively high explosive force tends to distort the surrounding ligaments. There are also limits to the pressure that hydroexpanding equipment can supply. However, both processes have been successful in producing strong, tight joints.
There are two major advantages to uniform pressure expanding: First, tubes can be expanded into the whole thickness of thick tubesheets in one application of pressure or exploding one explosive insert. The strain hardening effect of these processes is not so great as to preclude two stages of hydroexpanding or a second charge of explosive expanding. Two-stage uniform pressure expanding has the advantage that the first stage stiffens the tubesheet by increasing the ligament width by the amount of the tube wall. The second advantage is that there is considerably less residual tensile stress in the transition between the expanded and unexpanded tube. This is advantageous from the fatigue standpoint and also from the standpoint of Stress Corrosion Cracking in tubes made of material that is subject to SCC in the conditions of use.
Hybrid Expanding
Because the strain hardening created by roller expanding resists the tendency of residual stress in the tube joints to relax, combining a first stage of approximately 3% wall reduction by uniform pressure expanding with subsequent roller expanding to the final desired percent wall reduction can confer the benefits of both processes. Hybrid expanding is now widely used in such equipment as intermediate and high pressure feedwater heater manufacture.
ASME CODE REQUIREMENTS FOR PERCENT WALL REDUCTION
In response to the many requests for information about ASME Code requirements for wall thinning during expanding, expressed as percent wall reduction, readers are advised that the ASME Code does not specify percent wall reduction. As stated above, it is the Manufacturer's responsibility to determine the suitable percent wall reduction for the service.
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