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End-to-end joining of tubes by plastic instability
Accepted Manuscript Title: End-To-End Joining Of Tubes By Plastic Instability Author: L.M. Alves C.M.A. Silva P.A.F. Martins PII: DOI: Reference:
S0924-0136(14)00143-5 http://dx.doi.org/doi:10.1016/j.jmatprotec.2014.04.011 PROTEC 13963
To appear in:
Journal of Materials Processing Technology
Received date: Revised date: Accepted date:
6-2-2014 31-3-2014 13-4-2014
Please cite this article as: Alves, L.M.,End-To-End Joining Of Tubes By Plastic Instability, Journal of Materials Processing Technology (2014), http://dx.doi.org/10.1016/j.jmatprotec.2014.04.011 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
L.M. Alves, C.M.A. Silva and P.A.F. Martins*
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END-TO-END JOINING OF TUBES BY PLASTIC INSTABILITY
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Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001 Lisboa, Portugal
(*)
Corresponding author. E-mail: [email protected] First author. E-mail: [email protected] Second author. E-mail: [email protected]
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ABSTRACT This paper presents an innovative joining process for the longstanding challenge of connecting two tubes by their ends at room temperature by means of a simple, effective and environmental friendly solution. The process is performed in one stroke and makes use of tube expansion to put the mating surfaces of the two tubes in a correct position for subsequent locking by means
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of plastic instability and simultaneous compression beading.
The presentation combines experimentation with commercial S460MC (carbon steel) welded
tubes and finite element modelling with the purpose of characterizing the deformation
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mechanics of the process, identifying its major operating parameters and providing basic design
guidelines to successfully perform the end-to-end joining of tubes by plastic instability. The new
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proposed joining process has potential to easily and efficiently replace existing solutions based
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on the utilization of fastened, crimped, welded, brazed or adhesive joints.
Keywords: Joining by plastic deformation, End-to-end joining of tubes, Plastic instability, Finite
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element modelling, Experimentation
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1.
INTRODUCTION
Currently available solutions for the end-to-end joining of tubes make use of fastened, crimped, welded, brazed or adhesive joints (Figure 1). Each option offers advantages and disadvantages
Different types of joints currently used for the end-to-end joining of tubes: (a) fastened joints, (b) crimped joints, (c) welded joints, (d) brazed or adhesive joints, (e) friction welded joints and (f) flash butt welded joints.
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Figure 1 -
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that need to be considered for use in specific applications.
Fastened joints (with flanges or bulkhead unions, Figure 1a) make use of threads, screws, bolts
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and sometimes brazed interfaces to connect the tubes together. They are simple to design, easy to assemble and disassemble and available in standard sizes as indicated in Budynas and
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Nisbett (2008). Their major limitations are associated with aesthetic, dimensional and water or gas tightness requirements. Corrosion sensitivity may also prevent the utilization of fastened
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joints in case of tubes and joints made from dissimilar materials being exposed to moist environments.
Crimped joints (Figure 1b) make use of beads or dimples produced by reduction, swaging or electromagnetic forming. Zhang et al. (2014), for example, proposed the application of rotary swaging to join tubes of different diameters, whereas Psyk et al. (2011) provided a state-of-theart review of interference-fit and form-fit joints produced by electromagnetic forming. In contrast to fastened joints, crimped joints are not limited by aesthetic requirements or by the availability of standard size flanges or unions. However, they may be limited by the required pull-out force and water or gas tightness because the thickness of the two tubes to be connected must be thin and material ductility must be good enough to withstand large localized plastic deformations without fracture. The crimped joints produced by electromagnetic forming introduce additional material requirements of high electrical conductivity, which often limit its applicability to aluminium, copper and its alloys. A special type of crimped joints is the interference-fit joints that may be produced by electromagnetic forming or by shrink-fitting based on the thermal expansion or contraction. Thermal shrink-fitting was investigated by Golbakhshi et al., (2013) who compared the accuracy of analytical and finite element solutions in case of a connection between two steel rings.
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Welded joints (Figure 1c) are generally used in thick-walled tubes due to the need of heating the tubes to their melting temperature without causing significant distortion, warpage and metallurgical changes. The selection of welded joints must also consider the difficulties arising from the end-to-end joining of tubes made from dissimilar materials and the costs incurred to remove slag.
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Brazed joints (Figure 1d) are good alternative to welded joints in case of thin-walled tubes. They are produced by placing a filler metal (with a melting temperature below that of the tubes) between the counterfacing surfaces of the tubes and subsequently raising their temperature by
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a torch, an induction coil or in a furnace. The melted filler flows by capillarity and creates a
strong connection between the mating surfaces of the tubes upon cooling. The most important advantages of brazed joints is that they can be easily automated and effectively used to connect
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tubes made from dissimilar materials or exhibiting significant differences in wall thickness. Their major limitations are derived from distortion caused by the heating-cooling cycle and from the need to fabricate special purpose tube end-shapes with very tight tolerances and very good
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surface quality.
Adhesive joints (Figure 1d) are alternative to welded and brazed joints in situations where temperature cannot be applied or in applications involving dissimilar materials (e.g. metals and
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polymers). The joints are produced by placing a thin film of liquid or semisolid structural adhesive between the counterfacing surfaces of the tubes and keeping the assembly immobilized until complete solidification. Adhesive joints circumvent most of the limitations
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associated with the other type of joints but require careful surface preparation with tight tolerances, time for the adhesive to cure and may experience decrease in performance over
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time under adverse environmental conditions. Miller (2003) presents an overview of welding, brazing and adhesive technologies applied to tube joining.
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Other solutions for the end-to-end joining of tubes include the utilization of friction welding (Figure 1e) and flash butt welding (Figure 1f) technologies (ASM, 1993). In friction welding one tube remains stationary while the other is placed in a chuck and rotated at a high speed. The friction welded joint is produced when the tubes are brought into contact under an axial compression force. In flash butt welding, the arc produced at the tube ends, gives raise to local heating and material softening. The flash butt welded joint is also produced when the tubes are brought into contact by an axial compression force. Both types of joints can be easily automated but their application is limited to thick-walled tubes because thin-walled tubes have a tendency to buckle under the typical range of compression forces and temperatures. The state-of-the-art review of the existing technical solutions for the end-to-end joining of tubes allow us to conclude that there is a need to develop a new process that is capable of accomplishing the longstanding challenge of connecting two tubes by their ends by means of a simple, effective and environmental friendly solution. This paper is written in this perspective and introduces a new cold forming process for the endto-end joining of tubes. The process is performed in one stroke and employs two sequential forming stages, as it is schematically shown in Figure 2. The first stage produces the adjacent
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counterfacing surfaces and the second stage creates the lock between these surfaces by means of axisymmetric plastic instability. The process will be hereafter referred as ‘end-to-end
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joining of tubes by plastic instability’.
End-to-end joining of tubes by plastic instability.
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Figure 2 -
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(a) Schematic representation of the process with the notation that will be utilized throughout the paper; (b) Photograph showing the active tool components and two tubular specimens;
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(c) Photograph showing a detail of the cross section of two tubes connected by their ends.
Under these circumstances, and besides the main objective of presenting a new process for the end-to-end joining of tubes, the other aims and objectives of this paper are the following: (i) to understand the deformation mechanics of the new joining process, (ii) to characterize its modes of deformation, (iii) to set-up its feasibility window as a function of the major operating parameters and (iv) to show its applicability in case of end-to-end joining of commercial carbon steel tubes.
The organization of the paper is the following. Section 2 summarizes the mechanical characterization of the tubes, presents the fundamentals of the new proposed joining process, describes the associated tool system and provides information on the experimental work plan. Section 3 gives insight into the finite element modelling conditions that were utilized in the numerical simulations of the process. Section 4 is organized in two major parts. The first part presents and discusses the results obtained namely, the modes of deformation, the influence of the major operating parameters on the process feasibility window and the overall force requirements. The second part explores the application of the new proposed joining process to the connection of tubes of dissimilar materials by their ends. Section 5 concludes.
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2.
EXPERIMENTATION
2.1 Mechanical characterization of the material The investigation was performed on commercial S460MC (carbon steel) welded tubes belonging to the same batch of those used in the investigation on tube branching by asymmetric
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compression beading (Alves and Martins, 2011). The stress-strain curve was determined by means of tensile and stack compression tests carried out at room temperature and was approximated by the following Ludwik–Hollomon’s equation,
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σ = 616.4 ε 0.06 (MPa)
(1)
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The occurrence and development of plastic instability on S460MC tubes were characterized by compressing tubular specimens between flat parallel platens. A critical instability load
Pcr = 93.5 kN was determined for tubes with a reference radius r0 = 16 mm and a wall
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thickness t 0 = 1.5 mm.
Further informations on the methods and procedures that were utilized to obtain the stressstrain curve and the critical instability load of the S460MC tubes are provided in the
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aforementioned published work by Alves and Martins (2011).
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2.2 Tool system
The new process for the end-to-end joining of tubes by plastic instability is schematically shown
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in Figure 2a. As seen from observation of the open, intermediate and close positions of the tool system, joining is accomplished in one stroke by a sequence of two different elementary tube
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forming operations: expansion and compression beading. Expansion is performed by forcing the upper tube against the chamfered end of the lower tube in order to enlarge the unsupported height lo of the upper tube radially and to create adjacent counterfacing surfaces between the two tubes to connect. During the first stage of the joining process (refer to the left side of Figure 2a), the lower tube acts like a tapered punch and the slope of its chamfered edge plays a key role in the overall feasibility of the process. Once the unsupported height lo of the upper tube gets into contact with the lower die, there is a sudden change in the overall kinematics of the process. Expansion is replaced by plastic instability and locking is accomplished by simultaneous compression beading of the two tubes (refer to the right side of Figure 2a). The schematic representation of the tool system in Figure 2a allows identifying the major operating parameters of the process as: (i) the initial unsupported height lo of the upper tube, which expands radially, (ii) the initial unsupported height l i of the lower tube, which behaves as a tapered punch in the first stage of the process, and (iii) the angle α of the chamfered tube
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ends. The upper and lower dies are designed to a specific reference radius r0 of the tubes and the mandrel is also dedicated to a specific wall thickness t0 of the tubes to be joined. As will be seen later in the paper, the initial gap opening l gap = l o + l i between the upper and lower dies controls the number of compression beads that will be formed, whereas the ratio
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l o / l i of the initial unsupported height of the upper and lower tubes controls the possibility of the plastic instability waves to be triggered simultaneously or one after the other.
The photograph in Figure 2b shows the dies, the mandrel and two tubular specimens with
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chamfered ends. The other photograph in Figure 2c shows a detail of the cross section of the two tubular specimens after being joined.
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2.3 Plan of experiments
The tool system was mounted in the hydraulic testing machine (Instron SATEC 1200 kN) where
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the mechanical characterization of the material had previously been performed. The experiments were carried out at room temperature on tubular specimens with a reference radius
r0 = 16 mm and a wall thickness t 0 = 1.5 mm. The crosshead velocity of the testing machine
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was set equal to 100 mm/min (1.7 mm/s).
The plan of experiments was designed in order to study the influence of the three most important process parameters: (i) the ratio l gap r0 between the sum of the initial unsupported
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height of the upper ( lo ) and lower ( l i ) tubes and the reference radius r 0 of the tube (hereafter
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referred as ‘the slenderness ratio’), (ii) the ratio l o / l i of the initial unsupported height of the upper and lower tubes (hereafter referred as ‘the aspect ratio’) and (iii) the inclination
α
of the
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chamfered tube ends. Table 1 summarizes the experimental conditions.
Test case 1 2 3 4 5 6 7 8 9 10 11 12 13
lo
(mm)
5 10 15 20 25 22 25 30 20 20 20 20 20
li
(mm) 5 10 15 20 25 20 20 20 22 25 30 20 20
l gap (mm)
l gap / r0
lo / li
α (degrees)
10 20 30 40 50 42 45 50 42 45 50 40 40
0.625 1.25 1.875 2.5 3.125 2.625 2.813 3.125 2.625 2.813 3.125 2.5 2.5
1 1 1 1 1 1.1 1.25 1.5 0.91 0.8 0.67 1 1
25 25 25 25 25 25 25 25 25 25 25 45 90
Table 1 - The plan of experiments (nomenclature according to Figure 1).
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The ratio r0 t0 of the reference radius to the thickness of the tube wall and the influence of the mandrel in material flow were left out of the plan of experiments due to previous knowledge of the authors in the field of compression beading (Gouveia et al., 2006b). The influence of
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anisotropy was also left out of the investigation.
3. FINITE ELEMENT MODELLING
The development of plastic instability and compression beading is related to material behavior
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in the plastic regime. This explains the reason why the in-house finite element computer program I-form built upon the irreducible finite element flow formulation can successfully handle
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the end-to-end joining of tubes by plastic instability.
The irreducible finite element flow formulation is based on the following variational principle
Π = ∫ σ ε& dV +
1 2
K ∫ ε&v2 dV −
V
⎛
|u r |
∫ Ti u i dS + ∫ ⎜⎝ ∫0
ST
Sf
τ f du r ⎞⎟ dS ⎠
(2)
σ in (2) denotes the effective stress, ε& is the effective strain rate, ε&V is the
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The symbol
V
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(extended to account frictional effects),
volumetric strain rate, K is a large positive constant imposing the incompressibility constraint,
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Ti and u i are the surface tractions and velocities on ST , τ f are the friction shear stresses on
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the contact interface S f between tubes and tooling (dies and mandrel), and V is the control volume limited by the surfaces SU and ST . Further information on the finite element flow
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formulation and the computer program I-form can be found elsewhere (Nielsen et al., 2013). The numerical modelling of the end-to-end joining of tubes by plastic instability was performed in two different stages corresponding to the previously mentioned elementary tube forming operations by expansion and compression beading. In the first stage (expansion), the tubes were discretized by means of linear quadrilateral elements (Figure 3b) taking advantage of rotational symmetry, and sliding was allowed over the chamfered edge of the lower tube (Figure 3c). The dies and mandrel are schematically shown in Figure 3a and were discretized by means of contact-friction linear elements.
At the end of the expansion stage (that is, when the unsupported height lo of the upper tube gets into contact with the lower die), there was a need to perform a remeshing operation to increase the number of elements in the plastically deforming regions and to connect the meshes of the upper and lower tubes along the chamfered edge of the lower tube. The first objective was accomplished by raising the number of elements through the thickness from three to five in order to ensure an adequate geometric modelling of the compression beads (Figures 3d and 3e). The second objective was aimed to replicate the sticking conditions that develop along the
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chamfered edge of the lower tube and the counterfacing side of the upper tube when the kinematics of the plastically deforming region changes from expansion to compression beading. The finite element mesh resulting from the above mentioned procedure is made of approximately 7000 nodal points and 5000 linear quadrilateral elements and the overall CPU time for a typical analysis was below 2 minutes on a standard laptop computer equipped with an
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Numerical modeling of the ‘end-to-end joining of tubes by plastic instability’ (case 4 of Table 1) (a) Schematic representation showing the different entities that were utilized to model the tubes and the active tool parts; (b) Discretization of the upper and lower tubes by finite elements; (c) Finite element predicted geometry at the end of the radial expansion of the unsupported height of the upper tube; (d) Finite element predicted geometry showing the development of plastic instability in both tubes; (e) Finite element predicted geometry at the end of stroke (locking by compression beading). Note: The lower pictures provide details of the meshes of the upper and lower tubes at the gap opening.
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Figure 3 –
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Intel i7 CPU (2.7 GHz) processor and making use of 4 cores.
4. RESULTS AND DISCUSSION 4.1 Modes of deformation
End-to-end joining of tubes by plastic instability is dependent upon the development and propagation of sound compression beads at the gap opening between the upper and lower dies. Experimental observations and finite element modelling allowed identifying four different modes of deformation that are dependent on the combined influence of the slenderness ratio
l gap r0 and the aspect ratio l o / l i .
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In what concerns the influence of the slenderness ratio l gap r0 , the two leftmost specimens in Figure 4 (cases 1 and 2) clearly show that there is a threshold value (say, l gap r0 = 1.25 ) below which no tubes will be joined by their ends. This is because the gap opening l gap is not big enough for the upper tube to bend (after radial expansion) in order to place its counterfacing
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surface in a correct position for subsequent locking by compression beading with the lower tube. This mode of deformation (hereafter referred to as ‘mode 0’) corresponds to pure expansion and, therefore, is not suitable for the end-to-end joining of tubes by plastic instability.
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On the other hand, when the slenderness ratio is large (say, above l gap r0 = 3.125 ) as a result of outsized values of the unsupported free length of the upper and lower tubes there is a
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tendency to develop multiple plastic instability waves that are also unsuitable for the end-to-end joining of tubes. This is because the second plastic instability wave either results incomplete (refer to case 5 in Figure 4), or collides with the previously formed compression bead in order to
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form a poor quality double joint, when the gap opening l gap becomes extremely large. This mode of deformation (hereafter referred to as ‘mode 3’) is also unsuitable for the end-to-end
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joining of tubes by plastic instability.
Figure 4 –
Experimental and finite element predicted modes of deformation that occur in the end-to-end joining of tubes by plastic instability (cases 1 to 5 of Table 1).
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Compression beads are sound and good joints are formed between the edges of the two tubes for values of the slenderness ratio l gap r0 placed in-between the two aforementioned threshold values (say, 1.25 < l gap r0 < 3.125 ). The mode of deformation associated with the successful end-to-end joining of tubes by plastic instability will be hereafter designated as ‘mode 2’ (refer to case 3 and 4 in Figure 4). As seen in this figure, the differences in the final width of the
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compression beads corresponding to cases 3 and 4 result from differences in the initial gap
opening l gap . In other words, the width of the compression beads can be slightly altered by
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setting the value of the initial gap height l gap .
The influence of the aspect ratio lo / li in the overall performance of the process is illustrated in
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Figure 5. The specimens placed on the left of case 4 (cases 6, 7 and 8) possess increasingly larger values of lo / li while those placed on the right of case 4 (cases 9, 10, and 11) possess
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increasingly smaller values of lo / li .
Figure 5 –
Experimental and finite element predicted modes of deformation that occur during end-to-end joining of tubes by plastic instability (cases 4, 6, 7, 8, 9, 10 and 11 of Table 1).
As shown in the figure, there is a new deformation mode (hereafter referred to as ‘mode 1’) characterized by an incomplete locking between the two tubes. This deformation mode occurs for aspect ratios
lo / li ≥ 1.25 and is caused by plastic instability waves not being
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simultaneously triggered in both tubes at the same time, when the initial unsupported height lo of the upper tube is larger than the initial unsupported height li of the lower tube. The photograph and the finite element predicted detail of the cross section of the two tubes shows the incomplete locking and allows understanding the reason why an earlier development of plastic instability in the upper (outer) tube gives no chance (due to absence of free space) for
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the plastic instability wave of the lower (inner) tube to be locked with that of the upper tube. Thus, mode 1 is also not adequate for the end-to-end joining of tubes by plastic instability.
Conversely, when the aspect ratio lo / l i ≤ 0.8 , the plastic instability waves are first triggered in
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the lower (inner) tube and will push the top unsupported height of the upper (outer) tube towards the outside in order to produce a joint compression bead. A second plastic instability
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wave will be triggered shortly after the upper tube contacts the lower die and the overall result is a poor end-to-end joint similar to those produced by deformation mode 3.
The overall results from experimentation and finite element modelling are summarized in
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Table 2. The enclosed black dashed lines separate the process operating conditions for producing sound end-to-end joining of tubes by plastic instability (mode 2) from those giving rise
lo
5
(mm)
5
(mm)
10
Mode 1
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Mode 0
15
20
22
25
30
15
20 22 25 30
20 22 25 30
20 22 25 30
20 22 25 30
Mode 2
Mode 3
Process feasibility window for the end-to-end joining of S460MC tubes by plastic instability showing the modes of deformation as a function of the initial unsupported height of the upper
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Table 2 –
10
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li
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to non-existing (mode 0), incomplete (mode 1) or non-admissible double joints (mode 3).
( lo ) and lower ( li ) tubes.
However, it is very important to understand that the process feasibility window should not be confused with the potential range of applicability because a small process window like that shown in Table 2 only means that the unsupported heights of the upper and lower tubes must be controlled within a compact range of values in order to successfully connect any two tubes by their ends.
4.2 Load requirements Figure 6 presents the experimental and finite element predicted evolution of the load with displacement for selected operating conditions corresponding to cases 1, 3 and 5 of Table 1. The load-displacement trend of case 1 is typical of non-steady tube expansion (Gouveia et al., 2006a). In fact, after an initial stage (labelled as ‘A’ in Figure 6) characterized by a steep increase of the load resulting from the upper tube being forced into the chamfered edge of the lower tube, there is transition into the final stage (labelled as ‘B’) characterized by further steep
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increase of the load due to: (i) the progressive circumferential stretching of the unsupported region of the upper tube as it flows along the chamfered edge of the lower tube, (ii) the unsuccessful attempt of the lower tube to develop plastic instability and (iii) the final contact between the leading edge of the upper tube and the surface of the lower die. The load-displacement trend of cases 3 and 5 is different because it combines the initial stage
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that was previously observed in case 1 with a transition stage in which the upper tube bends axially in order to match the counterfacing surface of the lower tube and the development of
steady-stage expansion stage (refer to the regions labelled as ‘C’ in both case 3 and 5) in which
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the forming load is practically constant. The steep increase of the load up to peek values of
approximately 172~188 kN in the subsequent regions of the load-displacement curve that are labelled as ‘D’ derives from the development of a plastic instability wave after the leading edge
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of the upper tube reaches the surface of the lower die. In fact, the peek values of the forming loads that were determined for cases 3 and 5 of Figure 6 are approximately equal to twice the
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critical instability load Pcr of a single tube that had been previously determined by compressing tubular specimens between flat parallel platens (refer to Section 2.1 and to the dashed line labelled as ‘(2x) Plastic instability’ in Figure 6).
The reason why the critical instability load of the assembly can in some cases (e.g. case 3) be
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smaller than twice the value of the experimental critical instability load is because a closer look at the experimental load-displacement curve near the dashed line labelled as ‘Plastic instability’
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in Figure 6 indicates that there is a tube starting plastic instability slightly before the other.
Figure 6 – Experimental and finite element predicted evolution of the load-displacement curves for cases 1, 3 and 5 of Table 1.
The final upward tail of the load-displacement curve (labelled as ‘E’) corresponds to locking by compression beading of the upper and lower tubes. The overall agreement between experimental and finite element predicted evolutions of the load with displacement may be
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considered good taking into consideration the diversity and complexity of the phenomena taking place during end-to-end joining of tubes by plastic instability.
4.3 Angle of the chamfered edges The inclination α of the chamfered tube edges (Figure 1a) also plays a role in the deformation
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mechanics of the end-to-end joining of tubes by plastic instability. Figure 7a shows the result of
attempting to join two tubes by their ends without chamfering its edges ( α = 90º , case 13 of Table 1). As seen, local buckling due to plastic instability develops in a similar way to that commonly
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found in the axial compression of tubes between flat parallel platens and prevents the tubes of
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being joined by their ends.
Figure 7 –
End-to-end joining of tubes by plastic instability using different inclinations α of the chamfered tube edge. (a) Photographs of unsuccessful and successful attempts corresponding to cases 4, 12 and 13 of Table 1 with inclinations α of the chamfered tube ends respectively equal to 25º, 45º and 90º; (b) Experimental evolution of the early stages of the load-displacement curves corresponding to the test cases shown in (a).
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In contrast, cases 4 and 12 possessing inclination angles α of the chamfered edge to the vertical axis respectively equal to 25º and 45º are capable of providing good end-to-end joints. In fact, the major difference between these two operating conditions is not related to the overall success of the joint but to the evolution of the load-displacement curve at the early stages of the process. As shown in Figure 7b, the peak load at the end of the first stage of the joining process
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is larger in case of α = 45º (case 12 of Table 1) than in case of α = 25º (case 4 of Table 1). This is because the increase of the inclination angle α of the chamfered edges shifts material flow conditions towards local buckling by plastic instability ( α = 90º , case 13 of Table 1) in which the
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peak load reaches the value of the critical instability load Pcr = 93.5 kN.
It is worth noting that the inclination of the chamfered tube edge has no influence on the
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process window because it simply controls the feasibility of the upper tube to be expanded over the lower tube. Further investigation is needed to determine the possibility of performing end-toend joining of tubes by chamfering the edges of one tube (e.g. the upper tube) and using the
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other tube (e.g. the lower tube) without chamfer due to potential cost savings resulting from reducing by half the number of tubes to be prepared.
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4.4 Extension to dissimilar materials
The most important advantage of the new proposed joining process is the possibility of connecting tubes of dissimilar materials by their ends without resorting to heating-cooling cycles
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and to careful preparation of the counterfacing surfaces. The connection should be a simple, straightforward procedure in case of tubes with similar strengths but may require a two stroke
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variant of the process in case of tubes with significant differences in strength (Figure 8a). This is necessary to prevent the lower strength tube to be sheared while being forced against the
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chamfered edge of the higher strength tube or to be axially deformed when the higher strength tube is forced against it.
The application of the two stroke variant of the process to connect carbon steel S460MC and aluminium AA6060-T6 tubes by their ends is shown in Figure 8b and requires the unsupported height of the S460MC tube to be previously expanded by a mandrel and subsequently clamped to the AA6060-T6 by plastic instability and compression beading. The two stroke variant of the process also eliminates the need to produce chamfers at both tube ends.
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End-to-end joining of carbon steel S460MC and aluminium AA6060-T6 tubes by plastic instability.
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Figure 8 -
(a) Schematic representation of the two stroke variant of the new proposed joining process;
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5. CONCLUSIONS
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(b) Photograph showing the preforms and the final tubes connected by their ends.
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End-to-end joining of tubes by plastic instability is a step forward in the longstanding challenge of connecting two tubes by their ends at room temperature by means of a simple, effective and environmental friendly solution.
Experimental work with commercial carbon steel S460MC welded tubes and finite element modelling of the process allowed identifying and distinguishing the process operating conditions for producing sound joints from those giving rise to non-existing, incomplete or non-admissible double joints.
Two geometric ratios are proposed for establishing basic joining guidelines: (i) the slenderness ratio l gap r0 between the gap opening and the reference radius of the tube and (ii) the aspect ratio l o / l i
between the initial unsupported height of the upper and lower tubes. The
slenderness ratio controls the number of plastic instability waves that are triggered in the gap opening and design values in the range 1.25 < l gap r0 < 3.125 were found adequate for S460MC (carbon steel) welded tubes. Values of the aspect ratio l o / l i ≅ 1 are recommended in order to ensure that plastic instability waves are triggered simultaneously in both tubes instead of being triggered in one tube after the other.
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The inclination angle α of the chamfered edges is recommended not to take values close to 90º because of potential risk of the expansion of the upper tube being replaced by local buckling due to plastic instability. Inclination angles α of 25º and 45º degrees were found appropriate for connecting the two tubes by their ends. The process was successfully employed to connect carbon steel S460MC and aluminium
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AA6060-T6 tubes by their ends but further research is needed to explore its utilization in case of
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tubes of dissimilar materials.
ACKNOWLEDGMENTS
under the research contract PEst-OE/EME/LA0022/2011.
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The work was partially supported by the Portuguese Foundation for Science and Technology
The authors would also like to acknowledge the support provided by MCG – Mind for Metal,
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Carregado, Portugal.
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REFERENCES
Alves, L.M., Martins, P.A.F., 2011. Tube branching by asymmetric compression beading. Journal of Materials Processing Technology 212, 1200–1208.
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ASM, 1993. Welding, Brazing and Soldering (Ed. Olson, D.L., Siewert, T.A., Liu, S., Edwards, G.R.). ASM International, Metals Park, USA.
New York, USA.
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Budynas, R.G., Nisbett, J.K., 2008. Shigley’s Mechanical Engineering Design. McGraw Hill,
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Golbakhshi, H., Namjoo, M., Mohammadi, M., 2013. A 3D comprehensive finite element based simulation for best shrink fit design process. Mechanics & Industry 14, 23-30.
Gouveia, B.P.P.A., Alves, M.L., Rosa, P.A.R., Brito A.G., Martins, P.A.F., 2006a. Expansion and reduction of thin-walled tubes using a die: Experimental and theoretical investigation. International Journal of Machine Tools & Manufacture 46, 1643–1652
Gouveia, B.P.P.A., Alves, M.L., Rosa, P.A.R., Martins, P.A.F., 2006b. Compression beading and nosing of thin-walled tubes using a die: experimental and theoretical investigation. International Journal of Mechanics and Materials in Design 3, 7-16.
Miller, G., 2003. Tube Forming Processes: A Comprehensive Guide. SME – Society of Manufacturing Engineers, Dearborn, Michigan, USA. Nielsen, C.V., Zhang, W., Alves, L.M., Bay, N., Martins, P.A.F., 2013. Modeling of ThermoElectro-Mechanical Manufacturing Processes with Applications in Metal Forming and Resistance Welding, Springer-Verlag, London, UK. Psyk, V., Rischa, D., Kinsey, B.L., Tekkaya, A.E., Kleiner, M., 2011. Electromagnetic forming - A review. Journal of Materials Processing Technology 211, 787-829.
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Zhang, Q., Jin, K., Mu, D., 2014, Tube/tube joining technology by using rotary swaging forming
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method. Journal of Materials Processing Technology (accepted for publication)
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Different types of joints currently used for the end-to-end joining of tubes: (a) fastened joints, (b) crimped joints, (c) welded joints, (d) brazed or adhesive joints, (e) friction welded joints and (f) flash butt welded joints.
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Figure 1 -
Page 19 of 28
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Figure 2 -
End-to-end joining of tubes by plastic instability.
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(d) Schematic representation of the process with the notation that will be utilized throughout the paper; (e) Photograph showing the active tool components and two tubular specimens; Photograph showing a detail of the cross section of two tubes connected by their ends.
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(f)
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Numerical modeling of the ‘end-to-end joining of tubes by plastic instability’ (case 4 of Table 1) (f) Schematic representation showing the different entities that were utilized to model the tubes and the active tool parts; (g) Discretization of the upper and lower tubes by finite elements; (h) Finite element predicted geometry at the end of the radial expansion of the unsupported height of the upper tube; (i) Finite element predicted geometry showing the development of plastic instability in both tubes; (j) Finite element predicted geometry at the end of stroke (locking by compression beading). Note: The lower pictures provide details of the meshes of the upper and lower tubes at the gap opening.
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Figure 3 –
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Experimental and finite element predicted modes of deformation that occur in the end-to-end joining of tubes by plastic instability (cases 1 to 5 of Table 1).
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Figure 4 –
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Experimental and finite element predicted modes of deformation that occur during end-to-end joining of tubes by plastic instability (cases 4, 6, 7, 8, 9, 10 and 11 of Table 1).
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Figure 5 –
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Figure 6 – Experimental and finite element predicted evolution of the load-displacement curves for cases 1, 3 and 5 of Table 1.
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Figure 7 –
End-to-end joining of tubes by plastic instability using different inclinations α of the chamfered tube edge. (c) Photographs of unsuccessful and successful attempts corresponding to cases 4, 12 and 13 of Table 1 with inclinations α of the chamfered tube ends respectively equal to 25º, 45º and 90º; (d) Experimental evolution of the early stages of the load-displacement curves corresponding to the test cases shown in (a).
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Figure 8 -
End-to-end joining of carbon steel S460MC and aluminium AA6060-T6 tubes by plastic instability. (c) Schematic representation of the two stroke variant of the new proposed joining process;
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(d) Photograph showing the preforms and the final tubes connected by their ends.
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5 10 15 20 25 22 25 30 20 20 20 20 20
li
(mm) 5 10 15 20 25 20 20 20 22 25 30 20 20
l gap (mm)
l gap / r0
lo / li
α (degrees)
10 20 30 40 50 42 45 50 42 45 50 40 40
0.625 1.25 1.875 2.5 3.125 2.625 2.813 3.125 2.625 2.813 3.125 2.5 2.5
1 1 1 1 1 1.1 1.25 1.5 0.91 0.8 0.67 1 1
25 25 25 25 25 25 25 25 25 25 25 45 90
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(mm)
cr
1 2 3 4 5 6 7 8 9 10 11 12 13
lo
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Test case
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Table 1 - The plan of experiments (nomenclature according to Figure 1).
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lo
5
(mm)
10
5
(mm)
10
Mode 0 Table 2 –
15
20
22
25
30
15
20 22 25 30
20 22 25 30
20 22 25 30
20 22 25 30
Mode 1
Mode 2
Mode 3
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Process feasibility window for the end-to-end joining of S460MC tubes by plastic instability showing the modes of deformation as a function of the initial unsupported height of the upper
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( lo ) and lower ( li ) tubes.
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S0924-0136(14)00143-5 http://dx.doi.org/doi:10.1016/j.jmatprotec.2014.04.011 PROTEC 13963
To appear in:
Journal of Materials Processing Technology
Received date: Revised date: Accepted date:
6-2-2014 31-3-2014 13-4-2014
Please cite this article as: Alves, L.M.,End-To-End Joining Of Tubes By Plastic Instability, Journal of Materials Processing Technology (2014), http://dx.doi.org/10.1016/j.jmatprotec.2014.04.011 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
L.M. Alves, C.M.A. Silva and P.A.F. Martins*
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END-TO-END JOINING OF TUBES BY PLASTIC INSTABILITY
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Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001 Lisboa, Portugal
(*)
Corresponding author. E-mail: [email protected] First author. E-mail: [email protected] Second author. E-mail: [email protected]
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ABSTRACT This paper presents an innovative joining process for the longstanding challenge of connecting two tubes by their ends at room temperature by means of a simple, effective and environmental friendly solution. The process is performed in one stroke and makes use of tube expansion to put the mating surfaces of the two tubes in a correct position for subsequent locking by means
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of plastic instability and simultaneous compression beading.
The presentation combines experimentation with commercial S460MC (carbon steel) welded
tubes and finite element modelling with the purpose of characterizing the deformation
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mechanics of the process, identifying its major operating parameters and providing basic design
guidelines to successfully perform the end-to-end joining of tubes by plastic instability. The new
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proposed joining process has potential to easily and efficiently replace existing solutions based
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on the utilization of fastened, crimped, welded, brazed or adhesive joints.
Keywords: Joining by plastic deformation, End-to-end joining of tubes, Plastic instability, Finite
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element modelling, Experimentation
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1.
INTRODUCTION
Currently available solutions for the end-to-end joining of tubes make use of fastened, crimped, welded, brazed or adhesive joints (Figure 1). Each option offers advantages and disadvantages
Different types of joints currently used for the end-to-end joining of tubes: (a) fastened joints, (b) crimped joints, (c) welded joints, (d) brazed or adhesive joints, (e) friction welded joints and (f) flash butt welded joints.
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Figure 1 -
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that need to be considered for use in specific applications.
Fastened joints (with flanges or bulkhead unions, Figure 1a) make use of threads, screws, bolts
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and sometimes brazed interfaces to connect the tubes together. They are simple to design, easy to assemble and disassemble and available in standard sizes as indicated in Budynas and
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Nisbett (2008). Their major limitations are associated with aesthetic, dimensional and water or gas tightness requirements. Corrosion sensitivity may also prevent the utilization of fastened
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joints in case of tubes and joints made from dissimilar materials being exposed to moist environments.
Crimped joints (Figure 1b) make use of beads or dimples produced by reduction, swaging or electromagnetic forming. Zhang et al. (2014), for example, proposed the application of rotary swaging to join tubes of different diameters, whereas Psyk et al. (2011) provided a state-of-theart review of interference-fit and form-fit joints produced by electromagnetic forming. In contrast to fastened joints, crimped joints are not limited by aesthetic requirements or by the availability of standard size flanges or unions. However, they may be limited by the required pull-out force and water or gas tightness because the thickness of the two tubes to be connected must be thin and material ductility must be good enough to withstand large localized plastic deformations without fracture. The crimped joints produced by electromagnetic forming introduce additional material requirements of high electrical conductivity, which often limit its applicability to aluminium, copper and its alloys. A special type of crimped joints is the interference-fit joints that may be produced by electromagnetic forming or by shrink-fitting based on the thermal expansion or contraction. Thermal shrink-fitting was investigated by Golbakhshi et al., (2013) who compared the accuracy of analytical and finite element solutions in case of a connection between two steel rings.
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Welded joints (Figure 1c) are generally used in thick-walled tubes due to the need of heating the tubes to their melting temperature without causing significant distortion, warpage and metallurgical changes. The selection of welded joints must also consider the difficulties arising from the end-to-end joining of tubes made from dissimilar materials and the costs incurred to remove slag.
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Brazed joints (Figure 1d) are good alternative to welded joints in case of thin-walled tubes. They are produced by placing a filler metal (with a melting temperature below that of the tubes) between the counterfacing surfaces of the tubes and subsequently raising their temperature by
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a torch, an induction coil or in a furnace. The melted filler flows by capillarity and creates a
strong connection between the mating surfaces of the tubes upon cooling. The most important advantages of brazed joints is that they can be easily automated and effectively used to connect
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tubes made from dissimilar materials or exhibiting significant differences in wall thickness. Their major limitations are derived from distortion caused by the heating-cooling cycle and from the need to fabricate special purpose tube end-shapes with very tight tolerances and very good
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surface quality.
Adhesive joints (Figure 1d) are alternative to welded and brazed joints in situations where temperature cannot be applied or in applications involving dissimilar materials (e.g. metals and
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polymers). The joints are produced by placing a thin film of liquid or semisolid structural adhesive between the counterfacing surfaces of the tubes and keeping the assembly immobilized until complete solidification. Adhesive joints circumvent most of the limitations
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associated with the other type of joints but require careful surface preparation with tight tolerances, time for the adhesive to cure and may experience decrease in performance over
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time under adverse environmental conditions. Miller (2003) presents an overview of welding, brazing and adhesive technologies applied to tube joining.
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Other solutions for the end-to-end joining of tubes include the utilization of friction welding (Figure 1e) and flash butt welding (Figure 1f) technologies (ASM, 1993). In friction welding one tube remains stationary while the other is placed in a chuck and rotated at a high speed. The friction welded joint is produced when the tubes are brought into contact under an axial compression force. In flash butt welding, the arc produced at the tube ends, gives raise to local heating and material softening. The flash butt welded joint is also produced when the tubes are brought into contact by an axial compression force. Both types of joints can be easily automated but their application is limited to thick-walled tubes because thin-walled tubes have a tendency to buckle under the typical range of compression forces and temperatures. The state-of-the-art review of the existing technical solutions for the end-to-end joining of tubes allow us to conclude that there is a need to develop a new process that is capable of accomplishing the longstanding challenge of connecting two tubes by their ends by means of a simple, effective and environmental friendly solution. This paper is written in this perspective and introduces a new cold forming process for the endto-end joining of tubes. The process is performed in one stroke and employs two sequential forming stages, as it is schematically shown in Figure 2. The first stage produces the adjacent
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counterfacing surfaces and the second stage creates the lock between these surfaces by means of axisymmetric plastic instability. The process will be hereafter referred as ‘end-to-end
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joining of tubes by plastic instability’.
End-to-end joining of tubes by plastic instability.
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Figure 2 -
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(a) Schematic representation of the process with the notation that will be utilized throughout the paper; (b) Photograph showing the active tool components and two tubular specimens;
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(c) Photograph showing a detail of the cross section of two tubes connected by their ends.
Under these circumstances, and besides the main objective of presenting a new process for the end-to-end joining of tubes, the other aims and objectives of this paper are the following: (i) to understand the deformation mechanics of the new joining process, (ii) to characterize its modes of deformation, (iii) to set-up its feasibility window as a function of the major operating parameters and (iv) to show its applicability in case of end-to-end joining of commercial carbon steel tubes.
The organization of the paper is the following. Section 2 summarizes the mechanical characterization of the tubes, presents the fundamentals of the new proposed joining process, describes the associated tool system and provides information on the experimental work plan. Section 3 gives insight into the finite element modelling conditions that were utilized in the numerical simulations of the process. Section 4 is organized in two major parts. The first part presents and discusses the results obtained namely, the modes of deformation, the influence of the major operating parameters on the process feasibility window and the overall force requirements. The second part explores the application of the new proposed joining process to the connection of tubes of dissimilar materials by their ends. Section 5 concludes.
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2.
EXPERIMENTATION
2.1 Mechanical characterization of the material The investigation was performed on commercial S460MC (carbon steel) welded tubes belonging to the same batch of those used in the investigation on tube branching by asymmetric
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compression beading (Alves and Martins, 2011). The stress-strain curve was determined by means of tensile and stack compression tests carried out at room temperature and was approximated by the following Ludwik–Hollomon’s equation,
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σ = 616.4 ε 0.06 (MPa)
(1)
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The occurrence and development of plastic instability on S460MC tubes were characterized by compressing tubular specimens between flat parallel platens. A critical instability load
Pcr = 93.5 kN was determined for tubes with a reference radius r0 = 16 mm and a wall
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thickness t 0 = 1.5 mm.
Further informations on the methods and procedures that were utilized to obtain the stressstrain curve and the critical instability load of the S460MC tubes are provided in the
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aforementioned published work by Alves and Martins (2011).
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2.2 Tool system
The new process for the end-to-end joining of tubes by plastic instability is schematically shown
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in Figure 2a. As seen from observation of the open, intermediate and close positions of the tool system, joining is accomplished in one stroke by a sequence of two different elementary tube
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forming operations: expansion and compression beading. Expansion is performed by forcing the upper tube against the chamfered end of the lower tube in order to enlarge the unsupported height lo of the upper tube radially and to create adjacent counterfacing surfaces between the two tubes to connect. During the first stage of the joining process (refer to the left side of Figure 2a), the lower tube acts like a tapered punch and the slope of its chamfered edge plays a key role in the overall feasibility of the process. Once the unsupported height lo of the upper tube gets into contact with the lower die, there is a sudden change in the overall kinematics of the process. Expansion is replaced by plastic instability and locking is accomplished by simultaneous compression beading of the two tubes (refer to the right side of Figure 2a). The schematic representation of the tool system in Figure 2a allows identifying the major operating parameters of the process as: (i) the initial unsupported height lo of the upper tube, which expands radially, (ii) the initial unsupported height l i of the lower tube, which behaves as a tapered punch in the first stage of the process, and (iii) the angle α of the chamfered tube
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ends. The upper and lower dies are designed to a specific reference radius r0 of the tubes and the mandrel is also dedicated to a specific wall thickness t0 of the tubes to be joined. As will be seen later in the paper, the initial gap opening l gap = l o + l i between the upper and lower dies controls the number of compression beads that will be formed, whereas the ratio
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l o / l i of the initial unsupported height of the upper and lower tubes controls the possibility of the plastic instability waves to be triggered simultaneously or one after the other.
The photograph in Figure 2b shows the dies, the mandrel and two tubular specimens with
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chamfered ends. The other photograph in Figure 2c shows a detail of the cross section of the two tubular specimens after being joined.
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2.3 Plan of experiments
The tool system was mounted in the hydraulic testing machine (Instron SATEC 1200 kN) where
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the mechanical characterization of the material had previously been performed. The experiments were carried out at room temperature on tubular specimens with a reference radius
r0 = 16 mm and a wall thickness t 0 = 1.5 mm. The crosshead velocity of the testing machine
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was set equal to 100 mm/min (1.7 mm/s).
The plan of experiments was designed in order to study the influence of the three most important process parameters: (i) the ratio l gap r0 between the sum of the initial unsupported
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height of the upper ( lo ) and lower ( l i ) tubes and the reference radius r 0 of the tube (hereafter
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referred as ‘the slenderness ratio’), (ii) the ratio l o / l i of the initial unsupported height of the upper and lower tubes (hereafter referred as ‘the aspect ratio’) and (iii) the inclination
α
of the
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chamfered tube ends. Table 1 summarizes the experimental conditions.
Test case 1 2 3 4 5 6 7 8 9 10 11 12 13
lo
(mm)
5 10 15 20 25 22 25 30 20 20 20 20 20
li
(mm) 5 10 15 20 25 20 20 20 22 25 30 20 20
l gap (mm)
l gap / r0
lo / li
α (degrees)
10 20 30 40 50 42 45 50 42 45 50 40 40
0.625 1.25 1.875 2.5 3.125 2.625 2.813 3.125 2.625 2.813 3.125 2.5 2.5
1 1 1 1 1 1.1 1.25 1.5 0.91 0.8 0.67 1 1
25 25 25 25 25 25 25 25 25 25 25 45 90
Table 1 - The plan of experiments (nomenclature according to Figure 1).
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The ratio r0 t0 of the reference radius to the thickness of the tube wall and the influence of the mandrel in material flow were left out of the plan of experiments due to previous knowledge of the authors in the field of compression beading (Gouveia et al., 2006b). The influence of
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anisotropy was also left out of the investigation.
3. FINITE ELEMENT MODELLING
The development of plastic instability and compression beading is related to material behavior
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in the plastic regime. This explains the reason why the in-house finite element computer program I-form built upon the irreducible finite element flow formulation can successfully handle
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the end-to-end joining of tubes by plastic instability.
The irreducible finite element flow formulation is based on the following variational principle
Π = ∫ σ ε& dV +
1 2
K ∫ ε&v2 dV −
V
⎛
|u r |
∫ Ti u i dS + ∫ ⎜⎝ ∫0
ST
Sf
τ f du r ⎞⎟ dS ⎠
(2)
σ in (2) denotes the effective stress, ε& is the effective strain rate, ε&V is the
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The symbol
V
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(extended to account frictional effects),
volumetric strain rate, K is a large positive constant imposing the incompressibility constraint,
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Ti and u i are the surface tractions and velocities on ST , τ f are the friction shear stresses on
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the contact interface S f between tubes and tooling (dies and mandrel), and V is the control volume limited by the surfaces SU and ST . Further information on the finite element flow
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formulation and the computer program I-form can be found elsewhere (Nielsen et al., 2013). The numerical modelling of the end-to-end joining of tubes by plastic instability was performed in two different stages corresponding to the previously mentioned elementary tube forming operations by expansion and compression beading. In the first stage (expansion), the tubes were discretized by means of linear quadrilateral elements (Figure 3b) taking advantage of rotational symmetry, and sliding was allowed over the chamfered edge of the lower tube (Figure 3c). The dies and mandrel are schematically shown in Figure 3a and were discretized by means of contact-friction linear elements.
At the end of the expansion stage (that is, when the unsupported height lo of the upper tube gets into contact with the lower die), there was a need to perform a remeshing operation to increase the number of elements in the plastically deforming regions and to connect the meshes of the upper and lower tubes along the chamfered edge of the lower tube. The first objective was accomplished by raising the number of elements through the thickness from three to five in order to ensure an adequate geometric modelling of the compression beads (Figures 3d and 3e). The second objective was aimed to replicate the sticking conditions that develop along the
Page 8 of 28
chamfered edge of the lower tube and the counterfacing side of the upper tube when the kinematics of the plastically deforming region changes from expansion to compression beading. The finite element mesh resulting from the above mentioned procedure is made of approximately 7000 nodal points and 5000 linear quadrilateral elements and the overall CPU time for a typical analysis was below 2 minutes on a standard laptop computer equipped with an
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Numerical modeling of the ‘end-to-end joining of tubes by plastic instability’ (case 4 of Table 1) (a) Schematic representation showing the different entities that were utilized to model the tubes and the active tool parts; (b) Discretization of the upper and lower tubes by finite elements; (c) Finite element predicted geometry at the end of the radial expansion of the unsupported height of the upper tube; (d) Finite element predicted geometry showing the development of plastic instability in both tubes; (e) Finite element predicted geometry at the end of stroke (locking by compression beading). Note: The lower pictures provide details of the meshes of the upper and lower tubes at the gap opening.
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Figure 3 –
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Intel i7 CPU (2.7 GHz) processor and making use of 4 cores.
4. RESULTS AND DISCUSSION 4.1 Modes of deformation
End-to-end joining of tubes by plastic instability is dependent upon the development and propagation of sound compression beads at the gap opening between the upper and lower dies. Experimental observations and finite element modelling allowed identifying four different modes of deformation that are dependent on the combined influence of the slenderness ratio
l gap r0 and the aspect ratio l o / l i .
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In what concerns the influence of the slenderness ratio l gap r0 , the two leftmost specimens in Figure 4 (cases 1 and 2) clearly show that there is a threshold value (say, l gap r0 = 1.25 ) below which no tubes will be joined by their ends. This is because the gap opening l gap is not big enough for the upper tube to bend (after radial expansion) in order to place its counterfacing
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surface in a correct position for subsequent locking by compression beading with the lower tube. This mode of deformation (hereafter referred to as ‘mode 0’) corresponds to pure expansion and, therefore, is not suitable for the end-to-end joining of tubes by plastic instability.
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On the other hand, when the slenderness ratio is large (say, above l gap r0 = 3.125 ) as a result of outsized values of the unsupported free length of the upper and lower tubes there is a
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tendency to develop multiple plastic instability waves that are also unsuitable for the end-to-end joining of tubes. This is because the second plastic instability wave either results incomplete (refer to case 5 in Figure 4), or collides with the previously formed compression bead in order to
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form a poor quality double joint, when the gap opening l gap becomes extremely large. This mode of deformation (hereafter referred to as ‘mode 3’) is also unsuitable for the end-to-end
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joining of tubes by plastic instability.
Figure 4 –
Experimental and finite element predicted modes of deformation that occur in the end-to-end joining of tubes by plastic instability (cases 1 to 5 of Table 1).
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Compression beads are sound and good joints are formed between the edges of the two tubes for values of the slenderness ratio l gap r0 placed in-between the two aforementioned threshold values (say, 1.25 < l gap r0 < 3.125 ). The mode of deformation associated with the successful end-to-end joining of tubes by plastic instability will be hereafter designated as ‘mode 2’ (refer to case 3 and 4 in Figure 4). As seen in this figure, the differences in the final width of the
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compression beads corresponding to cases 3 and 4 result from differences in the initial gap
opening l gap . In other words, the width of the compression beads can be slightly altered by
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setting the value of the initial gap height l gap .
The influence of the aspect ratio lo / li in the overall performance of the process is illustrated in
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Figure 5. The specimens placed on the left of case 4 (cases 6, 7 and 8) possess increasingly larger values of lo / li while those placed on the right of case 4 (cases 9, 10, and 11) possess
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increasingly smaller values of lo / li .
Figure 5 –
Experimental and finite element predicted modes of deformation that occur during end-to-end joining of tubes by plastic instability (cases 4, 6, 7, 8, 9, 10 and 11 of Table 1).
As shown in the figure, there is a new deformation mode (hereafter referred to as ‘mode 1’) characterized by an incomplete locking between the two tubes. This deformation mode occurs for aspect ratios
lo / li ≥ 1.25 and is caused by plastic instability waves not being
Page 11 of 28
simultaneously triggered in both tubes at the same time, when the initial unsupported height lo of the upper tube is larger than the initial unsupported height li of the lower tube. The photograph and the finite element predicted detail of the cross section of the two tubes shows the incomplete locking and allows understanding the reason why an earlier development of plastic instability in the upper (outer) tube gives no chance (due to absence of free space) for
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the plastic instability wave of the lower (inner) tube to be locked with that of the upper tube. Thus, mode 1 is also not adequate for the end-to-end joining of tubes by plastic instability.
Conversely, when the aspect ratio lo / l i ≤ 0.8 , the plastic instability waves are first triggered in
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the lower (inner) tube and will push the top unsupported height of the upper (outer) tube towards the outside in order to produce a joint compression bead. A second plastic instability
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wave will be triggered shortly after the upper tube contacts the lower die and the overall result is a poor end-to-end joint similar to those produced by deformation mode 3.
The overall results from experimentation and finite element modelling are summarized in
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Table 2. The enclosed black dashed lines separate the process operating conditions for producing sound end-to-end joining of tubes by plastic instability (mode 2) from those giving rise
lo
5
(mm)
5
(mm)
10
Mode 1
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Mode 0
15
20
22
25
30
15
20 22 25 30
20 22 25 30
20 22 25 30
20 22 25 30
Mode 2
Mode 3
Process feasibility window for the end-to-end joining of S460MC tubes by plastic instability showing the modes of deformation as a function of the initial unsupported height of the upper
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Table 2 –
10
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li
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to non-existing (mode 0), incomplete (mode 1) or non-admissible double joints (mode 3).
( lo ) and lower ( li ) tubes.
However, it is very important to understand that the process feasibility window should not be confused with the potential range of applicability because a small process window like that shown in Table 2 only means that the unsupported heights of the upper and lower tubes must be controlled within a compact range of values in order to successfully connect any two tubes by their ends.
4.2 Load requirements Figure 6 presents the experimental and finite element predicted evolution of the load with displacement for selected operating conditions corresponding to cases 1, 3 and 5 of Table 1. The load-displacement trend of case 1 is typical of non-steady tube expansion (Gouveia et al., 2006a). In fact, after an initial stage (labelled as ‘A’ in Figure 6) characterized by a steep increase of the load resulting from the upper tube being forced into the chamfered edge of the lower tube, there is transition into the final stage (labelled as ‘B’) characterized by further steep
Page 12 of 28
increase of the load due to: (i) the progressive circumferential stretching of the unsupported region of the upper tube as it flows along the chamfered edge of the lower tube, (ii) the unsuccessful attempt of the lower tube to develop plastic instability and (iii) the final contact between the leading edge of the upper tube and the surface of the lower die. The load-displacement trend of cases 3 and 5 is different because it combines the initial stage
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that was previously observed in case 1 with a transition stage in which the upper tube bends axially in order to match the counterfacing surface of the lower tube and the development of
steady-stage expansion stage (refer to the regions labelled as ‘C’ in both case 3 and 5) in which
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the forming load is practically constant. The steep increase of the load up to peek values of
approximately 172~188 kN in the subsequent regions of the load-displacement curve that are labelled as ‘D’ derives from the development of a plastic instability wave after the leading edge
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of the upper tube reaches the surface of the lower die. In fact, the peek values of the forming loads that were determined for cases 3 and 5 of Figure 6 are approximately equal to twice the
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critical instability load Pcr of a single tube that had been previously determined by compressing tubular specimens between flat parallel platens (refer to Section 2.1 and to the dashed line labelled as ‘(2x) Plastic instability’ in Figure 6).
The reason why the critical instability load of the assembly can in some cases (e.g. case 3) be
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smaller than twice the value of the experimental critical instability load is because a closer look at the experimental load-displacement curve near the dashed line labelled as ‘Plastic instability’
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in Figure 6 indicates that there is a tube starting plastic instability slightly before the other.
Figure 6 – Experimental and finite element predicted evolution of the load-displacement curves for cases 1, 3 and 5 of Table 1.
The final upward tail of the load-displacement curve (labelled as ‘E’) corresponds to locking by compression beading of the upper and lower tubes. The overall agreement between experimental and finite element predicted evolutions of the load with displacement may be
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considered good taking into consideration the diversity and complexity of the phenomena taking place during end-to-end joining of tubes by plastic instability.
4.3 Angle of the chamfered edges The inclination α of the chamfered tube edges (Figure 1a) also plays a role in the deformation
ip t
mechanics of the end-to-end joining of tubes by plastic instability. Figure 7a shows the result of
attempting to join two tubes by their ends without chamfering its edges ( α = 90º , case 13 of Table 1). As seen, local buckling due to plastic instability develops in a similar way to that commonly
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found in the axial compression of tubes between flat parallel platens and prevents the tubes of
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being joined by their ends.
Figure 7 –
End-to-end joining of tubes by plastic instability using different inclinations α of the chamfered tube edge. (a) Photographs of unsuccessful and successful attempts corresponding to cases 4, 12 and 13 of Table 1 with inclinations α of the chamfered tube ends respectively equal to 25º, 45º and 90º; (b) Experimental evolution of the early stages of the load-displacement curves corresponding to the test cases shown in (a).
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In contrast, cases 4 and 12 possessing inclination angles α of the chamfered edge to the vertical axis respectively equal to 25º and 45º are capable of providing good end-to-end joints. In fact, the major difference between these two operating conditions is not related to the overall success of the joint but to the evolution of the load-displacement curve at the early stages of the process. As shown in Figure 7b, the peak load at the end of the first stage of the joining process
ip t
is larger in case of α = 45º (case 12 of Table 1) than in case of α = 25º (case 4 of Table 1). This is because the increase of the inclination angle α of the chamfered edges shifts material flow conditions towards local buckling by plastic instability ( α = 90º , case 13 of Table 1) in which the
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peak load reaches the value of the critical instability load Pcr = 93.5 kN.
It is worth noting that the inclination of the chamfered tube edge has no influence on the
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process window because it simply controls the feasibility of the upper tube to be expanded over the lower tube. Further investigation is needed to determine the possibility of performing end-toend joining of tubes by chamfering the edges of one tube (e.g. the upper tube) and using the
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other tube (e.g. the lower tube) without chamfer due to potential cost savings resulting from reducing by half the number of tubes to be prepared.
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4.4 Extension to dissimilar materials
The most important advantage of the new proposed joining process is the possibility of connecting tubes of dissimilar materials by their ends without resorting to heating-cooling cycles
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and to careful preparation of the counterfacing surfaces. The connection should be a simple, straightforward procedure in case of tubes with similar strengths but may require a two stroke
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variant of the process in case of tubes with significant differences in strength (Figure 8a). This is necessary to prevent the lower strength tube to be sheared while being forced against the
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chamfered edge of the higher strength tube or to be axially deformed when the higher strength tube is forced against it.
The application of the two stroke variant of the process to connect carbon steel S460MC and aluminium AA6060-T6 tubes by their ends is shown in Figure 8b and requires the unsupported height of the S460MC tube to be previously expanded by a mandrel and subsequently clamped to the AA6060-T6 by plastic instability and compression beading. The two stroke variant of the process also eliminates the need to produce chamfers at both tube ends.
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End-to-end joining of carbon steel S460MC and aluminium AA6060-T6 tubes by plastic instability.
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Figure 8 -
(a) Schematic representation of the two stroke variant of the new proposed joining process;
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5. CONCLUSIONS
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(b) Photograph showing the preforms and the final tubes connected by their ends.
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End-to-end joining of tubes by plastic instability is a step forward in the longstanding challenge of connecting two tubes by their ends at room temperature by means of a simple, effective and environmental friendly solution.
Experimental work with commercial carbon steel S460MC welded tubes and finite element modelling of the process allowed identifying and distinguishing the process operating conditions for producing sound joints from those giving rise to non-existing, incomplete or non-admissible double joints.
Two geometric ratios are proposed for establishing basic joining guidelines: (i) the slenderness ratio l gap r0 between the gap opening and the reference radius of the tube and (ii) the aspect ratio l o / l i
between the initial unsupported height of the upper and lower tubes. The
slenderness ratio controls the number of plastic instability waves that are triggered in the gap opening and design values in the range 1.25 < l gap r0 < 3.125 were found adequate for S460MC (carbon steel) welded tubes. Values of the aspect ratio l o / l i ≅ 1 are recommended in order to ensure that plastic instability waves are triggered simultaneously in both tubes instead of being triggered in one tube after the other.
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The inclination angle α of the chamfered edges is recommended not to take values close to 90º because of potential risk of the expansion of the upper tube being replaced by local buckling due to plastic instability. Inclination angles α of 25º and 45º degrees were found appropriate for connecting the two tubes by their ends. The process was successfully employed to connect carbon steel S460MC and aluminium
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AA6060-T6 tubes by their ends but further research is needed to explore its utilization in case of
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tubes of dissimilar materials.
ACKNOWLEDGMENTS
under the research contract PEst-OE/EME/LA0022/2011.
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The work was partially supported by the Portuguese Foundation for Science and Technology
The authors would also like to acknowledge the support provided by MCG – Mind for Metal,
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Carregado, Portugal.
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REFERENCES
Alves, L.M., Martins, P.A.F., 2011. Tube branching by asymmetric compression beading. Journal of Materials Processing Technology 212, 1200–1208.
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ASM, 1993. Welding, Brazing and Soldering (Ed. Olson, D.L., Siewert, T.A., Liu, S., Edwards, G.R.). ASM International, Metals Park, USA.
New York, USA.
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Budynas, R.G., Nisbett, J.K., 2008. Shigley’s Mechanical Engineering Design. McGraw Hill,
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Golbakhshi, H., Namjoo, M., Mohammadi, M., 2013. A 3D comprehensive finite element based simulation for best shrink fit design process. Mechanics & Industry 14, 23-30.
Gouveia, B.P.P.A., Alves, M.L., Rosa, P.A.R., Brito A.G., Martins, P.A.F., 2006a. Expansion and reduction of thin-walled tubes using a die: Experimental and theoretical investigation. International Journal of Machine Tools & Manufacture 46, 1643–1652
Gouveia, B.P.P.A., Alves, M.L., Rosa, P.A.R., Martins, P.A.F., 2006b. Compression beading and nosing of thin-walled tubes using a die: experimental and theoretical investigation. International Journal of Mechanics and Materials in Design 3, 7-16.
Miller, G., 2003. Tube Forming Processes: A Comprehensive Guide. SME – Society of Manufacturing Engineers, Dearborn, Michigan, USA. Nielsen, C.V., Zhang, W., Alves, L.M., Bay, N., Martins, P.A.F., 2013. Modeling of ThermoElectro-Mechanical Manufacturing Processes with Applications in Metal Forming and Resistance Welding, Springer-Verlag, London, UK. Psyk, V., Rischa, D., Kinsey, B.L., Tekkaya, A.E., Kleiner, M., 2011. Electromagnetic forming - A review. Journal of Materials Processing Technology 211, 787-829.
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Zhang, Q., Jin, K., Mu, D., 2014, Tube/tube joining technology by using rotary swaging forming
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cr
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method. Journal of Materials Processing Technology (accepted for publication)
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ip t cr
Different types of joints currently used for the end-to-end joining of tubes: (a) fastened joints, (b) crimped joints, (c) welded joints, (d) brazed or adhesive joints, (e) friction welded joints and (f) flash butt welded joints.
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Figure 1 -
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Figure 2 -
End-to-end joining of tubes by plastic instability.
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(d) Schematic representation of the process with the notation that will be utilized throughout the paper; (e) Photograph showing the active tool components and two tubular specimens; Photograph showing a detail of the cross section of two tubes connected by their ends.
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(f)
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Numerical modeling of the ‘end-to-end joining of tubes by plastic instability’ (case 4 of Table 1) (f) Schematic representation showing the different entities that were utilized to model the tubes and the active tool parts; (g) Discretization of the upper and lower tubes by finite elements; (h) Finite element predicted geometry at the end of the radial expansion of the unsupported height of the upper tube; (i) Finite element predicted geometry showing the development of plastic instability in both tubes; (j) Finite element predicted geometry at the end of stroke (locking by compression beading). Note: The lower pictures provide details of the meshes of the upper and lower tubes at the gap opening.
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Figure 3 –
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Experimental and finite element predicted modes of deformation that occur in the end-to-end joining of tubes by plastic instability (cases 1 to 5 of Table 1).
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Figure 4 –
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Experimental and finite element predicted modes of deformation that occur during end-to-end joining of tubes by plastic instability (cases 4, 6, 7, 8, 9, 10 and 11 of Table 1).
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Figure 5 –
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Figure 6 – Experimental and finite element predicted evolution of the load-displacement curves for cases 1, 3 and 5 of Table 1.
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Figure 7 –
End-to-end joining of tubes by plastic instability using different inclinations α of the chamfered tube edge. (c) Photographs of unsuccessful and successful attempts corresponding to cases 4, 12 and 13 of Table 1 with inclinations α of the chamfered tube ends respectively equal to 25º, 45º and 90º; (d) Experimental evolution of the early stages of the load-displacement curves corresponding to the test cases shown in (a).
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Figure 8 -
End-to-end joining of carbon steel S460MC and aluminium AA6060-T6 tubes by plastic instability. (c) Schematic representation of the two stroke variant of the new proposed joining process;
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(d) Photograph showing the preforms and the final tubes connected by their ends.
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5 10 15 20 25 22 25 30 20 20 20 20 20
li
(mm) 5 10 15 20 25 20 20 20 22 25 30 20 20
l gap (mm)
l gap / r0
lo / li
α (degrees)
10 20 30 40 50 42 45 50 42 45 50 40 40
0.625 1.25 1.875 2.5 3.125 2.625 2.813 3.125 2.625 2.813 3.125 2.5 2.5
1 1 1 1 1 1.1 1.25 1.5 0.91 0.8 0.67 1 1
25 25 25 25 25 25 25 25 25 25 25 45 90
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(mm)
cr
1 2 3 4 5 6 7 8 9 10 11 12 13
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Test case
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Table 1 - The plan of experiments (nomenclature according to Figure 1).
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lo
5
(mm)
10
5
(mm)
10
Mode 0 Table 2 –
15
20
22
25
30
15
20 22 25 30
20 22 25 30
20 22 25 30
20 22 25 30
Mode 1
Mode 2
Mode 3
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Process feasibility window for the end-to-end joining of S460MC tubes by plastic instability showing the modes of deformation as a function of the initial unsupported height of the upper
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( lo ) and lower ( li ) tubes.
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