Finite Element Analysis and Experimental Evaluation of Residual Stress of Zr-4 Alloys Processed Through Swaging

metals

Article Finite Element Analysis and Experimental Evaluation of Residual Stress of Zr-4 alloys Processed through Swaging

Gaurav Singh 1 , Bijit Kalita 1, K. I. Vishnu Narayanan 2, Umesh Kumar Arora 2, Manas M. Mahapatra 3 and Rengaswamy Jayaganthan 1,*

1 Department of Engineering Design, IIT Madras, Chennai 600036, India; [email protected] (G.S.); [email protected] (B.K.) 2 Nuclear Fuel Complex, Hyderabad, Telangana 500062, India; [email protected] (K.I.V.N.); [email protected] (U.K.A.) 3 School of Mechanical Sciences, Indian Institute of Technology Bhubaneswar, Argul, Jatani 751013, India; [email protected] * Correspondence: [email protected]; Tel.: +91-44-2257-4735

Received: 31 August 2020; Accepted: 19 September 2020; Published: 25 September 2020

Abstract: Zirconium alloy has been extensively used as a cladding material in nuclear power reactors due to its low neutron absorption cross section, excellent mechanical properties, and corrosion resistance. The influence of the swaging parameter, feed rate (0.7, 1.25, 2 m/min) on residual stress induced in Zr-4 alloy is investigated in the present work. A three-dimensional finite element model was implemented in the Deform 3D software to simulate the rotary swaging (RS) process over a circular rod of Zr-4 alloy. The simulation results based on the 3D framework provide a detailed insight of residual stress, true stress versus true strain and force applied over the rod during the multiple pass swaging process; the results are compared with experimental results. The experimental hole drilling method is used to determine the residual stresses on swaged zirconium alloy at different feed rates (0.7, 1.25, and 2 m/min). A similar trend of residual stress between experimental and numerical results from the surface to the center on the swaged rod samples is observed. The same magnitude of residual stress at the surface of the swaged Zr-4 rod is also observed. It is found to be compressive at the surface and tensile in the center of the samples, as observed in the present work.

Keywords: rotary swaging; FEM; residual stress; Zr-4 alloy; hole drilling; Deform 3D

1. Introduction Zirconium alloys processed through the swaging technique are used in nuclear power reactors and chemical industries due to their excellent tensile properties, fracture toughness and corrosion resistance. Swaging is a metal forming process by which the diameter of a rod or tube is reduced by forcing it into a die with the help of a reciprocating blow. The forming dies of the swaging machine are arranged concentrically around the work piece (Figure1a). The swaging dies perform high frequency radial movements with short strokes. Rotary swaging (RS) can be performed under hot and cold conditions, depending on the swaged material, required surface quality and ﬁnal properties [1,2]. Infeed rotary swaging, the work piece is fed axially inside the set of dies but in the recess swaging process, the work piece is not fed axially forward or outward (Figure1a). The sinking zone is much smaller than the forging zone. Therefore, the infeed swaging process is often utilized in the situation where the work piece is necked from one end. The recess swaging process is often used to reduce the diameter at a certain position of the work piece, or to form a concave proﬁle [1–6].

Metals 2020, 10, 1281; doi:10.3390/met10101281 www.mdpi.com/journal/metals Metals 2020, 10, x FOR PEER REVIEW 2 of 16 situation where the work piece is necked from one end. The recess swaging process is often used to reduce the diameter at a certain position of the work piece, or to form a concave profile [1–6]. The work piece can be classified into three zones when it is inside the dies; they are the sinking zone, the forging zone and the sizing zone (Figure 1b) [3]. Similarly, the dies can be classified into three zones such as the reduction, calibration and exit zones. The outside part at the sinking zone suffers from triaxial compressive stress as it is in direct contact with the die and therefore, the deformation of this part is more severe. The outside part at the sizing zone suffers from axial tensile stress due to the axial elongation. The axial elongation of the work piece as well as the necking predicted in the simulation are caused by the axial tensile stress by virtue of the deformation occurring in the sizing zone [1]. During the rotary swaging process, the forming of the work piece takes place in the swaging head in small steps by a radial oscillating movement of the tools. A rotary swaging process utilizing an energy-controlled method was discussed in [1]. The deformation of the tube mainly occurs at the sinking zone. The radial action of the dies is generated by rotation of the driven swaging spindle due to the cam shaped outline of the shoe. Through the roll-off-process between the shoes and the cylinder rollers, the dies are moved inwards simultaneously at every overrun of the cams. The cross section of the axially fed work piece becomes reduced. Due to the rotation of the swaging spindle relative to the work piece, a constant circumferential shaping can be obtained [7,8]. Various parameters of swaging can affect the microstructure, mechanical properties and residual stresses on the materials being processed. The die angle, die stroke, feed velocity, and the friction coefficient would affect the deformation of the work piece. Incremental forming processes have been studied in recent years, in most cases using finite element modelling (FEM) due to its high precision. Specifically, FEM is used in rotary swaging in order to study the strain and stress distributions in the work piece [4], especially the influence of the axial feed velocity on the strain field [5], the influence of friction and the die angle on residual stresses [6] and temperature distribution during the process [9,10]. Axisymmetric quadrilateral full integration elements were chosen to develop the finite element analysis (FEA) model of rotary swaging for an Mg alloy [11]. FEA was conducted for the tungsten heavy alloy using FORGE software; the highest strain was observed in theMetals surface2020, 10 ,regions, 1281 which were directly affected by the swaging dies [12]. Using Forge 2 NxT of 15 commercial software, FEA was conducted for an elastic-viscoplastic material model [12].

Figure 1. (a) A Lebel diagram of a swaging head [2] and (b) the zones of the swaging process [3], Figure 1. (a) A Lebel diagram of a swaging head [2] and (b) the zones of the swaging process [3], with with permission from Elsevier, 2020. permission from Elsevier, 2020.

The work piece can be classified into three zones when it is inside the dies; they are the sinking zone, the forging zone and the sizing zone (Figure1b) [ 3]. Similarly, the dies can be classified into three zones such as the reduction, calibration and exit zones. The outside part at the sinking zone suffers from triaxial compressive stress as it is in direct contact with the die and therefore, the deformation of this part is more severe. The outside part at the sizing zone suffers from axial tensile stress due to the axial elongation. The axial elongation of the work piece as well as the necking predicted in the simulation are caused by the axial tensile stress by virtue of the deformation occurring in the sizing zone [1]. During the rotary swaging process, the forming of the work piece takes place in the swaging head in small steps by a radial oscillating movement of the tools. A rotary swaging process utilizing an energy-controlled method was discussed in [1]. The deformation of the tube mainly occurs at the sinking zone. The radial action of the dies is generated by rotation of the driven swaging spindle due to the cam shaped outline of the shoe. Through the roll-off-process between the shoes and the cylinder rollers, the dies are moved inwards simultaneously at every overrun of the cams. The cross section of the axially fed work piece becomes reduced. Due to the rotation of the swaging spindle relative to the work piece, a constant circumferential shaping can be obtained [7,8]. Various parameters of swaging can affect the microstructure, mechanical properties and residual stresses on the materials being processed. The die angle, die stroke, feed velocity, and the friction coefficient would affect the deformation of the work piece. Incremental forming processes have been studied in recent years, in most cases using finite element modelling (FEM) due to its high precision. Specifically, FEM is used in rotary swaging in order to study the strain and stress distributions in the work piece [4], especially the influence of the axial feed velocity on the strain field [5], the influence of friction and the die angle on residual stresses [6] and temperature distribution during the process [9,10]. Axisymmetric quadrilateral full integration elements were chosen to develop the finite element analysis (FEA) model of rotary swaging for an Mg alloy [11]. FEA was conducted for the tungsten heavy alloy using FORGE software; the highest strain was observed in the surface regions, which were directly affected by the swaging dies [12]. Using Forge NxT commercial software, FEA was conducted for an elastic-viscoplastic material model [12]. Metals 2020, 10, 1281 3 of 15

Swaging has led to a substantial increase in the ultimate tensile strength and a decrease in ductility [13,14]. The finite element (FE) model has shown the variation of strain from surface to central axis of swaged Al–Cu clad composite [15]. The residual stress component in the axial direction is much larger than that in other directions and as a result, it becomes one of the basic factors causing transverse surface cracks in the subsequent rotary swaging (RS) passes [16]. The zones of swaging are explicitly shown using ABAQUS software (6.16, Dassault Systèmes®,Vélizy-Villacoublay, France). The axial reaction was compared using lubricant as well as without lubricant [17]. A combined friction law was used to model the friction in the die-workpiece interface for recess swaging [18]. Forge 2011 3D was used for FEA of copper AISI C11000 tube that suffers triaxial stress during the rotary swaging process [3]. Fluctuations in the stroke height, which are in the range of the tolerance of the components of the swaging head, has led to strong fluctuations in residual stress distribution [2]. The 2D axisymmetric and 3D FE analysis is used in modelling residual stresses and forging load in the cold radial forging process. Metal flow in the deformation gap has been performed using the finite element method in the real swaging process [19]. The Lagrange type incompressibility condition and boundary conditions for velocity were considered as reported in the literature [20]. The local strain distribution calculations were verified using experimentally available data on Inconel 718 [21]. FEM analysis based on plane 2D elements was used for determining the state of stress and analysis of the metal flow in swaging [8]. Zirconium alloy is used in nuclear fission reactor applications due to its superior mechanical properties compared to other structural material like stainless steel [22]. Zirconium alloys have a good combination of strength and ductility, high corrosion and oxidation resistance and a low neutron absorption cross section area [23–26]. Residual stresses are induced into the materials due to plastic deformation, annealing, phase transformation and welding in material components [27]. Residual stress is an important criterion for choosing the cladding material for nuclear applications because of severe plastic deformation processes such as rotary swaging, extrusion, the rolling process, and hot pressure torsion and dissimilar metal welding used for processing this alloy [28–30]. Residual stresses are measured by different methods such as, X-Ray diffraction (XRD), hole drilling and deep hole drilling, and the hole contour method and block removal [31]. XRD has the ability to measure only surface residual stresses, while semi destructive techniques like deep hole drilling are able to measure the residual stress up to 750 mm depth in the material [32]. Various studies have been carried out on other alloys such as titanium alloys, tungsten-based alloys and copper alloys. The effect of rotary swaging and annealing on residual stress for WNiCo powder-based pseudo alloy was predicted using numerical and experimental techniques (XRD technique) [33]. It was reported that swaging at room temperature introduced higher compressive stresses which decreased after the post heat treatment process [13,33]. Residual stress analyses through X-ray diffraction and the elastoplastic self-consistent (EPSC) model were made on cold pilgered zirconium alloy [34]. The contribution and magnitude of the first and second order residual stresses were evaluated using inputs from the modeling [34]. It is possible to determine the basic characteristics of strain distribution, the strain rate, the local strain intensities, and the displacement rates of the work piece, as well as the swaging force. To understand residual stresses, Henriksen et.al conducted a series of tests and stated that grain deformation in the surface layer generates residual stresses [35]. Therefore, according to his study, mechanical deformation is the key factor for residual stress generation in the materials. A parametric study of machining parameters in order to understand the impact on the residual stresses in materials is reported using an arbitrary Lagrangian-Eulerian (ALE) finite element approach [36].

2. Finite Element Analysis FE analysis is a consequence of the trend followed by industry in the past few decades towards an improvement of the process and the use of total quality programs. There is an increasing demand in recent times to produce more output with better quality and lower costs. Consequently, the use of computer modelling has become increasingly appealing to industry. Its application provides important Metals 2020, 10, 1281 4 of 15 design information on the shape and integrity of the part, the required force, wear on tools and an understanding of the metal working process, where conventional analytical methods are restricted to the steady-state stage of the process. Thus, conventional methods cannot provide an insight into the dynamic changes that occur during the initial stage of the process. In addition, the simulations are advantageous for their ability to easily vary geometry and boundary conditions, consequently facilitating detailed studies of deformation patterns. The process (billet, tools), once modelled, can be used for a large variety of investigations by simply changing the boundary conditions in the model. The literatures on determination of residual stress in zirconium alloy by numerical and experimental methods is limited. A 3D finite element model based on plastic as well as elastic-plastic formulation are developed using the commercial finite element software DEFORM 3D (12.1, Scientific Forming Technologies Corporation Columbus, Ohio, Unites States) in the present work to analyse the residual stress in zircaloy-4 (Zr-4 alloy). DEFORM 3D uses the finite element method to solve large deformation problems and an automatic mesh generator (AMG) to automatically provide an optimized remeshing capability. The implicit FE method was used for the analysis, where equilibrium global equations were simultaneously solved implicitly with the Newton-Raphson (N-R) method. The iterative approach used in the implicit FE method may have issues achieving convergence for non-linear material [37]. Explicit FE results are compared with the results of an implicit formulation and computing times were benchmarked for different problems [38]. Implicit FEA in 3D is computationally expensive, but recent works have shown that it can scale well on large high-performance computing machines or clouds [39].

2.1. Modelling Considering that rotary swaging is a cold forming process, the following assumptions were considered to analyze the processing of Zr-4 alloys: (a) the material is uniform and isotropic, (b) the interface of the dies and the work piece are under isothermal conditions, and (c) the gravity and inertial force are ignored. The friction condition in the die–work piece interface was modelled by the combined (hybrid) friction law, which is the combination of two friction models. The friction model is assumed to be sliding velocity dependent, with a friction coeﬃcient of 0.4, which is commonly used for cold forging conditions. The swaging dies moved radially toward the rod and deformed it. The initial length and diameter of the rod were 500 and 21 mm, respectively. Table1 shows some process parameters used for the FE modeling of Zircaloy-4.

Table1. List of parameters used in the ﬁnite element modelling (FEM) simulation of the swaging process.

Parameters for FEA Before Simulation After Simulation Diameter (mm) 21 20–19–18.2–17.4–16.2 Temperature (◦C) 20 20 Swaging stroke (mm) 10 10 Number of bites (L/f + 1) = 51 Length of work piece(L) 500 mm 580 mm Axial feed per bite (f) Varies (10 mm) Rotation per bite 45, 90 degree Die movement velocity 30 mm/sec Number of pass 1 to 5 Rotation per pass 180 degree (For multiple pass) 21 to 20 mm, 20 to 19 mm, 19 to 18.2 mm, Pass schedule for round bar 18.2 to 17.4 mm, 17.4 to 16.2 mm Swaging through feed rate for bars 0.7 m/min, 1.25 m/min, 2 m/min

The Lagrangian incremental model is generally used for all the conventional applications like forming, heat transfer or heat-treatment. It is also useful for modelling the transient phase of processes like rolling, machining, extrusion, drawing, cogging etc. The main advantage is due to easier remeshing, which is useful for large scale deformation as well. However, in case of large deformations, the mesh Metals 2020, 10, 1281 5 of 15 quality quickly degrades, leading to inaccuracy or even instability, and remeshing is inevitable. Mesh generation for such remeshing can not only be time and resource consuming, but there would also be an error associated with the projection of the solution onto the new mesh; it is the major drawback of the arbitrary Lagrangian-Eulerian (ALE) method. The convergence of an elasto-plastic solution is dependent on the initial guess of the stress–strain state. There are three initial guess solutions available: (1) the elastic solution, which uses purely elastic deformation data, (2) the plastic solution, which uses plastic deformation data to generate the initial guess, and (3) the previous step solution, which uses the elasto-plastic solution from the previous step to generate the initial guess. In most of the cases, the latter, previous step solution seems to give the best convergence. The Newton-Raphson (N-R) method is used to solve the problem. It is recommended because generally it converges in fewer iteration than the other available methods [37]. However, solutions are more likely to fail to converge with this method than with other methods. Whereas, the direct iteration method is more likely to converge than the N-R method, but to do so, will generally require more iterations. In the Deform software, matrix equations take care of solving especially large-scale deformation problems.

2.2. Material In order for a simulation to achieve a high level of accuracy, it is important to have an understanding of the material properties required to specify a material used in DEFORM 3D. The Zr-4 alloy, with an equivalent stress–strain relationship at room temperature, was used for the analysis. The Create a New Material option is used to define the Zr-4 alloy. The rod was assumed to be elasto-plastic. For elastic data, elastic properties like Young’s modulus, Poisson’s ratio and the thermal expansion coefficient were used for the deformation analysis. Assuming that there was no internal heat generation, a Young’s modulus of 99 GPa and a Poisson’s ratio of 0.37 were considered for the simulation. For plastic material, the tabular data format was used. This format is the most versatile format as it can represent any material where flow stress can be given as a function of strain, strain rate, and temperature. This flow stress curve is used to determine the residual stress analysis from the simulation. The Von Mises stress criterion is imposed during simulation. The die and manipulator are considered as rigid bodies for this analysis.

2.3. Mesh The geometry of the elasto-plastic work specimen is meshed with ﬁnite element meshes of tetrahedron elements (shown in Figure2a); the mesh of the work piece (initial diameter of 21 mm and length of 500 mm) consisted of 27,806 elements and 7142 nodes. For plastic material, brick mesh elements with 6500 elements and 7878 nodes are generated. Deform 3D provides the facilities for automatic remesh wherever necessary. Remeshing criteria were selected as it is the most convenient way to handle the remeshing of objects undergoing large plastic deformation. Remeshing is the process of replacing a distorted mesh with a new undistorted mesh and interpolating the ﬁeld variables (strain, velocity, damage, and temperature etc.) from the old mesh to the new mesh.

2.4. Boundary Condition Contact boundary conditions display inter-object boundary contact conditions on a given object. Contact boundary conditions are applied to nodes of a slave object (work piece), and specified contact between those nodes and the surface of a master object (die and manipulator). In master–slave combination, in case of a single deforming object, the deforming object should always be the slave object. In case of multiple deforming bodies, the object with the finer mesh at the interface of the two objects should be the slave object. Contact must be specified for every pair of deformable objects that may contact each other during the simulation. At the interface between two objects, the constant Metals 2020, 10, 1281 6 of 15 friction coefficient is specified. A separation criteria was imposed for inter object relationships. The dies areMetals assigned 2020, 10, a x slidingFOR PEER velocity REVIEW of 30 mm/s over the work piece. 6 of 16

Figure 2. (a) The mesh domain of the work piece, and (b) axial (X), circumferential (Y) and radial (Z) Figure 2. (a) The mesh domain of the work piece, and (b) axial (X), circumferential (Y) and radial (Z) directions are shown in Zr-4 swaged rod samples. directions are shown in Zr-4 swaged rod samples. 2.5. Residual Stress Analysis Using FEM 2.4. Boundary Condition Prediction and control of residual stresses and stress concentration in the materials is essential for understandingContact boundary the fracture condition toughnesss display inter and- fatigueobject boundary life of the contact components. conditions Residual on a given stresses object. in theContact work boundary piece are periodicallyconditions are introduced applied to during nodes of in a various slave object thermo-mechanical (work piece), and forming specified processes. contact Tobetween predict those residual nodes stress and values the surface from the of simulations a master object of the (die swaged and Zr-4 manipulator). alloy, 20 measuring In master points–slave werecombination, chosen along in case the of diameter, a single using deforming the point-tracking object, the deforming technique. object The dies should are takenalways away be the from slave the tube.object. These In case steps of multiple provide deforming significant bodies, time to the recover object the with elastic the finer part mesh of the at formulation. the interface Theof the stress two remainingobjects should in the be tube the afterslave theobject. relaxation Contac periodt must be was specified assumed for to every be the pair residual of deformable stress. objects that may contact each other during the simulation. At the interface between two objects, the constant 3.friction Experimental-Residual coefficient is specified. Stress A Measurement separation criteria was imposed for inter object relationships. The dies are assigned a sliding velocity of 30 mm/s over the work piece. The through thickness residual stresses are measured by using the deep hole drilling technique. The main advantage of using this technique is due to the fact that it can measure the residual stress 2.5. Residual Stress Analysis using FEM fields through the thickness of the swaged rod samples. The tests are carried out in four steps: Prediction and control of residual stresses and stress concentration in the materials is essential 1. A through reference hole is drilled at the measured location using gun drilling. for understanding the fracture toughness and fatigue life of the components. Residual stresses in the 2.workThe piece measurement are periodically of the introduced reference hole during diameter in variou is mades thermo at pre-decided-mechanical angles forming for each processes. increment To predictin the residual depth stress direction. values from the simulations of the swaged Zr-4 alloy, 20 measuring points 3.wereA chosen core of along material the containingdiameter, using the reference the point hole-tracking is trepanned technique. free ofThe the dies rest are of thetaken material away usingfrom the tube.an electric These dischargesteps provide machine significant (EDM) time (Makino, to recover Mason, the Ohio,elastic Unitedpart of States).the formulation. The stress 4.remainingThe reference in the tube hole after diameter the relaxation is again measured period was to calculateassumed theto be magnitude the residual of residualstress. stress fields from the amount of deformation observed in the inner core column of trepanning process. 3. Experimental-Residual Stress Measurement The following Equations (1) and (2) were used to determine the residual stresses (σy, σz): The through thickness residual stresses are measured by using the deep hole drilling technique. The main advantage of using this technique∆d isy due 1toh the fact ithat it can measure the residual stress εy = = 3σy σz (1) fields through the thickness of the swaged roddy samples.−E The− tests are carried out in four steps: 1. A through reference hole is drilled at the measured location using gun drilling. ∆dz 1 h i 2. The measurement of the referenceεz = hole= diameter3σz isσ y made at pre-decided angles for each(2) dz −E − increment in the depth direction. where, ε and ε are measured strains in the y and z directions, respectively; ∆d and ∆z are the change 3. A corey of zmaterial containing the reference hole is trepanned free of the resty of the material using in diameters in the y and z directions, respectively; d and d are the initial diameters, in the y and z an electric discharge machine (EDM) (Makino, Mason,y zOhio, United States). directions, respectively; E is Young’s modulus; and σ and σ are the stresses in the y and z directions, 4. The reference hole diameter is again measured toy calculatez the magnitude of residual stress fields respectively [31,40]. The through thickness residual stress measurement is explained in detail in our from the amount of deformation observed in the inner core column of trepanning process. earlier work [40]. TheThe Zr-4 following alloys Equation are produceds (1) and by the (2) inductionwere used melting to determine process the and residual swaged stresses up to (σ a 16.2y, σz) mm: rod from 21 mm rod samples in 5 passes (NFC Hyderabad,∆ 1 India). The composition of Zr-4 alloy is shown = = − 3 − (1) in Table2. The through thickness residual stresses measured by the deep hole drilling technique of 25%

∆ 1 = = − 3 − (2)

Metals 2020, 10, x FOR PEER REVIEW 7 of 16 where, and are measured strains in the y and z directions, respectively; ∆ and ∆ are the change in diameters in the y and z directions, respectively; and are the initial diameters, in the y and z directions, respectively; E is Young’s modulus; and and are the stresses in the y and z directions, respectively [31,40]. The through thickness residual stress measurement is explained in detail in our earlier work [40]. The Zr-4 alloys are produced by the induction melting process and swaged up to a 16.2 mm rod from 21 mm rod samples in 5 passes (NFC Hyderabad, India). The composition of Zr-4 alloy is shown inMetals Table2020 2. ,The10, 1281 through thickness residual stresses measured by the deep hole drilling technique7 of 15 25% (18.2 mm rod) swaged samples (0.7 m/min, 1.25 m/min and 2 m/min) and 40% (16.2 mm rod) swaged samples (0.7 m/min). The residual stresses along both the directions (axial and radial direction(18.2 mms) peak rod) swagednear the samples middle (0.7point m /inmin, the 1.25thickness m/min direction and 2 m /andmin) accordingly and 40% (16.2 themm stress rod) patterns swaged aresamples represented (0.7 m for/min). the Theswaged residual bars stresses, as shown along in bothFigure the 2b. directions Samples (axialare polished and radial by directions)emery papers peak becausenear the surface middle defects point inmay the affect thickness the strain direction relaxation and accordingly readings. theYoung’s stress modulus patterns areand representedPoisson’s ratiofor theof Zr swaged-4 alloy bars,are 99 as GPa shown and in0.37 Figure, respectively2b. Samples [23,24]. are polishedThe tensile by properties emery papers (yield because strength surface and tensiledefects strength) may aff ect of the Zr- strain4 alloys relaxation are taken readings. from Young’s our earlier modulus work and [23]. Poisson’s The scanning ratio of Zr-4electron alloy microscopyare 99 GPa-based and 0.37, electron respectively backscattered [23,24 ].diffraction The tensile (EBSD properties) (FEI, (yieldHillsboro, strength OH, and USA tensile) was strength)carried outof on Zr-4 25% alloys of the are samples taken from at different our earlier feed work rates [ 23for]. kernel The scanning average electron misorientation microscopy-based (KAM) mapping. electron Thebackscattered samples were diff polishedraction (EBSD) with up (FEI, to Hillsboro,2000 µm emery OH, USA) papers was, followed carried out by onalumina 25% of and the samplescolloidalat clothdiff erentpolishing. feed ratesElectropolis for kernelhing average was done misorientation using 80% methanol (KAM) mapping. and 20% Theperchloric samples acid were for polished17 s at −30with °C. up to 2000 µm emery papers, followed by alumina and colloidal cloth polishing. Electropolishing was done using 80% methanol and 20% perchloric acid for 17 s at 30 C. − ◦ Table 2. The composition of Zr-4 alloy. Table 2. The composition of Zr-4 alloy. Alloying Element Sn% Fe% Cr% O% H ppm Zr% CompositionAlloying Element (Wt.%) Sn%1.46 Fe%0.11 0.22 Cr% 0.13 O% H21ppm Bal. Zr% Composition (Wt.%) 1.46 0.11 0.22 0.13 21 Bal. 4. Results and Discussions 4. Results and Discussion 4.1. FEM Results 4.1. FEM Results A rod with initial diameter of 21 mm and length of 500 mm was considered for plastic deformationA rod, with with initial single diameter pass to reduce of 21 mm theand diameter length of of the 500 rod mm by was 1 mm. considered The final for length plastic is deformation,calculated aswith 513.21 single mm. pass The to true reduce σ versus the diameter the true ofε curve the rod is plotted by 1 mm. using The origin final length software is calculated for the swaged as 513.21 piece mm. andThe is trueshownσ versus in Figure the true3a. ε curve is plotted using origin software for the swaged piece and is shown in Figure3a.

Figure 3. (a) The true σ versus the true ε of the work piece, obtained from numerical data, and (b) the Figure 3. (a) The true σ versus the true ε of the work piece, obtained from numerical data, and (b) the flash produced over the outer surface of the work piece flash produced over the outer surface of the work piece During the swaging process, due to the tolerance applied to the dies (3 or 4), the swaged work pieceDuring is not the uniform, swaging as someprocess flash, due was to produced the tolerance on the applied outer surfaceto the dies of the (3 rodor 4) as, the shown swaged in Figure work3b. pieceTo avoid is not this uniform problem, as some the work flash piece was isproduced allowed toon rotatethe outer after surface each bite of /theblow. rod With as shown this rotation, in Figure it is possible to have a uniform surface of the swaged rod. The rotation angle per bite of 15 degrees was assumed, which does not lead to a uniform surface. Later, the rotation of 90 degrees was used to ensure a better surface after the operation. Now, considering an elasto-plastic case, the rod of 500 mm length was deformed for three consecutive passes; in the first pass the diameter of the work piece was reduced from 21 mm to 20 mm and in the next two passes, it was reduced to a final diameter of 18.2 mm. The final length obtained after two subsequent passes is 540.671 mm, as shown in Figure4a. The stress distribution contour over a particular cross section of the rod is displayed after slicing the rod as shown in Figure4b. Metals 2020, 10, x FOR PEER REVIEW 8 of 16

3(b). To avoid this problem the work piece is allowed to rotate after each bite/blow. With this rotation, itMetals is possible 2020, 10, xto FOR have PEER a REVIEWuniform surface of the swaged rod. The rotation angle per bite of 158 degree of 16 s was assumed, which does not lead to a uniform surface. Later, the rotation of 90 degrees was used to 3(b). To avoid this problem the work piece is allowed to rotate after each bite/blow. With this rotation, ensure a better surface after the operation. it is possible to have a uniform surface of the swaged rod. The rotation angle per bite of 15 degrees was Now,assumed considering, which does an not elasto lead- plasticto a uniform case, surface. the rod Later, of 500 the mm rotation length of 90was degree deformeds was used for to three consecutiveensure a bette passesr surface; in afterthe first the operation.pass the diameter of the work piece was reduced from 21 mm to 20 mm andNow, in considering the next two an passes, elasto-plastic it was case,reduced the rod to a of final 500 diameter mm length of was18.2 deformedmm. The forfinal three length obtainedconsecutive after passes two ; subsequentin the first pass passes the is diameter 540.671 ofmm the, as work shown piece in wasFigure reduced 4a. The from stress 21 mm distribution to 20 contourmm and over in the a particular next two cross passes, section it was of reduced the rod is to displayeda final diameter after slicing of 18.2 the mm. rod Theas shown final length in Figure 4b.obtained after two subsequent passes is 540.671 mm, as shown in Figure 4a. The stress distribution Metalscontour2020 over, 10, 1281 a particular cross section of the rod is displayed after slicing the rod as shown in Figure8 of 15 4b.

Figure 4. (a) The final length of the swaged rod, and (b) the stress distribution over a particular cross Figuresection.4. (a) The ﬁnal length of the swaged rod, and (b) the stress distribution over a particular Figure 4. (a) The final length of the swaged rod, and (b) the stress distribution over a particular cross cross section. section. A path operation was performed over the swaged work piece for a random cross section, as A path operation was performed over the swaged work piece for a random cross section, as shown shownA inpath Figure operation 5, using was the performed point tracki overng theoption swaged of the work software piece tofor see a randomthe σ and cross ϵ variation section, acrossas in Figure5, using the point tracking option of the software to see the σ and variation across the cross theshown cross in Figure section. 5, Stress/strainusing the point generated tracking isoption the maximumof the software at the to see surface the σ andand graduallyϵ variation decreasesacross section. Stress/strain generated is the maximum at the surface and gradually decreases towards the towardsthe cross the section. center Stress/strain of the work generatedpiece. Hence, is the the maximum surface is atthe the highly surface stressed and gradually region, as decreases can be seen center of the work piece. Hence, the surface is the highly stressed region, as can be seen from Figure4b. fromtowards Figure the 4b.center of the work piece. Hence, the surface is the highly stressed region, as can be seen from Figure 4b.

Figure 5. Point tracking along the cross section of the rod. FigureFigure 5. 5. PointPoint tracking tracking along along the the cross cross section section of ofthe the rod. rod. From this analysis, the load applied by the die on the work piece has been generated. Figure 6a FromFrom thisthis analysis, the the load load applied applied by by the the die die on on the the work work piece piece has has been been generated. generated. Figure Figure 6a 6a indicates the Z-load and Figure 6b indicates the Y-load. The load at the top and bottom are almost indicatesindicates thethe Z-loadZ-load andand FigureFigure6 6bb indicates indicates the the Y-load. Y-load. The The load load at at the the top top and and bottom bottom are are almost almost the same. The maximum value is located where the load is exerted by the right and the minimum value is exerted by the left; as measured along the Z direction. In Figure6b, the load exerted by the right die and the left die, which are in the horizontal direction, are the maximum and the top/bottom die exerts minimum load on the work piece as it measures the load in the Y direction. At the same time, all four dies exert the same amount of load over the work piece, to have uniform deformation. The eﬀective stress with respect to time is plotted from elasto-plastic data undergoing multi-pass swaging. From Figure7, it is clear that the value of stress increases with the number of passes. Actually, the results presented here refer to the working stress during the swaging process and the results give the value of the residual stress after successful completion of the swaging process. From the load curve, it can be observed that at the same time Metals 2020, 10, x FOR PEER REVIEW 9 of 16 the same. The maximum value is located where the load is exerted by the right and the minimum value is exerted by the left; as measured along the Z direction.

Metals 2020, 10, 1281 9 of 15 Metals 2020, 10, x FOR PEER REVIEW 9 of 16 theall foursame dies. The exert maximum equal amounts value is oflocated load over where the the work load piece; is exerted this leads by the to aright uniform and homogeneousthe minimum valuedeformation is exerted in theby axialthe left; direction as measure of thed swagedalong the Zr-4 Z direction. rod.

Figure 6. The load applied on the rod (a) along the Z direction, and (b) along the Y direction.

In Figure 6b, the load exerted by the right die and the left die, which are in the horizontal direction, are the maximum and the top/bottom die exerts minimum load on the work piece as it measures the load in the Y direction. At the same time, all four dies exert the same amount of load over the work piece, to have uniform deformation. The effective stress with respect to time is plotted from elasto-plastic data undergoing multi-pass swaging. From Figure 7, it is clear that the value of stress increases with the number of passes. Actually, the results presented here refer to the working stress during the swaging process and the results give the value of the residual stress after successful completion of the swaging process. From the load curve, it can be observed that at the same time all four dies exert equal amounts of load over the work piece; this leads to a uniform homogeneous deformationFigure in 6.theThe axial load direction applied on of the the rod swaged (a) along Zr- the4 rod. Z direction, and (b) along the Y direction. Figure 6. The load applied on the rod (a) along the Z direction, and (b) along the Y direction.

Figure 7. TheThe e effectiveﬀective stress for three subsequent swaging passes.

Moreover, for the above cases, the die has been designed for the optimum value of the required diameter of the rod. However, However, as our analysis is limited to a very small value of of diameter diameter reduction, reduction, the appropriate consideration of the die geometry would play a significantsignificant role. Here, the dies have been designed according to the required diameter (e.g., 21-20, 20-19, etc.), i.e., different die geometry is used for each 1 mm reduction of diameter. As a post-processing result of this analysis, a 20 mm diameter rod is obtained with an incremental length. Now, instead of a multi pass operation, the obtained 20 mm diameter rod is imported to the next set of simulations using the respective die. Assuming a similar condition of all other parameters involved, the swaging process is completed for the next 1 mm diameter reduction. Repeating this procedure for subsequent steps (e.g., 19 to 18.2 mm and 18.2 to 17.4 mm), a final swaged rod of Figure 7. The effective stress for three subsequent swaging passes. diameter nearly equal to 16.2 mm is obtained (Figure8a). True σ versus the curve is obtained from experimentalMoreover, as for well the as above numerical cases, analysis the die andhas been they designed are plotted for together the optimum and shown value in of Figure the required8b. diameter of the rod. However, as our analysis is limited to a very small value of diameter reduction, the appropriate consideration of the die geometry would play a significant role. Here, the dies have

Metals 2020, 10, x FOR PEER REVIEW 10 of 16

been designed according to the required diameter (e.g., 21-20, 20-19, etc.), i.e., different die geometry is used for each 1 mm reduction of diameter. As a post-processing result of this analysis, a 20 mm diameter rod is obtained with an incremental length. Now, instead of a multi pass operation, the obtained 20 mm diameter rod is imported to the next set of simulations using the respective die. Assuming a similar condition of all other parameters involved, the swaging process is completed for the next 1 mm diameter reduction. Repeating this procedure for subsequent steps (e.g., 19 to 18.2 mm and 18.2 to 17.4 mm), a final swaged rod of diameter nearly equal to 16.2 mm is obtained (Figure 8a). True σ versus the ϵ curve is obtained from experimental as well as numerical analysis and they are plotted together and shown Metalsin Figure2020, 108b., 1281 10 of 15

Figure 8. (a) The cross section of the 16.2 mm rod, and (b) the comparison of numerical and experimental trueFigureσ and 8. (acurves) The ofcross the swagedsection ofpiece. the 16.2 mm rod, and (b) the comparison of numerical and experimental true σ and ϵ curves of the swaged piece. Our analysis is based on a varying axial feed rate. The variation of effective stress was estimated for diOfferentur analysis feed ratesis based (0.7 on m a/min, varying 1.25 axial m/min feed and rate. 2 The m/min). variation Using of Deformeffective 3D,stress the was time estimated step is specifiedfor different as 0.5 feed s for rates a bite (0.7 and m/min, accordingly, 1.25 m/min the axial and feed 2 m/min). per bite Using has been Deform calculated 3D, the and time is given step as is inputspecified in the as pre-processor.0.5 s for a bite Accordingand accordingly, to the parameters,the axial feed die per velocity bite has and been stroke calculated in the radial and is direction given as isinput fixed. in Thethe pre obtained-processor. results According are shown to below.the parameters, die velocity and stroke in the radial direction is fixedResidual. The obtained stresses inresults the work are shown material below. are periodically distributed during the forming process. To ensureResidual a stress stresses value in the from work the material simulations are periodically that describe distributed a homogeneous during residualthe forming stress process. state, 20To measuring ensure a stress points value were from chosen the along simulations the diameter; that describe the positions a homogeneous are seen in residual Figure5 .stress The residual state, 20 stressesmeasuring were points extracted were after chosen the die along was the released diameter from; the workpositions piece, are with seen subsequent in Figure cooling5. The toresidual room temperature.stresses were It extracted is observed after that the with die anwas increasing released numberfrom the of work passes, piece the, valuewith subsequent of residual stresscooling also to increases.room tem Thisperature. can be It observedis observed from that the with FEM an analysisincreasing for number the different of pass numberes, the ofvalue passes. of residual The residual stress stressesalso increases. were measured This can alongbe observed the radial from direction the FEM of analysis the rodat for di thefferent different cross sectionsnumber ofof thepasses. swaged The workresidual piece. stresses were measured along the radial direction of the rod at different cross sections of the swagedNumerical work piece. simulation was performed to predict the residual stress over the surface as well as over the cross-sectionNumerical simulation of the 25% was swaged performed samples, to withpredict diff erentthe residual feed rates stress using over DEFORM the surface 3D as software. well as Thisover result the cross (Figure-section9a–c) ofshows the the25% compressive swaged samples residual, with stress different at the surface feed rates and using the tensile DEFORM residual 3D stresssoftwar ate. the This center result in the(Figure radial 9a direction–c) shows of the the compressive rod. The obtained residual results stress qualitativelyat the surface match and the with tensile the experimentresidual stress data. at Itthe may center be becausein the radial of varying direction parameters of the rod. involved The obtained in the completeresults qualitatively swaging process, match suchwith asthe die experiment geometry, data. die movement It may be because velocity, of and varying swaging parameters stroke. In involved the next in step, the diecomplete geometry swaging was variedprocess, according such as todie the geometry, required diameter,die movement i.e., 5 nos. velocity, of die and sets swaging (one die stroke. set contains In the 4 segments) next step, for die swaginggeometry the was bar varied from φ according21 to φ 16.2 to the mm: required 1 set: φ diameter21 to φ 20, i.e. mm;, 5 nos. 1 set: ofφ die20 sets to φ (one19 mm; die set 1 set: containφ 19s to 4 segments) for swaging the bar from ϕ 21 to ϕ 16.2 mm: 1 set: ϕ 21 to ϕ 20 mm; 1 set: ϕ 20 to ϕ 19 mm; φMetals18.2 2020 mm;, 10 1, x set: FORφ PEER18.2 REVIEW to φ 17.4 mm; 1 set: φ 17.4 to φ 16.2 mm. 11 of 16 1 set: ϕ 19 to ϕ 18.2 mm; 1 set: ϕ 18.2 to ϕ 17.4 mm; 1 set: ϕ 17.4 to ϕ 16.2 mm.

FigureFigure 9.9. The p predictedredicted residual residual stresses stresses in in the the radial radial direction direction for for the the 25% 25% swaged swaged sample sampless (a) at (a )0.7 at 0.7m/min m/min feed feed rate, rate, (b) (atb) 1.25 at 1.25 m/min m/min feed feed rate rate and and (c) (atc) 2 at m/min 2 m/min feed feed rate. rate.

Parameters play a significant role in the variation of residual stresses. A better value of the obtained residual stresses has been noticed in the below figures (Figure 10) when appropriate die geometry is used. Also, in next step, simulated results have shown a better trend with values matching with the experimental results, obtained by employing 30 mm/sec die movement velocity. There is evidence of inhomogeneous deformation of swaged Zr-4 alloy as the feed rate is increased from 0.7 m/min to 2 m/min in the case of the 25% swaged rod, measured in the radial direction. As seen from Figure 10a–c, the magnitude of the residual stress at the surface is −0.588 MPa at 0.7 m/min. It increases to −62.8 MPa at 1.25 m/min and −88.2 MPa for 2 m/min.

Figure 10. The residual stresses in the radial direction with different die geometries and die movement velocities (a) at 0.7 m/min, (b) at 1.25 m/min and (c) at 2 m/min feed rate.

4.2. Deep Hole Drilling For the 25% swaged samples (18.2 mm swaged rod), residual stress results are shown in Figure 11a–c. It is observed that as the diameter decreases through swaging operation, and the magnitude of the residual stresses increases as is evident from Figure 11d for the 16.2 mm rod (0.7 m/min feed rate). This is attributed to high cold work, which would lead to higher flow stress as well as higher residual stress.

Metals 2020, 10, x FOR PEER REVIEW 11 of 16

Metals Figure2020, 10 9., 1281 The predicted residual stresses in the radial direction for the 25% swaged samples (a) at 0.711 of 15 m/min feed rate, (b) at 1.25 m/min feed rate and (c) at 2 m/min feed rate.

ParametersParameters play a signiﬁcantsignificant role in the variation of residual stresses. stresses. A A better better value value of of the the obtainedobtained residualresidual stresses has been noticed in in the the below below figures ﬁgures ( (FigureFigure 10) 10 )when when appropriate appropriate die die geometrygeometry is is used. used Also,. Also, in nextin next step, step, simulated simulated results results have haveshown shown a better a trendbetter with trend values with matching values withmatching the experimental with the experimental results, obtained results, obtained by employing by employing 30 mm/sec 30 diemm/sec movement die movement velocity. velocity. There is evidenceThere is evidence of inhomogeneous of inhomogeneous deformation deformation of swaged of swaged Zr-4 alloy Zr-4 asalloy the as feed the ratefeed israte increased is increased from 0.7from m /0.7min m/min to 2 m to/min 2 m/min in the in case the ofcase the of 25% the swaged25% swaged rod, measuredrod, measured in the inradial the radial direction. direction. As seenAs fromseen from Figure Figure 10a–c, 10a the–c, magnitudethe magnitude of theof the residual residual stress stress at at the the surface surface isis −0.588 MPa MPa at at 0.7 0.7 m/min. m/min. − ItIt increasesincreases toto −62.8 MPa at 1.25 m/min m/min and and −88.288.2 MPa MPa for for 2 2m/min. m/min. − −

FigureFigure 10.10. The r residualesidual stresses stresses in in the the radial radial direction direction with with different diﬀerent die die geometr geometriesies and and die die movement movement velocitiesvelocities ((aa)) atat 0.70.7 mm/min,/min, ((bb)) atat 1.251.25 mm/min/min and (c) at 2 m/min m/min feed rate. 4.2. Deep Hole Drilling 4.2. Deep Hole Drilling For the 25% swaged samples (18.2 mm swaged rod), residual stress results are shown in Figure 11a–c. It is observedFor the 25% that swaged as the diametersamples (18.2 decreases mm swaged through rod), swaging residual operation, stress results and theare magnitudeshown in Figure of the 11a–c. It is observed that as the diameter decreases through swaging operation, and the magnitude residual stresses increases as is evident from Figure 11d for the 16.2 mm rod (0.7 m/min feed rate). This is of the residual stresses increases as is evident from Figure 11d for the 16.2 mm rod (0.7 m/min feed attributedMetals 2020, to10, highx FOR cold PEER work, REVIEW which would lead to higher ﬂow stress as well as higher residual stress.12 of 16 rate). This is attributed to high cold work, which would lead to higher flow stress as well as higher residual stress.

FigureFigure 11.11. The r residualesidual stress stress variation variation with with depth depth for for the the 25% 25% swaged swaged samples samples:: (a) (0.7a) 0.7m/min, m/min, (b) (b1.25) 1.25/min/min,, (c) (2c )m/min 2 m/min and and (d) ( d0.7) 0.7 m/min m/min for for the the 40% 40% swaged swaged sample. sample. For the 25% swaged alloy, deep hole drilling results indicate the compressive stresses at the surface For the 25% swaged alloy, deep hole drilling results indicate the compressive stresses at the and tensile stresses at center for 0.7 m/min, 1.25 m/min and 2 m/min feed rates. The magnitude of surface and tensile stresses at center for 0.7 m/min, 1.25 m/min and 2 m/min feed rates. The magnitude compressive residual stress increases with increasing feed rates. This is due to the higher amount of of compressive residual stress increases with increasing feed rates. This is due to the higher amount of deformation induced during higher feed rates. Deep hole drilling measurements show the compressive stress at the surface and the tensile stress at the center for both the axial and radial directions. Figure 12a–c shows the kernel average misorientation of 25% swaged Zr-4 alloys at different feed rates. This result shows that the amount of strain increases with increasing feed rates (from 0.7 m/min to 2 m/min). That also supports the trend of surface residual stress measured through experimental and numerical methods.

Figure 12. Kernel average misorientation (KAM) images of (a) 0.7 m/min, (b) 1.25 m/min and (c) 2 m/min of the 25% swaged (surface).

4.3. Experimental vs. Numerical Experimental and numerical results obtained from the FE analysis of residual stresses are plotted together and compared in Figure 13a–c.

Metals 2020, 10, x FOR PEER REVIEW 12 of 16

Figure 11. The residual stress variation with depth for the 25% swaged samples: (a) 0.7 m/min, (b) 1.25/min, (c) 2 m/min and (d) 0.7 m/min for the 40% swaged sample.

For the 25% swaged alloy, deep hole drilling results indicate the compressive stresses at the

Metalssurface2020 and, 10, tensile 1281 stresses at center for 0.7 m/min, 1.25 m/min and 2 m/min feed rates. The magnitu12 ofde 15 of compressive residual stress increases with increasing feed rates. This is due to the higher amount of deformation induced during higher feed rates. Deep hole drilling measurements show the deformationcompressive induced stress at during the surface higher andfeed the rates. tensile Deep stress holedrilling at the center measurements for both show the axial the compressive and radial stressdirection at thes. surface and the tensile stress at the center for both the axial and radial directions. FigureFigure 12 12aa–c–c shows shows the the kernel kernel average average misorientation misorientation of 25%of 25% swaged swaged Zr-4 Zr alloys-4 alloys at di atﬀerent different feed rates.feed rates. This resultThis result shows shows that the that amount the amount of strain of strain increases increases with increasing with increasing feed rates feed (from rates 0.7(from m/min 0.7 tom/min 2 m/min). to 2 That m/min). also Thatsupports also the supports trend of the surface trend residual of surface stress residual measured stress through measured experimental through andexperimental numerical and methods. numerical methods.

Figure 12. Kernel average misorientation (KAM) images of (a) 0.7 m/min, (b) 1.25 m/min and (c) Figure 12. Kernel average misorientation (KAM) images of (a) 0.7 m/min, (b) 1.25 m/min and (c) 2 2 m/min of the 25% swaged (surface). m/min of the 25% swaged (surface). 4.3. Experimental vs. Numerical 4.3. Experimental vs. Numerical Experimental and numerical results obtained from the FE analysis of residual stresses are plotted Experimental and numerical results obtained from the FE analysis of residual stresses are plotted togetherMetals 2020 and, 10, comparedx FOR PEER inREVIEW Figure 13a–c. 13 of 16 together and compared in Figure 13a–c.

FigureFigure 13. 13.The The comparisoncomparison betweenbetween experimentalexperimental residualresidual stressesstresses ((aa)) 0.70.7 mm/min,/min,( b(b)) 1.25 1.25 m m/min/minand and c ((c)) 2 2 m m/min/min and and the the numerically numerically predicted predicted residual residual stresses stresses for for the the 25% 25% swaged swaged Zr-4 Zr-4 sample. sample. The residual stress predicted by numerical modelling is in tandem with the deep hole drilling The residual stress predicted by numerical modelling is in tandem with the deep hole drilling technique for the 25% (18.2 mm rod) swaged samples. For the 25% swaged alloy, deep hole drilling technique for the 25% (18.2 mm rod) swaged samples. For the 25% swaged alloy, deep hole drilling results reveal compressive stresses at the surface and tensile stresses at the center. For the 25% swaged results reveal compressive stresses at the surface and tensile stresses at the center. For the 25% swaged alloy, numerical modelling showed (in the radial direction, Z) compressive stresses at the surface and alloy, numerical modelling showed (in the radial direction, Z) compressive stresses at the surface and tensile stresses at the center. Both experimental and numerical methods show similar residual stress tensile stresses at the center. Both experimental and numerical methods show similar residual stress magnitudes quantitatively at the surface of the swaged rod. For the 0.7 m/min feed rate, deep hole magnitudes quantitatively at the surface of the swaged rod. For the 0.7 m/min feed rate, deep hole drilling and numerical methods have shown 6 MPa and 0.9 MP, respectively. In the case of 1.25 m/min drilling and numerical methods have shown 6 MPa −and −0.9 MP, respectively. In the case of 1.25 feed rate, deep hole drilling technique showed 52 MPa and 41.4 MPa from the numerical method. m/min feed rate, deep hole drilling technique −showed −52 MPa− and −41.4 MPa from the numerical For the 2 m/min feed rate, deep hole drilling showed 86 MPa and 74 MPa with the numerical method. For the 2 m/min feed rate, deep hole drilling− showed −86− MPa and −74 MPa with the method. Both numerical and experimental methods predicted a similar trend in variation of tensile numerical method. Both numerical and experimental methods predicted a similar trend in variation residual stresses but they diﬀer slightly in their magnitude. These results are for swaged samples at of tensile residual stresses but they differ slightly in their magnitude. These results are for swaged diﬀerent feed rates and it suggests that increasing the feed rate increases the compressive residual samples at different feed rates and it suggests that increasing the feed rate increases the compressive stresses on the surface while tensile stresses are nearly similar on increasing the feed rates. With these residual stresses on the surface while tensile stresses are nearly similar on increasing the feed rates. With these results, we suggest that 1.25 m/min feed rate is good for producing swaged Z-4 alloy, because of the good combination of mechanical properties of tensile strength (535.50 MPa), ductility (19.84%) and fracture toughness (44.37 MPa·m0.5) reported in our earlier work [24]. Further annealing treatment will decrease the tensile residual stress at the center of Zr-4 alloy rod. Numerical results could be improved further by using more refined meshes and minor time steps in order to match closely with experimental results. To improve the die design, die movement velocity with or without lubricant during swaging could also contribute to obviate the detrimental effect of residual stress in the alloy.

5. Conclusions Numerical and experimental investigations are carried out to investigate the influence of the feed rate in the radial direction on residual stresses of a swaged zircaloy-4 rod. The following conclusions are made based on the present work: 1. Numerical and experimental results both show a similar trend of residual stresses from the surface to center on the 25% swaged rod at different feed rates (0.7 m/min, 1.25 m/min and 2 m/min). Almost the same magnitude of residual stress on the surface as well as center of the 25% swaged rod are observed. 2. Deep hole drilling results show an increase in magnitude of residual stress on increasing the percentage of cold work. This is due to increase in the amount of deformation, which leads to an increase in yield strength at higher cold work on zirconium alloys. 3. The inhomogeneous deformation observed from the surface to the center (in the radial direction) on the 25% swaged rod (0.7 m/min, 1.25 m/min and 2 m/min) as observed in residual stress magnitude for both experimental and numerical methods. 4. It can be concluded from the load curve that at the same time all four dies exert an equal amount of load over the work piece, it results in a uniform homogeneous deformation in the axial direction of the swaged Zr-4 rod.

Metals 2020, 10, 1281 13 of 15 results, we suggest that 1.25 m/min feed rate is good for producing swaged Z-4 alloy, because of the good combination of mechanical properties of tensile strength (535.50 MPa), ductility (19.84%) and fracture toughness (44.37 MPa m0.5) reported in our earlier work [24]. Further annealing treatment · will decrease the tensile residual stress at the center of Zr-4 alloy rod. Numerical results could be improved further by using more reﬁned meshes and minor time steps in order to match closely with experimental results. To improve the die design, die movement velocity with or without lubricant during swaging could also contribute to obviate the detrimental eﬀect of residual stress in the alloy.

5. Conclusions Numerical and experimental investigations are carried out to investigate the inﬂuence of the feed rate in the radial direction on residual stresses of a swaged zircaloy-4 rod. The following conclusions are made based on the present work:

1. Numerical and experimental results both show a similar trend of residual stresses from the surface to center on the 25% swaged rod at diﬀerent feed rates (0.7 m/min, 1.25 m/min and 2 m/min). Almost the same magnitude of residual stress on the surface as well as center of the 25% swaged rod are observed. 2. Deep hole drilling results show an increase in magnitude of residual stress on increasing the percentage of cold work. This is due to increase in the amount of deformation, which leads to an increase in yield strength at higher cold work on zirconium alloys. 3. The inhomogeneous deformation observed from the surface to the center (in the radial direction) on the 25% swaged rod (0.7 m/min, 1.25 m/min and 2 m/min) as observed in residual stress magnitude for both experimental and numerical methods. 4. It can be concluded from the load curve that at the same time all four dies exert an equal amount of load over the work piece, it results in a uniform homogeneous deformation in the axial direction of the swaged Zr-4 rod. 5. The axial (X) and radial (Z) residual stresses on the surface are compressive and thus, can help in preventing crack propagation and can enhance product life. On the other hand, the stresses towards the center of the rod are tensile and thus, may assist the propagation of possible cracks. Hence, there is a need to undergo heat treatment before use.

Author Contributions: G.S. and B.K., conceptualized, procured and analyzed data, and wrote the manuscript; K.I.V.N. and U.K.A., provided the methodology (the swaging process) and resources for samples; M.M.M., provided the facilities for hole drilling and carrying out the experiments; R.J., directed the research, wrote the manuscript and provided comments in the manuscript. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the Board of Research in Nuclear Sciences (BRNS), Mumbai, India (grant no. EDD/16/17/034/BRNS/RJAG.) Acknowledgments: The authors would like to thank the Board of Research in Nuclear Sciences (BRNS), Mumbai, India for sponsoring this work. Conﬂicts of Interest: The authors declare that they have no conﬂict of interest.

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