- Email: [email protected]
Experimental and Theoretical Study of Deformation Processes in a Flange Connection of Iron Beams
Available online at www.sciencedirect.com Available online at www.sciencedirect.com
ScienceDirect ScienceDirect
Structural Integrity Procedia 00 (2018) 000–000 Available online www.sciencedirect.com Available online at at www.sciencedirect.com Structural Integrity Procedia 00 (2018) 000–000
ScienceDirect ScienceDirect
Procedia Structural (2018) 207–214 Structural IntegrityIntegrity Procedia900 (2016) 000–000
www.elsevier.com/locate/procedia www.elsevier.com/locate/procedia
www.elsevier.com/locate/procedia
IGF Workshop “Fracture and Structural Integrity” IGF Workshop “Fracture and Structural Integrity”
Experimental and Theoretical Study of Deformation Processes in a Experimental and Theoretical Study of Deformation Processes in a Flange Connection IronFebruary Beams XV Portuguese Conference on Fracture, PCF 2016,of 2016, Paço de Arcos, Portugal Flange Connection of10-12 Iron Beams a a I.Shardakov *, A.Shestakov , I.Glotaa turbine blade of an Thermo-mechanical modeling of a high a apressure I.Shardakov *, A.Shestakov , I.Glot Institute of Continuous Media Mechanics UB RAS, 1, Korolev street, Perm, 614013, Russia airplane gas turbine engine Institute of Continuous Media Mechanics UB RAS, 1, Korolev street, Perm, 614013, Russia a a
P. Brandãoa, V. Infanteb, A.M. Deusc*
Abstract AbstractaDepartment of Mechanical Engineering, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1, 1049-001 Lisboa, Flange connections are the critical elements of metal structures,Portugal as they determine the whole structure rigidity and strength. In this b IDMEC, Departmentthe of Mechanical Engineering, Instituto Superior Universidade de Lisboa, Av. Rovisco Pais, 1, strength. 1049-001 In Lisboa, Flange connections elements of structures, asTécnico, they determine the whole rigidity and this paper, we present theare resultscritical of experimental andmetal theoretical studies performed to evaluate the structure deformation behavior of the elements Portugal paper, we present the results of experimental and theoretical studies performed to evaluate the deformation behavior of the elements c of metal beam-to-column flange connections. The experimental investigations were carried out on samples subjected to elastic and CeFEMA, Department of Mechanical Engineering, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1, 1049-001 Lisboa, of metal beam-to-column experimental investigations were carried out samples on samples subjected to elastic inelastic deformations up flange to theirconnections. full failure. The Displacements at Portugal the characteristic points of the were registered during and the inelastic deformations up deformations to their full failure. Displacements the characteristic points of strain the samples were registered the loading process. Relative were measured at theatpoints of greatest stress and concentration. The dataduring obtained loading process. Relative deformations were measured at the points of greatest stress and strain concentration. The data obtained at different scales accurately characterize the interrelations between the deformed elements, especially when the deformation at different scales Our accurately characterize the concerned interrelations the deformed elements, especially when the deformation Abstract becomes inelastic. theoretical studies were withbetween the development of a mathematical model capable of providing an becomes inelastic. Our were concernedstates withinthethedevelopment a mathematical model capable of providing an adequate description of theoretical elastic and studies inelastic stress-strain elements of of flange connections. During description their operation, modern aircraft stress-strain engine components areelements subjected to increasingly demanding operating conditions, adequate of elastic and inelastic states in the of flange connections. especially the high pressure turbine (HPT) blades. Such conditions cause these parts to undergo different types of time-dependent © 2018 The Authors. Published by Elsevier B.V. © 2018 Published Elsevier B.V. degradation, oneresponsibility of Published which by is creep. AGruppo model using theFrattura finite element method (FEM) was developed, in order to be able to predict © 2018The TheAuthors. Authors. by Elsevier B.V. Peer-review under of the Italiano (IGF) ExCo. Peer-review responsibility of the GruppoFlight Italianodata Frattura (IGF) ExCo. for a specific aircraft, provided by a commercial aviation the creepunder behaviour of HPT blades. records Peer-review under responsibility of the Gruppo Italiano Frattura(FDR) (IGF) ExCo. company, were used to obtain thermal and mechanical data for three different flight cycles. In order to create the 3D model Keywords: flange connection; failure; load-carrying capacity; monitoring; simulation; experiment needed flange for the FEM analysis, a HPT blade scrap monitoring; was scanned, and itsexperiment chemical composition and material properties were Keywords: connection; failure; load-carrying capacity; simulation; obtained. The data that was gathered was fed into the FEM model and different simulations were run, first with a simplified 3D rectangular block shape, in order to better establish the model, and then with the real 3D mesh obtained from the blade scrap. The 1. overall Introduction expected behaviour in terms of displacement was observed, in particular at the trailing edge of the blade. Therefore such a 1. model Introduction can be useful in the goal of predicting turbine blade life, given a set of FDR data.
Flange connections are used as an alternative to welding because they can be easily disassembled for shipping, connections are usedbyas an alternative to welding because they can be easily disassembled for shipping, ©Flange 2016inspection, The Authors. Published Elsevier B.V. There routine maintenance, or replacement. have been numerous studies considering the specific features routine inspection, maintenance, or replacement. There have been numerous studies considering the specific under responsibility of the ScientificofCommittee of PCF 2016. ofPeer-review the deformation capacity of the elements flange connections in various embodiments. It is known thatfeatures flange of the deformation capacity ofcan thebeelements connections in various known flangea column-to-beam connections realizedofinflange different ways, Ghindea and embodiments. Ballok (2015).ItInisthe past that decades, Keywords: High Pressure Turbine Blade; Creep; Finite Element Method; 3D Model; Simulation. column-to-beam connections can be realized in different ways, Ghindea and Ballok (2015). In the past decades, a
* Corresponding author. Tel.: +7-342-237-8318; fax: +7-342-237-8487 * Corresponding Tel.: +7-342-237-8318; fax: +7-342-237-8487 E-mail address:author. [email protected] E-mail address: [email protected] 2452-3216 © 2018 The Authors. Published by Elsevier B.V. 2452-3216 © 2018 Authors. Published Elsevier B.V. Frattura (IGF) ExCo. Peer-review underThe responsibility of theby Gruppo Italiano Peer-review underauthor. responsibility the Gruppo Italiano Frattura (IGF) ExCo. * Corresponding Tel.: +351of218419991. E-mail address: [email protected]
2452-3216 © 2016 The Authors. Published by Elsevier B.V.
Peer-review under responsibility of the Scientific Committee of PCF 2016. 2452-3216 2018 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the Gruppo Italiano Frattura (IGF) ExCo. 10.1016/j.prostr.2018.06.032
208 2
I. Shardakov et al. / Procedia Structural Integrity 9 (2018) 207–214 Author name / Structural Integrity Procedia 00 (2018) 000–000
number of studies on the mechanical properties of the flange connection have been carried out; in particular, the results of tests performed on full-scale samples are described in Prinz et al. (2014). The samples consisting of a column and an adjacent beam were subjected to loading, and a bending moment was applied to the beam until the column-to-beam connection was broken. The size of the flange and the number of connecting bolts varied. Reinforcement of the flange plate using additional stiffeners increases the strength of the connection, but reduces its deformation capacity, Abidelah et al. (2012). The amount of plastic deformation in the reinforced connection decreases and, as a result, the capability of this connection to dissipate vibrations caused by seismic loads decreases. One of the approaches toward improving the stability of the structure under the action of seismic loads implies the reduction of the beam flange width near beam-to-column connections, which increases the deformation capacity of the beam and reduces the loads carried out by the column, Roudsari et al. (2018). A proper analysis for the element with a non-orthogonal beam-to-column joint under seismic loads is given in Hunn et al. (2018). The behavior of a column-to-column bolted joint was explored both theoretically and experimentally taking into account the three-dimensional geometry of the columns, flanges and bolts, Li, He et al. (2018). The dry friction contact conditions were specified for the flanges, and the bolt pretension was taken into consideration. Analysis of the structure, consisting of a large number of beams connected by bolted connections, is presented in Blachowski and Gutkowski (2016). A nonlinear calculation of the construction using the method of subconstructions has been performed, which makes it possible to significantly save the calculation time. The behavior of the structure is modeled when one of the flange connection bolts is removed. In experimental-theoretical work Meng et al. (2018), the influence of the characteristics of the bolted flange column-to-beam connection on progressing breakdown of the structure is investigated. It should be noted that, along with flange connections, welded connections of columns and beams are widely used nowadays. Both in-situ and numerical studies of such connections are carried out Li et al. (2018), Rong et al. (2018) under constant and cyclic loads. Compared to bolted connections, such connections have a number of significant disadvantages. When constructing a structure, the installation of welding connections takes a considerable period of time, requires high qualification of the personnel, and the quality of welded seams can depend on the environmental conditions. The manufacture of flanges for the bolted connection can be performed under stable factory conditions using automated welding lines. Each version of the flange connection has its own peculiarities of the deformation behavior, which become especially significant under inelastic deformation. In the engineering environment, the development and implementation of verified mathematical models that allow analyzing the deformation processes in the elements of flange connections from the elastic state to the complete loss of bearing capacity is an urgent issue. This paper presents a series of experimental and theoretical studies conducted to analyze the specific features of quasistatic deformation processes in bolted flange connections. Mathematical modeling of the stress-strain state of the elements of such connections is complicated by the following three factors: three-dimensional geometry of mating parts, contact interactions between the bolted connections at the stages of their installation and operation, and the availability of large elastoplastic deformations. The first challenge has been overcome through the use of the FEM software, but the remaining two have required the performance of a number of experimental and theoretical studies to provide a reliable mathematical modeling of the stress-strain state in the elements of this joint. 2. Experiment description The schematic drawing of the sample of the flange connection is shown in Fig. 1. The sample consists of a vertical column and two symmetrically located horizontal beams adjacent to it. The horizontal beams are connected to the vertical column by eight bolts. The I-Beam shape of the beam and column is considered. For the experimental study of the deformation processes in the connection elements, a test stand has been developed. The structural diagram of the stand, the load scheme and the system for measuring during the tests are shown in Fig. 2. The sample consisting of a column 3 and a beam 4 is loaded in the power frame 1 using hydraulic jacks 5 connected to the common hydraulic line, which ensures symmetrical loading of the sample throughout the experiment. The figure shows: F, 2F – reaction forces arising, respectively, in the horizontal beams and the column from the action of the jacks; U1, U2, U3 – location of vertical displacement sensors;
I. Shardakov et al. / Procedia Structural Integrity 9 (2018) 207–214 Author name / Structural Integrity Procedia 00 (2018) 000–000
209 3
Fig. 1. The diagram of the flange connection (dimensions are in millimeters).
E1, E2 – location of sensors for measuring deformation in a horizontal direction, EF – location of sensor for measuring deformation along the beam axis. The system for measuring deformation parameters consisted of three displacement sensors and three deformation ones. Fig. 2 shows the arrangement of the displacement sensors. Relative to the independent reference base the vertical displacements of the horizontal beams in the vicinity of the places of application of forces from the hydraulic jacks, as well as the vertical movement of the lower end of the vertical column, were measured. Such a scheme for measuring vertical displacements made it possible to control the symmetry of the deformation relative to the vertical column, and also to determine the value of the vertical displacement of the column only due to the entire set of the deformation processes in the flange connection. The positions of sensors E1, E2 on the vertical column and EF on the horizontal beam are determined from the results of mathematical modeling of the quasistatic deformation process in the framework of the elasto-plastic deformation. The E1, E2 sensors are designed to record the dominant strain values along the horizontal axis on the shelf of the vertical column. The EF sensor is fixed on the upper shelf of the horizontal beam at a distance of 33 cm from the flange. Such a position of this sensor ensures absence of plastic deformations and allows one to control the effort from the jacks.
Fig. 2. The structural diagram of the test stand with a sample: 1 – power frame; 2 – support for the jacks; 3 – vertical column of the flange connection; 4 – horizontal beam of the flange connection; 5 – hydraulic jack
I. name Shardakov et al. /Integrity ProcediaProcedia Structural00Integrity 9 (2018) 207–214 Author / Structural (2018) 000–000
4210
Fig. 3. External force F t (N) vs. time t (min)
Fig. 3 shows a graph of the dependence of the external force F, given by the jacks, on the time t. This force in the time sweep has a periodic character with increasing maximum value and unloading to zero on each cycle. Such a character makes it possible to determine the force at which inelastic components appear in the recorded deformations, and also to estimate the measure of accumulated inelastic deformations caused by an external force. These results are used to verify the mathematical model. 3. Mathematical model The computational model consists of 19 parts: one column, two beams, and sixteen bolts. To describe the mathematical model of the group of these elements, we introduce the superscript k, which indicates that the variable belongs to the corresponding body. The initial position of the points of each element is given by the radius vectors X , and the deformed position by the vectors x . The radius vectors, determining the initial state and the deformed one, are determined in the initial coordinate system E j . The relationship between the initial and deformed states is calculated by the deformation gradient tensor F with components Fij xi / X j . Indices i , j take the values 1, 2 and 3. The moving coordinate system associated with the body ei is found as follows e1
e '1 e ' e '2 , e2 1 , e3 e1 e2 , e '1 e '1 e '2
(1)
where e'i F Ei are the auxiliary vectors. The rotation tensor, connecting the original coordinate system with the moving one, has the form of R ei E j . The mechanical behavior of each element is determined as follows: - Equilibrium equations ijk x j
0,
(2)
where ijk is the stress tensor; and x j is the Cartesian coordinates in the reference configuration. – Geometric relationships ε k R k Lk R k , T
(3)
I. Shardakov et al. / Procedia Structural Integrity 9 (2018) 207–214 Author name / Structural Integrity Procedia 00 (2018) 000–000
211 5
T 1 Fk Fk I is the deformation tensor where ε k is the deformation tensor in the moving coordinate system; Lk 2 in the original coordinate system; I is the unit tensor. – Physical equations, which take into account plastic deformations and are given in increments
dσ k Dk dε k dε k , pl ,
(4)
where dσ k is the stress tensor increment; Dk is the tensor of elastic constants; dε k the deformation tensor increment; Q(σ, w) dε k , pl is the plastic deformation tensor increment, Q is yield surface (this form corresponds to the σ associated plastic flow law); w is the work of plastic deformations. – Contact conditions on the adjacent (beam-column, bolt-beam, and bolt-column) surfaces are specified in terms of the dry friction model and are given by two inequalities, of which one expresses the condition of non-penetration of surfaces
(Uk 2 Uk1 ) nk1k 2 0
(5)
and the other describes a limitation to the tangential force on the contact area
K fr P ,
(6)
where U k 1 and U k 2 are the displacement vectors at the contact points of adjacent elements with numbers k1 and k2, respectively; n k 1 k 2 is the normal vector to the contact surface calculated with respect to the body k1 in the contact
σ k 1 n k 1 k 2 n k 1 k 2 is the area of bodies k1 and k2, σ is the stress tensor on the contact surface of the body k2, P normal stress at the contact point; σ k 1 nk 1 k 2 P n k 1 k 2 is the tangential stress at the contact point; K fr is the k1
friction coefficient. - Boundary conditions Uk
k
XSuk
XSk
f uk ,
(7)
fk ,
(8)
k
k
where f u is the displacement distribution function on the contact surface (for the body number k); f is the stress vector distribution function on the surface under the action of external forces are applied (for the body number k). The mathematical model described above is solved numerically by the finite element method. Fig. 4 shows the finite element mesh. The elements are based on the quadratic approximation of displacements. The number of nodes in the design scheme is 52491. The size of the element in the contact area is 2 centimeters.
4. Comparison of calculations and experimental results Five samples of flange connections were studied. The results obtained during the first experiments allowed us to make the developed mathematical model more accurate. In particular, the conditions for contact interaction were specified, and corrections to the parameters of constitutive equations were made. The measured and calculated deformation parameters are given below. These data were obtained for the jacks under the action of the external force F t varying according to the law illustrated in Fig. 3. Fig. 5 shows the time variation of the averaged value of vertical displacements at points U1 and U3 on the horizontal beams relative to the displacement of the vertical column at point U2 (Fig. 2):
6212
I. name Shardakov et al. /Integrity ProcediaProcedia Structural00Integrity 9 (2018) 207–214 Author / Structural (2018) 000–000
U t U1 t U3 t / 2 U2 t , where U1 t , U 2 t , U 3 t are the vertical displacements relative to the reference base at the corresponding point of the structure. The simulation results are shown by the red line, and the experimental data by the blue line.
Fig. 4. The FEM model of a column-to-beam connection
Figure 1. Vertical displacement U t (mm) vs. time t (min). (red line – simulation, blue line – experiment)
The value U t is a macro parameter that integrally reflects all the deformation processes occurring in the vicinity of the bolted connection, including inelasticity and contact interaction. Therefore, U t can be used as an informative parameter in the deformation monitoring of the flange connection. It follows from the obtained results that the application of the force F t 150kN to the jacks and its subsequent removal are not accompanied by the return-tozero of the value U t due to the elastic behavior of the material, i.e. inelastic deformation begins. Fig. 6 shows the time variations of the local deformations (in the horizontal direction) of the vertical column in the vicinity of the bolted connection. These deformations correspond to points E1 and E2 (Fig. 2) with mounted strain gauges.
I. Shardakov et al. / Procedia (2018) 207–214 Author name / Structural IntegrityStructural ProcediaIntegrity 00 (2018)9 000–000
(a)
2137
(b)
Figure 2. Deformations 1 (μm / m) at point E1 (a) and 2 (μm / m) at point E2 (b) depending on time t (min). (red line - simulation, blue line experiment)
Analysis of the results has indicated that compression, 1 0 , is realized at point E1 and tension, 1 0 , at point E2. It is interesting that the inelastic behavior of the elements in the compressed zone begins at higher loads compared to the stretched zone (at jack forces of 225kN and 190kN, respectively). At the same time, the value of the vertical displacement U t at which the inelasticty zone starts corresponds to the jack force of ~ 150 kN. This fact can be attributed to the peculiarities of inelastic contact deformations in the bolted joint.
5. Conclusion A number of experimental and theoretical studies on the deformation behavior of metal bolted flange connections under quasistatic deformation have been carried out. The experimental measurements of the deformation parameters for the samples representing full-scale flange joints made it possible to verify the developed mathematical model describing deformation processes based on the elastic-plastic flow. The analysis of the numerical simulation results and the experimental measurements allowed us to determine deformation parameters that reflect the specific features of the stress-strain state in the vicinity of the bolted joint. The proposed parameters can be used in monitoring the structures with bolted flange connections.
Acknowledgements The research was performed at the Institute of Continuous Media Mechanics Ural Branch of Russian Academy of Science, with the support of the Russian Science Foundation (project №14-29-00172).
References Abidelah, A., Bouchair, A., Kerdal, D.E., 2012. Experimental and analytical behavior of bolted end-plate connections with or withour stiffeners. J Constr Steel Res, 76, 13–27. Blachowski, B., Gutkowski, W., 2016. Effect of damaged circular flange-bolted connections on behaviour of tall towers, modelled by multilevel substructuring. Engineering Structures, 111, 93-103. Ghindea, M., Ballok, R., 2015. State-of-the-art review on bolted steel beam-to-column connections. Bulletin of the Transilvania University of Braşov, 8 (57). Hunn, Z.D., et al., 2018. A Finite Element Study of Non-Orthogonal Bolted Flange Plate Connections for Seismic Applications. Key Engineering Materials, 763, 525-532. Li, B., Yang, Y., Chen, Y., Cheng, W., Zhang, L., 2018. Behavior of connections between square CFST columns and H-section steel beams. Journal of Constructional Steel Research, 145, 10-27. Li, X.C., He, X.N., Wang, H.X., Zhang, A.L., 2018. Compression-bend-shearing performance of column-to-column bolted-flange connections in prefabricated multi-high-rise steel structures. Engineering Structures, 160, 439-460.
214 8
I. Shardakov et al. / Procedia Structural Integrity 9 (2018) 207–214 Author name / Structural Integrity Procedia 00 (2018) 000–000
Meng, B., Zhong, W., Hao, J., 2018. Anti-collapse performances of steel beam-to-column assemblies with different span ratios. Journal of Constructional Steel Research, 140, 125-138. Prinz, G.S., Nussbaumer, A., Borges, L., Khadka, S., 2014. Experimental testing and simulation of bolted beam-column connections having thick extended endplates and multiple bolts per row. Engineering Structures, 59, 434–447. Rong, B., Liu, S., Yan, J., Zhang, R., 2018. Shear behaviour of panel zone in through-diaphragm connections to steel tubular columns. Thin-Walled Structures, 122, 286-299. Roudsari, M.T., Jamshidi, H.K., Moradi, S.H., 2018. Experimental and Numerical Assessment of Reduced IPE Beam Sections Connections with Box-Stiffener. International Journal of Steel Structures, 18(1), 255–263.
ScienceDirect ScienceDirect
Structural Integrity Procedia 00 (2018) 000–000 Available online www.sciencedirect.com Available online at at www.sciencedirect.com Structural Integrity Procedia 00 (2018) 000–000
ScienceDirect ScienceDirect
Procedia Structural (2018) 207–214 Structural IntegrityIntegrity Procedia900 (2016) 000–000
www.elsevier.com/locate/procedia www.elsevier.com/locate/procedia
www.elsevier.com/locate/procedia
IGF Workshop “Fracture and Structural Integrity” IGF Workshop “Fracture and Structural Integrity”
Experimental and Theoretical Study of Deformation Processes in a Experimental and Theoretical Study of Deformation Processes in a Flange Connection IronFebruary Beams XV Portuguese Conference on Fracture, PCF 2016,of 2016, Paço de Arcos, Portugal Flange Connection of10-12 Iron Beams a a I.Shardakov *, A.Shestakov , I.Glotaa turbine blade of an Thermo-mechanical modeling of a high a apressure I.Shardakov *, A.Shestakov , I.Glot Institute of Continuous Media Mechanics UB RAS, 1, Korolev street, Perm, 614013, Russia airplane gas turbine engine Institute of Continuous Media Mechanics UB RAS, 1, Korolev street, Perm, 614013, Russia a a
P. Brandãoa, V. Infanteb, A.M. Deusc*
Abstract AbstractaDepartment of Mechanical Engineering, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1, 1049-001 Lisboa, Flange connections are the critical elements of metal structures,Portugal as they determine the whole structure rigidity and strength. In this b IDMEC, Departmentthe of Mechanical Engineering, Instituto Superior Universidade de Lisboa, Av. Rovisco Pais, 1, strength. 1049-001 In Lisboa, Flange connections elements of structures, asTécnico, they determine the whole rigidity and this paper, we present theare resultscritical of experimental andmetal theoretical studies performed to evaluate the structure deformation behavior of the elements Portugal paper, we present the results of experimental and theoretical studies performed to evaluate the deformation behavior of the elements c of metal beam-to-column flange connections. The experimental investigations were carried out on samples subjected to elastic and CeFEMA, Department of Mechanical Engineering, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1, 1049-001 Lisboa, of metal beam-to-column experimental investigations were carried out samples on samples subjected to elastic inelastic deformations up flange to theirconnections. full failure. The Displacements at Portugal the characteristic points of the were registered during and the inelastic deformations up deformations to their full failure. Displacements the characteristic points of strain the samples were registered the loading process. Relative were measured at theatpoints of greatest stress and concentration. The dataduring obtained loading process. Relative deformations were measured at the points of greatest stress and strain concentration. The data obtained at different scales accurately characterize the interrelations between the deformed elements, especially when the deformation at different scales Our accurately characterize the concerned interrelations the deformed elements, especially when the deformation Abstract becomes inelastic. theoretical studies were withbetween the development of a mathematical model capable of providing an becomes inelastic. Our were concernedstates withinthethedevelopment a mathematical model capable of providing an adequate description of theoretical elastic and studies inelastic stress-strain elements of of flange connections. During description their operation, modern aircraft stress-strain engine components areelements subjected to increasingly demanding operating conditions, adequate of elastic and inelastic states in the of flange connections. especially the high pressure turbine (HPT) blades. Such conditions cause these parts to undergo different types of time-dependent © 2018 The Authors. Published by Elsevier B.V. © 2018 Published Elsevier B.V. degradation, oneresponsibility of Published which by is creep. AGruppo model using theFrattura finite element method (FEM) was developed, in order to be able to predict © 2018The TheAuthors. Authors. by Elsevier B.V. Peer-review under of the Italiano (IGF) ExCo. Peer-review responsibility of the GruppoFlight Italianodata Frattura (IGF) ExCo. for a specific aircraft, provided by a commercial aviation the creepunder behaviour of HPT blades. records Peer-review under responsibility of the Gruppo Italiano Frattura(FDR) (IGF) ExCo. company, were used to obtain thermal and mechanical data for three different flight cycles. In order to create the 3D model Keywords: flange connection; failure; load-carrying capacity; monitoring; simulation; experiment needed flange for the FEM analysis, a HPT blade scrap monitoring; was scanned, and itsexperiment chemical composition and material properties were Keywords: connection; failure; load-carrying capacity; simulation; obtained. The data that was gathered was fed into the FEM model and different simulations were run, first with a simplified 3D rectangular block shape, in order to better establish the model, and then with the real 3D mesh obtained from the blade scrap. The 1. overall Introduction expected behaviour in terms of displacement was observed, in particular at the trailing edge of the blade. Therefore such a 1. model Introduction can be useful in the goal of predicting turbine blade life, given a set of FDR data.
Flange connections are used as an alternative to welding because they can be easily disassembled for shipping, connections are usedbyas an alternative to welding because they can be easily disassembled for shipping, ©Flange 2016inspection, The Authors. Published Elsevier B.V. There routine maintenance, or replacement. have been numerous studies considering the specific features routine inspection, maintenance, or replacement. There have been numerous studies considering the specific under responsibility of the ScientificofCommittee of PCF 2016. ofPeer-review the deformation capacity of the elements flange connections in various embodiments. It is known thatfeatures flange of the deformation capacity ofcan thebeelements connections in various known flangea column-to-beam connections realizedofinflange different ways, Ghindea and embodiments. Ballok (2015).ItInisthe past that decades, Keywords: High Pressure Turbine Blade; Creep; Finite Element Method; 3D Model; Simulation. column-to-beam connections can be realized in different ways, Ghindea and Ballok (2015). In the past decades, a
* Corresponding author. Tel.: +7-342-237-8318; fax: +7-342-237-8487 * Corresponding Tel.: +7-342-237-8318; fax: +7-342-237-8487 E-mail address:author. [email protected] E-mail address: [email protected] 2452-3216 © 2018 The Authors. Published by Elsevier B.V. 2452-3216 © 2018 Authors. Published Elsevier B.V. Frattura (IGF) ExCo. Peer-review underThe responsibility of theby Gruppo Italiano Peer-review underauthor. responsibility the Gruppo Italiano Frattura (IGF) ExCo. * Corresponding Tel.: +351of218419991. E-mail address: [email protected]
2452-3216 © 2016 The Authors. Published by Elsevier B.V.
Peer-review under responsibility of the Scientific Committee of PCF 2016. 2452-3216 2018 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the Gruppo Italiano Frattura (IGF) ExCo. 10.1016/j.prostr.2018.06.032
208 2
I. Shardakov et al. / Procedia Structural Integrity 9 (2018) 207–214 Author name / Structural Integrity Procedia 00 (2018) 000–000
number of studies on the mechanical properties of the flange connection have been carried out; in particular, the results of tests performed on full-scale samples are described in Prinz et al. (2014). The samples consisting of a column and an adjacent beam were subjected to loading, and a bending moment was applied to the beam until the column-to-beam connection was broken. The size of the flange and the number of connecting bolts varied. Reinforcement of the flange plate using additional stiffeners increases the strength of the connection, but reduces its deformation capacity, Abidelah et al. (2012). The amount of plastic deformation in the reinforced connection decreases and, as a result, the capability of this connection to dissipate vibrations caused by seismic loads decreases. One of the approaches toward improving the stability of the structure under the action of seismic loads implies the reduction of the beam flange width near beam-to-column connections, which increases the deformation capacity of the beam and reduces the loads carried out by the column, Roudsari et al. (2018). A proper analysis for the element with a non-orthogonal beam-to-column joint under seismic loads is given in Hunn et al. (2018). The behavior of a column-to-column bolted joint was explored both theoretically and experimentally taking into account the three-dimensional geometry of the columns, flanges and bolts, Li, He et al. (2018). The dry friction contact conditions were specified for the flanges, and the bolt pretension was taken into consideration. Analysis of the structure, consisting of a large number of beams connected by bolted connections, is presented in Blachowski and Gutkowski (2016). A nonlinear calculation of the construction using the method of subconstructions has been performed, which makes it possible to significantly save the calculation time. The behavior of the structure is modeled when one of the flange connection bolts is removed. In experimental-theoretical work Meng et al. (2018), the influence of the characteristics of the bolted flange column-to-beam connection on progressing breakdown of the structure is investigated. It should be noted that, along with flange connections, welded connections of columns and beams are widely used nowadays. Both in-situ and numerical studies of such connections are carried out Li et al. (2018), Rong et al. (2018) under constant and cyclic loads. Compared to bolted connections, such connections have a number of significant disadvantages. When constructing a structure, the installation of welding connections takes a considerable period of time, requires high qualification of the personnel, and the quality of welded seams can depend on the environmental conditions. The manufacture of flanges for the bolted connection can be performed under stable factory conditions using automated welding lines. Each version of the flange connection has its own peculiarities of the deformation behavior, which become especially significant under inelastic deformation. In the engineering environment, the development and implementation of verified mathematical models that allow analyzing the deformation processes in the elements of flange connections from the elastic state to the complete loss of bearing capacity is an urgent issue. This paper presents a series of experimental and theoretical studies conducted to analyze the specific features of quasistatic deformation processes in bolted flange connections. Mathematical modeling of the stress-strain state of the elements of such connections is complicated by the following three factors: three-dimensional geometry of mating parts, contact interactions between the bolted connections at the stages of their installation and operation, and the availability of large elastoplastic deformations. The first challenge has been overcome through the use of the FEM software, but the remaining two have required the performance of a number of experimental and theoretical studies to provide a reliable mathematical modeling of the stress-strain state in the elements of this joint. 2. Experiment description The schematic drawing of the sample of the flange connection is shown in Fig. 1. The sample consists of a vertical column and two symmetrically located horizontal beams adjacent to it. The horizontal beams are connected to the vertical column by eight bolts. The I-Beam shape of the beam and column is considered. For the experimental study of the deformation processes in the connection elements, a test stand has been developed. The structural diagram of the stand, the load scheme and the system for measuring during the tests are shown in Fig. 2. The sample consisting of a column 3 and a beam 4 is loaded in the power frame 1 using hydraulic jacks 5 connected to the common hydraulic line, which ensures symmetrical loading of the sample throughout the experiment. The figure shows: F, 2F – reaction forces arising, respectively, in the horizontal beams and the column from the action of the jacks; U1, U2, U3 – location of vertical displacement sensors;
I. Shardakov et al. / Procedia Structural Integrity 9 (2018) 207–214 Author name / Structural Integrity Procedia 00 (2018) 000–000
209 3
Fig. 1. The diagram of the flange connection (dimensions are in millimeters).
E1, E2 – location of sensors for measuring deformation in a horizontal direction, EF – location of sensor for measuring deformation along the beam axis. The system for measuring deformation parameters consisted of three displacement sensors and three deformation ones. Fig. 2 shows the arrangement of the displacement sensors. Relative to the independent reference base the vertical displacements of the horizontal beams in the vicinity of the places of application of forces from the hydraulic jacks, as well as the vertical movement of the lower end of the vertical column, were measured. Such a scheme for measuring vertical displacements made it possible to control the symmetry of the deformation relative to the vertical column, and also to determine the value of the vertical displacement of the column only due to the entire set of the deformation processes in the flange connection. The positions of sensors E1, E2 on the vertical column and EF on the horizontal beam are determined from the results of mathematical modeling of the quasistatic deformation process in the framework of the elasto-plastic deformation. The E1, E2 sensors are designed to record the dominant strain values along the horizontal axis on the shelf of the vertical column. The EF sensor is fixed on the upper shelf of the horizontal beam at a distance of 33 cm from the flange. Such a position of this sensor ensures absence of plastic deformations and allows one to control the effort from the jacks.
Fig. 2. The structural diagram of the test stand with a sample: 1 – power frame; 2 – support for the jacks; 3 – vertical column of the flange connection; 4 – horizontal beam of the flange connection; 5 – hydraulic jack
I. name Shardakov et al. /Integrity ProcediaProcedia Structural00Integrity 9 (2018) 207–214 Author / Structural (2018) 000–000
4210
Fig. 3. External force F t (N) vs. time t (min)
Fig. 3 shows a graph of the dependence of the external force F, given by the jacks, on the time t. This force in the time sweep has a periodic character with increasing maximum value and unloading to zero on each cycle. Such a character makes it possible to determine the force at which inelastic components appear in the recorded deformations, and also to estimate the measure of accumulated inelastic deformations caused by an external force. These results are used to verify the mathematical model. 3. Mathematical model The computational model consists of 19 parts: one column, two beams, and sixteen bolts. To describe the mathematical model of the group of these elements, we introduce the superscript k, which indicates that the variable belongs to the corresponding body. The initial position of the points of each element is given by the radius vectors X , and the deformed position by the vectors x . The radius vectors, determining the initial state and the deformed one, are determined in the initial coordinate system E j . The relationship between the initial and deformed states is calculated by the deformation gradient tensor F with components Fij xi / X j . Indices i , j take the values 1, 2 and 3. The moving coordinate system associated with the body ei is found as follows e1
e '1 e ' e '2 , e2 1 , e3 e1 e2 , e '1 e '1 e '2
(1)
where e'i F Ei are the auxiliary vectors. The rotation tensor, connecting the original coordinate system with the moving one, has the form of R ei E j . The mechanical behavior of each element is determined as follows: - Equilibrium equations ijk x j
0,
(2)
where ijk is the stress tensor; and x j is the Cartesian coordinates in the reference configuration. – Geometric relationships ε k R k Lk R k , T
(3)
I. Shardakov et al. / Procedia Structural Integrity 9 (2018) 207–214 Author name / Structural Integrity Procedia 00 (2018) 000–000
211 5
T 1 Fk Fk I is the deformation tensor where ε k is the deformation tensor in the moving coordinate system; Lk 2 in the original coordinate system; I is the unit tensor. – Physical equations, which take into account plastic deformations and are given in increments
dσ k Dk dε k dε k , pl ,
(4)
where dσ k is the stress tensor increment; Dk is the tensor of elastic constants; dε k the deformation tensor increment; Q(σ, w) dε k , pl is the plastic deformation tensor increment, Q is yield surface (this form corresponds to the σ associated plastic flow law); w is the work of plastic deformations. – Contact conditions on the adjacent (beam-column, bolt-beam, and bolt-column) surfaces are specified in terms of the dry friction model and are given by two inequalities, of which one expresses the condition of non-penetration of surfaces
(Uk 2 Uk1 ) nk1k 2 0
(5)
and the other describes a limitation to the tangential force on the contact area
K fr P ,
(6)
where U k 1 and U k 2 are the displacement vectors at the contact points of adjacent elements with numbers k1 and k2, respectively; n k 1 k 2 is the normal vector to the contact surface calculated with respect to the body k1 in the contact
σ k 1 n k 1 k 2 n k 1 k 2 is the area of bodies k1 and k2, σ is the stress tensor on the contact surface of the body k2, P normal stress at the contact point; σ k 1 nk 1 k 2 P n k 1 k 2 is the tangential stress at the contact point; K fr is the k1
friction coefficient. - Boundary conditions Uk
k
XSuk
XSk
f uk ,
(7)
fk ,
(8)
k
k
where f u is the displacement distribution function on the contact surface (for the body number k); f is the stress vector distribution function on the surface under the action of external forces are applied (for the body number k). The mathematical model described above is solved numerically by the finite element method. Fig. 4 shows the finite element mesh. The elements are based on the quadratic approximation of displacements. The number of nodes in the design scheme is 52491. The size of the element in the contact area is 2 centimeters.
4. Comparison of calculations and experimental results Five samples of flange connections were studied. The results obtained during the first experiments allowed us to make the developed mathematical model more accurate. In particular, the conditions for contact interaction were specified, and corrections to the parameters of constitutive equations were made. The measured and calculated deformation parameters are given below. These data were obtained for the jacks under the action of the external force F t varying according to the law illustrated in Fig. 3. Fig. 5 shows the time variation of the averaged value of vertical displacements at points U1 and U3 on the horizontal beams relative to the displacement of the vertical column at point U2 (Fig. 2):
6212
I. name Shardakov et al. /Integrity ProcediaProcedia Structural00Integrity 9 (2018) 207–214 Author / Structural (2018) 000–000
U t U1 t U3 t / 2 U2 t , where U1 t , U 2 t , U 3 t are the vertical displacements relative to the reference base at the corresponding point of the structure. The simulation results are shown by the red line, and the experimental data by the blue line.
Fig. 4. The FEM model of a column-to-beam connection
Figure 1. Vertical displacement U t (mm) vs. time t (min). (red line – simulation, blue line – experiment)
The value U t is a macro parameter that integrally reflects all the deformation processes occurring in the vicinity of the bolted connection, including inelasticity and contact interaction. Therefore, U t can be used as an informative parameter in the deformation monitoring of the flange connection. It follows from the obtained results that the application of the force F t 150kN to the jacks and its subsequent removal are not accompanied by the return-tozero of the value U t due to the elastic behavior of the material, i.e. inelastic deformation begins. Fig. 6 shows the time variations of the local deformations (in the horizontal direction) of the vertical column in the vicinity of the bolted connection. These deformations correspond to points E1 and E2 (Fig. 2) with mounted strain gauges.
I. Shardakov et al. / Procedia (2018) 207–214 Author name / Structural IntegrityStructural ProcediaIntegrity 00 (2018)9 000–000
(a)
2137
(b)
Figure 2. Deformations 1 (μm / m) at point E1 (a) and 2 (μm / m) at point E2 (b) depending on time t (min). (red line - simulation, blue line experiment)
Analysis of the results has indicated that compression, 1 0 , is realized at point E1 and tension, 1 0 , at point E2. It is interesting that the inelastic behavior of the elements in the compressed zone begins at higher loads compared to the stretched zone (at jack forces of 225kN and 190kN, respectively). At the same time, the value of the vertical displacement U t at which the inelasticty zone starts corresponds to the jack force of ~ 150 kN. This fact can be attributed to the peculiarities of inelastic contact deformations in the bolted joint.
5. Conclusion A number of experimental and theoretical studies on the deformation behavior of metal bolted flange connections under quasistatic deformation have been carried out. The experimental measurements of the deformation parameters for the samples representing full-scale flange joints made it possible to verify the developed mathematical model describing deformation processes based on the elastic-plastic flow. The analysis of the numerical simulation results and the experimental measurements allowed us to determine deformation parameters that reflect the specific features of the stress-strain state in the vicinity of the bolted joint. The proposed parameters can be used in monitoring the structures with bolted flange connections.
Acknowledgements The research was performed at the Institute of Continuous Media Mechanics Ural Branch of Russian Academy of Science, with the support of the Russian Science Foundation (project №14-29-00172).
References Abidelah, A., Bouchair, A., Kerdal, D.E., 2012. Experimental and analytical behavior of bolted end-plate connections with or withour stiffeners. J Constr Steel Res, 76, 13–27. Blachowski, B., Gutkowski, W., 2016. Effect of damaged circular flange-bolted connections on behaviour of tall towers, modelled by multilevel substructuring. Engineering Structures, 111, 93-103. Ghindea, M., Ballok, R., 2015. State-of-the-art review on bolted steel beam-to-column connections. Bulletin of the Transilvania University of Braşov, 8 (57). Hunn, Z.D., et al., 2018. A Finite Element Study of Non-Orthogonal Bolted Flange Plate Connections for Seismic Applications. Key Engineering Materials, 763, 525-532. Li, B., Yang, Y., Chen, Y., Cheng, W., Zhang, L., 2018. Behavior of connections between square CFST columns and H-section steel beams. Journal of Constructional Steel Research, 145, 10-27. Li, X.C., He, X.N., Wang, H.X., Zhang, A.L., 2018. Compression-bend-shearing performance of column-to-column bolted-flange connections in prefabricated multi-high-rise steel structures. Engineering Structures, 160, 439-460.
214 8
I. Shardakov et al. / Procedia Structural Integrity 9 (2018) 207–214 Author name / Structural Integrity Procedia 00 (2018) 000–000
Meng, B., Zhong, W., Hao, J., 2018. Anti-collapse performances of steel beam-to-column assemblies with different span ratios. Journal of Constructional Steel Research, 140, 125-138. Prinz, G.S., Nussbaumer, A., Borges, L., Khadka, S., 2014. Experimental testing and simulation of bolted beam-column connections having thick extended endplates and multiple bolts per row. Engineering Structures, 59, 434–447. Rong, B., Liu, S., Yan, J., Zhang, R., 2018. Shear behaviour of panel zone in through-diaphragm connections to steel tubular columns. Thin-Walled Structures, 122, 286-299. Roudsari, M.T., Jamshidi, H.K., Moradi, S.H., 2018. Experimental and Numerical Assessment of Reduced IPE Beam Sections Connections with Box-Stiffener. International Journal of Steel Structures, 18(1), 255–263.