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Procedia Structural (2017) 777–784 Structural IntegrityIntegrity Procedia500 (2016) 000–000

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2nd International Conference on Structural Integrity, ICSI 2017, 4-7 September 2017, Funchal, Madeira, Portugal

Fracture for 2016, Steel10-12 Structures operated thePortugal XVBrittle Portuguese ConferenceModeling on Fracture, PCF February 2016, Paço dein Arcos, Extreme Thermo-mechanical modeling of a high pressure turbine blade of an a Valeriy Lepova*, Albertairplane Grigorievgas , Mbelle Samuel Bisongb, Kyunna Lepovaa turbine engine aa V.P.Larionov’s

of the North SB RAS, Yakutsk-677980, Russia, Oktyabrskaja, 1 V.P.Larionov’s Institute of Physical-Technical Problems a b c b bENSET Douala, Cameroon

P. Brandão , V. Infante , A.M. Deus *

a

Department of Mechanical Engineering, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1, 1049-001 Lisboa, Portugal IDMEC, Department of Mechanical Engineering, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1, 1049-001 Lisboa, Abstract Portugal c CeFEMA, Department of Mechanical Engineering, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1, 1049-001 Lisboa, T he Extreme here is an environment that contains conditionsPortugal that are hard to survive even for steel structures due to extreme b

temperature, corrosion, inappropriate service and repair. S o not only the mechanical properties and behavior of steel structures are important for structural integrity but also the phase transition processes, inhomogeneity and uncertainty factors. T hese problems are observed and discussed in the paper consisting of three main theoretical parts: the multiscale modeling approach for Abstract structural damage accumulation, the theory of low-temperature brittle-ductile transition for bcc steels, and uncertainty factors During their operation, modern aircraft engine are lifetime subjectedestimation to increasingly conditions, at low demanding temperatureoperating conditions, weld estimation concept. T he applications describe thecomponents locomotive tire especially the calculation high pressure Such conditions cause these parts tobased undergo types of time-dependent inhomogeneity andturbine bridge(HPT) serviceblades. life prediction. T he modeling approach on different K achanov-R abotnov structural degradation, one of which A model using finite element method was developed, in orderhas to be ableused to predict damage accumulation theoryis creep. and stochastic crack the growth modeling. B ay(FEM) esian probability approach been for the creep behaviour of HPT blades. Flight data records (FDR) for a specific aircraft, provided by a commercial aviation uncertainty factor estimation. T he experimental research included the internal friction study of bcc steel, the mechanical tension company, were usedtesting to obtain thermalprepared and mechanical for three differentofflight cycles. to create 3D model and impact toughness for probes from useddata in climatic condition C entral Y ak In utiaorder locomotive tirethe steel, the needed for testing the FEM analysis,steel a HPT bladeand scrap was scanned, and its chemical composition and material properties were low-cy cling for welded probes, microhardness estimation. T he inhomogeneity of probes used for stress and obtained. The data that was gathered was fed into the FEM model and different simulations were run, first with a simplified 3D strain state modeling. T he microstructural study reveals the small crack s in heat affected z one so the siz e and distance between rectangular block shape, in order to better establish the model, and then with the real 3D mesh obtained from the blade scrap. The such defects used for stochastic modeling visualiz ation of observed, crack propagation andatcrack velocity he concept of a overall expected behaviour in terms of displacement was in particular the trailing edgeestimation. of the blade.TTherefore such service life estimation for welded steel bearing for bridges has been presented. model can be useful in the goal of predicting turbine blade life, given a set of FDR data. © 2017 The Authors. Published by Elsevier B.V. © 2017 The Authors. Published by Elsevier B.V. Peer-review under responsibility ofby theElsevier Scientific Committee ICSI 2017. © 2016 The Authors. Published B.V. Peer-review under responsibility of the Scientific Committee of ICSIof2017 Peer-review under responsibility of the Scientific Committee of PCF 2016. Keywords: Extreme environment; mechanical behavior; low-cycle fatigue; fatigue; giga-cycle fatigue; brittle fracture; damage accumulation; modeling; welded steel probes; locomotive tire; microhardness; stress state; stochastic crack growth; service life; structural Keywords: High Pressure Turbine Blade; Creep; Finite Element Method; 3D Model; Simulation.

* Corresponding author. Tel.: +7-411-239-0578; fax: +7-411-239-0599. E-mail address: [email protected] 2452-3216 © 2017 The Authors. Published by Elsevier B.V. Peer-review underauthor. responsibility the Scientific Committee of ICSI 2017. * 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  2017 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the Scientific Committee of ICSI 2017 10.1016/j.prostr.2017.07.169

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1. Introduction The brittle fracture mechanics begins from Griffith (1920) study, when he revealed an influence of discrete invisible cracks for the materials strength. Then Ioffe (1928) shows that the small cracks arranged in a surface layer and could be managed by technology. But only past decades shows the whole spectrum of sizes and forms of defects and significance of damage accumulation processes in structural materials due to both the experimental and numerical mechanics development, including the electron microscopy achievements and fracture modeling noted in Fracture (1968), by Cherepanov (1977), Broek (1982), than in last years by Arkhangelskaja and Lepov (2003), Lepov (2008), Hell (2015), and other. The significantly loss of safety and economic efficiency is occurred in the operation of transport infrastructure such as railway equipment and bridge bearing in extreme climatic conditions. This leads to grows of energy and resource intensity of transportation. Special actuality of this problem is considering the construction of new rail lines and increase of cargo turnover. One of the most important units of railway equipment for example is the tire and rail system for low climatic temperatures, many tests was made by Grigoriev and Lepov (2012). For the bridges it was just shown for the weld steel bearing by Lepov and Mbelle (2017). Their durability and reliability significantly affect operating costs, and destruction is unacceptable because they pose a clear threat to traffic safety. The paper also underlines the significance of structural approach for strength and lifetime of construction members and system elements on the base of stochastic modeling of damage accumulation and fracture processes did by Broberg (1990) and Lepov et al (2007, 2016). New visualization possibilities of the Web-oriented programming for the fracture modeling due to developed algorithm of stochastic growth of the microcracks and micropores has been presented. 2. Materials and methods 2.1. Structural modeling approach The importance of considering internal heterogeneity and material structure leads to the development and wide use of the so-called structural models of damage accumulation and fracture. The main advantage of using a structured approach, including evaluation of the lifetime of metal structures, is to overcome known limitations of the semiempirical models that do not include an explicit description of the physical phenomena occurring in the material. Another important aspect when modeling of the processes of damage accumulation and destruction in real materials is the taking into account the hierarchy of structural damage and non-homogeneity of material properties at different levels described in detail in Computational and Experimental Methods (2009). In many cases the statistical modeling only could resolve this problem. Those models that are based on the simple generalization of experimental data on scattering characteristics of material resistance to deformation and fracture, are essentially the same semi-empirical as based on the hypothesis of homogeneity. The models considering the statistical variability of the properties of materials at micro - and macroscopic levels are more physically reasonable and give more opportunities to predict the effect of anisotropy of properties on the regularities of deformation and fracture of materials. The important advantage of combined structural models should be mentioned also, such as the ability to find a way of experimental data obtained for one of the kinds of loading and behavior of one material to another independently of composition and structure, and combine experimental data related to various kinds of stress state and external influence. The scheme of assessment of limit state and resource of structure element on the basis of structural and stochastic modeling shown on Fig. 1a. The initial and boundary data for the models are the sizes and quantitative characteristics of the distribution of defects at different structural levels or scales obtained by the scanning probes and optical microscopy and fractography methods, characterized quantitative by fractal dimension, and it in situ evolution during the damage accumulation process. Structural level or scale in this case means the area of the extent to which the prevailing is a certain defect structures (for example, vacancy, dislocation, the accumulation of dislocations, crack, micropore, strip shift, non-metallic inclusion, etc.). Deformation surface image of plane probe of low-alloyed steel near the rupture presented on Fig. 1b made by Lepov et al (2008, 2016). The image was obtained by STM and has 5×5 µm size. Just through the middle of the image a grain boundary passed with some structural defects around (small cracks, slip bends, twins etc.).

ValeriyValeriy Lepov Lepov et al. /etStructural Integrity Procedia 00 (2017) 000–000 al. / Procedia Structural Integrity 5 (2017) 777–784

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STM-, ASM- and optical microscopy and fractography of deformation and fracture surfaces Size distribution of microdefects on different structural levels Fractal parameters of damage Damage accumulation law Coherent model of elastoplasticity and damage accumulation

A

1 mkm

Estimation the limit size of parameters Stochastic modeling of growth and branching of small crack Statistical regularity of fracture

Estimation of limit state and lifetime of structure element or construction

B

Fig. 1. (a) Scheme of assessment of the strength and lifetime on the basis of structural modeling; (b) STM-image of deformation surface of steel probe with grain boundary and inhomogeneities.

2.2. Materials and method for mechanical tests The locomotive tires are exposed to influence of various loadings during operation. Material of the wheel of this locomotive element is merged in the complex stress state. So the internal and superficial defects are developed and damage plastic deformation and difficult tension takes place. The standard tension test for the steel does not a great gulf fixed for mechanical properties (as yielding, breaking point, and tensile strain) at room and low temperature (see Table 1). But because the bandage of locomotive tire is operated not only in a wide range of working temperatures, but in static and dynamic loading too the principle is to study the impact toughness of the material of the band, as positive (20 C) and below freezing (-20, -40, -60 C) also. Table 2 shows the results of impact test of bandage steel and average values for three or five samples. For welded steel probes the 30 run were carried out during the arc welding process, and a total of four different beads were achieved, such as the root run, hot pass, the filling and the capping. But before these welding runs were made, the steel alloy of 8 mm thickness was cut into the required dimension with the help of lathe machine. The initial joint configuration was obtained by securing the plates in position using tack welding. Single V butt joint configuration was used to fabricate the joints using manual metal arc welding process. This welding was done on the both side of the material. All the necessary cares were taken to avoid the joint distortion and the joints were made with applying clamping fixtures. The specimens for testing were sectioned to the required sizes.


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Table 3 shows the average values of chemical elements in welded steel probes. Table 1. Results of standard tensile test T, C

T, MPa

B, MPa

, %

20

690,16

1037,2

10,28

-50

755,74

1066,67

8,63

Table 2. Results of test for impact toughness KCV 20

T, C

-20

-40

-60

2,29 KCV, J/cm2

0,70

1,75

1,33

0,71

0,58

1,69

1,37

0,54

0,74

1,72

1,38

0,96

0,51

1,36

0,73

1,64 Average

0,67

1,82

0,62

Table 3. Result of chemical analysis of material, % Fe

C

Si

Mn

P

S

Cr

Mo

Ni

Al

Co

Cu

Nb

Ti

V

Zr

As

98.9

.183

.236

.397

.004

.32

.029

.011

.034

.046

.006

.04

.002

.002

.002

.002

.005

Analysis of the microstructure of the base metal, weld metal and heat affected zone of the sample numbered by 7 was performed using metallographic optical microscope. Composition of pearlite and ferrite was seen with the print of the indenter of the micro hardness test. The formation of pearlite and ferrite in base metal is composed of 20/80 respectively. For weld zone and HAZ it changes due to thermal processes. So the microstructure analysis shows that the base metal is a ferrite and pearlite having a grain size of 11-12 on a scale corresponding to an average grain diameter ≈ 7 microns (see Fig. 2c). The structure of the weld metal is also made up of ferrite and pearlite (see Fig. 2a) with columnar crystals of cast metal. The HAZ is made up of Widmanstätten figures (see Fig. 2b). The width of the HAZ zone is about 1,5 mm. In different areas of heat affected zone is observed fine-grained ferrite-pearlite structure with a high degree of dispersion [9]. Fig. 2b shows a micro crack with the length 1,7 mm in the HAZ of sample number 7. In the weld zone of this probe 1,2 mm length micro crack was revealed also.

50 mkm A

50 mkm B

50 mkm C

Fig. 2. (a) Microstructure of the weld; (b) HAZ and (c) base metal in the probe, ×250.

The un-notched smooth tensile specimens were prepared to evaluate transverse tensile properties of the joints such as tensile strength and yield strength (see Table 4). One result was removed due to very low strength. Also the un-notched smooth cyclic loading specimens were prepared to evaluate fatigue properties under low cyclic loading. Two points were obtainable from the tensile test results like the average tensile loading Rm and the average

Valeriy Lepov et al. / Procedia Structural Integrity 5 (2017) 777–784 Valeriy Lepov et al. / Structural Integrity Procedia 00 (2017) 000–000

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Rp 0.2. An interval between these two values serve us as maximum starting point for the fatigue loading for each specimen. This cyclic loading was constant on the specimens under a constant frequency of 5 Hz until fracture and complete rupture occurs on the specimen (see Fig.3). Table 4. Corrected tensile test result. No 1 2 3 4 5 6 7 8 9

S0, [mm] 84.08 85.67 73.92 84.16 80.67 removed 83.21 85.91 83.37

L0, [mm] 52.00 52.00 52.00 52.00 52.00

p0.2, [МPа] 328.35 322.08 314.62 335.97 335.90

b, [МPа] 484.50 477.24 488.12 482.68 485.46

, % 22.18 20.95 23.55 21.72 25.93

52.00 52.00 52.00

323.45 318.22 340.22

484.79 479.69 485.18

21.83 20.91 23.20

, MPa

N, cycles Fig. 3. S-N curve for a low cycle tested fatigue tested specimens.

Amongst the ten specimens used for the test, nine of the specimens were broken not at the welded portion but on the base metal. This can only interpret a good weld done with little or no defect. However one of the sample was broken on the welded portion before reaching its elastic limit, this signified a defect that could be due to WPS (Welding Procedure Specification), hydrogen inclusion, amongst others. A further research on the microstructure will give more light to the cause of this problem. 3. Modeling results and discussion The modeling of damage accumulation processes should consider the complex effects of high-cycle fatigue and low-cycle impact loading and also friction damage. The impact toughness as shown in Table 3 greatly depends on the test temperature. So the overall damage  could differentiate for high-cycle fatigue damage F and low-cycle impact damage L and contact wear damage Fr:


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1 N 1 K 1 M f i l k  , N i 1 K k 1 M j 1 fr j 

   F   L   Fr 







(1)

where f i – damage during fatigue i-cycle, l k – damage during contact impact k-cycle, fr j – damage during j-cycle of wear, N, K – appropriate cycles value. For operation at low temperatures the fatigue and friction damage of tire and rail way has been reduced, but the impact damage significantly grown. In summer contrariwise the contact impact damage low-to-nonexistent. The calculation of F and F is known before by Lepov et al (2016), but the contact wear damage was very hard to estimate due to complex process in contact spot and necessity of coherent thermal and mechanical problem solution. Here the thermal kinetic of interaction model used for two rough surfaces by Goryacheva (2013) and averaging of stress in contact spot of wheel-rail system. So the contact wear damage will be calculated by: M  U   i   U   (t )  1 exp dt    ,  kTi  j 1   kT (t )  

T

1  0

 Fr   exp 

(2)

where T – wheel resource, U – activation energy,  and  – material parameters, k – Boltzmann constant, (t) – stress in contact spot of wheel-rail system in point of time t, T(t) – temperature-time cycle, j=1,2… M – number of months when the wheel was exploited, – averaging stress in contact spot. Summation in (2) is performed by months with the known average temperature on railway spot. The stress value in this case will be equal to strength of steel and could be calculated by microhardness value. Here for locomotive tire b· 3,5·365 = 1277,5 MPa.  and  calculated by initial and boundary data for damage accumulation: t = 0, Fr = 0; t = T, Fr = 1. The condition of extreme uncertainty of tire stress and temperature state is defined by lack of information during operation of locomotive. The calculation shows that the locomotive tire lifetime de facto is three times as little in extreme conditions. To taking into account another undefined factors the some expert system and the Bayesian approach are need for most appropriate case of damage assessment by Al-Najjar and Weinstein (2015) approach: M

1

j 1

 

 U   i    p  j Tj , j kTi  

 Fr   exp   where p

 j Tj , j

 , 

(3)

- probability of j-damage at extreme uncertainty conditions.

The stress-strain state analysis is based on the models of linear elasticity, which are described by Lame equations for displacement. The discretization of the system of equations is done through the finite element method, and the numerical realization of the method is performed on collection of free software FEniCS. The result obtained shows that, the distribution of displacement in all samples are almost the same. Between the welded zone, the heat affected zone and the external elliptic zone, the Von Mizes stress is almost the same in all three samples (see Fig.4). Numerical results of Von Mizes stress for tension around the welded zone of three samples are presented in fig. 4. The maximum value located around the boundary between heat affected and welded zones is significantly lesser than total maximum value of Von Mizes stress. Stochastic model of crack growth and fracture in multiphase heterogeneous material is based on the mechanism triggered by stresses opening small cracks or pores on particles or ruptures of material, further viscoplastic growth and mutual coalescence of defects provide the crack propagation proposed by Broberg (1990) and modified by Lepov (2007). The model could visualize the crack propagation in heterogeneous media in real time. It is assumed that the length of the crack is a mean value of fraction and has a stochastic nature and normal distribution. The distance between cracks is the mean value also.

Valeriy al. / Procedia Structural Integrity 5 (2017) 777–784 Valeriy LepovLepov et al. /etStructural Integrity Procedia 00 (2017) 000–000

A

7837

B

C Fig. 4. Stress distribution in tension: a) for sample 1, b) for sample 3, c) for sample 7.

The length of cracks revealed in weld and heat affected zone is measured by metallography using the optical microscope “Neophot-32” and equal to 1.2 and 1.68 mm subsequently. The distance between the bottom edges of the cracks equals to 1.46 mm. The local flow stress could be calculated from microhardness values. Thus all parameters to simulate the crack growth, observe the possible path and calculate the crack velocity as an averaged discrete propagation of the crack tip are known. But another aspect of the modelling is the scale problem. The macroscopic cracks (with length of 1 mm and more) here has the same mechanical behaviour as microscopic cracks (length 1 mkm and above) so the algorithm is right, but the size of calculation zone is significantly large. So for velocity of crack the dimension factor used was equal to 100. Web-oriented visualization examples of crack growth on microdefects shown on Fig.5. Algorithm has realized by modern version of Java script language (http://iptpn.ysn.ru/hdr). Further modification of the model connected with application to a wide range of phenomena, such as accumulation of damage in porous media, materials with multiple phase transitions, including evaporation, melting and freezing, as well as the second order phase transition at lower temperature.

A

B Fig. 5. Java script visualization examples of crack growth on: a) micropores, b) small cracks

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4. Conclusion The mechanical properties and structure evaluation after the weld and low-cycle loading is significant for structural members of transport system. The differences in failure for low-cycling fatigue test probes caused by weld defects and heterogeneity could be modeled both by mechanics of continua and fracture mechanics. The influence of the mechanical heterogeneity in the low-alloyed steel welded probes on state-strain state and crack resistance has been estimated by the FE and stochastic modelling. Common defects were noticed on some welded samples, and these samples during the tensile test were broken on the welded zone under the normal estimated tensile strength and before the elastic limit. This failure could be as a result of one of the following reasons: poor welding procedure specification, poor welding skills, amongst others. The new criterion and approach of damage estimation for locomotive tire in extreme uncertainty conditions are offered. It is revealed that the lifetime of tire is significantly sensitive to impact strength at low temperature during operation. The new visualization possibilities of programming of damage accumulation and fracture processes has been presented also. The possibility of crack growth under the low-cycling and dynamic load, and in cases of complex loading is examined. To avoid the catastrophic failure of welded structures, special techniques should be applied to reduce hardness of the material. Systematic monitoring of structures like railway, locomotive tire, bridges, pipe lines, energy stations and buildings is necessary. One of the good methods of nondestructive testing could be the microhardness control of the weld and heat affected zone to avoid the significant modification of mechanical properties of welded structures. Acknowledgements This research has been partially supported by Russian Foundation for Basic Research (Project 15-41-05010) and Federal Agency of Scientific Organization of Ministry of Science and Education of Russian Federation. References Al-Najjar, N.I., Weinstein J., 2015, A Bayesian model of Knightian uncertainty, Theory Dec. 78, 1–22. Arkhangelskaya, E.A., Lepov, V.V., Larionov, V.P., 2003, The Role of Defects in the Development of Delayed Fracture of a Damaged Medium under the Effect of Hydrogen, Materialovedenie 8, 7–10. Broberg, K.B., 1990, Computer demonstration of crack growth, Int. J. Fracture 42, 277-285. Broek, D., 1982, Elementary engineering fracture mechanics, Martinus Nijhoff Publishers, Boston. Cherepanov, G.P., 1974, Mechanics of Brittle Fracture, Nauka Press, Moscow. Computational and Experimental Methods in Structures: Vol.3. Multiscale Modeling in Solid Mechanics, 2009, ed. Ugo Galvanetto and M.H. Ferri Aliabadi, World Scientific, London. Goryacheva, I.G., Soshenkov, S.N., and Torskaya, E.V., 2013, Modelling of Wear and Fatigue Defect Formation in Wheel-Rail Contact, Vehicle Syst. Dyn. 51, 6, 767–783. Griffith, A.A., 1920, The phenomenon of rupture and flow in solids, Phil. Trans. Roy. Soc. Ser. A 221, 163–198. Fracture. An Advanced Treatise, ed. Liebovitz, H., 1968, Academic Press, New York and London. Hell, S.W., et al, 2015, The 2015 super-resolution microscopy roadmap, J. Phys. D: Appl. Phys. 48, 443001 Ιοffe, A.F., 1928, The Physics of Crystals, McGraw Hill, New York and London. Lepov, V., Ivanova, A., Achikasova, V., Lepova, K., 2007, Modeling of the damage accumulation and fracture: structural-statistical aspects, Key Engineering Materials 345-346, I, 809-812. Lepov, V.V., et al., 2008, The Mechanism of Nanostructured Steel Fracture at Low Temperatures, Nanotechnologies in Russia 3, 734–742 Lepov, V., Grigoriev, A., Achikasova, V., Lepova, K., 2016, Some Aspects of Structural Modeling of Damage Accumulation and Fracture Processes in Metal Structures at Low Temperature, Modelling and Simulation in Engineering 2016, 7178028. Lepov, V., Mbelle, S.B., 2017, Microhardness and Elasticity Study of Fatigue Tested Weld Samples, DEStech Transactions on Engineering and Technology Research, International Conference on Mechanical and Mechatronics Engineering (ICMME 2017), 8611.