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Are the mechanical field parameters sufficient to predict uniquely the failure due to the ductile or cleavage mechanisms?
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Procedia Structural Structural IntegrityIntegrity Procedia1300(2018) (2016)285–291 000–000
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ECF22 - Loading and Environmental effects on Structural Integrity ECF22 - Loading and Environmental effects on Structural Integrity
Are the mechanical field parameters sufficient to predict uniquely Are the mechanical field parameters sufficient to predict uniquely the failure dueontoFracture, the ductile or10-12 cleavage mechanisms? XV Portuguese Conference PCF 2016, February 2016, Paço de Arcos, Portugal the failure due to the ductile or cleavage mechanisms? a Andrzej Neimitzaa,of Jaroslaw Galkiewicz * Thermo-mechanical modeling a high pressure Andrzej Neimitz , Jaroslaw Galkiewicza* turbine blade of an Kielce University of Technology, Aleja Tysiaclecia Panstwa Polskiego 7, 25-314 Kielce, Poland airplane gas turbine engine Kielce University of Technology, Aleja Tysiaclecia Panstwa Polskiego 7, 25-314 Kielce, Poland a
b
c
Abstract P. Brandão , V. Infante , A.M. Deus * Abstract a of Mechanical Instituto Superior Técnico, Lisboa, Av. Rovisco Pais,ductile. 1, 1049-001 Lisboa, The mostDepartment often observed failureEngineering, mechanisms in metallic alloys areUniversidade divided in de two groups: brittle and Brittle failure Portugal The b most often observedalong failure mechanisms metallic are divided groups:environment) brittle and ductile. failure mechanism may proceed grain boundariesin(failure duealloys to the creep processinortwo aggressive or alongBrittle the cleavage IDMEC, Department of Mechanical Engineering, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1, 1049-001 Lisboa, mechanism may along grain boundaries (failure dueoften to Portugal thethe creep process or aggressive environment) or alongprocess the cleavage planes within theproceed grain. Ductile fracture mechanism is most result of voids nucleation–growth–coalescence or by c planes within thealong grain.slip Ductile fracture mechanism is most often resultUniversidade of voids nucleation–growth–coalescence process or by dislocation slip Tests were performed at three the different temperatures: –20C, –50C, on1049-001 five different CeFEMA, Department of planes. Mechanical Engineering, Instituto Superior Técnico, de +20C, Lisboa, Av. Rovisco Pais, 1, Lisboa, dislocationgeometries, slip along slip planes. were performed three different temperatures: +20C, –20C,strains –50C,and onstresses five different Portugal specimen designed to Tests provide different stressattriaxialities, Lode factors as well as critical at the specimen to provide stress triaxialities, factorsofasthe well critical strains andstrains stresses at the moment ofgeometries, final failure.designed Numerical analysesdifferent were performed after carefulLode calibration realasstress – logarithmic uniaxial moment of final failure. Numerical analyses were performed after careful calibration of the real stress – logarithmic strains uniaxial curves. Calibration followed modified Bai–Wierzbicki procedure. Abstract curves. Calibration followed modified Bai–Wierzbicki procedure. © 2018 The Authors. Published by Elsevier B.V. © 2018 Thetheir Authors. Publishedmodern by Elsevier B.V. engine components are subjected to increasingly demanding operating conditions, operation, aircraft © During 2018 The Authors. Published by B.V. Peer-review under responsibility of Elsevier the ECF22 organizers. Peer-review under responsibility ofturbine the ECF22 organizers. especially the high pressure (HPT) blades. Such conditions cause these parts to undergo different types of time-dependent Peer-review under responsibility of the ECF22 organizers. degradation, one of which is creep. A model using the finite element method (FEM) was developed, in order to be able to predict Keywords: triaxiality; Lode angle; fracture mechanisms; stress-strain curve the creep behaviour HPT blades. Flight data records curve (FDR) for a specific aircraft, provided by a commercial aviation Keywords: triaxiality; Lodeof angle; fracture mechanisms; stress-strain company, were used to obtain thermal and mechanical data for three different flight cycles. In order to create the 3D model needed for the FEM analysis, a HPT blade scrap was scanned, and its chemical composition and material properties were 1. obtained. Introduction The data that was gathered was fed into the FEM model and different simulations were run, first with a simplified 3D 1. rectangular Introduction block shape, in order to better establish the model, and then with the real 3D mesh obtained from the blade scrap. The overall behaviour terms ofofdisplacement observed, at the different trailing edge of the blade. Therefore such a In thisexpected paper the failure in analysis ferritic steel,was heat treated intoparticular receive three microstructures is presented. Inexperiments thiscan paper the failure analysis of ferritic steel, heatlife, treated receive three different microstructures is specimens presented. model be useful inperformed the goal of at predicting turbine blade given set of FDR data. The were three different temperatures oftoa+20C, –20C and –50C on five different
The experiments performed at three temperatures of +20C, –20C and –50C onplastic five different specimens geometries. Both were ductile and brittle failuredifferent mechanisms were observed, preceded by extensive deformation. The © 2016 TheBoth Authors. Published by Elsevier B.V. geometries. ductile and brittle failure mechanisms were observed, preceded by extensive plastic deformation. The analysis of these mechanisms was carried on within the scope of the isotropic continuum mechanics of solids. It is Peer-review undermechanisms responsibilitywas of the Scientific Committee of PCF of 2016. analysis of these carried on within the scope the isotropic continuum mechanics of solids. It is believed that the normal (to fracture surface) stress tensor component is responsible for brittle (cleavage) micro, meso, believed that the normal (to fracture surface) stress tensor component is responsible for brittle (cleavage) micro, meso, macro – crack extension [1–3] when it isFinite greater thanMethod; the critical value over the distance (area) also greater than the Keywords: High Pressure Turbine Blade; Creep; Element 3D Model; Simulation. macro – crack extension [1–3] when it is greater than the critical value over the distance (area) also greater than the
* Corresponding author. Tel.: +48-41-342-4711; fax: +48-41-342-4295. * Corresponding Tel.: +48-41-342-4711; fax: +48-41-342-4295. 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. Peer-review underThe responsibility of theby ECF22 organizers. Peer-review underauthor. responsibility the ECF22 organizers. * 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 ECF22 organizers. 10.1016/j.prostr.2018.12.048
Andrzej Neimitz et al. / Procedia Structural Integrity 13 (2018) 285–291 Author name / Structural Integrity Procedia 00 (2018) 000–000
286 2
critical value. In turn, the ductile failure mechanisms is controlled by plastic deformation (effective accumulated), stress triaxiality: =σm/σe, where σm and σe are first stress tensor invariant and effective stress respectively, e 3 J 2 , J2 is the second stress deviator invariant [4–6]. In the last two decades another quantity has been introduced to characterize the ductile failure process: the Lode angle, θ, which is related to the third invariant of the stress tensor deviator: 1/3 3 1/3 cos 3 r / e 27 / 2 J 3 / e3 , r 27 / 2 det sij 27 / 2 1 m 2 m 3 m In this paper equivalent Lode parameter, L, will be used: L 2 II I III / I III and the relation between ξ and L parameter is as 3 L 9 L2 / L2 3 . The Lode angle influences the localization of plastic deformation and the process of follows: void's evolution [4–6]. In this paper we will try to answer the question: are the above listed mechanical field parameters sufficient to characterize failure mechanisms and to predict the failure due to the ductile or cleavage mechanism? 2. Experimental program The specimen shapes were selected to cover a wide range of triaxiality factors and Lode parameters L. However, because of the purposes of the research program we were interested in a relatively large values (positive) of the η factor and positive values of the L factors. The specimen shapes are shown in Fig.1.
a) Symbol C04 or C1
b) Symbol PN c) Symbol PR Fig.1 The geometries of the tested specimens
d) Symbol S
In the case of the specimen shown in Fig. 1a two radii of notches were machined R=0.4 mm (symbol C04) and R=1.0 mm (symbol C1) to provoke ductile fracture nucleation process in two different locations. The specimens were machined from the S355JR steel after three different heat treatments. The properties measured in uniaxial tensile tests are shown in Table 1. Table 1. Heat treatments and tensile properties of the tested S355JR steel at 20C. Symbol
Heat Treatment
Microstructure
E [GPa]
ReH [MPa]
ReL [MPa]
Rm [MPa]
N
Normalized at 950C Normalized and annealed (600C, 150 h)
Ferrite–pearlite Ferrite containing spheroidized carbide particles
197a) 198b) 210
375a) 380 b) 382
367 a) 378 b) 368
496 a) 614 b) 470
211
393
380
588
Ferrite containing Quenched in oil and 197 412 spheroidized carbide annealed (600C, 198 415 particles 150 h) Structure in the first line – values obtained from the nominal stress–strain curve in the second line – values obtained from the true stress−logarithmic strain curve
406
511
411
603
NW
HW a) b)
In order to receive different level of plasticity the specimens were tested at three different temperatures of +20C, –20C and –50C. The η and L factors were recorded as follows: a) two notched cylindrical specimens with R=0.4mm (from 0.5 to 1.0; Lfrom 0.6 to 1.0) and R=1mm (from 0.4 to 1.4; Lfrom 0.85 to 1.0), b) plate with two symmetrical notches, R=1mm; (0.4, L=0.4), c) R=10mm (0.5, L=0.5), d ) pure shear (0.4, L=0). The microstructures are shown in Fig. 2. Numerical analysis was performed with the ABAQUS 6.12 computer program, after careful calibration of the constitutive equations. The procedure of calibration was presented elsewhere [7,8].
2873
Author / Structural Integrity Structural Procedia 00 (2018)13 000–000 Andrzejname Neimitz et al. / Procedia Integrity (2018) 285–291
a
b
c
Fig.2. Microstructures of HW material (a), N material (b) and NW material (c)
3. Failure mechanisms During the experimental tests several fracture mechanisms were observed, depending on the specimen shape, material and test temperature. The failure mechanism observed in almost all materials, specimens and test temperatures was due to voids nucleation–growth–coalescence. In some cases ductile fracture was not observed at very low temperatures (–80C or –100C; not shown in this paper). Voids were growing along surfaces perpendicular to the external loading and inclined to the external loading. The purpose of this stage of research was to determine the values of the critical effective plastic strain (εpl_e) as a function of computed parameters: η, L at the critical moment. It was assumed that the initiation of the rapid failure process due to the voids coalescence started at last or at next to last step of integration (loading). Rapid cleavage fracture was observed in some cases and it started at the last step of integration. No irregularities were observed along the force–elongation curves indicating the sudden jumps of cleavage fracture during the loading process. The locations of cleavage fracture initiation spot could be identified, to some extent, analyzing the fracture surface images and orientation of river pattern on the cleavage planes. The locations of the ductile fracture initial spot were usually not possible or not unique by observation of fracture surface by the scanning electron microscope. In the most cases, both within cylindrical and PN specimens, the differences between the sizes and shapes of caverns in a fracture surface were not noticeable. Thus, some working hypothesis had to be assumed to localize the critical spot. The origin of this hypothesis is Rice and Tracy [5] result concerning the rate of growth of the isolated spherical void surrounded by an ideally plastic material. Their numerical results were well approximated by the formula: R0 / R0 0.263 exp m / 2 0 . Since the whole critical cross–section of loaded specimen is stretched at the same time, it is proposed to compare the quantity representing, in a very rough approximation, the extension of the voids’ radii, recorded along the fractured surface at the presumed moment of the rapid evolution of damage. The simplified formula is as follows: R pl _ e exp
(1)
The results concerning two cylindrical specimens with different radii of the circumferential notch are shown in Fig. 3 and Table 2. It was concluded from the results listed in Table 2 that the final ductile failure process started at the centre of the C1 specimen and next to the notch in the C04 specimen. Table 2. Values of the mechanical field parameters at the critical moment η εpl_e_cr Specimen centre 0.24 1.6 R=0.4 Next to the notch 0.93 0.497 Specimen centre 0.36 1.33 R=1.0 Next to the notch 0.57 0.42
L 0.99 0.54 0.996 0.78
σ 1443 789 1298 619
εpl_e_cr ·exp(η) 1.19 1.53 1.36 0.86
With lower temperatures one expects failure mechanism to change from ductile to cleavage. However, it did not happen in all specimen tested. Specimens C1 and PR never failed by cleavage mechanism in the temperature range from +20C to –50C (they did at lower temperatures). The examples of cleavage surfaces are shown in Fig. 4.
288 4
Andrzej Neimitz et al. / Procedia Structural Integrity 13 (2018) 285–291 Author name / Structural Integrity Procedia 00 (2018) 000–000
Fig. 3a. Distribution of η, L, εpl_e; specimen C04, material HW, temp. +20C, last step of integration
Fig. 4a. Specimen C04; material N, temp. –50C, ductile zone inside
Fig. 3b. Distribution of η, L, εpl_e; specimen C1, material HW, temp. +20C, last step of integration
Fig. 4b. Specimen C04; material N, temp. –50C, cleavage fracture surface
Fig. 4c. Specimen PN; material N, temp. –50C, cleavage area shape and size; left side of specimen
Fig.4d. Cleavage surface; specimen PN; material N, temp. –50C
Evolution of the cleavage failure mechanism and the analysis of this process in terms of mechanical field parameters is not unique, at least authors are not able, at the moment, propose a unique not controversial hypothesis. It strongly depends on a history of plastic deformation evolution and evolution of voids' growth. According to accepted so far hypotheses [1, 2], this process is controlled by normal stress tensor component and a scale parameter (critical length or area). In the case of the N material and –50C, two specimens failed by cleavage after intensive evolution of voids. They were PN specimen and C04 specimen. The specimen C1 failed according to ductile failure mechanism. The normal to the fracture surface stress tensor components are shown for all four specimen geometries C04, C1, PN, PR in Fig. 5. Since the specimen C1 failed due to the ductile mechanism the normal stresses within this specimen should be lower than in the C04 and PN specimens. It happens in between two vertical lines 1 and 2 in Fig. 5. Along the abscissa the normalized distance from the specimen centre is measured. Thus, the critical stress should be sought in between vertical lines 1 and 2. The observations of the cleavage surface in PN specimens suggest that the cleavage started at the distance about 6.6 mm from the specimen centre. If this estimation is correct the critical stress is about 1240 MPa and the origin of cleavage is at the distance 1.29 mm from the centre of C04 specimen. The values of other parameters at the critical moment for two specimens which failed according to cleavage mechanisms are shown in Fig. 6. Observing evolution of mechanical field parameters with external loading some questions arise: 1) Why caverns are not observed on a cleavage fracture surfaces? Are voids not nucleated in the domain where cleavage fracture is nucleated at the last step of loading? 2) Why cleavage is not initiated in the domain where ductile failure is observed, even though the opening stress level is higher than the presumed critical stress. It is easier to give a qualitative answer for the second question than to the first one. The cleavage can happen when the opening stress is greater than the critical value. It was estimated at the level of 1240 MPa. In the case of PN specimen such a level of the opening stress may happen at 13/17 or 14/17 step of loading (Fig. 7 and 8) at the centre of the specimen. In the C04 specimen it may happen at 11/15 step of loading also in the centre of the specimen. However, in both specimens the
Andrzej Neimitz et al. / Procedia Structural Integrity 13 (2018) 285–291 Author name / Structural Integrity Procedia 00 (2018) 000–000
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triaxiality parameters, η at the central part of these specimens are very high from the very beginning of the loading process; and they are higher in the specimen centers than at other locations. Also, effective plastic strains are high at this stage of loading and one can expect that many voids had already nucleated and grown before the critical stress was reached and cleavage at this location was not possible. One should also notice that effective plastic strain reaches the highest values at the specimen centre in the PN specimen and it is not so in the case of the C04 specimen. The Lode factor at this stage of loading was in the range 0.4-0.6 for the PN specimen and 1.0 for the C04 specimen. The answer for the first question is not so unambiguous. Distribution of equivalent plastic strains and Lode factors are different in both discussed specimens. In the case of PN and C04 specimens the plastic strains are distributed uniformly through the critical cross-section only at the beginning of loading. In the C04 specimen the Lode parameter is equal to one at the specimen centre during the whole loading history and this value decreases along the specimen radius. Different behavior is observed in the case of the PN specimen. Only the η parameter behaves similarly in both specimens. In Fig. 9 the distribution of the ΔR parameter (Eq. 1) is shown along the normalized distance from the specimens' centers. In all three specimens (C04, C1, PN) the specimens' surfaces to the left from ellipsis (Fig. 9) are covered by caverns. In two cases (specimens C04, PN) the specimens' fracture surfaces to the right of the ellipsis are the results of the cleavage fracture process. It is not so in the case of the C1 specimen. Thus, using the mechanical field parameters discussed in this paper, there is no strong reasonable explanation why the C04 specimen broke due to the cleavage mechanics not to the ductile one.
Fig.5. Stress vs. normalized distance computed at the critical moment
Fig.6a. Distribution of the mechanical parameters at the critical moment along the critical plane, measured from the specimen centre; temp. -50C, material N, specimen PN
Fig.6b. Distribution of the mechanical parameters at the critical moment
Fig.7a. Specimen PN, material N, temp.-500C, history of the plastic
along the critical plane, measured from the specimen centre; temp. -50C,
strain distribution along longer axis
material N, specimen C04
6 290
Author name / Structural 00Integrity (2018) 000–000 Andrzej Neimitz et al. /Integrity ProcediaProcedia Structural 13 (2018) 285–291
Fig.7b. Specimen PN, material N, temp.-500C, history of the η factor
Fig.7c. Specimen PN, material N, temp.-500C, history of the L factor
distribution along longer axis
distribution along longer axis
Fig.7d. Specimen PN, material N, temp.-500C, history of the opening
Fig.8a. Specimen C04, material N, temp.-500C, history of the plastic strain
stress distribution along longer axis
Fig.8b. Specimen C04, material N, temp.-500C, history of the η factor distribution along specimen axis
distribution along specimen axis
Fig.8c. Specimen C04, material N, temp.-500C, history of the L factor distribution along specimen axis
Andrzej Neimitz et al. / Procedia Structural Integrity 13 (2018) 285–291 Author name / Structural Integrity Procedia 00 (2018) 000–000
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Fig.8d. Specimen C04, material N, temp.-500C, history of the opening
Fig.9. Distribution of the ΔR parameter (Eq.6) for C04 (last loading
stress distribution along specimen axis
step), C1 (last loading step), PN (steps 12, 14, 15(last))
4. Concluding remark In the Introduction the following question was formulated: "...are the above listed mechanical field parameters sufficient to characterize failure mechanisms and to predict the failure due to the ductile or cleavage mechanism?". Unfortunately, the results of the analysis performed in this paper do not allow for a positive answer. There is no unique explanation to determine the competition between the cleavage and ductile fracture mechanism. At the moment there are two possible explanations: 1) The triaxiality factor η alone may decide on a failure due to the ductile mechanism. It must be high enough to stop the cleavage fracture. 2) another parameter must be sought to explain the observed controversies. Acknowledgements This research was performed with financial support from the Polish National Science Committee (NCN), grant no. UMO–2014/15/B/ST8/00205 References Ritchie R.O., Knott J.F., Rice J.R., On the relationship between critical tensile stress and fracture toughness in mild steel. Journal of the Mechanics and Physics of Solids, 21:395-410 1973. Neimitz A., Graba M., Galkiewicz J., An alternative formulation of the Ritchie–Knott–Rice local fracture criterion, Engeering Fracture Mechanics, 74, 8, pp. 1308–1322, 2007. Neimitz A., Galkiewicz J., Dzioba I., The ductile to cleavage transition in ferritic Cr-Mo-V steel: A detailed microscopic and numerical analysis, Engineering Fracture Mechanics, vol.77, pp. 2504-2526, 2010. McClintock FA. A Criterion for Ductile Fracture by Growth of Holes. Journal of Applied Mechanics, (1968), Vol.4, pp. 363–371. Rice, J.R., Tracey, D.M. On the ductile enlargement of voids in triaxial stress fields, J. of the Mechanics and Physics of Solids, Vol. 17, pp. 201–217, 1969. Bao, Y., Wierzbicki, T., On fracture locus in the equivalent strain and stress triaxiality space. Int J Mech. Sci. 46(1), 81–98, 2004. Neimitz A., Galkiewicz J., Dzioba I., Calibration of constitutive equations under conditions of large strains and stress triaxiality, Archives of Civil and Mechanical Engineering, Volume 18, Issue 4, pp. 1123–1135, September 2018. Neimitz A., Dzioba I., Lipiec S., Calibration of constitutive equations for the stress level estimation in domain with the large strains, This conference.
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Structural Integrity Procedia 00 (2018) 000–000 Available online www.sciencedirect.com Available online at at www.sciencedirect.com
www.elsevier.com/locate/procedia www.elsevier.com/locate/procedia
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Procedia Structural Structural IntegrityIntegrity Procedia1300(2018) (2016)285–291 000–000
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ECF22 - Loading and Environmental effects on Structural Integrity ECF22 - Loading and Environmental effects on Structural Integrity
Are the mechanical field parameters sufficient to predict uniquely Are the mechanical field parameters sufficient to predict uniquely the failure dueontoFracture, the ductile or10-12 cleavage mechanisms? XV Portuguese Conference PCF 2016, February 2016, Paço de Arcos, Portugal the failure due to the ductile or cleavage mechanisms? a Andrzej Neimitzaa,of Jaroslaw Galkiewicz * Thermo-mechanical modeling a high pressure Andrzej Neimitz , Jaroslaw Galkiewicza* turbine blade of an Kielce University of Technology, Aleja Tysiaclecia Panstwa Polskiego 7, 25-314 Kielce, Poland airplane gas turbine engine Kielce University of Technology, Aleja Tysiaclecia Panstwa Polskiego 7, 25-314 Kielce, Poland a
b
c
Abstract P. Brandão , V. Infante , A.M. Deus * Abstract a of Mechanical Instituto Superior Técnico, Lisboa, Av. Rovisco Pais,ductile. 1, 1049-001 Lisboa, The mostDepartment often observed failureEngineering, mechanisms in metallic alloys areUniversidade divided in de two groups: brittle and Brittle failure Portugal The b most often observedalong failure mechanisms metallic are divided groups:environment) brittle and ductile. failure mechanism may proceed grain boundariesin(failure duealloys to the creep processinortwo aggressive or alongBrittle the cleavage IDMEC, Department of Mechanical Engineering, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1, 1049-001 Lisboa, mechanism may along grain boundaries (failure dueoften to Portugal thethe creep process or aggressive environment) or alongprocess the cleavage planes within theproceed grain. Ductile fracture mechanism is most result of voids nucleation–growth–coalescence or by c planes within thealong grain.slip Ductile fracture mechanism is most often resultUniversidade of voids nucleation–growth–coalescence process or by dislocation slip Tests were performed at three the different temperatures: –20C, –50C, on1049-001 five different CeFEMA, Department of planes. Mechanical Engineering, Instituto Superior Técnico, de +20C, Lisboa, Av. Rovisco Pais, 1, Lisboa, dislocationgeometries, slip along slip planes. were performed three different temperatures: +20C, –20C,strains –50C,and onstresses five different Portugal specimen designed to Tests provide different stressattriaxialities, Lode factors as well as critical at the specimen to provide stress triaxialities, factorsofasthe well critical strains andstrains stresses at the moment ofgeometries, final failure.designed Numerical analysesdifferent were performed after carefulLode calibration realasstress – logarithmic uniaxial moment of final failure. Numerical analyses were performed after careful calibration of the real stress – logarithmic strains uniaxial curves. Calibration followed modified Bai–Wierzbicki procedure. Abstract curves. Calibration followed modified Bai–Wierzbicki procedure. © 2018 The Authors. Published by Elsevier B.V. © 2018 Thetheir Authors. Publishedmodern by Elsevier B.V. engine components are subjected to increasingly demanding operating conditions, operation, aircraft © During 2018 The Authors. Published by B.V. Peer-review under responsibility of Elsevier the ECF22 organizers. Peer-review under responsibility ofturbine the ECF22 organizers. especially the high pressure (HPT) blades. Such conditions cause these parts to undergo different types of time-dependent Peer-review under responsibility of the ECF22 organizers. degradation, one of which is creep. A model using the finite element method (FEM) was developed, in order to be able to predict Keywords: triaxiality; Lode angle; fracture mechanisms; stress-strain curve the creep behaviour HPT blades. Flight data records curve (FDR) for a specific aircraft, provided by a commercial aviation Keywords: triaxiality; Lodeof angle; fracture mechanisms; stress-strain company, were used to obtain thermal and mechanical data for three different flight cycles. In order to create the 3D model needed for the FEM analysis, a HPT blade scrap was scanned, and its chemical composition and material properties were 1. obtained. Introduction The data that was gathered was fed into the FEM model and different simulations were run, first with a simplified 3D 1. rectangular Introduction block shape, in order to better establish the model, and then with the real 3D mesh obtained from the blade scrap. The overall behaviour terms ofofdisplacement observed, at the different trailing edge of the blade. Therefore such a In thisexpected paper the failure in analysis ferritic steel,was heat treated intoparticular receive three microstructures is presented. Inexperiments thiscan paper the failure analysis of ferritic steel, heatlife, treated receive three different microstructures is specimens presented. model be useful inperformed the goal of at predicting turbine blade given set of FDR data. The were three different temperatures oftoa+20C, –20C and –50C on five different
The experiments performed at three temperatures of +20C, –20C and –50C onplastic five different specimens geometries. Both were ductile and brittle failuredifferent mechanisms were observed, preceded by extensive deformation. The © 2016 TheBoth Authors. Published by Elsevier B.V. geometries. ductile and brittle failure mechanisms were observed, preceded by extensive plastic deformation. The analysis of these mechanisms was carried on within the scope of the isotropic continuum mechanics of solids. It is Peer-review undermechanisms responsibilitywas of the Scientific Committee of PCF of 2016. analysis of these carried on within the scope the isotropic continuum mechanics of solids. It is believed that the normal (to fracture surface) stress tensor component is responsible for brittle (cleavage) micro, meso, believed that the normal (to fracture surface) stress tensor component is responsible for brittle (cleavage) micro, meso, macro – crack extension [1–3] when it isFinite greater thanMethod; the critical value over the distance (area) also greater than the Keywords: High Pressure Turbine Blade; Creep; Element 3D Model; Simulation. macro – crack extension [1–3] when it is greater than the critical value over the distance (area) also greater than the
* Corresponding author. Tel.: +48-41-342-4711; fax: +48-41-342-4295. * Corresponding Tel.: +48-41-342-4711; fax: +48-41-342-4295. 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. Peer-review underThe responsibility of theby ECF22 organizers. Peer-review underauthor. responsibility the ECF22 organizers. * 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 ECF22 organizers. 10.1016/j.prostr.2018.12.048
Andrzej Neimitz et al. / Procedia Structural Integrity 13 (2018) 285–291 Author name / Structural Integrity Procedia 00 (2018) 000–000
286 2
critical value. In turn, the ductile failure mechanisms is controlled by plastic deformation (effective accumulated), stress triaxiality: =σm/σe, where σm and σe are first stress tensor invariant and effective stress respectively, e 3 J 2 , J2 is the second stress deviator invariant [4–6]. In the last two decades another quantity has been introduced to characterize the ductile failure process: the Lode angle, θ, which is related to the third invariant of the stress tensor deviator: 1/3 3 1/3 cos 3 r / e 27 / 2 J 3 / e3 , r 27 / 2 det sij 27 / 2 1 m 2 m 3 m In this paper equivalent Lode parameter, L, will be used: L 2 II I III / I III and the relation between ξ and L parameter is as 3 L 9 L2 / L2 3 . The Lode angle influences the localization of plastic deformation and the process of follows: void's evolution [4–6]. In this paper we will try to answer the question: are the above listed mechanical field parameters sufficient to characterize failure mechanisms and to predict the failure due to the ductile or cleavage mechanism? 2. Experimental program The specimen shapes were selected to cover a wide range of triaxiality factors and Lode parameters L. However, because of the purposes of the research program we were interested in a relatively large values (positive) of the η factor and positive values of the L factors. The specimen shapes are shown in Fig.1.
a) Symbol C04 or C1
b) Symbol PN c) Symbol PR Fig.1 The geometries of the tested specimens
d) Symbol S
In the case of the specimen shown in Fig. 1a two radii of notches were machined R=0.4 mm (symbol C04) and R=1.0 mm (symbol C1) to provoke ductile fracture nucleation process in two different locations. The specimens were machined from the S355JR steel after three different heat treatments. The properties measured in uniaxial tensile tests are shown in Table 1. Table 1. Heat treatments and tensile properties of the tested S355JR steel at 20C. Symbol
Heat Treatment
Microstructure
E [GPa]
ReH [MPa]
ReL [MPa]
Rm [MPa]
N
Normalized at 950C Normalized and annealed (600C, 150 h)
Ferrite–pearlite Ferrite containing spheroidized carbide particles
197a) 198b) 210
375a) 380 b) 382
367 a) 378 b) 368
496 a) 614 b) 470
211
393
380
588
Ferrite containing Quenched in oil and 197 412 spheroidized carbide annealed (600C, 198 415 particles 150 h) Structure in the first line – values obtained from the nominal stress–strain curve in the second line – values obtained from the true stress−logarithmic strain curve
406
511
411
603
NW
HW a) b)
In order to receive different level of plasticity the specimens were tested at three different temperatures of +20C, –20C and –50C. The η and L factors were recorded as follows: a) two notched cylindrical specimens with R=0.4mm (from 0.5 to 1.0; Lfrom 0.6 to 1.0) and R=1mm (from 0.4 to 1.4; Lfrom 0.85 to 1.0), b) plate with two symmetrical notches, R=1mm; (0.4, L=0.4), c) R=10mm (0.5, L=0.5), d ) pure shear (0.4, L=0). The microstructures are shown in Fig. 2. Numerical analysis was performed with the ABAQUS 6.12 computer program, after careful calibration of the constitutive equations. The procedure of calibration was presented elsewhere [7,8].
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a
b
c
Fig.2. Microstructures of HW material (a), N material (b) and NW material (c)
3. Failure mechanisms During the experimental tests several fracture mechanisms were observed, depending on the specimen shape, material and test temperature. The failure mechanism observed in almost all materials, specimens and test temperatures was due to voids nucleation–growth–coalescence. In some cases ductile fracture was not observed at very low temperatures (–80C or –100C; not shown in this paper). Voids were growing along surfaces perpendicular to the external loading and inclined to the external loading. The purpose of this stage of research was to determine the values of the critical effective plastic strain (εpl_e) as a function of computed parameters: η, L at the critical moment. It was assumed that the initiation of the rapid failure process due to the voids coalescence started at last or at next to last step of integration (loading). Rapid cleavage fracture was observed in some cases and it started at the last step of integration. No irregularities were observed along the force–elongation curves indicating the sudden jumps of cleavage fracture during the loading process. The locations of cleavage fracture initiation spot could be identified, to some extent, analyzing the fracture surface images and orientation of river pattern on the cleavage planes. The locations of the ductile fracture initial spot were usually not possible or not unique by observation of fracture surface by the scanning electron microscope. In the most cases, both within cylindrical and PN specimens, the differences between the sizes and shapes of caverns in a fracture surface were not noticeable. Thus, some working hypothesis had to be assumed to localize the critical spot. The origin of this hypothesis is Rice and Tracy [5] result concerning the rate of growth of the isolated spherical void surrounded by an ideally plastic material. Their numerical results were well approximated by the formula: R0 / R0 0.263 exp m / 2 0 . Since the whole critical cross–section of loaded specimen is stretched at the same time, it is proposed to compare the quantity representing, in a very rough approximation, the extension of the voids’ radii, recorded along the fractured surface at the presumed moment of the rapid evolution of damage. The simplified formula is as follows: R pl _ e exp
(1)
The results concerning two cylindrical specimens with different radii of the circumferential notch are shown in Fig. 3 and Table 2. It was concluded from the results listed in Table 2 that the final ductile failure process started at the centre of the C1 specimen and next to the notch in the C04 specimen. Table 2. Values of the mechanical field parameters at the critical moment η εpl_e_cr Specimen centre 0.24 1.6 R=0.4 Next to the notch 0.93 0.497 Specimen centre 0.36 1.33 R=1.0 Next to the notch 0.57 0.42
L 0.99 0.54 0.996 0.78
σ 1443 789 1298 619
εpl_e_cr ·exp(η) 1.19 1.53 1.36 0.86
With lower temperatures one expects failure mechanism to change from ductile to cleavage. However, it did not happen in all specimen tested. Specimens C1 and PR never failed by cleavage mechanism in the temperature range from +20C to –50C (they did at lower temperatures). The examples of cleavage surfaces are shown in Fig. 4.
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Fig. 3a. Distribution of η, L, εpl_e; specimen C04, material HW, temp. +20C, last step of integration
Fig. 4a. Specimen C04; material N, temp. –50C, ductile zone inside
Fig. 3b. Distribution of η, L, εpl_e; specimen C1, material HW, temp. +20C, last step of integration
Fig. 4b. Specimen C04; material N, temp. –50C, cleavage fracture surface
Fig. 4c. Specimen PN; material N, temp. –50C, cleavage area shape and size; left side of specimen
Fig.4d. Cleavage surface; specimen PN; material N, temp. –50C
Evolution of the cleavage failure mechanism and the analysis of this process in terms of mechanical field parameters is not unique, at least authors are not able, at the moment, propose a unique not controversial hypothesis. It strongly depends on a history of plastic deformation evolution and evolution of voids' growth. According to accepted so far hypotheses [1, 2], this process is controlled by normal stress tensor component and a scale parameter (critical length or area). In the case of the N material and –50C, two specimens failed by cleavage after intensive evolution of voids. They were PN specimen and C04 specimen. The specimen C1 failed according to ductile failure mechanism. The normal to the fracture surface stress tensor components are shown for all four specimen geometries C04, C1, PN, PR in Fig. 5. Since the specimen C1 failed due to the ductile mechanism the normal stresses within this specimen should be lower than in the C04 and PN specimens. It happens in between two vertical lines 1 and 2 in Fig. 5. Along the abscissa the normalized distance from the specimen centre is measured. Thus, the critical stress should be sought in between vertical lines 1 and 2. The observations of the cleavage surface in PN specimens suggest that the cleavage started at the distance about 6.6 mm from the specimen centre. If this estimation is correct the critical stress is about 1240 MPa and the origin of cleavage is at the distance 1.29 mm from the centre of C04 specimen. The values of other parameters at the critical moment for two specimens which failed according to cleavage mechanisms are shown in Fig. 6. Observing evolution of mechanical field parameters with external loading some questions arise: 1) Why caverns are not observed on a cleavage fracture surfaces? Are voids not nucleated in the domain where cleavage fracture is nucleated at the last step of loading? 2) Why cleavage is not initiated in the domain where ductile failure is observed, even though the opening stress level is higher than the presumed critical stress. It is easier to give a qualitative answer for the second question than to the first one. The cleavage can happen when the opening stress is greater than the critical value. It was estimated at the level of 1240 MPa. In the case of PN specimen such a level of the opening stress may happen at 13/17 or 14/17 step of loading (Fig. 7 and 8) at the centre of the specimen. In the C04 specimen it may happen at 11/15 step of loading also in the centre of the specimen. However, in both specimens the
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triaxiality parameters, η at the central part of these specimens are very high from the very beginning of the loading process; and they are higher in the specimen centers than at other locations. Also, effective plastic strains are high at this stage of loading and one can expect that many voids had already nucleated and grown before the critical stress was reached and cleavage at this location was not possible. One should also notice that effective plastic strain reaches the highest values at the specimen centre in the PN specimen and it is not so in the case of the C04 specimen. The Lode factor at this stage of loading was in the range 0.4-0.6 for the PN specimen and 1.0 for the C04 specimen. The answer for the first question is not so unambiguous. Distribution of equivalent plastic strains and Lode factors are different in both discussed specimens. In the case of PN and C04 specimens the plastic strains are distributed uniformly through the critical cross-section only at the beginning of loading. In the C04 specimen the Lode parameter is equal to one at the specimen centre during the whole loading history and this value decreases along the specimen radius. Different behavior is observed in the case of the PN specimen. Only the η parameter behaves similarly in both specimens. In Fig. 9 the distribution of the ΔR parameter (Eq. 1) is shown along the normalized distance from the specimens' centers. In all three specimens (C04, C1, PN) the specimens' surfaces to the left from ellipsis (Fig. 9) are covered by caverns. In two cases (specimens C04, PN) the specimens' fracture surfaces to the right of the ellipsis are the results of the cleavage fracture process. It is not so in the case of the C1 specimen. Thus, using the mechanical field parameters discussed in this paper, there is no strong reasonable explanation why the C04 specimen broke due to the cleavage mechanics not to the ductile one.
Fig.5. Stress vs. normalized distance computed at the critical moment
Fig.6a. Distribution of the mechanical parameters at the critical moment along the critical plane, measured from the specimen centre; temp. -50C, material N, specimen PN
Fig.6b. Distribution of the mechanical parameters at the critical moment
Fig.7a. Specimen PN, material N, temp.-500C, history of the plastic
along the critical plane, measured from the specimen centre; temp. -50C,
strain distribution along longer axis
material N, specimen C04
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Fig.7b. Specimen PN, material N, temp.-500C, history of the η factor
Fig.7c. Specimen PN, material N, temp.-500C, history of the L factor
distribution along longer axis
distribution along longer axis
Fig.7d. Specimen PN, material N, temp.-500C, history of the opening
Fig.8a. Specimen C04, material N, temp.-500C, history of the plastic strain
stress distribution along longer axis
Fig.8b. Specimen C04, material N, temp.-500C, history of the η factor distribution along specimen axis
distribution along specimen axis
Fig.8c. Specimen C04, material N, temp.-500C, history of the L factor distribution along specimen axis
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Fig.8d. Specimen C04, material N, temp.-500C, history of the opening
Fig.9. Distribution of the ΔR parameter (Eq.6) for C04 (last loading
stress distribution along specimen axis
step), C1 (last loading step), PN (steps 12, 14, 15(last))
4. Concluding remark In the Introduction the following question was formulated: "...are the above listed mechanical field parameters sufficient to characterize failure mechanisms and to predict the failure due to the ductile or cleavage mechanism?". Unfortunately, the results of the analysis performed in this paper do not allow for a positive answer. There is no unique explanation to determine the competition between the cleavage and ductile fracture mechanism. At the moment there are two possible explanations: 1) The triaxiality factor η alone may decide on a failure due to the ductile mechanism. It must be high enough to stop the cleavage fracture. 2) another parameter must be sought to explain the observed controversies. Acknowledgements This research was performed with financial support from the Polish National Science Committee (NCN), grant no. UMO–2014/15/B/ST8/00205 References Ritchie R.O., Knott J.F., Rice J.R., On the relationship between critical tensile stress and fracture toughness in mild steel. Journal of the Mechanics and Physics of Solids, 21:395-410 1973. Neimitz A., Graba M., Galkiewicz J., An alternative formulation of the Ritchie–Knott–Rice local fracture criterion, Engeering Fracture Mechanics, 74, 8, pp. 1308–1322, 2007. Neimitz A., Galkiewicz J., Dzioba I., The ductile to cleavage transition in ferritic Cr-Mo-V steel: A detailed microscopic and numerical analysis, Engineering Fracture Mechanics, vol.77, pp. 2504-2526, 2010. McClintock FA. A Criterion for Ductile Fracture by Growth of Holes. Journal of Applied Mechanics, (1968), Vol.4, pp. 363–371. Rice, J.R., Tracey, D.M. On the ductile enlargement of voids in triaxial stress fields, J. of the Mechanics and Physics of Solids, Vol. 17, pp. 201–217, 1969. Bao, Y., Wierzbicki, T., On fracture locus in the equivalent strain and stress triaxiality space. Int J Mech. Sci. 46(1), 81–98, 2004. Neimitz A., Galkiewicz J., Dzioba I., Calibration of constitutive equations under conditions of large strains and stress triaxiality, Archives of Civil and Mechanical Engineering, Volume 18, Issue 4, pp. 1123–1135, September 2018. Neimitz A., Dzioba I., Lipiec S., Calibration of constitutive equations for the stress level estimation in domain with the large strains, This conference.