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Influence of crack closure and local near-tip stress on crack growth life estimation
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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 Structural IntegrityIntegrity Procedia1400(2019) (2016)429–434 000–000
www.elsevier.com/locate/procedia www.elsevier.com/locate/procedia
www.elsevier.com/locate/procedia
2nd International Conference on Structural Integrity and Exhibition 2018 2nd International Conference on Structural Integrity and Exhibition 2018
Influence of crack closure and local near-tip stress on crack growth XV Portuguese Conference on Fracture, PCF 2016, 10-12 February 2016, Paço de Arcos, Portugal Influence of crack closure life and estimation local near-tip stress on crack growth life estimation Thermo-mechanical modeling of a high pressure blade a, b a a a A.N. Savkina, R. Sunder , D.S. Denisevich , K.A. Badikovturbine , A.A. Sedov * of an airplane gasAvenue turbine engine a a, b a a A.N. Savkin , R. Sunder , D.S.Lenin Denisevich , K.A. Badikov A.A. Sedova* Volgograd State Technical University, 28, Volgograd 400005, Russian ,Federation a
Bangalore Integrated System Solutions (P) Ltd., No. 497 E, 14th Cross, 4th Phase, Peenya Industrial Area, Bangalore 560058, India. a b c Volgograd State Technical University,a Lenin Avenue 28, Volgograd 400005, Russian Federation b Bangalore Integrated System Solutions (P) Ltd., No. 497 E, 14th Cross, 4th Phase, Peenya Industrial Area, Bangalore 560058, India. b
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, Portugal Abstract Currently, among other models for crack growth prediction, crack closure models that consider the decrease in stress intensity c CeFEMA, Department of Mechanical Engineering, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1, 1049-001 Lisboa, factor (SIF) range associated with cyclic loading asymmetry arePortugal more popular. One of drawbacks of these models is impossibility
Abstract b
Currently, among other models crack growth prediction, crack closure models that consider the decrease in stress intensity of considering the loading historyfor sequence. factor (SIF) range associated with cyclic loading asymmetry are more popular. One by of drawbacks of these modelsthat is impossibility local near-tip stresses, induced overloads, and postulated the overload The theory related threshold SIF range and ΔKth and of considering the loading history sequence. effect in the near-threshold region of growth rates is caused by residual local stresses. The proposed model applies the local stress Abstract The theoryapproach related threshold SIFstress rangeσ*and ΔKstress th and local near-tip stresses, induced by overloads, and postulated that the overload and strain to estimate in the concentration region for fatigue analysis. This region is characterized by local effect in stress the near-threshold region growth rates is caused by residual local at stresses. TheFurther proposed model applies themodel local stress During their modernofisaircraft engine components arereaction subjected to increasingly demanding operating conditions, near-tip σ*,operation, whose amplitude determined by cyclic inelastic crack tip. development of the is due and strain approach to estimate stress σ* in the stress concentration region for fatigue analysis. This region is characterized by local the high pressure turbine (HPT)ΔK blades. Such conditions cause these parts to undergo different types of time-dependent to especially varying nature of the threshold SIF range th. near-tip stress amplitude is determined by which cyclic inelastic reaction at crack Further development the ispredict due onewhose of which isformula creep. Awas model using the finite element (FEM) was developed, in order bemodel able Asdegradation, a basis, theσ*, Forman-Mettu adopted, describes themethod fatigue cracktip. growth curve in all threeofto regions of to fatigue . to varying nature of the threshold SIF range ΔK thdata the creep behaviour of HPT blades. Flight records (FDR) for a specific aircraft, provided by a commercial aviation crack growth rate. The range ΔK was determined by the peak load ΔP of the load history. The crack closure was considered by the Ascompany, a basis, the Forman-Mettu formula was and adopted, which describes the and fatigue crack growth curve allby three regions fatigue were used to obtain thermal data three different flight cycles. Ininorder to theof3D model Schijve equation, considering the asymmetry ofmechanical the half-cycle U for = f(R), effective SIF was estimated ΔKcreate eff = ΔK*U. Given crack growth rate. The range ΔK was determined by the peak load ΔP of the load history. The crack closure was considered by the needed for the FEM analysis, a HPT blade scrap was scanned, and its chemical composition and material properties were known SIF range ΔK, the value of the local stress σ* at distance from the crack tip r* was determined for each half cycle by Neuber obtained. The data that was gathered was fed into the FEM model and different simulations were run, first with a simplified Given Schijve equation, considering the asymmetry of the half-cycle U = f(R), and effective SIF was estimated by ΔK eff = ΔK*U. and Ramberg-Osgood equations, and threshold SIF was estimated from the analytical formula of Кth=f(σ). Thus, known loading3D rectangular block shape, in order to local better establish model,from and the thencrack withtip ther*real mesh obtained from the blade The known range ΔK, thetovalue of the σ* atKthe distance was3D determined for each half cycle byscrap. Neuber history SIF made it possible determine ΔKeff, stress Kmax, and th on each cycle for fatigue life estimation. overall expected behaviour in terms of displacement was observed, in particular at theformula trailingofedge of the blade. Therefore such a =f(σ). Thus, known loading and Ramberg-Osgood equations, and threshold SIF was estimated from the analytical К th Mathematical modeling of fatigue crack growth life, especially in near-threshold region of its growth, according to the Sunder’s modelmade can be useful intothe goal of predicting blade life, cycle givenfor a set of FDR data. history it possible determine ΔK , and K on each fatigue life estimation. eff, Kmaxturbine th scheme, showed that investigated aluminum alloy 2024-T3 exhibited crack growth sensitivity to various types of force action, Mathematical modeling ofrandom fatigue loading. crack growth life, especially in near-threshold region of its growth, according to the Sunder’s including various types of © 2016showed The Authors. Published by Elsevier alloy B.V. 2024-T3 exhibited crack growth sensitivity to various types of force action, scheme, that investigated aluminum Peer-review under responsibility of the Scientific Committee of PCF 2016. © 2019 The Authors. Published by Elsevier B.V. including various types of random loading. © 2018 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Pressure Turbine Blade; Creep; Finite Element Method; 3D Model; Simulation. Selection and High peer-review under responsibility ofB.V. Peer-review under responsibility of the SICE 2018 organizers. © Keywords: 2018 The Authors. Published by Elsevier * Corresponding author. Tel.: +7-905-062-68-80. E-mail address: [email protected] * Corresponding author. Tel.: +7-905-062-68-80. E-mail address: [email protected] 2452-3216 © 2018 The Authors. Published by Elsevier B.V.
This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/)
2452-3216 © 2018 The Authors. Published by Elsevier Selection and peer-review under responsibility of B.V. Peer-review under responsibility of the SICE 2018 organizers.
This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) * Corresponding author. Tel.: +351 218419991. Selection and peer-review under responsibility of Peer-review under responsibility of the SICE 2018 organizers. 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 2019 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Selection and peer-review under responsibility of Peer-review under responsibility of the SICE 2018 organizers. 10.1016/j.prostr.2019.05.052
2
Author name / Structural Integrity Procedia 00 (2018) 000–000
This BY-NC-ND (https://creativecommons.org/licenses/by-nc-nd/4.0/) 430 is an open access article under the CC A.N. Savkin et al.license / Procedia Structural Integrity 14 (2019) 429–434 Selection and peer-review under responsibility of Peer-review under responsibility of the SICE 2018 organizers. Keywords: crack growth rate, crack closure, stress intensity factor, variable amplitude loading.
1. Introduction The machines and structures are experienced variable loads in operation. The microcracks can arise in stress concentrators areas, which are the overstrained micro-entities of metal structures. The growth of such cracks under service loading can lead to catastrophic failure. Crack growth kinetics depends on the magnitude as well as sequence of applied loads (Panasjuk, 1991). For example, overloads promote crack growth retardation while underloads accelerate growth. Random loading contains all those elements and analysis of their interaction is made difficult by gaps in understanding. Therefore, experimental studies of the effect of load history continue to be relevant. A common approach to handling the mix of load amplitudes under random loading is to ignore their interaction and merely apply the linear damage accumulation rule. 2. The crack closure model and the near-tip stress influence Currently, among other models for crack growth life estimation, crack closure models that consider the decrease in the stress intensity factor (SIF) magnitude are more popular (Kiciak et al. (2003). One of the negative sides of these models is the impossibility of considering the loading history.
Fig. 1. The ralationship between near-tip stress and ΔKth
The Sunder’s crack resistance model, considering the local near-tip stress, explains the nature of crack slowing based on the active particles from moisture accumulates at the crack tip in the most stressed volume under increasing load, which affects the dependence of the threshold SIF Kth = f ( * ) from stresses near the crack [Sunder (2005) and (2012). Theory bound threshold SIF ΔKth and local near-tip stress and postulated that the overloading effect at the threshold crack growth rates caused by local residual stresses. The proposed model applies the local stress and strain approach to estimate the stress σ* in the stress concentrator region in the fatigue analysis. In this study, the Neuber and Ramberg-Osgood equations were used for making associating SIF K or its range ΔK with the local stress σ* at a distance from the crack tip r* for static and cyclic loading, respectively:
A.N. Savkin et al. / Procedia Structural Integrity 14 (2019) 429–434 Author name / Structural Integrity Procedia 00 (2018) 000–000 1 * * n' K 2 r * E * E K' , 1 * * n' . K 2 r * E * 2 2K ' E
431 3
(1)
(2)
Fig. 2. (a) Illustration of combination of Neuber’s rule and Ramberg-Osgood equation; (b) local near-tip stress at some distance from crack tip
Further development of the model is connected with considering the variable nature of the threshold SIF range ΔKth. Below is the equation proposed for calculating the fatigue crack growth rate:
K th 1 K eff da C K eff n dN K max 1 Kc
p
, q .
(3)
The Forman-Mettu formula was used as a basis, which describes the fatigue crack growth rate curve in all three regions. The Paris coefficients C and n are proposed to be determined by the so-called “three tests” method. 3. Material and test schedule The tests were conducted on servohydraulic test system BISS Nano-25 using C(T)-specimens as per ASTM-647. The specimens were cut from aluminum alloy 2024-Т3 A series of three tests under constant amplitude loading were performed with maximum load Pmax = 2 kN, loading frequency F = 5 Hz and cycle ratios R1 = 0,1, R2 = 0,3 and R3 = 0,5. The asymmetry ratio was varied from 0 to 0.75 for the tests with overloads. The range ΔK was determined by the peak load ΔP of the load history. The Schijve equation U=f(R) was used for considering the crack closure, and the effective SIF was estimated by formula ΔKeff = ΔK*U. The local stress σ* was calculated by formula (2) with using range of SIF. The threshold SIF Kth was estimated
A.N. Savkin et al. / Procedia Structural Integrity 14 (2019) 429–434 Author name / Structural Integrity Procedia 00 (2018) 000–000
432 4
from the analytical dependence Kth = f ( * ), substituting it into Eq. (3). Thus, a known loading history made it possible to determine ΔKeff, Kmax and Kth at each cycle for fatigue life estimation (Savkin et al. (2016). The constant amplitude loading was carried out with Рmax = 1750 N, R = 0.7, N = 104. The level of overload is 1.5 times higher in comparison with the subsequent constant amplitude loading. The factors с, m, p, q и Kc are constant and are known, and the loading history introduced determines the change ΔK, Kmax and ΔKth. Summation of crack length increments on each cycle of loading history allows to determine the fatigue crack life:
Nf
a f a0 n da j 1 i 1 dN ij m
(4)
where af is the critical crack length; a0 is the initial crack length; n is the loading history cycles number; m is the number of iterations of loading sequence; (da/dN)ij is the crack growth rate and increment on i-th cycle of j-th iteration of loading sequence. The blocks of spectra MiniFALSTAFF, MiniTWIST, SAETRANS differ from the original quazi-random sequences, because negative loads were truncated to zero. Thus, all tests were carried out without compressive loading. The load value was Pmax1 = 2500 N, Pmax2 = 3000 N and Pmax3 = 3500 N. 4. Test results and discussion The test simulation under constant amplitude loading with overload-underload (curve 1) and underload-overload (curve 2) sequences overlapping is shown on Fig. 3.
Fig. 3. The local near-tip stress σ* (a), threshold SIF Кth (b) and fatigue crack length (c) under cyclic loading with overload-underload (1) and underload-overload (2)
The overload unit of loading block, consisting of underload-overload, slows the crack growth by 6 times compared to the block with underload-overload sequence, which is close to the results obtained in the experiment. Here, the change of SIF Kth (Fig. 3 b) as a function of the calculated near-tip stress σ* is shown in these tests (Fig. 3 a). The crack growth rate slowing with the underload-overload sequence in comparison with overload-underload is associated with the local near-tip stress σ* decreasing and threshold SIF Kth increasing.
A.N. Savkin et al. / Procedia Structural Integrity 14 (2019) 429–434 Author name / Structural Integrity Procedia 00 (2018) 000–000
433 5
The simulation of the test under MiniFalstaff-spectrum loading is shown in Fig. 4
Fig. 4. The local near-tip stress σ* (a), threshold SIF Кth (b) and fatigue crack length (c) under variable amplitude loading with MiniFalstaff spectrum
A Sunder model feature of the use is the definition of the asymmetry ratio for each semi-cycle of random cyclic loading and crack closing factor U and the local near-tip stresses and the values of the threshold SIF Kth used in Eq. (3). However, the random nature of the loads applied to the specimen leads with the field of spread of the points of change of the threshold SIF as a function of the local near-tip stress, which makes it difficult to study the function of the change of these parameters as the fatigue crack grew. The mean values were calculated for studying the kinetics of these parameters during the loading process. Their variation during the loading process is shown on Fig. 4 b and 4 c. It is noted that, the local near-tip stress σ* during 100-200 load blocks remains constant, and then increases up to failure, and irrespective Pmax. These stresses are negative at Pmax = 2500 N, with Pmax increasing it move to the positive area. SIF Kth remains practically constant in the initial period of loading. As the fatigue crack grows, the SIF at the crack tip increases, and its threshold value decreases, contributing to an increase in the rate of crack growth. Comparison of the calculated and experimental data on the fatigue cracks growth life with different nature of variable loading with allowance for local near-tip stress and the change in the value of the threshold stress intensity factor are shown in Fig. 5.
Fig. 5. Comparison of the calculated and experimental fatigue crack growth lives for tests under different types of loading
434 6
A.N. Savkin et al. / Procedia Structural Integrity 14 (2019) 429–434 Author name / Structural Integrity Procedia 00 (2018) 000–000
5. Conclusion The fatigue crack growth life estimation, especially in the near-threshold area of its growth, according to the Sunder model, showed that for the investigated aluminum alloy 2024-T3, the crack growth sensitivity to features of force action was revealed. The correlation factor calculated by the Sounder model and experimental data on the fatigue crack growth life for different types of loading was r = 0.97. Acknowledgements This paper was financially supported by the RFBR grant 17-08-01648 A, № 17-08-01742 A and the President of the Russian Federation grant MK-943.2017.8. References Panasiuk V. V., 1991. Mehanika kvazikhrupkogo razrusheniia materialov. Naukova dumka, Kiev, pp. 416. Kiciak A., Glinka G., Burns D. J., 2003. Calculation of stress intensity factors and crack opening displacements for cracks subjected to complex stress fields. Journal of Pressure Vessel Technology, Vol. 125, p. 260-266. Sunder R., 2012. Unraveling the Science of Variable Amplitude Fatigue. Journal of ASTM International, Vol. 9, №1, pp. 32. Sunder R., 2005. Fatigue as process of brittle micro-fracture. Fatigue and Fracture of Engineering Materials and Structures, Vol.28, №3, pp. 289300. Savkin A.N., Andronik A.V., Koraddi R., 2016. Approximation Algorithms of Crack Growth Rate Curve Based on Crack Size Variations. Journal of Testing and Evaluation, Vol. 44, No. 1, pp. 310-319.
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 Structural IntegrityIntegrity Procedia1400(2019) (2016)429–434 000–000
www.elsevier.com/locate/procedia www.elsevier.com/locate/procedia
www.elsevier.com/locate/procedia
2nd International Conference on Structural Integrity and Exhibition 2018 2nd International Conference on Structural Integrity and Exhibition 2018
Influence of crack closure and local near-tip stress on crack growth XV Portuguese Conference on Fracture, PCF 2016, 10-12 February 2016, Paço de Arcos, Portugal Influence of crack closure life and estimation local near-tip stress on crack growth life estimation Thermo-mechanical modeling of a high pressure blade a, b a a a A.N. Savkina, R. Sunder , D.S. Denisevich , K.A. Badikovturbine , A.A. Sedov * of an airplane gasAvenue turbine engine a a, b a a A.N. Savkin , R. Sunder , D.S.Lenin Denisevich , K.A. Badikov A.A. Sedova* Volgograd State Technical University, 28, Volgograd 400005, Russian ,Federation a
Bangalore Integrated System Solutions (P) Ltd., No. 497 E, 14th Cross, 4th Phase, Peenya Industrial Area, Bangalore 560058, India. a b c Volgograd State Technical University,a Lenin Avenue 28, Volgograd 400005, Russian Federation b Bangalore Integrated System Solutions (P) Ltd., No. 497 E, 14th Cross, 4th Phase, Peenya Industrial Area, Bangalore 560058, India. b
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, Portugal Abstract Currently, among other models for crack growth prediction, crack closure models that consider the decrease in stress intensity c CeFEMA, Department of Mechanical Engineering, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1, 1049-001 Lisboa, factor (SIF) range associated with cyclic loading asymmetry arePortugal more popular. One of drawbacks of these models is impossibility
Abstract b
Currently, among other models crack growth prediction, crack closure models that consider the decrease in stress intensity of considering the loading historyfor sequence. factor (SIF) range associated with cyclic loading asymmetry are more popular. One by of drawbacks of these modelsthat is impossibility local near-tip stresses, induced overloads, and postulated the overload The theory related threshold SIF range and ΔKth and of considering the loading history sequence. effect in the near-threshold region of growth rates is caused by residual local stresses. The proposed model applies the local stress Abstract The theoryapproach related threshold SIFstress rangeσ*and ΔKstress th and local near-tip stresses, induced by overloads, and postulated that the overload and strain to estimate in the concentration region for fatigue analysis. This region is characterized by local effect in stress the near-threshold region growth rates is caused by residual local at stresses. TheFurther proposed model applies themodel local stress During their modernofisaircraft engine components arereaction subjected to increasingly demanding operating conditions, near-tip σ*,operation, whose amplitude determined by cyclic inelastic crack tip. development of the is due and strain approach to estimate stress σ* in the stress concentration region for fatigue analysis. This region is characterized by local the high pressure turbine (HPT)ΔK blades. Such conditions cause these parts to undergo different types of time-dependent to especially varying nature of the threshold SIF range th. near-tip stress amplitude is determined by which cyclic inelastic reaction at crack Further development the ispredict due onewhose of which isformula creep. Awas model using the finite element (FEM) was developed, in order bemodel able Asdegradation, a basis, theσ*, Forman-Mettu adopted, describes themethod fatigue cracktip. growth curve in all threeofto regions of to fatigue . to varying nature of the threshold SIF range ΔK thdata the creep behaviour of HPT blades. Flight records (FDR) for a specific aircraft, provided by a commercial aviation crack growth rate. The range ΔK was determined by the peak load ΔP of the load history. The crack closure was considered by the Ascompany, a basis, the Forman-Mettu formula was and adopted, which describes the and fatigue crack growth curve allby three regions fatigue were used to obtain thermal data three different flight cycles. Ininorder to theof3D model Schijve equation, considering the asymmetry ofmechanical the half-cycle U for = f(R), effective SIF was estimated ΔKcreate eff = ΔK*U. Given crack growth rate. The range ΔK was determined by the peak load ΔP of the load history. The crack closure was considered by the needed for the FEM analysis, a HPT blade scrap was scanned, and its chemical composition and material properties were known SIF range ΔK, the value of the local stress σ* at distance from the crack tip r* was determined for each half cycle by Neuber obtained. The data that was gathered was fed into the FEM model and different simulations were run, first with a simplified Given Schijve equation, considering the asymmetry of the half-cycle U = f(R), and effective SIF was estimated by ΔK eff = ΔK*U. and Ramberg-Osgood equations, and threshold SIF was estimated from the analytical formula of Кth=f(σ). Thus, known loading3D rectangular block shape, in order to local better establish model,from and the thencrack withtip ther*real mesh obtained from the blade The known range ΔK, thetovalue of the σ* atKthe distance was3D determined for each half cycle byscrap. Neuber history SIF made it possible determine ΔKeff, stress Kmax, and th on each cycle for fatigue life estimation. overall expected behaviour in terms of displacement was observed, in particular at theformula trailingofedge of the blade. Therefore such a =f(σ). Thus, known loading and Ramberg-Osgood equations, and threshold SIF was estimated from the analytical К th Mathematical modeling of fatigue crack growth life, especially in near-threshold region of its growth, according to the Sunder’s modelmade can be useful intothe goal of predicting blade life, cycle givenfor a set of FDR data. history it possible determine ΔK , and K on each fatigue life estimation. eff, Kmaxturbine th scheme, showed that investigated aluminum alloy 2024-T3 exhibited crack growth sensitivity to various types of force action, Mathematical modeling ofrandom fatigue loading. crack growth life, especially in near-threshold region of its growth, according to the Sunder’s including various types of © 2016showed The Authors. Published by Elsevier alloy B.V. 2024-T3 exhibited crack growth sensitivity to various types of force action, scheme, that investigated aluminum Peer-review under responsibility of the Scientific Committee of PCF 2016. © 2019 The Authors. Published by Elsevier B.V. including various types of random loading. © 2018 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Pressure Turbine Blade; Creep; Finite Element Method; 3D Model; Simulation. Selection and High peer-review under responsibility ofB.V. Peer-review under responsibility of the SICE 2018 organizers. © Keywords: 2018 The Authors. Published by Elsevier * Corresponding author. Tel.: +7-905-062-68-80. E-mail address: [email protected] * Corresponding author. Tel.: +7-905-062-68-80. E-mail address: [email protected] 2452-3216 © 2018 The Authors. Published by Elsevier B.V.
This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/)
2452-3216 © 2018 The Authors. Published by Elsevier Selection and peer-review under responsibility of B.V. Peer-review under responsibility of the SICE 2018 organizers.
This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) * Corresponding author. Tel.: +351 218419991. Selection and peer-review under responsibility of Peer-review under responsibility of the SICE 2018 organizers. 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 2019 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Selection and peer-review under responsibility of Peer-review under responsibility of the SICE 2018 organizers. 10.1016/j.prostr.2019.05.052
2
Author name / Structural Integrity Procedia 00 (2018) 000–000
This BY-NC-ND (https://creativecommons.org/licenses/by-nc-nd/4.0/) 430 is an open access article under the CC A.N. Savkin et al.license / Procedia Structural Integrity 14 (2019) 429–434 Selection and peer-review under responsibility of Peer-review under responsibility of the SICE 2018 organizers. Keywords: crack growth rate, crack closure, stress intensity factor, variable amplitude loading.
1. Introduction The machines and structures are experienced variable loads in operation. The microcracks can arise in stress concentrators areas, which are the overstrained micro-entities of metal structures. The growth of such cracks under service loading can lead to catastrophic failure. Crack growth kinetics depends on the magnitude as well as sequence of applied loads (Panasjuk, 1991). For example, overloads promote crack growth retardation while underloads accelerate growth. Random loading contains all those elements and analysis of their interaction is made difficult by gaps in understanding. Therefore, experimental studies of the effect of load history continue to be relevant. A common approach to handling the mix of load amplitudes under random loading is to ignore their interaction and merely apply the linear damage accumulation rule. 2. The crack closure model and the near-tip stress influence Currently, among other models for crack growth life estimation, crack closure models that consider the decrease in the stress intensity factor (SIF) magnitude are more popular (Kiciak et al. (2003). One of the negative sides of these models is the impossibility of considering the loading history.
Fig. 1. The ralationship between near-tip stress and ΔKth
The Sunder’s crack resistance model, considering the local near-tip stress, explains the nature of crack slowing based on the active particles from moisture accumulates at the crack tip in the most stressed volume under increasing load, which affects the dependence of the threshold SIF Kth = f ( * ) from stresses near the crack [Sunder (2005) and (2012). Theory bound threshold SIF ΔKth and local near-tip stress and postulated that the overloading effect at the threshold crack growth rates caused by local residual stresses. The proposed model applies the local stress and strain approach to estimate the stress σ* in the stress concentrator region in the fatigue analysis. In this study, the Neuber and Ramberg-Osgood equations were used for making associating SIF K or its range ΔK with the local stress σ* at a distance from the crack tip r* for static and cyclic loading, respectively:
A.N. Savkin et al. / Procedia Structural Integrity 14 (2019) 429–434 Author name / Structural Integrity Procedia 00 (2018) 000–000 1 * * n' K 2 r * E * E K' , 1 * * n' . K 2 r * E * 2 2K ' E
431 3
(1)
(2)
Fig. 2. (a) Illustration of combination of Neuber’s rule and Ramberg-Osgood equation; (b) local near-tip stress at some distance from crack tip
Further development of the model is connected with considering the variable nature of the threshold SIF range ΔKth. Below is the equation proposed for calculating the fatigue crack growth rate:
K th 1 K eff da C K eff n dN K max 1 Kc
p
, q .
(3)
The Forman-Mettu formula was used as a basis, which describes the fatigue crack growth rate curve in all three regions. The Paris coefficients C and n are proposed to be determined by the so-called “three tests” method. 3. Material and test schedule The tests were conducted on servohydraulic test system BISS Nano-25 using C(T)-specimens as per ASTM-647. The specimens were cut from aluminum alloy 2024-Т3 A series of three tests under constant amplitude loading were performed with maximum load Pmax = 2 kN, loading frequency F = 5 Hz and cycle ratios R1 = 0,1, R2 = 0,3 and R3 = 0,5. The asymmetry ratio was varied from 0 to 0.75 for the tests with overloads. The range ΔK was determined by the peak load ΔP of the load history. The Schijve equation U=f(R) was used for considering the crack closure, and the effective SIF was estimated by formula ΔKeff = ΔK*U. The local stress σ* was calculated by formula (2) with using range of SIF. The threshold SIF Kth was estimated
A.N. Savkin et al. / Procedia Structural Integrity 14 (2019) 429–434 Author name / Structural Integrity Procedia 00 (2018) 000–000
432 4
from the analytical dependence Kth = f ( * ), substituting it into Eq. (3). Thus, a known loading history made it possible to determine ΔKeff, Kmax and Kth at each cycle for fatigue life estimation (Savkin et al. (2016). The constant amplitude loading was carried out with Рmax = 1750 N, R = 0.7, N = 104. The level of overload is 1.5 times higher in comparison with the subsequent constant amplitude loading. The factors с, m, p, q и Kc are constant and are known, and the loading history introduced determines the change ΔK, Kmax and ΔKth. Summation of crack length increments on each cycle of loading history allows to determine the fatigue crack life:
Nf
a f a0 n da j 1 i 1 dN ij m
(4)
where af is the critical crack length; a0 is the initial crack length; n is the loading history cycles number; m is the number of iterations of loading sequence; (da/dN)ij is the crack growth rate and increment on i-th cycle of j-th iteration of loading sequence. The blocks of spectra MiniFALSTAFF, MiniTWIST, SAETRANS differ from the original quazi-random sequences, because negative loads were truncated to zero. Thus, all tests were carried out without compressive loading. The load value was Pmax1 = 2500 N, Pmax2 = 3000 N and Pmax3 = 3500 N. 4. Test results and discussion The test simulation under constant amplitude loading with overload-underload (curve 1) and underload-overload (curve 2) sequences overlapping is shown on Fig. 3.
Fig. 3. The local near-tip stress σ* (a), threshold SIF Кth (b) and fatigue crack length (c) under cyclic loading with overload-underload (1) and underload-overload (2)
The overload unit of loading block, consisting of underload-overload, slows the crack growth by 6 times compared to the block with underload-overload sequence, which is close to the results obtained in the experiment. Here, the change of SIF Kth (Fig. 3 b) as a function of the calculated near-tip stress σ* is shown in these tests (Fig. 3 a). The crack growth rate slowing with the underload-overload sequence in comparison with overload-underload is associated with the local near-tip stress σ* decreasing and threshold SIF Kth increasing.
A.N. Savkin et al. / Procedia Structural Integrity 14 (2019) 429–434 Author name / Structural Integrity Procedia 00 (2018) 000–000
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The simulation of the test under MiniFalstaff-spectrum loading is shown in Fig. 4
Fig. 4. The local near-tip stress σ* (a), threshold SIF Кth (b) and fatigue crack length (c) under variable amplitude loading with MiniFalstaff spectrum
A Sunder model feature of the use is the definition of the asymmetry ratio for each semi-cycle of random cyclic loading and crack closing factor U and the local near-tip stresses and the values of the threshold SIF Kth used in Eq. (3). However, the random nature of the loads applied to the specimen leads with the field of spread of the points of change of the threshold SIF as a function of the local near-tip stress, which makes it difficult to study the function of the change of these parameters as the fatigue crack grew. The mean values were calculated for studying the kinetics of these parameters during the loading process. Their variation during the loading process is shown on Fig. 4 b and 4 c. It is noted that, the local near-tip stress σ* during 100-200 load blocks remains constant, and then increases up to failure, and irrespective Pmax. These stresses are negative at Pmax = 2500 N, with Pmax increasing it move to the positive area. SIF Kth remains practically constant in the initial period of loading. As the fatigue crack grows, the SIF at the crack tip increases, and its threshold value decreases, contributing to an increase in the rate of crack growth. Comparison of the calculated and experimental data on the fatigue cracks growth life with different nature of variable loading with allowance for local near-tip stress and the change in the value of the threshold stress intensity factor are shown in Fig. 5.
Fig. 5. Comparison of the calculated and experimental fatigue crack growth lives for tests under different types of loading
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5. Conclusion The fatigue crack growth life estimation, especially in the near-threshold area of its growth, according to the Sunder model, showed that for the investigated aluminum alloy 2024-T3, the crack growth sensitivity to features of force action was revealed. The correlation factor calculated by the Sounder model and experimental data on the fatigue crack growth life for different types of loading was r = 0.97. Acknowledgements This paper was financially supported by the RFBR grant 17-08-01648 A, № 17-08-01742 A and the President of the Russian Federation grant MK-943.2017.8. References Panasiuk V. V., 1991. Mehanika kvazikhrupkogo razrusheniia materialov. Naukova dumka, Kiev, pp. 416. Kiciak A., Glinka G., Burns D. J., 2003. Calculation of stress intensity factors and crack opening displacements for cracks subjected to complex stress fields. Journal of Pressure Vessel Technology, Vol. 125, p. 260-266. Sunder R., 2012. Unraveling the Science of Variable Amplitude Fatigue. Journal of ASTM International, Vol. 9, №1, pp. 32. Sunder R., 2005. Fatigue as process of brittle micro-fracture. Fatigue and Fracture of Engineering Materials and Structures, Vol.28, №3, pp. 289300. Savkin A.N., Andronik A.V., Koraddi R., 2016. Approximation Algorithms of Crack Growth Rate Curve Based on Crack Size Variations. Journal of Testing and Evaluation, Vol. 44, No. 1, pp. 310-319.