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The influence of grain size on cleavage crack propagation resistance in ferritic steels
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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
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Procedia Structural Integrity 13 00 (2018) 1221–1225 Structural Integrity Procedia (2016) 000–000
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ECF22 - Loading and Environmental effects on Structural Integrity ECF22 - Loading and Environmental effects on Structural Integrity
The influence of grain size on cleavage crack propagation resistance The influence of grain size on cleavage crack propagation resistance in ferritic steels XV Portuguese Conference on Fracture, PCF 2016, 10-12 February 2016, Paço de Arcos, Portugal in ferritic steels a a Yuta Suzukia* , Takuhiromodeling Hemmiaa, Fuminori Yanagimoto , Kazuki Shibanuma Thermo-mechanical of a high pressure turbine blade a* a Yuta Suzuki , Takuhiro Hemmi , Fuminori Yanagimoto , Kazuki Shibanumaa of an Department of Systems Innovation, the University of Tojyo, 7-3-1, Hongo, Bunkyo-ku, Tokyo, Japan airplane gas turbine engine Department of Systems Innovation, the University of Tojyo, 7-3-1, Hongo, Bunkyo-ku, Tokyo, Japan a a
Abstract Abstract P. Brandãoa, V. Infanteb, A.M. Deusc* Cleavagea crack propagation in steels occurs suddenly and at high speed, and has a risk of giving structures crucial damage. Thus, Department of be Mechanical Engineering, Instituto Superior Técnico, Universidade Lisboa, Av. Rovisco 1, 1049-001 Lisboa, Cleavage crack propagation in steels occurs suddenly and at high speed, and has ade risk ofexample giving structures damage. Thus,a it is a phenomenon to prevented absolutely. It is well known that microstructures, for grain Pais, size crucial or orientation, make Portugal it is ba phenomenon to beto prevented It is well known that but microstructures, example grain or orientation, make isa substantial contribution material absolutely. resistance to cleavage fracture, the effect of for microstructures onsize mechanism of fracture IDMEC,contribution Department of Engineering, Instituto Superior Universidade de Lisboa, Pais, 1049-001 Lisboa, substantial toMechanical material to cleavage fracture, but the effectout of arrest microstructures on mechanism of fracture is practically hardly elucidated at the resistance present moment. This study Técnico, firstly carried tests Av. to Rovisco evaluate the 1,relation between Portugal practically hardly elucidatedand at grain the present moment. carried of outmicrostructures, arrest tests to evaluate the relation between cleavage crack propagation size that was theThis moststudy basic firstly characteristic and experimented to describe c CeFEMA, Department of Mechanical Engineering, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1, 1049-001 Lisboa, cleavage crack process propagation and grain size mechanism. that was the The mostnumerical basic characteristic of microstructures, and experimented to describe the elementary on the microscopic Portugalanalysis model was developed to express the results of these the elementaryand process on that the microscopic mechanism. numerical analysis model was developed to express experiments, showed the larger grain size was,The the larger cleavage crack propagation resistance was. the results of these experiments, and showed that the larger grain size was, the larger cleavage crack propagation resistance was. © Abstract 2018 The Authors. Published by Elsevier B.V. © 2018 Published by Elsevier B.V. B.V. © 2018The TheAuthors. Authors. Published by Peer-review underresponsibility responsibility of Elsevier the ECF22 organizers. Peer-review under of the ECF22 organizers. Peer-review under responsibility of the ECF22 organizers. During their operation, modern aircraft engine components are subjected to increasingly demanding operating conditions, Keywords: Cleavage; Crack propagation; Arrest toughness; Microstructure; especially the high pressure turbine (HPT) blades. Such conditionsXFEM; cause these parts to undergo different types of time-dependent Keywords: Cleavage; Crack propagation; toughness; Microstructure; XFEM; degradation, one of which is creep. Arrest A model using the finite element method (FEM) was developed, in order to be able to predict the creep behaviour of HPT blades. Flight data records (FDR) for a specific aircraft, provided by a commercial aviation were used to obtain thermal and mechanical data for three different flight cycles. In order to create the 3D model 1. company, Introduction 1. needed Introduction for the FEM analysis, a HPT blade scrap was scanned, and its chemical composition and material properties were obtained. data that was gathered was fed into thegrain FEMsize, model andorientation, different simulations wereeffect run, first with a simplified It can beThe easily inferred that microstructures, like grain have a strong on cleavage fracture.3D rectangular blockinferred shape, inthat order to better establish the model, and thenorientation, with the realhave 3D mesh obtained from the bladefracture. scrap. The It can be easily microstructures, like grain size, grain a strong effect on cleavage Grain size is the most basic characteristic to describe microstructures, and it is empirically known that the smaller it is, overall expected behaviour in terms of displacement was observed, in particular at the trailing edge of the blade. Therefore such a Grain sizeeasily is thecrack mostarrests. basic characteristic describe and it isthe empirically known that the smaller it is, the more However, notoattempt hasmicrostructures, been elucidate model can be useful in the goal of predicting turbine blade life, made given atoset of FDR data.relation between grain size and arrest
the more easily crack However, no attempt has been made which to elucidate betweencomposition grain size and arrest toughness directly by arrests. measuring each arrest toughness for steels have the the relation same chemical and the toughness directly by measuring each arrest toughness for steels which have the same chemical composition and the different size because producing such steels requires advanced technology. Therefore, there is no firm evidence © 2016 grain The Authors. Published by Elsevier B.V. different grainunder size responsibility because producing such steels requires technology. Therefore, theretests is no evidence Peer-review of the Scientific Committee ofadvanced PCF 2016. that empirical knowledge is correct, and it is necessary to perform cleavage crack arrest toughness to firm ascertain it. thatThe empirical knowledge is correct, and it is necessary to perform cleavage crack arrest toughness tests to ascertain it. absorbed energy in cleavage crack propagation is composed of the energy of forming cleavage plane at the (100) Keywords: Highand Pressure Turbine Blade; Creep; Finite Element Method; 3D Model; Simulation. Theinabsorbed energy in cleavage crackunbroken propagation is composed of the energy of forming at the small (100) plane grains tear-ridge by breaking portion of the grain boundary. The formercleavage energy isplane negligibly plane in grains and tear-ridge by breaking unbroken portion of the grain boundary. The former energy is negligibly small compared to the latter energy, so it can be calculated by considering the formation energy of tear-ridge between grains compared to the latter energy, so However, it can be calculated by considering theestimated formation of tear-ridge betweensurface grains as the energy absorption amount. this derivation is a formula byenergy observing a part of fracture as the energy absorption amount. However, this derivation is a formula estimated by observing a part of fracture surface and contains many uncertain terms. In other words, it cannot be said that there is an experimental fact to prove it. and contains many uncertain terms. In other words, it cannot be said that there is an experimental fact to prove it. 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.2018.12.251
Yuta Suzuki et al. / Procedia Structural Integrity 13 (2018) 1221–1225 Author name / Structural Integrity Procedia 00 (2018) 000–000
1222 2
In the first place, the relation between average grain size and crack propagation resistance was revealed by performing systematic crack arrest toughness tests on steels whose average grain size was only different. Secondly, we experimentally measured the fracture condition at the grain level and the absorbed energy at the failure, and verified the validity of the estimation of the energy absorption amount. Finally, by applying the formula of the absorbed energy derived from experiments to the developed model, we compared the experimental fact with the result by model calculation. 2. Evaluation of macroscopic resistance against cleavage crack propagation 2.1. Material In this study, cleavage crack propagation tests were carried out using two types of ferrite-pearlite steels with different grain size. The chemical compositions are shown in Table 1. Mechanical properties of these steels are shown in Table 2. Microstructures of these steels by optic microscope observation are shown in Fig. 1. Table 1 Chemical compositions of steels employed (mass%) C
Si
Mn
P
S
Al
N
S1
0.1
0.19
1.5
0.01
0.003
0.028
0.0029
S2
0.1
0.2
1.48
0.011
0.003
0.03
0.0028
Table 2 Mechanical properties of steels employed Yield stress at room temperature [MPa]
Tensile strength at room temperature [MPa]
FATT[℃]
Average grain size[μm]
S1
319
459
-48.1
31.3
S2
231
405
-32.0
53.1
㻌
S1
S2
Fig. 1 Microstructures of steels employed by optic microscope observation (magnitude: 100)
2.2. Experimental procedure Using the two types of steels shown in 2.1, cleavage crack propagation resistance was evaluated by DCB tests at multiple temperatures from -90℃ to -50℃. In these tests, as the crack arrested due to the decrease of the stress intensity factor with crack growth, the temperature in these specimens was set to a constant value. The specimen of DCB tests is shown in Fig. 2.
Yuta Suzuki et al. / Procedia Structural Integrity 13 (2018) 1221–1225 Author name / Structural Integrity Procedia 00 (2018) 000–000 unit:mm
50 8 y
8
8
8
x
1223 3
z
30
x
0.2 Chevron notch
76
z y Rolling direction
Fig. 2 Configuration of crack arrest specimens
2.3. Evaluation result
Estimated local fracture stress [MPa]
When evaluating the arrest characteristic of a material from the result of the arrest toughness tests, arrest toughness using the stress intensity factor is often adopted as an indicator. However, this arrest toughness is only an apparent crack propagation resistance value. Therefore, based on the accomplishment of Yanagimoto et al., local fracture stress was adopted (Yanagimoto et al., 2018). Considering the crack opening displacement and the position of crack arrest at the time of occurrence of fracture, local fracture stress was evaluated by the finite element analysis with Abaqus 6.14 (SIMULIA, 2014). In this analysis, the estimation of local fracture stress was carried out by evaluating stress in the vicinity of crack tip when crack arresting. Fig. 3 shows the local fracture stress based on the average grain size. As a result, it can be said that experimentally showed that the larger grain size is, the larger cleavage crack propagation resistance. 1400 1200
S1
1000
S2
800 600 400 200 0
0
20 40 Average grain size [μm]
60
Fig. 3 Result of the estimated local fracture stresses
3. Calculation of absorbed energy In fact, it is nearly impossible to obtain effective surface energy directly from cleavage crack propagation experiments because it is extremely fast and complicated phenomenon. Therefore, microscopic cleavage fracture surface simulated by a numerical model was employed to calculate energy absorption during cleavage crack propagation. The accomplishment of Aihara and Tanaka was unique attempt to model cleavage crack propagation in bcc solids (Aihara and Tanaka, 2011). However, the model had problems in reproducing the actual phenomenon because of simplification such as discretization by a single rectangular unit cell and evaluation of the stress intensity factor of crack front by superposition of approximate solutions. Therefore, Shibanuma et al. developed a new cleavage crack
1224 4
Yuta Suzuki et al. / Procedia Structural Integrity 13 (2018) 1221–1225 Author name / Structural Integrity Procedia 00 (2018) 000–000
propagation model based on XFEM (Moës et al., 2002; Gonzalez et al., 2013; Shibanuma et al., 2018). This model made it possible to reproduce fracture surface with very complicated cleavage crack propagation with high precision and easily by defining finite elements independently of cracks and grains. In cleavage crack propagation in steels, it is pointed out that the absorbed energy due to cleavage plane formation is just a little and energy dissipation by ductile fracture of ligaments between cleavage planes along grain boundaries amounts for a large proportion (Shibanuma et al., 2016; Yamamoto et al.,2016). The broken ligament is called as tear ridge. Therefore, in accordance with previous studies (Aihara and Tanaka, 2011; Shibanuma et al., 2016; Yamamoto et al.,2016), the energy absorption calculation considered only tear ridge formation in this study. Plastic work in forming tear-ridge per unit volume has been expressed by the shear yield stress 𝜏𝜏𝑌𝑌 and the critical strain 𝜀𝜀𝑓𝑓𝑓𝑓 . Based on Tresca’s yielding condition assuming perfectly plastic solids, the energy absorption amountγ due to tear ridge formation was calculated by
1 ∫ 𝑐𝑐ℎ2 𝜏𝜏𝑌𝑌 𝜀𝜀𝑓𝑓𝑓𝑓 𝑑𝑑𝑑𝑑 2𝐴𝐴 𝑆𝑆
γ=
(1)
where 𝐴𝐴 is target area, and 𝑐𝑐 is the ratio of the thickness of the unbroken ligament to the height. Here, 𝑐𝑐 was set to0.1 and 𝜀𝜀𝑓𝑓𝑓𝑓 was set to 0.7 based on SEM observation conducted in previous studies (Shibanuma et al., 2016; Yamamoto et al., 2016).
S1
S2
Fig. 4 Simulation result of tear-ridge formation
Using the grain size distribution of S1, and S2 shown in 2.1, we evaluated the fracture surface formation energy of each steel. The obtained results are shown in Fig. 5. From this figure, similarly to the experimental result of Section 2, it could be said that the larger grain size is, the larger the fracture surface formation energy, that is, cleavage crack propagation resistance is.
Absorbed energy [J/mm2]
2.500 S1 S2
2.000 1.500 1.000 500 0
0
20 40 Average Grain size [μm]
60
Fig. 5 Influence of grain size on absorbed stress (Model simulation)
Yuta Suzuki et al. / Procedia Structural Integrity 13 (2018) 1221–1225 Author name / Structural Integrity Procedia 00 (2018) 000–000
1225 5
4. Conclusion In this study, the relation between grain size which was the most basic characteristic of microstructures and cleavage crack propagation resistance was evaluated by experiments and numerical analysis model development. From the macroscopic arrest toughness tests, it was found that the crack resistance tended to increase for steels which had large grain size. In the cleavage crack propagation model, the fracture surface corresponding the tear-ridge was reproduced, the absorbed energy was quantitatively derived from the formula based on the experimental result. As a result, on the both sides of experiments and numerical calculations by model, the results showed that the cleavage crack propagation resistance was larger for steels with larger grain size. References F. Yanagimoto, K. Shibanuma, K. Suzuki, T. Matsumoto, S. Aihara, Local stress in the vicinity of the propagating cleavage crack tip in ferritic steel, Materials & Design, Vol.144, pp.361-373, 2018. K. Shibanuma, Y. Suzuki, K. Kiriyama, T. Hemmi, H. Shirahata, A numerical simulation model of microscopic cleavage crack propagation based on 3D XFEM, ECF22_364 K. Shibanuma, Y. Yamamoto, F. Yanagimoto, K. Suzuki, S. Aihara, Multiscale Model Synthesis to Clarify the Relationship between Microstructures of Steel and Macroscopic Brittle Crack Arrest Behavior - Part I : Model Presentation. ISIJ Int. 56, 341–349. doi:10.2355/isijinternational.ISIJINT-2015-450, 2016. N. Moës, A. Gravouil, T. Belytschko, Non-planar 3D crack growth by the extended finite element and level sets, International Journal for Numerical Methods in Engineering, Vol.53, pp.2549-2568, 2002. S. Aihara, Y. Tanaka, A simulation model for cleavage crack propagation in bcc polycrystalline solids, Acta Materialia, Vol.59, pp.46414652, 2011. SIMULIA, 2014. Abaqus Analysis User’s Guide Version 6.14. Dassault Systemes. V.F. Gonzalez-Albuixech, E. Giner, J.E. Tarancon, F.J. Fuenmayor, A. Gravouil, Domain integral formulation for 3D curved and nonplanar cracks with the extended finite element method, Computational Methods in Applied Mechanics and Engineering, Vol.264, pp.129-144, 2013. Y. Yamamoto, K. Shibanuma, F. Yanagimoto, K. Suzuki, S. Aihara, Multiscale Model Synthesis to Clarify the Relationship between Microstructures of Steel and Macroscopic Brittle Crack Arrest Behavior - Part II : Application to Crack Arrest Test. ISIJ Int. 56, 350–358. doi:10.2355/isijinternational.ISIJINT-2015-450, 2016.
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 Integrity 13 00 (2018) 1221–1225 Structural Integrity Procedia (2016) 000–000
www.elsevier.com/locate/procedia www.elsevier.com/locate/procedia
www.elsevier.com/locate/procedia
ECF22 - Loading and Environmental effects on Structural Integrity ECF22 - Loading and Environmental effects on Structural Integrity
The influence of grain size on cleavage crack propagation resistance The influence of grain size on cleavage crack propagation resistance in ferritic steels XV Portuguese Conference on Fracture, PCF 2016, 10-12 February 2016, Paço de Arcos, Portugal in ferritic steels a a Yuta Suzukia* , Takuhiromodeling Hemmiaa, Fuminori Yanagimoto , Kazuki Shibanuma Thermo-mechanical of a high pressure turbine blade a* a Yuta Suzuki , Takuhiro Hemmi , Fuminori Yanagimoto , Kazuki Shibanumaa of an Department of Systems Innovation, the University of Tojyo, 7-3-1, Hongo, Bunkyo-ku, Tokyo, Japan airplane gas turbine engine Department of Systems Innovation, the University of Tojyo, 7-3-1, Hongo, Bunkyo-ku, Tokyo, Japan a a
Abstract Abstract P. Brandãoa, V. Infanteb, A.M. Deusc* Cleavagea crack propagation in steels occurs suddenly and at high speed, and has a risk of giving structures crucial damage. Thus, Department of be Mechanical Engineering, Instituto Superior Técnico, Universidade Lisboa, Av. Rovisco 1, 1049-001 Lisboa, Cleavage crack propagation in steels occurs suddenly and at high speed, and has ade risk ofexample giving structures damage. Thus,a it is a phenomenon to prevented absolutely. It is well known that microstructures, for grain Pais, size crucial or orientation, make Portugal it is ba phenomenon to beto prevented It is well known that but microstructures, example grain or orientation, make isa substantial contribution material absolutely. resistance to cleavage fracture, the effect of for microstructures onsize mechanism of fracture IDMEC,contribution Department of Engineering, Instituto Superior Universidade de Lisboa, Pais, 1049-001 Lisboa, substantial toMechanical material to cleavage fracture, but the effectout of arrest microstructures on mechanism of fracture is practically hardly elucidated at the resistance present moment. This study Técnico, firstly carried tests Av. to Rovisco evaluate the 1,relation between Portugal practically hardly elucidatedand at grain the present moment. carried of outmicrostructures, arrest tests to evaluate the relation between cleavage crack propagation size that was theThis moststudy basic firstly characteristic and experimented to describe c CeFEMA, Department of Mechanical Engineering, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1, 1049-001 Lisboa, cleavage crack process propagation and grain size mechanism. that was the The mostnumerical basic characteristic of microstructures, and experimented to describe the elementary on the microscopic Portugalanalysis model was developed to express the results of these the elementaryand process on that the microscopic mechanism. numerical analysis model was developed to express experiments, showed the larger grain size was,The the larger cleavage crack propagation resistance was. the results of these experiments, and showed that the larger grain size was, the larger cleavage crack propagation resistance was. © Abstract 2018 The Authors. Published by Elsevier B.V. © 2018 Published by Elsevier B.V. B.V. © 2018The TheAuthors. Authors. Published by Peer-review underresponsibility responsibility of Elsevier the ECF22 organizers. Peer-review under of the ECF22 organizers. Peer-review under responsibility of the ECF22 organizers. During their operation, modern aircraft engine components are subjected to increasingly demanding operating conditions, Keywords: Cleavage; Crack propagation; Arrest toughness; Microstructure; especially the high pressure turbine (HPT) blades. Such conditionsXFEM; cause these parts to undergo different types of time-dependent Keywords: Cleavage; Crack propagation; toughness; Microstructure; XFEM; degradation, one of which is creep. Arrest A model using the finite element method (FEM) was developed, in order to be able to predict the creep behaviour of HPT blades. Flight data records (FDR) for a specific aircraft, provided by a commercial aviation were used to obtain thermal and mechanical data for three different flight cycles. In order to create the 3D model 1. company, Introduction 1. needed Introduction for the FEM analysis, a HPT blade scrap was scanned, and its chemical composition and material properties were obtained. data that was gathered was fed into thegrain FEMsize, model andorientation, different simulations wereeffect run, first with a simplified It can beThe easily inferred that microstructures, like grain have a strong on cleavage fracture.3D rectangular blockinferred shape, inthat order to better establish the model, and thenorientation, with the realhave 3D mesh obtained from the bladefracture. scrap. The It can be easily microstructures, like grain size, grain a strong effect on cleavage Grain size is the most basic characteristic to describe microstructures, and it is empirically known that the smaller it is, overall expected behaviour in terms of displacement was observed, in particular at the trailing edge of the blade. Therefore such a Grain sizeeasily is thecrack mostarrests. basic characteristic describe and it isthe empirically known that the smaller it is, the more However, notoattempt hasmicrostructures, been elucidate model can be useful in the goal of predicting turbine blade life, made given atoset of FDR data.relation between grain size and arrest
the more easily crack However, no attempt has been made which to elucidate betweencomposition grain size and arrest toughness directly by arrests. measuring each arrest toughness for steels have the the relation same chemical and the toughness directly by measuring each arrest toughness for steels which have the same chemical composition and the different size because producing such steels requires advanced technology. Therefore, there is no firm evidence © 2016 grain The Authors. Published by Elsevier B.V. different grainunder size responsibility because producing such steels requires technology. Therefore, theretests is no evidence Peer-review of the Scientific Committee ofadvanced PCF 2016. that empirical knowledge is correct, and it is necessary to perform cleavage crack arrest toughness to firm ascertain it. thatThe empirical knowledge is correct, and it is necessary to perform cleavage crack arrest toughness tests to ascertain it. absorbed energy in cleavage crack propagation is composed of the energy of forming cleavage plane at the (100) Keywords: Highand Pressure Turbine Blade; Creep; Finite Element Method; 3D Model; Simulation. Theinabsorbed energy in cleavage crackunbroken propagation is composed of the energy of forming at the small (100) plane grains tear-ridge by breaking portion of the grain boundary. The formercleavage energy isplane negligibly plane in grains and tear-ridge by breaking unbroken portion of the grain boundary. The former energy is negligibly small compared to the latter energy, so it can be calculated by considering the formation energy of tear-ridge between grains compared to the latter energy, so However, it can be calculated by considering theestimated formation of tear-ridge betweensurface grains as the energy absorption amount. this derivation is a formula byenergy observing a part of fracture as the energy absorption amount. However, this derivation is a formula estimated by observing a part of fracture surface and contains many uncertain terms. In other words, it cannot be said that there is an experimental fact to prove it. and contains many uncertain terms. In other words, it cannot be said that there is an experimental fact to prove it. 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.2018.12.251
Yuta Suzuki et al. / Procedia Structural Integrity 13 (2018) 1221–1225 Author name / Structural Integrity Procedia 00 (2018) 000–000
1222 2
In the first place, the relation between average grain size and crack propagation resistance was revealed by performing systematic crack arrest toughness tests on steels whose average grain size was only different. Secondly, we experimentally measured the fracture condition at the grain level and the absorbed energy at the failure, and verified the validity of the estimation of the energy absorption amount. Finally, by applying the formula of the absorbed energy derived from experiments to the developed model, we compared the experimental fact with the result by model calculation. 2. Evaluation of macroscopic resistance against cleavage crack propagation 2.1. Material In this study, cleavage crack propagation tests were carried out using two types of ferrite-pearlite steels with different grain size. The chemical compositions are shown in Table 1. Mechanical properties of these steels are shown in Table 2. Microstructures of these steels by optic microscope observation are shown in Fig. 1. Table 1 Chemical compositions of steels employed (mass%) C
Si
Mn
P
S
Al
N
S1
0.1
0.19
1.5
0.01
0.003
0.028
0.0029
S2
0.1
0.2
1.48
0.011
0.003
0.03
0.0028
Table 2 Mechanical properties of steels employed Yield stress at room temperature [MPa]
Tensile strength at room temperature [MPa]
FATT[℃]
Average grain size[μm]
S1
319
459
-48.1
31.3
S2
231
405
-32.0
53.1
㻌
S1
S2
Fig. 1 Microstructures of steels employed by optic microscope observation (magnitude: 100)
2.2. Experimental procedure Using the two types of steels shown in 2.1, cleavage crack propagation resistance was evaluated by DCB tests at multiple temperatures from -90℃ to -50℃. In these tests, as the crack arrested due to the decrease of the stress intensity factor with crack growth, the temperature in these specimens was set to a constant value. The specimen of DCB tests is shown in Fig. 2.
Yuta Suzuki et al. / Procedia Structural Integrity 13 (2018) 1221–1225 Author name / Structural Integrity Procedia 00 (2018) 000–000 unit:mm
50 8 y
8
8
8
x
1223 3
z
30
x
0.2 Chevron notch
76
z y Rolling direction
Fig. 2 Configuration of crack arrest specimens
2.3. Evaluation result
Estimated local fracture stress [MPa]
When evaluating the arrest characteristic of a material from the result of the arrest toughness tests, arrest toughness using the stress intensity factor is often adopted as an indicator. However, this arrest toughness is only an apparent crack propagation resistance value. Therefore, based on the accomplishment of Yanagimoto et al., local fracture stress was adopted (Yanagimoto et al., 2018). Considering the crack opening displacement and the position of crack arrest at the time of occurrence of fracture, local fracture stress was evaluated by the finite element analysis with Abaqus 6.14 (SIMULIA, 2014). In this analysis, the estimation of local fracture stress was carried out by evaluating stress in the vicinity of crack tip when crack arresting. Fig. 3 shows the local fracture stress based on the average grain size. As a result, it can be said that experimentally showed that the larger grain size is, the larger cleavage crack propagation resistance. 1400 1200
S1
1000
S2
800 600 400 200 0
0
20 40 Average grain size [μm]
60
Fig. 3 Result of the estimated local fracture stresses
3. Calculation of absorbed energy In fact, it is nearly impossible to obtain effective surface energy directly from cleavage crack propagation experiments because it is extremely fast and complicated phenomenon. Therefore, microscopic cleavage fracture surface simulated by a numerical model was employed to calculate energy absorption during cleavage crack propagation. The accomplishment of Aihara and Tanaka was unique attempt to model cleavage crack propagation in bcc solids (Aihara and Tanaka, 2011). However, the model had problems in reproducing the actual phenomenon because of simplification such as discretization by a single rectangular unit cell and evaluation of the stress intensity factor of crack front by superposition of approximate solutions. Therefore, Shibanuma et al. developed a new cleavage crack
1224 4
Yuta Suzuki et al. / Procedia Structural Integrity 13 (2018) 1221–1225 Author name / Structural Integrity Procedia 00 (2018) 000–000
propagation model based on XFEM (Moës et al., 2002; Gonzalez et al., 2013; Shibanuma et al., 2018). This model made it possible to reproduce fracture surface with very complicated cleavage crack propagation with high precision and easily by defining finite elements independently of cracks and grains. In cleavage crack propagation in steels, it is pointed out that the absorbed energy due to cleavage plane formation is just a little and energy dissipation by ductile fracture of ligaments between cleavage planes along grain boundaries amounts for a large proportion (Shibanuma et al., 2016; Yamamoto et al.,2016). The broken ligament is called as tear ridge. Therefore, in accordance with previous studies (Aihara and Tanaka, 2011; Shibanuma et al., 2016; Yamamoto et al.,2016), the energy absorption calculation considered only tear ridge formation in this study. Plastic work in forming tear-ridge per unit volume has been expressed by the shear yield stress 𝜏𝜏𝑌𝑌 and the critical strain 𝜀𝜀𝑓𝑓𝑓𝑓 . Based on Tresca’s yielding condition assuming perfectly plastic solids, the energy absorption amountγ due to tear ridge formation was calculated by
1 ∫ 𝑐𝑐ℎ2 𝜏𝜏𝑌𝑌 𝜀𝜀𝑓𝑓𝑓𝑓 𝑑𝑑𝑑𝑑 2𝐴𝐴 𝑆𝑆
γ=
(1)
where 𝐴𝐴 is target area, and 𝑐𝑐 is the ratio of the thickness of the unbroken ligament to the height. Here, 𝑐𝑐 was set to0.1 and 𝜀𝜀𝑓𝑓𝑓𝑓 was set to 0.7 based on SEM observation conducted in previous studies (Shibanuma et al., 2016; Yamamoto et al., 2016).
S1
S2
Fig. 4 Simulation result of tear-ridge formation
Using the grain size distribution of S1, and S2 shown in 2.1, we evaluated the fracture surface formation energy of each steel. The obtained results are shown in Fig. 5. From this figure, similarly to the experimental result of Section 2, it could be said that the larger grain size is, the larger the fracture surface formation energy, that is, cleavage crack propagation resistance is.
Absorbed energy [J/mm2]
2.500 S1 S2
2.000 1.500 1.000 500 0
0
20 40 Average Grain size [μm]
60
Fig. 5 Influence of grain size on absorbed stress (Model simulation)
Yuta Suzuki et al. / Procedia Structural Integrity 13 (2018) 1221–1225 Author name / Structural Integrity Procedia 00 (2018) 000–000
1225 5
4. Conclusion In this study, the relation between grain size which was the most basic characteristic of microstructures and cleavage crack propagation resistance was evaluated by experiments and numerical analysis model development. From the macroscopic arrest toughness tests, it was found that the crack resistance tended to increase for steels which had large grain size. In the cleavage crack propagation model, the fracture surface corresponding the tear-ridge was reproduced, the absorbed energy was quantitatively derived from the formula based on the experimental result. As a result, on the both sides of experiments and numerical calculations by model, the results showed that the cleavage crack propagation resistance was larger for steels with larger grain size. References F. Yanagimoto, K. Shibanuma, K. Suzuki, T. Matsumoto, S. Aihara, Local stress in the vicinity of the propagating cleavage crack tip in ferritic steel, Materials & Design, Vol.144, pp.361-373, 2018. K. Shibanuma, Y. Suzuki, K. Kiriyama, T. Hemmi, H. Shirahata, A numerical simulation model of microscopic cleavage crack propagation based on 3D XFEM, ECF22_364 K. Shibanuma, Y. Yamamoto, F. Yanagimoto, K. Suzuki, S. Aihara, Multiscale Model Synthesis to Clarify the Relationship between Microstructures of Steel and Macroscopic Brittle Crack Arrest Behavior - Part I : Model Presentation. ISIJ Int. 56, 341–349. doi:10.2355/isijinternational.ISIJINT-2015-450, 2016. N. Moës, A. Gravouil, T. Belytschko, Non-planar 3D crack growth by the extended finite element and level sets, International Journal for Numerical Methods in Engineering, Vol.53, pp.2549-2568, 2002. S. Aihara, Y. Tanaka, A simulation model for cleavage crack propagation in bcc polycrystalline solids, Acta Materialia, Vol.59, pp.46414652, 2011. SIMULIA, 2014. Abaqus Analysis User’s Guide Version 6.14. Dassault Systemes. V.F. Gonzalez-Albuixech, E. Giner, J.E. Tarancon, F.J. Fuenmayor, A. Gravouil, Domain integral formulation for 3D curved and nonplanar cracks with the extended finite element method, Computational Methods in Applied Mechanics and Engineering, Vol.264, pp.129-144, 2013. Y. Yamamoto, K. Shibanuma, F. Yanagimoto, K. Suzuki, S. Aihara, Multiscale Model Synthesis to Clarify the Relationship between Microstructures of Steel and Macroscopic Brittle Crack Arrest Behavior - Part II : Application to Crack Arrest Test. ISIJ Int. 56, 350–358. doi:10.2355/isijinternational.ISIJINT-2015-450, 2016.