- Email: [email protected]
Multi-scale simulation of hydrogen influenced critical stress intensity in high Co–Ni secondary hardening steel
Materials and Design 87 (2015) 501–506
Contents lists available at ScienceDirect
Materials and Design journal homepage: www.elsevier.com/locate/jmad
Multi-scale simulation of hydrogen influenced critical stress intensity in high Co–Ni secondary hardening steel Chenchong Wang a, Chi Zhang a,⁎, Zhigang Yang a, Jie Su b, Yuqing Weng a,b a b
Key Laboratory of Advanced Materials of Ministry of Education, School of Materials Science and Engineering, Tsinghua University, Beijing 100084, China Institute for Structural Materials, Central, Iron and Steel Research Institute, Beijing 100081, China
a r t i c l e
i n f o
Article history: Received 4 May 2015 Received in revised form 19 June 2015 Accepted 9 August 2015 Available online 14 August 2015 Keywords: Multi-scale simulation Fracture toughness Hydrogen embrittlement
a b s t r a c t Hydrogen embrittlement was an important and long-standing problem in the fields of steels, especially ultrahigh strength steels. In order to simulate the ability of hydrogen embrittlement resistance for high Co–Ni secondary hardening steels, a multi-scale simulation method with four steps was used to calculate the critical stress intensity (KIC) and hydrogen influenced critical stress intensity (KISCC). For the four steps: the atomic scale and nm scale simulation were mainly used to simulate the effect of stress-assisted hydrogen diffusion at the crack tip; the μm scale simulation was used to handle the effect of microstructure; the cm simulation was used to analyze the size effect. As the effect of hydrogen concentration at the crack tip, the simulation results of critical cohesive strength of the Fe(110) at the crack tip decreased by 82.3%. The μm scale simulation showed the improvement of fracture toughness with the help of austenite layer between martensite laths. Compared with the mechanical properties of 300 M and AerMet100 steels, the accuracy of this simulation method was proved. © 2015 Elsevier Ltd. All rights reserved.
1. Introduction Hydrogen embrittlement (HE), which remained incompletely understood from the mechanistic point of view, was an important problem in the fields of steels for ships and subsea pipelines [1–3]. The susceptibility to hydrogen-induced delayed fracture of steels increased with strength increasing, therefore hydrogen embrittlement was one of the most serious challenges for ultra-high strength steels [4–6]. Since 1990s, much attention was paid to the strength and toughness improvement in high Co–Ni secondary hardening steels as AF1410 and AerMet 100, however, few of these steels had high ability of HE resistance [7–10]. Recently, several studies were made to develop new ultra-high strength steels, which had better HE resistance ability than usual high Co–Ni secondary hardening steels [11]. However, few details about the design methods of these steels, especially the mechanism of HE resistance, were reported. As a long-standing problem, HE was studied many great experts and many models were built to simulate the hydrogen influenced critical stress intensity in different kinds of steels [12–19]. Two of the most classical models for hydrogen-induced fracture simulation were the hydrogen enhanced local plasticity model (HELP) [18,19] and the hydrogen enhanced decohesion model (HEDE) [13]. In both of the models, the diffusion of hydrogen in the steels was considered and hydrogen fracture was regarded as a result of a critical combination of stress, strain and hydrogen concentration [12,16]. However, the microstructure of the ⁎ Corresponding author. E-mail address: [email protected] (C. Zhang).
http://dx.doi.org/10.1016/j.matdes.2015.08.040 0264-1275/© 2015 Elsevier Ltd. All rights reserved.
steels, which was also important for the fracture toughness for steels, was not considered in these two models [20–22]. In Jiang's model [15], first principle method was used to explain the cohesion–reduction mechanism of hydrogen embrittlement in steels, but its simulation results were limited to the atomic scale. It could not obtain the mechanical properties of steels without combining first principle method with other simulation methods. Finite element method (FEM) was widely used to simulate the macro-mechanical properties of steels [14], however, it probably ignored details in microscales as hydrogen diffusion at the crack tip and microstructure of the steels. In summary, HE was a complicated problem, which was affected by many factors from atomic scale to macroscale. In atomic scale, the hydrogen atom in the interstitial site could decrease the bonding strength of Fe atoms and make steels brittle. In nm scales, the hydrogen content at the crack tip was an important parameter which can affect the crack propagation. In μm scale, the microstructure had great effect on most mechanical properties of steels. In cm scale, the size effect was also an important factor for the fracture toughness of materials. All these factors were in different scales and they could not be solved by just one simulation method. Therefore, many multi-scale simulation models were developed to solve the problem [26–28]. Recently, Olden's study [28] reported a multi-scale simulation model which included both atomic and microstructure simulations. This model could clearly express the effect of microstructure on the diffusion of hydrogen. However, the model was not focused on calculating the value of macro properties. Hénaff [27] and Vergani [26] also did a lot of work on multiscale simulation which considered the effect of microstructure. However, the microstructure analysis in these models was focused on dislocation
502
C. Wang et al. / Materials and Design 87 (2015) 501–506
or plastic zone at the crack tip, not the phases in the steels. In present study, a multi-scale simulation model, which considered the phases in the steels, was used to calculate the value of hydrogen influenced critical stress intensity in high Co–Ni secondary hardening steels. Considering about the development of high Co–Ni secondary hardening steels, two hotspot steels (300 M and AerMet100 steels) were taken as examples to prove the accuracy of this simulation method. The details of simulation method were given in Section 2, followed by results and discussion in Section 3, and the conclusion was in Section 4. 2. Simulation method The applied model consisted of a four-step simulation procedure including atomic scale, nm scale, μm scale and cm scales. The export of every step was the import of next step. Table 1 showed the whole simulation procedure of this multi-scale simulation model. More details were explained as follows. 2.1. Atomic scale Several studies reported that hydrogen in steels preferred to stay on the Fe surface or subsurface as Fe(100) and Fe(110), instead of in bulk [29,30]. The first principle calculation showed that hydrogen atoms would decrease the cohesive strength of the Fe surface or subsurface when they concentrated on the Fe surface or subsurface [30]. In Jiang's model [15], the relation between hydrogen coverage (θ) and the critical cohesive strength (σc(θ)) of surface or subsurfaces in metal materials could be expressed by Eq. 1. According to Eq. 1, the value of σc(θ)/ σc(0) decreased from 1 to almost 0 with the increasing of hydrogen coverage (θ) at surface or subsurface. σ c ðθÞ ¼ 1−a1 θ þ a2 θ2 σ c ð0Þ
ð1Þ
[13], the stress-assisted diffusion of hydrogen was expressed by a modified Fick's law with respect to the hydrostatic stress (p) as Eq. 3. ∂C DV H DV H ∇C ∇p− C∇2 p ¼ D∇2 C− RT RT ∂t
ð3Þ
where C was the hydrogen concentration; D was the diffusion coefficient; VH was the partial molar volume of hydrogen in steel; R was the mole gas constant (8.314 J/mol K); and T was the absolute temperature (K). The relation between stress field (σ) and hydrostatic stress was p = Tr(σ)/3. The boundary condition was C ¼ C 0 epV H =RT . The hydrogen coverage was defined as a function of the hydrogen concentration as Eq. 4 [13]. θ¼
C C þ expð−Hs =RT Þ
ð4Þ
where Hs was the Gibbs free energy difference between interface and the surrounding materials. A 10 × 10 nm 2D model of crack tip was built by COMSOL Multiphysics as shown in Fig. 1(a). A time dependant load was applied on the top of the models in the y direction as shown in Fig. 1(b) and the bottom of the model was encastred. With the increase of the load, the stress at the crack tip would increase and hydrogen would concentrate to the crack tip based on Eq. 3. Therefore, with the increase of hydrogen coverage at the crack tip, the cohesive strength of Fe(110) at the crack tip would decrease based on Eq. 2. When the stress at the crack tip became equal to the cohesive strength, the crack propagation would form. It meant this model of crack tip could explain the effect of stress-assisted hydrogen diffusion on cohesive strength at crack tip and calculate the value of the critical cohesive strength of Fe(110) at the crack tip (σcc(θ)). 2.3. μm scale
As the matrix of most high Co–Ni secondary hardening steels was martensite, whose crystal structure was b.c.c. [31]. And the main fracture mode of high Co–Ni secondary hardening steels was quasicleavage fracture [9]. Therefore, to simplify the simulation process, Fe(110) was set as fracture plane. According to Jiang's model [15], the relation between hydrogen coverage and the cohesive strength of Fe(110) in Fe/H system was expressed by Eq. 2. σ c ðθÞ ¼ 1−1:0467θ þ 0:1687θ2 σ c ð0Þ
ð2Þ
2.2. nm scale In nm scale simulation, the stress-assisted diffusion of hydrogen at the crack tip was simulated by FEM, using the software of COMSOL Multiphysics. Eq. 2 was used as the import of nm scale simulation by processing it into the software of COMSOL Multiphysics. The nm scale simulation was based on HEDE mode [13]. According to HEDE mode
In μm scale simulation, FEM models based on the microstructure of steels were built using the software of ABAQUS. The value of σcc(0) and σcc(θ) obtained from atomic and nm scale simulation was used as the import of μm scale simulation. We optimized the loading values in μm scale simulation based on the critical cohesive stress obtained by nm scale simulation to make the cohesive strength in μm scale simulation equal to the value of σcc(0) and σcc(θ) obtained from atomic and nm scale simulation. According to TEM observation results reported by previous work [31], two contour integral models were built: martensite without austenite layer (model of 300 M) and martensite with 15 nm austenite layer (model of AerMet100). The property of martensite was elasticity with Em = 200GPa and v = 0.3 [32–34]. Austenite layers in the models were considered to be an elastic–plastic solid with Ea = Em/10GPa, v = 0.3, and σb = 580 MPa [35–38]. Because the crack propagation formed across the martensite as quasi-cleavage crack [9], the interface between martensite and austenite layer was set as ‘fixed’. A 4-node bilinear plane stress elements (CPS4R) were used in these 2D contour integral models. The uniaxial tensile loading was
Table 1 Simulation procedure of the multi-scale simulation model. Scales
Methods
Import
Export
Atomic (1–20 Å)
First principle
–
σ c ðθÞ σ c ð0Þ
nm (1–20 nm)
FEM (COMSOL)
σ c ðθÞ σ c ð0Þ
μm (1–10 μm) cm (1–5 cm)
FEM (ABAQUS) Empirical formula
¼ 1−a1 θ þ a2 θ2 σ cc ð0Þ σcc(θ), σcc(0) Microstructure information KIC(s), KISCC(s) (For μm scale)
¼ 1−a1 θ þ a2 θ σ cc ð0Þ θ, σcc(θ)
Influence factors 2
KIC(s), KISCC(s) (For small samples) KIC, KISCC (For actual samples)
Crystal orientation, composition Hydrogen diffusion Microstructure Size effect
C. Wang et al. / Materials and Design 87 (2015) 501–506
503
Fig. 1. 2D model of crack tip built by COMSOL Multiphysics: (a) structure and mesh; (b) time dependant load.
applied on the top of the models in the y direction and the bottom of the models was encastred. As Fig. 2 shows that, the crack region was meshed as annular units around the crack tip in order to calculate the KIC value of the models by contour integral. In contour integral models, the initial crack propagation direction was not only perpendicular to the austenite layer. The models in which the initial crack propagation direction was 30°, 45° and 60° to the austenite layers were built and their simulation results were similar with the models in which the initial crack propagation direction was just perpendicular to the austenite layer. It meant that the angles between the initial crack propagation direction and the austenite layer had little effect on the simulation results of KIC. Therefore, considering the length limit of the paper, only models in which the initial crack propagation direction was perpendicular to the austenite layer were shown in this paper. As the sizes of the contour integral models were only about 1 μm, only KIC and KISCC for μm scale (KIC(s), KISCC(s)) could be obtained by the μm scale simulation.
2.4. cm scale As the models used in nm and μm scale simulations were all 2D models with small sizes, the size effect should be considered in order to calculate the value of KIC and KISCC for actual samples used for experiment, so that the simulation results could be compared with the experiment results and the accuracy of the simulation could be analyzed. According to Weibull brittle failure theory [39], for the heterogeneous material with same ratio of crack length (a) and sample height (h), the ratio of KIC for μm scale (KIC(s)) and actual samples (KIC) was expressed by Eq. 5 [40]. KICðsÞ ¼ KIC
sffiffiffiffiffiffiffi hðsÞ V 1=α h V ð sÞ
ð5Þ
where V = sth; V(s) = s(s)t(s)h(s); s was length of the actual sample; t was thickness of the actual sample; h was height of the actual sample; s(s)
Fig. 2. Contour integral models built by ABAQUS.
504
C. Wang et al. / Materials and Design 87 (2015) 501–506
Table 2 Parameters used in the four-step simulation procedure. Name
Value
Name
Value
Name
Value
D VH C0 R T
1 × 10−9 cm2/s 2 cm3/mol 4.0 × 10−5 mol/cm3 8.314 J/(mol · K) 293 K
s t h a α
140 mm 15 mm 30 mm 15 mm 5
s(s) t(s) h(s) a(s) σcc(0)
600 nm 0.01 nm 300 nm 150 nm 500 MPa
was length of the μm scale sample; t(s) was thickness of the μm scale sample; h(s) was height of the μm scale sample; and α was Weibull coefficient. In cm scale simulation, the value of KIC and KISCC for μm scale (KIC(s), KISCC(s)) obtained from μm scale simulation was used as the import. Therefore, based on Eq. 5, the simulation results of KIC and KISCC for actual samples could be obtained. All the parameters used in the fourstep simulation procedure were shown in Table 2 [9,12,13,16,39–41].
Fig. 4. The change of total stress and cohesive strength at the crack tip with the increase of load.
3. Results and discussion 3.1. Stress-assisted hydrogen diffusion at the crack tip Fig. 3(a) showed the simulation results of the stress field at the crack tip given by COMSOL Multiphysics. It was clear that significant stress concentration formed at the crack tip. This stress concentration leaded to the hydrogen concentration as stress-assisted hydrogen diffusion (Fig. 3(b)). Similar simulation results of stress-assisted hydrogen diffusion were also reported by several previous works [12,13,16] and all the results also showed stress-assisted hydrogen concentration at the crack tip. It was certain that the stress at the crack tip increased with the increase of load. However, based on Eq. 2, the cohesive strength of the crack tip decreased with the increase of load because of the stressassisted hydrogen concentration at the crack tip. Fig. 4 showed the change of total stress (σt) and cohesive strength (σc) at the crack tip with the increase of load. At the cross point of the curves of total stress and cohesive strength, σt = σc = 88.3 MPa. It meant that the critical cohesive strength at the crack tip σcc(θ) = 88.3 MPa, at which the crack propagation began. As the effect of hydrogen concentration at the crack tip, the simulation results of critical cohesive strength of Fe(110) at the crack tip decreased by 82.3% (1 − σcc(θ)/σcc(0) ≈ 0.823). 3.2. Effect of microstructure on fracture toughness Fig. 5 showed the simulation results of the stress field obtained by ABAQUS. Significant stress concentration could be observed at the crack tip in the model of martensite without austenite layer as shown
in Fig. 5(a). However, with the same load, the stress concentration at the crack tip was greatly reduced by austenite layer in the model of martensite with 15 nm austenite layer as shown in Fig. 5(b). Therefore, the model of martensite with 15 nm austenite layer would have higher value of KIC than the model of martensite without austenite layer. In previous works, several reports about the simulation of natural biological materials or layered composites drew similar conclusion that soft layers in a hard material would probably reduce the stress concentration at the crack tip and improve the fracture toughness of the material [42,43]. After adding the value of σcc(0) and σcc(θ) into the contour integral models (make the stress at the crack tip meet the predetermined value by changing the load applied on the models), the results of KIC and KISCC for small samples were obtained as shown in Table 3. The calculation results clearly showed the improvement of fracture toughness with the help of austenite layer. 3.3. Comparison of simulation and experiment results The simulation results of actual samples were obtained by cm scale simulation. As the mechanical properties of high Co–Ni secondary hardening steels were studied by several previous works [23–25], it would not be tested again in this study. The comparison of simulation and experiment results was shown as Table 4. According to the TEM observation results in previous works [9,28], martensite without austenite layer model was used to simulate 300 M steel and martensite with 15 nm austenite layer model was used to simulate AerMet100 steel in μm scale simulation. Because the experiment results of KISCC for 300 M
Fig. 3. The results of nm scale simulation: (a) stress distribution; (b) hydrogen distribution.
C. Wang et al. / Materials and Design 87 (2015) 501–506
505
Fig. 5. The results of μm scale simulation: (a) martensite without austenite layer; (b) martensite with 15 nm austenite layer.
models and more factors should be considered in order to obtain reasonable results.
Table 3 pffiffiffiffiffi The results of KIC and KISCC for μm scale (unit: MPa m).
KIC(s) KISCC(s)
Martensite without austenite layer
Martensite with 15 nm austenite layer
4. Conclusion
1321 241
3104 554
A four-step multi-scale simulation model was built to calculate the KIC and KISCC value for 300 M and AerMet100 steels. The effect of stress-assisted hydrogen diffusion, microstructure and size effect had been mainly considered in this model.
was too small with a big error range, so the simulation and experiment results of KISCC for 300 M had a difference. For other values, the difference between the simulation results and the experiment results were less than 8%. Therefore, the simulation results were basically consistent with the experiment results for 300 M and AerMet 100 steels. As the calculation results reported by Olson [11], all the main alloy elements (Ni, Co, Cr, Mo) in 300 M and AerMet100 had little effect on the cohesive strength of crystal plane. Therefore, for the atomic scale simulation in this paper, the system was simplified as Fe/H system without considering the effect of other elements. However, for other kinds of high Co–Ni secondary hardening steels, such as M54 which contained W and V [41], the effect of composition could not be ignored. If the steels contained the elements which had significant effect on cohesive strength (as W, V, B and Re), more work about first principle method should be added to the atomic scale simulation in order to revise Eq. 2, which showed the effect of elements on cohesive strength. For the nm scale simulation, Eq. 3 could be revised by adding the effect of strain [12]. Also, the initial hydrogen content (C0) and hydrogen diffusion coefficient (D) for different steels could be tested by hydrogen permeation technique or galvanostatic charging technique [9], in order to optimize the parameters in the models. For the μm scale simulation, the model should been built based on the actual microstructure of the steels. For AerMet100, the precipitates in the matrix were very small (10 nm in length) [28,43], so the FEM models for μm scale simulation were built as martensite and austenite layer, without considering the precipitates formed in the matrix. However, for the steels which had inclusions in large size and belonged to inclusion induced failure, the structure of precipitates should be added into the FEM models. In summary, the simulation process in this paper just provided a basic framework of multi-scale simulation, which was suitable for several common maraging steels. For other kinds of steels, more details should be added into the Table 4 pffiffiffiffiffi Comparison of simulation and experiment results (unit: MPa m). 300 M
Simulation results Experiment results
AerMet100
KIC
KISCC
KIC
KISCC
51.5 50
9.4 5–30
121.1 115
21.6 20
(1) As the increase of the load applied on the crack tip area, the hydrogen concentration formed at the crack tip by stress-assisted hydrogen diffusion. With the effect of hydrogen, value of the critical cohesive strength of Fe(110) at the crack tip decreased by 82.3%. (2) Stress concentration at the crack tip was greatly reduced by austenite layer. The KIC value for the model of martensite with 15 nm austenite layer (AerMet100) was 1.6 times larger than the KIC value for the model of martensite without austenite layer (300 M). (3) Because the experiment results of KISCC for 300 M was too small with a big error range, so the simulation and experiment results of KISCC for 300 M had a difference. For other values, the simulation results were basically consistent with the experiment results.
Acknowledgments This work was financially supported by National Basic Research Programs of China (No. 2015CB654802 and No. 2015GB118001). The financial support provided by the National Natural Science Foundation of China (Grant No. 51471094) was greatly acknowledged. References [1] Y. Qi, H. Luo, S. Zheng, C. Chen, Z. Lv, M. Xiong, Comparison of tensile and impact behavior of carbon steel in H2S environments, Mater. Des. 58 (2014) 234–241. [2] T.E. García, C. Rodríguez, F.J. Belzunce, I. Peñuelas, B. Arroyo, Development of a methodology to study the hydrogen embrittlement of steels by means of the small punch test, Mater. Sci. Eng. A 626 (2015) 342–351. [3] K. Jeong-Hyeon, K. Seul-Kee, K. Myung-Hyun, L. Jae-Myung, Numerical model to predict deformation of corrugated austenitic stainless steel sheet under cryogenic temperatures for design of liquefied natural gas insulation system, Mater. Des. 57 (2014) 26–39. [4] S. Zhang, Y. Huang, B. Sun, Q. Liao, H. Lu, B. Jian, et al., Effect of Nb on hydrogeninduced delayed fracture in high strength hot stamping steels, Mater. Sci. Eng. A 626 (2015) 136–143. [5] X. Zhu, W. Li, T.Y. Hsu, S. Zhou, L. Wang, X. Jin, Improved resistance to hydrogen embrittlement in a high-strength steel by quenching–partitioning–tempering treatment, Scr. Mater. 97 (2015) 21–24.
506
C. Wang et al. / Materials and Design 87 (2015) 501–506
[6] J. Rehrl, K. Mraczek, A. Pichler, E. Werner, Mechanical properties and fracture behavior of hydrogen charged AHSS/UHSS grades at high- and low strain rate tests, Mater. Sci. Eng. A 590 (2014) 360–367. [7] C. Yao, T. Wang, J. Ren, W. Xiao, A comparative study of residual stress and affected layer in Aermet100 steel grinding with alumina and cBN wheels, Int. J. Adv. Manuf. Technol. 74 (2014) 125–137. [8] G. Ji, F. Li, Q. Li, H. Li, Z. Li, A comparative study on Arrhenius-type constitutive model and artificial neural network model to predict high-temperature deformation behaviour in Aermet100 steel, Mater. Sci. Eng. A 528 (2011) 4774–4782. [9] D. Figueroa, M.J. Robinson, Hydrogen transport and embrittlement in 300 M and AerMet100 ultra high strength steels, Corros. Sci. 52 (2010) 1593–1602. [10] M.D. Mulholland, D.N. Seidman, Nanoscale co-precipitation and mechanical properties of a high-strength low-carbon steel, Acta Mater. 59 (2011) 1881–1897. [11] G.B. Olson, Genomic materials design: the ferrous frontier, Acta Mater. 61 (2013) 771–781. [12] A. Alvaro, V. Olden, O.M. Akselsen, 3D cohesive modelling of hydrogen embrittlement in the heat affected zone of an X70 pipeline steel—part II, Int. J. Hydrog. Energy 39 (2014) 3528–3541. [13] S. Serebrinsky, A quantum-mechanically informed continuum model of hydrogen embrittlement, J. Mech. Phys. Solids 52 (2004) 2403–2430. [14] M. Sun, K. Xiao, C. Dong, X. Li, P. Zhong, Effect of stress on electrochemical characteristics of pre-cracked ultrahigh strength stainless steel in acid sodium sulphate solution, Corros. Sci. 89 (2014) 137–145. [15] D.E. Jiang, E.A. Carter, First principles assessment of ideal fracture energies of materials with mobile impurities: Implications for hydrogen embrittlement of metals, Acta Mater. 52 (2004) 4801–4807. [16] V. Olden, A. Alvaro, O.M. Akselsen, Hydrogen diffusion and hydrogen influenced critical stress intensity in an API X70 pipeline steel welded joint—experiments and FE simulations, Int. J. Hydrog. Energy 37 (2012) 11474–11486. [17] A.H.M. Krom, H.J. Maier, R.W.J. Koers, A. Bakker, The effect of strain rate on hydrogen distribution in round tensile specimens, Mater. Sci. Eng. A 271 (1999) 22–30. [18] C. Beachem, A new model for hydrogen-assisted cracking, Metall. Mater. Trans. B 441–55 (1972). [19] H.K. Birnbaum, P. Sofronis, Hydrogen-enhanced localized plasticity-a mechanism for hydrogen-related fracture, Mater. Sci. Eng. A 176 (1994) 191–202. [20] X. Li, Y. Fan, X. Ma, S.V. Subramanian, C. Shang, Influence of martensite–austenite constituents formed at different intercritical temperatures on toughness, Mater. Des. 67 (2015) 457–463. [21] A. García-Prieto, M.D. Ramos-Lotito, D. Gutiérrez-Campos, P. Pena, C. Baudín, Influence of microstructural characteristics on fracture toughness of refractory materials, J. Eur. Ceram. Soc. 35 (2015) 1955–1970. [22] M. Javanbakht, M.J. Hadianfard, E. Salahinejad, Microstructure and mechanical properties of a new group of nanocrystalline medical-grade stainless steels prepared by powder metallurgy, J. Alloys Compd. 624 (2015) 17–21. [23] L. Vergani, G. Gobbi, C. Colombo, A numerical model to study the hydrogen embrittlement effect on low-alloy steels, in: A. Milazzo, MH. Aliabadi (Eds.), Key Eng. Mater. 2015, pp. 513–516.
[24] A. Tonneau, M. Gerland, G. Henaff, Environment-sensitive fracture of iron aluminides during cyclic crack growth, Metall. Mater. Trans. A 32 (2001) 2345–2356. [25] V. Olden, A. Saai, L. Jemblie, R. Johnsen, FE simulation of hydrogen diffusion in duplex stainless steel, Int. J. Hydrog. Energy 39 (2014) 1156–1163. [26] D.E. Jiang, C. Carter, Diffusion of interstitial hydrogen into and through bcc Fe from first principles, Phys. Rev. B 70 (2004). [27] J.H. Rose, F. Guinea, J. Ferrante, Universal features of the equation of state of metals, Phys. Rev. B 29 (1984) 2963–2969. [28] C. Wang, C. Zhang, Z. Yang, Austenite layer and precipitation in high Co–Ni maraging steel, Micron 67 (2014) 112–116. [29] K.J. Handerhan, W.M. Garrison, N.R. Moody, A comparison of the fracture behavior of two heats of the secondary hardening steel AF1410, Metall. Trans. A 20A (1989) 105–123. [30] T. Skiba, B. Baufeld, O. Van der Biest, Shaped metal deposition of 300 M steel, Proc. Inst. Mech. Eng. B J. Eng. Manuf. 225 (2011) 831–839. [31] A. Inoue, B.L. Shen, C.T. Chang, Fe- and Co-based bulk glassy alloys with ultrahigh strength of over 4000 MPa, Intermetallics 14 (2006) 936–944. [32] K.V. Rajkumar, A. Kumar, T. Jayakumar, B. Raj, K.K. Ray, Characterization of aging behavior in m250 grade maraging steel using ultrasonic measurements, Metall. Mater. Trans. A 38 (2007) 236–243. [33] H. Terasaki, H. Yamagishi, K. Moriguchi, Y. Tomio, Y. Komizo, Correlation between the thermodynamic stability of austenite and the shear modulus of polycrystalline steel alloy, J. Appl. Phys. 111 (2012) 93523. [34] F. Barrie, D.B. Futch, D.H.D. Hsu, M.V. Manuel, Effect of phase on debond strength in shape memory alloy reinforced composites, Mater. Des. 57 (2014) 98–102. [35] I.F. Golovnev, E.I. Golovneva, V.M. Fomin, Molecular-dynamic modeling of mechanical properties of free defect metal nanocrystals, Comput. Mater. Sci. 37 (2006) 336–348. [36] G. Pascale, Probabilistic approach and size effect in brittle materials under multiaxial stress states, Meccanica 19 (1984) 214–222. [37] L. Cao, X. Wang, Modification of size effect formula of fracture toughness of concrete for three-point bending specimens, J. Hohai Univ. Nat. Sci. 35 (2007) 63–66. [38] D. Figueroa, M.J. Robinson, The effects of sacrificial coatings on hydrogen embrittlement and re-embrittlement of ultra high strength steels, Corros. Sci. 50 (2008) 1066–1079. [39] B. Ji, H. Gao, Mechanical properties of nanostructure of biological materials, J. Mech. Phys. Solids 52 (2004) 1963–1990. [40] D.K. Yi, Z.M. Xiao, S.K. Tan, M. Fan, On elastic–plastic fracture behavior of a bi-layered composite plate with a sub-interface crack under mixed mode loading, Compos. Part B 60 (2014) 60–73. [41] G.B. Olson, Ferrium® m54® overview, http://www.questek.com/ferrium-m54.html2013. [42] J. Liang, L. Wang, Z. Li, B. Wang, F. Ding, Refinement of effective grain and enhancement of reverted austenite stability for AerMet 100 steel, Trans. Mater. Heat Treat. 31 (2010) 57–60. [43] R. Ayer, P.M. Machneier, Transmission electron-microscopy examination of hardening and toughening phenomena in Aermet-100, Metall. Trans. A 24 (1993) 1943–1955.
Contents lists available at ScienceDirect
Materials and Design journal homepage: www.elsevier.com/locate/jmad
Multi-scale simulation of hydrogen influenced critical stress intensity in high Co–Ni secondary hardening steel Chenchong Wang a, Chi Zhang a,⁎, Zhigang Yang a, Jie Su b, Yuqing Weng a,b a b
Key Laboratory of Advanced Materials of Ministry of Education, School of Materials Science and Engineering, Tsinghua University, Beijing 100084, China Institute for Structural Materials, Central, Iron and Steel Research Institute, Beijing 100081, China
a r t i c l e
i n f o
Article history: Received 4 May 2015 Received in revised form 19 June 2015 Accepted 9 August 2015 Available online 14 August 2015 Keywords: Multi-scale simulation Fracture toughness Hydrogen embrittlement
a b s t r a c t Hydrogen embrittlement was an important and long-standing problem in the fields of steels, especially ultrahigh strength steels. In order to simulate the ability of hydrogen embrittlement resistance for high Co–Ni secondary hardening steels, a multi-scale simulation method with four steps was used to calculate the critical stress intensity (KIC) and hydrogen influenced critical stress intensity (KISCC). For the four steps: the atomic scale and nm scale simulation were mainly used to simulate the effect of stress-assisted hydrogen diffusion at the crack tip; the μm scale simulation was used to handle the effect of microstructure; the cm simulation was used to analyze the size effect. As the effect of hydrogen concentration at the crack tip, the simulation results of critical cohesive strength of the Fe(110) at the crack tip decreased by 82.3%. The μm scale simulation showed the improvement of fracture toughness with the help of austenite layer between martensite laths. Compared with the mechanical properties of 300 M and AerMet100 steels, the accuracy of this simulation method was proved. © 2015 Elsevier Ltd. All rights reserved.
1. Introduction Hydrogen embrittlement (HE), which remained incompletely understood from the mechanistic point of view, was an important problem in the fields of steels for ships and subsea pipelines [1–3]. The susceptibility to hydrogen-induced delayed fracture of steels increased with strength increasing, therefore hydrogen embrittlement was one of the most serious challenges for ultra-high strength steels [4–6]. Since 1990s, much attention was paid to the strength and toughness improvement in high Co–Ni secondary hardening steels as AF1410 and AerMet 100, however, few of these steels had high ability of HE resistance [7–10]. Recently, several studies were made to develop new ultra-high strength steels, which had better HE resistance ability than usual high Co–Ni secondary hardening steels [11]. However, few details about the design methods of these steels, especially the mechanism of HE resistance, were reported. As a long-standing problem, HE was studied many great experts and many models were built to simulate the hydrogen influenced critical stress intensity in different kinds of steels [12–19]. Two of the most classical models for hydrogen-induced fracture simulation were the hydrogen enhanced local plasticity model (HELP) [18,19] and the hydrogen enhanced decohesion model (HEDE) [13]. In both of the models, the diffusion of hydrogen in the steels was considered and hydrogen fracture was regarded as a result of a critical combination of stress, strain and hydrogen concentration [12,16]. However, the microstructure of the ⁎ Corresponding author. E-mail address: [email protected] (C. Zhang).
http://dx.doi.org/10.1016/j.matdes.2015.08.040 0264-1275/© 2015 Elsevier Ltd. All rights reserved.
steels, which was also important for the fracture toughness for steels, was not considered in these two models [20–22]. In Jiang's model [15], first principle method was used to explain the cohesion–reduction mechanism of hydrogen embrittlement in steels, but its simulation results were limited to the atomic scale. It could not obtain the mechanical properties of steels without combining first principle method with other simulation methods. Finite element method (FEM) was widely used to simulate the macro-mechanical properties of steels [14], however, it probably ignored details in microscales as hydrogen diffusion at the crack tip and microstructure of the steels. In summary, HE was a complicated problem, which was affected by many factors from atomic scale to macroscale. In atomic scale, the hydrogen atom in the interstitial site could decrease the bonding strength of Fe atoms and make steels brittle. In nm scales, the hydrogen content at the crack tip was an important parameter which can affect the crack propagation. In μm scale, the microstructure had great effect on most mechanical properties of steels. In cm scale, the size effect was also an important factor for the fracture toughness of materials. All these factors were in different scales and they could not be solved by just one simulation method. Therefore, many multi-scale simulation models were developed to solve the problem [26–28]. Recently, Olden's study [28] reported a multi-scale simulation model which included both atomic and microstructure simulations. This model could clearly express the effect of microstructure on the diffusion of hydrogen. However, the model was not focused on calculating the value of macro properties. Hénaff [27] and Vergani [26] also did a lot of work on multiscale simulation which considered the effect of microstructure. However, the microstructure analysis in these models was focused on dislocation
502
C. Wang et al. / Materials and Design 87 (2015) 501–506
or plastic zone at the crack tip, not the phases in the steels. In present study, a multi-scale simulation model, which considered the phases in the steels, was used to calculate the value of hydrogen influenced critical stress intensity in high Co–Ni secondary hardening steels. Considering about the development of high Co–Ni secondary hardening steels, two hotspot steels (300 M and AerMet100 steels) were taken as examples to prove the accuracy of this simulation method. The details of simulation method were given in Section 2, followed by results and discussion in Section 3, and the conclusion was in Section 4. 2. Simulation method The applied model consisted of a four-step simulation procedure including atomic scale, nm scale, μm scale and cm scales. The export of every step was the import of next step. Table 1 showed the whole simulation procedure of this multi-scale simulation model. More details were explained as follows. 2.1. Atomic scale Several studies reported that hydrogen in steels preferred to stay on the Fe surface or subsurface as Fe(100) and Fe(110), instead of in bulk [29,30]. The first principle calculation showed that hydrogen atoms would decrease the cohesive strength of the Fe surface or subsurface when they concentrated on the Fe surface or subsurface [30]. In Jiang's model [15], the relation between hydrogen coverage (θ) and the critical cohesive strength (σc(θ)) of surface or subsurfaces in metal materials could be expressed by Eq. 1. According to Eq. 1, the value of σc(θ)/ σc(0) decreased from 1 to almost 0 with the increasing of hydrogen coverage (θ) at surface or subsurface. σ c ðθÞ ¼ 1−a1 θ þ a2 θ2 σ c ð0Þ
ð1Þ
[13], the stress-assisted diffusion of hydrogen was expressed by a modified Fick's law with respect to the hydrostatic stress (p) as Eq. 3. ∂C DV H DV H ∇C ∇p− C∇2 p ¼ D∇2 C− RT RT ∂t
ð3Þ
where C was the hydrogen concentration; D was the diffusion coefficient; VH was the partial molar volume of hydrogen in steel; R was the mole gas constant (8.314 J/mol K); and T was the absolute temperature (K). The relation between stress field (σ) and hydrostatic stress was p = Tr(σ)/3. The boundary condition was C ¼ C 0 epV H =RT . The hydrogen coverage was defined as a function of the hydrogen concentration as Eq. 4 [13]. θ¼
C C þ expð−Hs =RT Þ
ð4Þ
where Hs was the Gibbs free energy difference between interface and the surrounding materials. A 10 × 10 nm 2D model of crack tip was built by COMSOL Multiphysics as shown in Fig. 1(a). A time dependant load was applied on the top of the models in the y direction as shown in Fig. 1(b) and the bottom of the model was encastred. With the increase of the load, the stress at the crack tip would increase and hydrogen would concentrate to the crack tip based on Eq. 3. Therefore, with the increase of hydrogen coverage at the crack tip, the cohesive strength of Fe(110) at the crack tip would decrease based on Eq. 2. When the stress at the crack tip became equal to the cohesive strength, the crack propagation would form. It meant this model of crack tip could explain the effect of stress-assisted hydrogen diffusion on cohesive strength at crack tip and calculate the value of the critical cohesive strength of Fe(110) at the crack tip (σcc(θ)). 2.3. μm scale
As the matrix of most high Co–Ni secondary hardening steels was martensite, whose crystal structure was b.c.c. [31]. And the main fracture mode of high Co–Ni secondary hardening steels was quasicleavage fracture [9]. Therefore, to simplify the simulation process, Fe(110) was set as fracture plane. According to Jiang's model [15], the relation between hydrogen coverage and the cohesive strength of Fe(110) in Fe/H system was expressed by Eq. 2. σ c ðθÞ ¼ 1−1:0467θ þ 0:1687θ2 σ c ð0Þ
ð2Þ
2.2. nm scale In nm scale simulation, the stress-assisted diffusion of hydrogen at the crack tip was simulated by FEM, using the software of COMSOL Multiphysics. Eq. 2 was used as the import of nm scale simulation by processing it into the software of COMSOL Multiphysics. The nm scale simulation was based on HEDE mode [13]. According to HEDE mode
In μm scale simulation, FEM models based on the microstructure of steels were built using the software of ABAQUS. The value of σcc(0) and σcc(θ) obtained from atomic and nm scale simulation was used as the import of μm scale simulation. We optimized the loading values in μm scale simulation based on the critical cohesive stress obtained by nm scale simulation to make the cohesive strength in μm scale simulation equal to the value of σcc(0) and σcc(θ) obtained from atomic and nm scale simulation. According to TEM observation results reported by previous work [31], two contour integral models were built: martensite without austenite layer (model of 300 M) and martensite with 15 nm austenite layer (model of AerMet100). The property of martensite was elasticity with Em = 200GPa and v = 0.3 [32–34]. Austenite layers in the models were considered to be an elastic–plastic solid with Ea = Em/10GPa, v = 0.3, and σb = 580 MPa [35–38]. Because the crack propagation formed across the martensite as quasi-cleavage crack [9], the interface between martensite and austenite layer was set as ‘fixed’. A 4-node bilinear plane stress elements (CPS4R) were used in these 2D contour integral models. The uniaxial tensile loading was
Table 1 Simulation procedure of the multi-scale simulation model. Scales
Methods
Import
Export
Atomic (1–20 Å)
First principle
–
σ c ðθÞ σ c ð0Þ
nm (1–20 nm)
FEM (COMSOL)
σ c ðθÞ σ c ð0Þ
μm (1–10 μm) cm (1–5 cm)
FEM (ABAQUS) Empirical formula
¼ 1−a1 θ þ a2 θ2 σ cc ð0Þ σcc(θ), σcc(0) Microstructure information KIC(s), KISCC(s) (For μm scale)
¼ 1−a1 θ þ a2 θ σ cc ð0Þ θ, σcc(θ)
Influence factors 2
KIC(s), KISCC(s) (For small samples) KIC, KISCC (For actual samples)
Crystal orientation, composition Hydrogen diffusion Microstructure Size effect
C. Wang et al. / Materials and Design 87 (2015) 501–506
503
Fig. 1. 2D model of crack tip built by COMSOL Multiphysics: (a) structure and mesh; (b) time dependant load.
applied on the top of the models in the y direction and the bottom of the models was encastred. As Fig. 2 shows that, the crack region was meshed as annular units around the crack tip in order to calculate the KIC value of the models by contour integral. In contour integral models, the initial crack propagation direction was not only perpendicular to the austenite layer. The models in which the initial crack propagation direction was 30°, 45° and 60° to the austenite layers were built and their simulation results were similar with the models in which the initial crack propagation direction was just perpendicular to the austenite layer. It meant that the angles between the initial crack propagation direction and the austenite layer had little effect on the simulation results of KIC. Therefore, considering the length limit of the paper, only models in which the initial crack propagation direction was perpendicular to the austenite layer were shown in this paper. As the sizes of the contour integral models were only about 1 μm, only KIC and KISCC for μm scale (KIC(s), KISCC(s)) could be obtained by the μm scale simulation.
2.4. cm scale As the models used in nm and μm scale simulations were all 2D models with small sizes, the size effect should be considered in order to calculate the value of KIC and KISCC for actual samples used for experiment, so that the simulation results could be compared with the experiment results and the accuracy of the simulation could be analyzed. According to Weibull brittle failure theory [39], for the heterogeneous material with same ratio of crack length (a) and sample height (h), the ratio of KIC for μm scale (KIC(s)) and actual samples (KIC) was expressed by Eq. 5 [40]. KICðsÞ ¼ KIC
sffiffiffiffiffiffiffi hðsÞ V 1=α h V ð sÞ
ð5Þ
where V = sth; V(s) = s(s)t(s)h(s); s was length of the actual sample; t was thickness of the actual sample; h was height of the actual sample; s(s)
Fig. 2. Contour integral models built by ABAQUS.
504
C. Wang et al. / Materials and Design 87 (2015) 501–506
Table 2 Parameters used in the four-step simulation procedure. Name
Value
Name
Value
Name
Value
D VH C0 R T
1 × 10−9 cm2/s 2 cm3/mol 4.0 × 10−5 mol/cm3 8.314 J/(mol · K) 293 K
s t h a α
140 mm 15 mm 30 mm 15 mm 5
s(s) t(s) h(s) a(s) σcc(0)
600 nm 0.01 nm 300 nm 150 nm 500 MPa
was length of the μm scale sample; t(s) was thickness of the μm scale sample; h(s) was height of the μm scale sample; and α was Weibull coefficient. In cm scale simulation, the value of KIC and KISCC for μm scale (KIC(s), KISCC(s)) obtained from μm scale simulation was used as the import. Therefore, based on Eq. 5, the simulation results of KIC and KISCC for actual samples could be obtained. All the parameters used in the fourstep simulation procedure were shown in Table 2 [9,12,13,16,39–41].
Fig. 4. The change of total stress and cohesive strength at the crack tip with the increase of load.
3. Results and discussion 3.1. Stress-assisted hydrogen diffusion at the crack tip Fig. 3(a) showed the simulation results of the stress field at the crack tip given by COMSOL Multiphysics. It was clear that significant stress concentration formed at the crack tip. This stress concentration leaded to the hydrogen concentration as stress-assisted hydrogen diffusion (Fig. 3(b)). Similar simulation results of stress-assisted hydrogen diffusion were also reported by several previous works [12,13,16] and all the results also showed stress-assisted hydrogen concentration at the crack tip. It was certain that the stress at the crack tip increased with the increase of load. However, based on Eq. 2, the cohesive strength of the crack tip decreased with the increase of load because of the stressassisted hydrogen concentration at the crack tip. Fig. 4 showed the change of total stress (σt) and cohesive strength (σc) at the crack tip with the increase of load. At the cross point of the curves of total stress and cohesive strength, σt = σc = 88.3 MPa. It meant that the critical cohesive strength at the crack tip σcc(θ) = 88.3 MPa, at which the crack propagation began. As the effect of hydrogen concentration at the crack tip, the simulation results of critical cohesive strength of Fe(110) at the crack tip decreased by 82.3% (1 − σcc(θ)/σcc(0) ≈ 0.823). 3.2. Effect of microstructure on fracture toughness Fig. 5 showed the simulation results of the stress field obtained by ABAQUS. Significant stress concentration could be observed at the crack tip in the model of martensite without austenite layer as shown
in Fig. 5(a). However, with the same load, the stress concentration at the crack tip was greatly reduced by austenite layer in the model of martensite with 15 nm austenite layer as shown in Fig. 5(b). Therefore, the model of martensite with 15 nm austenite layer would have higher value of KIC than the model of martensite without austenite layer. In previous works, several reports about the simulation of natural biological materials or layered composites drew similar conclusion that soft layers in a hard material would probably reduce the stress concentration at the crack tip and improve the fracture toughness of the material [42,43]. After adding the value of σcc(0) and σcc(θ) into the contour integral models (make the stress at the crack tip meet the predetermined value by changing the load applied on the models), the results of KIC and KISCC for small samples were obtained as shown in Table 3. The calculation results clearly showed the improvement of fracture toughness with the help of austenite layer. 3.3. Comparison of simulation and experiment results The simulation results of actual samples were obtained by cm scale simulation. As the mechanical properties of high Co–Ni secondary hardening steels were studied by several previous works [23–25], it would not be tested again in this study. The comparison of simulation and experiment results was shown as Table 4. According to the TEM observation results in previous works [9,28], martensite without austenite layer model was used to simulate 300 M steel and martensite with 15 nm austenite layer model was used to simulate AerMet100 steel in μm scale simulation. Because the experiment results of KISCC for 300 M
Fig. 3. The results of nm scale simulation: (a) stress distribution; (b) hydrogen distribution.
C. Wang et al. / Materials and Design 87 (2015) 501–506
505
Fig. 5. The results of μm scale simulation: (a) martensite without austenite layer; (b) martensite with 15 nm austenite layer.
models and more factors should be considered in order to obtain reasonable results.
Table 3 pffiffiffiffiffi The results of KIC and KISCC for μm scale (unit: MPa m).
KIC(s) KISCC(s)
Martensite without austenite layer
Martensite with 15 nm austenite layer
4. Conclusion
1321 241
3104 554
A four-step multi-scale simulation model was built to calculate the KIC and KISCC value for 300 M and AerMet100 steels. The effect of stress-assisted hydrogen diffusion, microstructure and size effect had been mainly considered in this model.
was too small with a big error range, so the simulation and experiment results of KISCC for 300 M had a difference. For other values, the difference between the simulation results and the experiment results were less than 8%. Therefore, the simulation results were basically consistent with the experiment results for 300 M and AerMet 100 steels. As the calculation results reported by Olson [11], all the main alloy elements (Ni, Co, Cr, Mo) in 300 M and AerMet100 had little effect on the cohesive strength of crystal plane. Therefore, for the atomic scale simulation in this paper, the system was simplified as Fe/H system without considering the effect of other elements. However, for other kinds of high Co–Ni secondary hardening steels, such as M54 which contained W and V [41], the effect of composition could not be ignored. If the steels contained the elements which had significant effect on cohesive strength (as W, V, B and Re), more work about first principle method should be added to the atomic scale simulation in order to revise Eq. 2, which showed the effect of elements on cohesive strength. For the nm scale simulation, Eq. 3 could be revised by adding the effect of strain [12]. Also, the initial hydrogen content (C0) and hydrogen diffusion coefficient (D) for different steels could be tested by hydrogen permeation technique or galvanostatic charging technique [9], in order to optimize the parameters in the models. For the μm scale simulation, the model should been built based on the actual microstructure of the steels. For AerMet100, the precipitates in the matrix were very small (10 nm in length) [28,43], so the FEM models for μm scale simulation were built as martensite and austenite layer, without considering the precipitates formed in the matrix. However, for the steels which had inclusions in large size and belonged to inclusion induced failure, the structure of precipitates should be added into the FEM models. In summary, the simulation process in this paper just provided a basic framework of multi-scale simulation, which was suitable for several common maraging steels. For other kinds of steels, more details should be added into the Table 4 pffiffiffiffiffi Comparison of simulation and experiment results (unit: MPa m). 300 M
Simulation results Experiment results
AerMet100
KIC
KISCC
KIC
KISCC
51.5 50
9.4 5–30
121.1 115
21.6 20
(1) As the increase of the load applied on the crack tip area, the hydrogen concentration formed at the crack tip by stress-assisted hydrogen diffusion. With the effect of hydrogen, value of the critical cohesive strength of Fe(110) at the crack tip decreased by 82.3%. (2) Stress concentration at the crack tip was greatly reduced by austenite layer. The KIC value for the model of martensite with 15 nm austenite layer (AerMet100) was 1.6 times larger than the KIC value for the model of martensite without austenite layer (300 M). (3) Because the experiment results of KISCC for 300 M was too small with a big error range, so the simulation and experiment results of KISCC for 300 M had a difference. For other values, the simulation results were basically consistent with the experiment results.
Acknowledgments This work was financially supported by National Basic Research Programs of China (No. 2015CB654802 and No. 2015GB118001). The financial support provided by the National Natural Science Foundation of China (Grant No. 51471094) was greatly acknowledged. References [1] Y. Qi, H. Luo, S. Zheng, C. Chen, Z. Lv, M. Xiong, Comparison of tensile and impact behavior of carbon steel in H2S environments, Mater. Des. 58 (2014) 234–241. [2] T.E. García, C. Rodríguez, F.J. Belzunce, I. Peñuelas, B. Arroyo, Development of a methodology to study the hydrogen embrittlement of steels by means of the small punch test, Mater. Sci. Eng. A 626 (2015) 342–351. [3] K. Jeong-Hyeon, K. Seul-Kee, K. Myung-Hyun, L. Jae-Myung, Numerical model to predict deformation of corrugated austenitic stainless steel sheet under cryogenic temperatures for design of liquefied natural gas insulation system, Mater. Des. 57 (2014) 26–39. [4] S. Zhang, Y. Huang, B. Sun, Q. Liao, H. Lu, B. Jian, et al., Effect of Nb on hydrogeninduced delayed fracture in high strength hot stamping steels, Mater. Sci. Eng. A 626 (2015) 136–143. [5] X. Zhu, W. Li, T.Y. Hsu, S. Zhou, L. Wang, X. Jin, Improved resistance to hydrogen embrittlement in a high-strength steel by quenching–partitioning–tempering treatment, Scr. Mater. 97 (2015) 21–24.
506
C. Wang et al. / Materials and Design 87 (2015) 501–506
[6] J. Rehrl, K. Mraczek, A. Pichler, E. Werner, Mechanical properties and fracture behavior of hydrogen charged AHSS/UHSS grades at high- and low strain rate tests, Mater. Sci. Eng. A 590 (2014) 360–367. [7] C. Yao, T. Wang, J. Ren, W. Xiao, A comparative study of residual stress and affected layer in Aermet100 steel grinding with alumina and cBN wheels, Int. J. Adv. Manuf. Technol. 74 (2014) 125–137. [8] G. Ji, F. Li, Q. Li, H. Li, Z. Li, A comparative study on Arrhenius-type constitutive model and artificial neural network model to predict high-temperature deformation behaviour in Aermet100 steel, Mater. Sci. Eng. A 528 (2011) 4774–4782. [9] D. Figueroa, M.J. Robinson, Hydrogen transport and embrittlement in 300 M and AerMet100 ultra high strength steels, Corros. Sci. 52 (2010) 1593–1602. [10] M.D. Mulholland, D.N. Seidman, Nanoscale co-precipitation and mechanical properties of a high-strength low-carbon steel, Acta Mater. 59 (2011) 1881–1897. [11] G.B. Olson, Genomic materials design: the ferrous frontier, Acta Mater. 61 (2013) 771–781. [12] A. Alvaro, V. Olden, O.M. Akselsen, 3D cohesive modelling of hydrogen embrittlement in the heat affected zone of an X70 pipeline steel—part II, Int. J. Hydrog. Energy 39 (2014) 3528–3541. [13] S. Serebrinsky, A quantum-mechanically informed continuum model of hydrogen embrittlement, J. Mech. Phys. Solids 52 (2004) 2403–2430. [14] M. Sun, K. Xiao, C. Dong, X. Li, P. Zhong, Effect of stress on electrochemical characteristics of pre-cracked ultrahigh strength stainless steel in acid sodium sulphate solution, Corros. Sci. 89 (2014) 137–145. [15] D.E. Jiang, E.A. Carter, First principles assessment of ideal fracture energies of materials with mobile impurities: Implications for hydrogen embrittlement of metals, Acta Mater. 52 (2004) 4801–4807. [16] V. Olden, A. Alvaro, O.M. Akselsen, Hydrogen diffusion and hydrogen influenced critical stress intensity in an API X70 pipeline steel welded joint—experiments and FE simulations, Int. J. Hydrog. Energy 37 (2012) 11474–11486. [17] A.H.M. Krom, H.J. Maier, R.W.J. Koers, A. Bakker, The effect of strain rate on hydrogen distribution in round tensile specimens, Mater. Sci. Eng. A 271 (1999) 22–30. [18] C. Beachem, A new model for hydrogen-assisted cracking, Metall. Mater. Trans. B 441–55 (1972). [19] H.K. Birnbaum, P. Sofronis, Hydrogen-enhanced localized plasticity-a mechanism for hydrogen-related fracture, Mater. Sci. Eng. A 176 (1994) 191–202. [20] X. Li, Y. Fan, X. Ma, S.V. Subramanian, C. Shang, Influence of martensite–austenite constituents formed at different intercritical temperatures on toughness, Mater. Des. 67 (2015) 457–463. [21] A. García-Prieto, M.D. Ramos-Lotito, D. Gutiérrez-Campos, P. Pena, C. Baudín, Influence of microstructural characteristics on fracture toughness of refractory materials, J. Eur. Ceram. Soc. 35 (2015) 1955–1970. [22] M. Javanbakht, M.J. Hadianfard, E. Salahinejad, Microstructure and mechanical properties of a new group of nanocrystalline medical-grade stainless steels prepared by powder metallurgy, J. Alloys Compd. 624 (2015) 17–21. [23] L. Vergani, G. Gobbi, C. Colombo, A numerical model to study the hydrogen embrittlement effect on low-alloy steels, in: A. Milazzo, MH. Aliabadi (Eds.), Key Eng. Mater. 2015, pp. 513–516.
[24] A. Tonneau, M. Gerland, G. Henaff, Environment-sensitive fracture of iron aluminides during cyclic crack growth, Metall. Mater. Trans. A 32 (2001) 2345–2356. [25] V. Olden, A. Saai, L. Jemblie, R. Johnsen, FE simulation of hydrogen diffusion in duplex stainless steel, Int. J. Hydrog. Energy 39 (2014) 1156–1163. [26] D.E. Jiang, C. Carter, Diffusion of interstitial hydrogen into and through bcc Fe from first principles, Phys. Rev. B 70 (2004). [27] J.H. Rose, F. Guinea, J. Ferrante, Universal features of the equation of state of metals, Phys. Rev. B 29 (1984) 2963–2969. [28] C. Wang, C. Zhang, Z. Yang, Austenite layer and precipitation in high Co–Ni maraging steel, Micron 67 (2014) 112–116. [29] K.J. Handerhan, W.M. Garrison, N.R. Moody, A comparison of the fracture behavior of two heats of the secondary hardening steel AF1410, Metall. Trans. A 20A (1989) 105–123. [30] T. Skiba, B. Baufeld, O. Van der Biest, Shaped metal deposition of 300 M steel, Proc. Inst. Mech. Eng. B J. Eng. Manuf. 225 (2011) 831–839. [31] A. Inoue, B.L. Shen, C.T. Chang, Fe- and Co-based bulk glassy alloys with ultrahigh strength of over 4000 MPa, Intermetallics 14 (2006) 936–944. [32] K.V. Rajkumar, A. Kumar, T. Jayakumar, B. Raj, K.K. Ray, Characterization of aging behavior in m250 grade maraging steel using ultrasonic measurements, Metall. Mater. Trans. A 38 (2007) 236–243. [33] H. Terasaki, H. Yamagishi, K. Moriguchi, Y. Tomio, Y. Komizo, Correlation between the thermodynamic stability of austenite and the shear modulus of polycrystalline steel alloy, J. Appl. Phys. 111 (2012) 93523. [34] F. Barrie, D.B. Futch, D.H.D. Hsu, M.V. Manuel, Effect of phase on debond strength in shape memory alloy reinforced composites, Mater. Des. 57 (2014) 98–102. [35] I.F. Golovnev, E.I. Golovneva, V.M. Fomin, Molecular-dynamic modeling of mechanical properties of free defect metal nanocrystals, Comput. Mater. Sci. 37 (2006) 336–348. [36] G. Pascale, Probabilistic approach and size effect in brittle materials under multiaxial stress states, Meccanica 19 (1984) 214–222. [37] L. Cao, X. Wang, Modification of size effect formula of fracture toughness of concrete for three-point bending specimens, J. Hohai Univ. Nat. Sci. 35 (2007) 63–66. [38] D. Figueroa, M.J. Robinson, The effects of sacrificial coatings on hydrogen embrittlement and re-embrittlement of ultra high strength steels, Corros. Sci. 50 (2008) 1066–1079. [39] B. Ji, H. Gao, Mechanical properties of nanostructure of biological materials, J. Mech. Phys. Solids 52 (2004) 1963–1990. [40] D.K. Yi, Z.M. Xiao, S.K. Tan, M. Fan, On elastic–plastic fracture behavior of a bi-layered composite plate with a sub-interface crack under mixed mode loading, Compos. Part B 60 (2014) 60–73. [41] G.B. Olson, Ferrium® m54® overview, http://www.questek.com/ferrium-m54.html2013. [42] J. Liang, L. Wang, Z. Li, B. Wang, F. Ding, Refinement of effective grain and enhancement of reverted austenite stability for AerMet 100 steel, Trans. Mater. Heat Treat. 31 (2010) 57–60. [43] R. Ayer, P.M. Machneier, Transmission electron-microscopy examination of hardening and toughening phenomena in Aermet-100, Metall. Trans. A 24 (1993) 1943–1955.