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Analysis of fracture toughness in high Co–Ni secondary hardening steel using FEM
Author’s Accepted Manuscript Analysis of fracture toughness in High CO-NI secondary hardening steel using FEM Chenchong Wang, Chi Zhang, Zhigang Yang, Jie Su, Yuqing Weng www.elsevier.com/locate/msea
PII: DOI: Reference:
S0921-5093(15)30251-3 http://dx.doi.org/10.1016/j.msea.2015.08.003 MSA32637
To appear in: Materials Science & Engineering A Received date: 5 May 2015 Revised date: 30 July 2015 Accepted date: 1 August 2015 Cite this article as: Chenchong Wang, Chi Zhang, Zhigang Yang, Jie Su and Yuqing Weng, Analysis of fracture toughness in High CO-NI secondary hardening steel using FEM, Materials Science & Engineering A, http://dx.doi.org/10.1016/j.msea.2015.08.003 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Analysis of Fracture Toughness in High Co-Ni Secondary Hardening Steel Using FEM
Chenchong Wang1,Chi Zhang1,*, Zhigang Yang1, Jie Su2, Yuqing Weng1,2
1.
Key Laboratory of Advanced Materials of Ministry of Education, School of Materials Science and
Engineering, Tsinghua University, Beijing 100084, China
2.
Institute for Structural Materials,Central, Iron and Steel Research Institute,Beijing 100081, China
Corresponding AuthorE-mail address: [email protected]
Abstract The microstructure and mechanical properties of ultrahigh strength steels (300M, Aermet100 and M54) was analyzed. The experiment results showed that the steels with austenite layers at the boundary of martensite laths had higher KIC than those without austenite layers. Finite element method (FEM) was used to establish models based on the actual microstructure of the steels. Extended finite element method (XFEM) was used to study the crack path and crack growth rate. Contour integral method(CIM) was used to study the best thickness of austenite layer, the effect of crack propagation direction and the value of KIC. According to the simulation results,
10-15nm was the best thickness of austenite layer for the fracture toughness of the steels with martensite as matrix. The simulation results of normalized value of KIC were close to the experimental results.
Keywords: Austenite layer; fracture toughness; finite element method.
1. Introduction Ultrahigh strength steels have been receiving great attention for a long time[1-3]. Before the development of high Co-Ni secondary hardening steels, experimental study on the ultrahigh strength steel was mainly limited to increasing strength and few reports were on the breakthrough of optimizing both strength and toughness[4]. Over the past several decades, the studies on high Co-Ni secondary hardening steels resulted in the successful development of HY-180, AF 1410, AerMet100, and more recently, M54[5, 6]. As commercial steels, AerMet100 and M54 greatly increased the fracture toughness (especially KIC) of the traditional ultrahigh strength steels and partly replaced 300M steel in application[7, 8]. It is generally accepted that fracture toughness of steels strongly depends on the microstructure[9].In 1970’s, Rice and Johnson[10] reported that decreasing the size of precipitates in the matrix of the steel could decrease the crack growth rate effectively and increase the fracture toughness. Recently, several studies about material design suggested that soft phase layer had an important role in crack trapping and inhibiting the crack propagation[11, 12]. Therefore, in order to further enhance fracture toughness and hydrogen embrittlement (HE) resistence of secondary hardening steel,
the austenite layers formed between martensite lath boundaries in AerMet100 and M54 were of great concern[6, 8, 13, 14]. Although TEM observation results of austenite layers were reported in several studies about AerMet100 and M54[6, 8, 13], few discussion was made on the specific function of the austenite layers and the mechanism of fracture toughness improvement in high Co-Ni secondary hardening steels. In this paper, the actual microstructure of AerMet100 and M54 was observed by TEM and the relationship between austenite layers and fracture toughness was analyzed. According to the characteristic of actual microstructure, Extended finite element method (XFEM) and contour integral method (CIM) finite element models were developed to analyze the crack propagation and fracture toughness in high Co-Ni secondary hardening steel.
2. Materials and methods 300M, AerMet100 and M54 steels were chosen for the present study. The main composition of the steels in this study was listed in Table.1. All the steels subjected the optimum heat treatment. Specimens of M54 were austenitized at 1060oC for 1.5h and quenched in oil to room temperature. Then immediately transferred to a cryogenic bath held at -73oC for 2h, and finally aged at 515oC for 8h. The specimens of AerMet100 were austenitized at 890oC for 1h and quenched in oil to room temperature. Then immediately transferred to a cryogenic bath held at -73oC for 2h, and finally aged at 482oC for 8h. Specimens of 300M were austenitized at 870oC for 1h and quenched in oil to room temperature, then aged at 315oC for 2h.
Thin foils for TEM were cut from the specimens and ground to a thickness of about 50μm. The thin foils were electropolished in a perchloric acid-ethanol solution at -30 to -40oC. All the TEM samples were observed by JEOL JEM2011 (Japan Electron Optics Ltd., Tokyo) at 200kV. KIC was measured by precracked (W/B=2, a/W = 0.45 to 0.55) three-point single edge bend specimens (10×10×55mm) and standard compact tension specimens (25.4mm in thickness) using linear elastic fracture mechanics (LEFM) criteria per ASTM 399-90.
3.Microstructure and fracture toughness results As traditional ultra-high strength steel, the microstructure of 300M was reported in detail by many studies[15-17]. The conclusion in previous studies was that the microstructure of 300M included martensite/bainite laths as matrix and carbides as precipitation in matrix[15-17]. No austenite layers were observed in the previous or present studies of 300M. In 1993, Ayer and Machmeier[8] reported the microstructure of AerMet100. In Ayer and Machmeier’s study, besides martensite laths and carbides precipitation (M2C), austenite layers were observed at the boundary of martensite laths in AerMet100 and the thickness of the austenite layers were about 3nm[8]. In present study, austenite layers at the boundary of martensite laths in AerMet100 were also observed (Fig.1), but the thickness was from 3 to 10nm. Recently, M54, as new kind of high Co-Ni secondary hardening steel, was developed and studied. Wang et al.[5] reported the microstructure of M54 in detail. In Wang’s study[5], the austenite layers, which were very similar with those in AerMet100, was also observed in M54.
In present study, the thickness of the austenite layers in M54 was from 5 to 20nm as Fig.2 showed. The electron diffraction of the austenite layers and XRD results were reported by previous work, so it would not be mentioned again in this study. These special austenite layers were reported by many studies[5, 8], but few studies reported the formation mechanism of these austenite layers. More experiments and analysis should be made to explain the formation mechanism of these austenite layers in future studies. Traditional mechanical properties as tensile strength, yield strength and hardness of high Co-Ni secondary hardening steels were reported by many studies[4, 8], so these traditional data would not be reported in this study again. Now, most experts mainly paid attention to the fracture toughness of high Co-Ni secondary hardening steels, which was mainly discussed in this study. Fracture toughness (KIC) of the steels was measured and the results were close to the optimal value reported in the previous studies[4, 8]. Based on the results from both previous and present studies, the microstructure and fracture toughness of 300M, AerMet100 and M54 was summarized in Table.2. As Table.2 shown, the steels with austenite layers at the boundary of martensite laths (AerMet100/M54) had higher KIC than those without austenite layers (300M).
4. Finite element models 4.1 XFEM model Based on TEM observation results, two XFEM models were built: martensite
without austenite layer (XFEM model 1) and martensite with austenite layer (XFEM model 2) as Fig.3. The thickness of martensite laths in all the models was set to 150nm according to the TEM observation results. The property of martensite was elasticity with EM= 200GPa and v=0.3[18-20]. As the austenite layer in AerMet100 and M54 was very different with traditional austenite. It has great lattice distortion which make its lattice constant instable. Also, the residual stress in this layer may cause the deformation of the layer before loading[5]. Therefore, austenite layers in the models were considered to be an elastic-plastic solid with EA= EM/10GPa,v = 0.3,
s 380 MPa and b 580 MPa[21-24]. Because the crack propagation formed across the martensite as quasi-cleavage crack[6, 7], the interface between martensite and austenite layer was set as ‘fixed’. A 4-node bilinear plane strain elements (CPE4R) were used in these 2D XFEM models. The uniform increasing displacement loading was applied on the top and bottom of the models in the y direction. In actual material, the thickness of austenite layers was only 3-20nm. However, for simulation, this thickness was too small for us to see the effect of austenite layers on crack propagation. In order to make the simulation results of crack propagation direction clear, the thickness of the austenite layer in XFEM model 2 was set to 50nm, instead of 3-20nm. Also, in these XFEM models, the initial crack propagation direction was perpendicular to the austenite layer and no crystal orientation was considered in the models. In these situations, these XFEM models still had big differences with actual materials, so it could only qualitatively explain the effect of austenite layers on crack propagation. The simulation results could not show the real crack propagation in
actual materials. 4.2 CIM model Based on TEM observation results, five CIM models were built: martensite without austenite layer (CIM model 1), martensite with 5nm austenite layer (CIM model 2), 10nm austenite layer (CIM model 3), 15nm austenite layer (CIM model 4) and 20nm austenite layer (CIM model 5). Other parameters, as the thickness of martensite laths and the property of phases, were the same with XFEM models. A 4-node bilinear plane stress elements (CPS4R) were used in these 2D CIM models. In CIM models, we simulated the critical state when crack propagation just began, in order to calculate the KIC value. So, the loading value used in CIM models was a constant value. According to the simulation results of crack propagation by XFEM models, we could determine the loading value, which could make the material in the critical state when crack propagation just began. The uniaxial tensile loading was applied on the top of the models in the y direction and the bottom of the models was encastred. As Fig.4 shown, 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 CIM models, the initial crack propagation direction was not only perpendicular to the austenite layer. The models in which the initial crack propagation direction was 30o (CIM model 6) and 45o (CIM model 7) to the austenite layers were built as Fig.5. Their simulation results were compared with the models in which the initial crack propagation direction was just perpendicular to the austenite layer (CIM model 4). In CIM models, the sizes of the materials built in the models were much smaller than the
sizes of actual specimens which were used for the KIC testing in experiments. Therefore, without considering the size effect and crystal orientation, the absolute values of KIC calculated by these contour integral models were meaningless. However, the normalized value could be used to prove the accuracy of these models.
5. Simulation results and discussion 5.1 Crack propagation XFEM method was widely used to simulate the crack propagation in steels, especially dual-phase steels[9, 25, 26]. Based on previous study, when the longitudinal tensile loading was applied on an isotropic material with a transverse micro-crack, the direction of crack propagation tended to be transverse as a straight line[27]. However, for the dual-phase steels, the different properties between two phases (martensite/bainite or martensite/ferrite) in the steels could change the direction of crack propagation[9, 25, 26]. Fig.6 showed the simulation results of XFEM models in present study. For XFEM model 1 (martensite without austenite layer), crack propagation was along the X axis as a straight line and the spending time for the crack propagation process was about 0.2 (Fig.6 (a)). For XFEM model 2 (martensite with austenite layer), the direction of crack propagation was changed by austenite layer and the spending time for the crack to path through austenite layer was about 0.6 (Fig.6 (b)). Although these models were only qualitative models which couldn’t show the real crack propagation in actual materials as mentioned in Part 4.1, but we can draw the basic conclusion from the simulation results that austenite layer
could change the direction of crack propagation and decreased the crack growth rate. That meant, compared with the steels without austenite layers, energy consumption of crack propagation increased and fracture toughness was improved for the steels with austenite layers. Therefore, the simulation results of XFEM models qualitatively explained that austenite layers could improve the fracture toughness of high Co-Ni secondary hardening steel
5.2 Effect of crack propagation direction As the results of XFEM simulation, the austenite layer could change the crack propagation direction. Therefore, not all the crack propagation direction was just perpendicular to the austenite layer and the effect of crack propagation direction on the calculation of KIC should be analyzed. Fig.7 showed the results of stress field at the crack tip in CIM model 4, CIM model 6 and CIM model 7. All these models had 15nm austenite layer, but their crack propagation direction was different. As Fig.7, the stress field at the crack tip in all these models was similar. The value of KIC for CIM model 4, CIM model 6 and CIM model 7 was respectively 334.4, 320.5 and 307.0 MPa m . It meant the angles between the initial crack propagation direction and the austenite layer had little effect on the simulation results of K IC. Therefore, during the calculation of KIC, the models can be simplified, without considering the difference of initial crack propagation direction.
5.3 Stress field and KIC
Fig.8 showed the simulation results of stress field at the crack tip in CIM model 1 to CIM model 5. As the results in Fig.8 (a), significant stress concentration formed at the crack tip of CIM model 1(martensite without austenite layer). This stress concentration was greatly reduced by adding austenite layer at the boundary of matensite laths (Fig.8 (b)-(e)). However, when the thickness of the austenite layer was only 5nm, stress concentration formed behind the austenite layer (Fig.8 (b)). Fig.9 showed the relations between stress and distance from the crack tip for CIM models. It could be seen that stress concentration formed behind the layer when the layer’s thickness was less than 10nm. And when the thickness of austenite layer was larger than 15nm, the results were similar with the CIM model 4, whose thickness of austenite layer was just 15nm. All the simulation results in CIM models were similar with the well known solutions for crack propagation in layered materials with alternating hard and soft layers[11]. Based on the simulation results in CIM models, if the thickness of austenite layer was less than 10nm, the stress concentration still formed behind the austenite layer. That meant the austenite layer was too thin to reduce the stress concentration in this case. Also, if the thickness of austenite layer was larger than 15nm, its function is the same with the layers which was just 15nm in thickness. In addition, for the actual materials, an austenite in large size would become less homogeneous than an austenite in small size. Therefore, for austenite layer, the increase of its size would probably lead to the decrease of its property. In summary, although the simulation results showed no difference between the materials with 15nm and 20nm austenite layers, but the materials with 15nm austenite layers
would probably have better mechanical properties than the materials with 20nm austenite layers in actual situation because 15nm austenite layers would probably be more homogeneous and have better properties than 20nm austenite layers. In this case, there is no need to increase the thickness of austenite layer to larger than 15nm. Therefore, 10-15nm is the best thickness of austenite layer for the fracture toughness of the steels with martensite as matrix. The simulation and experimental results of KIC was listed in Table.3. As all the CIM models were 2D shell models without considering size effect and crystal orientation, all the simulation results of KIC belong to plane stress state. But the experimental results of KIC belong to plane strain state. According to theory of elastic mechanics[28], the calculation results of KIC should be larger than the experimental results. Therefore, as Table.3 shown, the absolute value of KIC obtained by simulation was larger than the value obtained by experiments. But the simulation results of normalized value were close to the experimental results.
6. Conclusion (1) As experimental results, the steels with austenite layers at the boundary of martensite laths (AerMet100/M54) had higher KIC than those without austenite layers (300M). (2) As XFEM simulation results, austenite layer changed the direction of crack propagation and decreased the crack growth rate. Therefore, compared with the steels without austenite layers, energy consumption of crack propagation increased and
fracture toughness was improved for the steels with austenite layers. (3) As CIM simulation results. 10-15nm is the best thickness of austenite layer for the fracture toughness of the steels with martensite as matrix. The angles between the initial crack propagation direction and the austenite layer had little effect on the simulation results of KIC. (4) Because the models used in present study were all 2D shell models without considering size effect and crystal orientation, the absolute value of KIC obtained by simulation was larger than the value obtained by experiments. But the simulation results of normalized value were close to the experimental results.
Acknowledgements This work was financially supported by National Basic Research Programs of China (No.2015GB118001 and No.2015CB654802). Greatly acknowledged the financial support provided by the National Natural Science Foundation of China (Grant No. 51471094). The authors acknowledge the assistance of J.M. Zhao and her group in Department of Engineering Mechanics in Tsinghua University with the FEM modeling.
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Figure Captions Fig.1 Austenite layers at the boundary of martensite laths in AerMet100: (a) 5nm in thickness;
(b) 10nm in thickness.
Fig.2 Austenite layers at the boundary of martensite laths in M54: (a) 5nm in thickness;
(b) 10nm in thickness;
(c) bright-field image;
(d) dark-field image.
Fig.3 The structure and mesh of XFEM models. Fig.4 The structure and mesh of CIM models. Fig.5 The CIM models with different crack propagation direction. Fig.6 The simulation results of XFEM models: (a) XFEM model 1; model 2.
(b) XFEM
Fig.7 The simulation results of CIM models with different crack propagation direction: (a) CIM model 4;
(b) CIM model 6;
(c) CIM model 7.
Fig.8 The simulation results of CIM models: (a) CIM model 1; (c) CIM model 3;
(d) CIM model 4;
(b) CIM model 2;
(e) CIM model 5.
Fig.9 The relations between stress and distance from the crack tip for CIM models.
Table.1 Main composition of the steels (wt. %). Table.2 Microstructure and fracture toughness of the steels. Table.3 The simulation and experimental results of KIC.
Table.1 Main composition of the steels (wt. %) Main composition (wt.%) Steel
C
Ni
Co
Mo
W
Cr
V
Si
Mn
M54
0.3
10.07
7.31
2.31
1.3
1.17
0.11
0.13
--
AerMet100
0.25
11.59
13.64
1.40
--
3.26
--
0.14
--
300M
0.4
1.83
--
0.40
--
0.85
0.1
1.56
0.75
Table.2 Microstructure and fracture toughness of the steels Steel
With/Without austenite layer
Thichness of austenite layer (nm)
KIC (MPa m )
300M AerMet100
Without With
-3-10
50 110
M54
With
5-20
115
Table.3The simulation and experimental results of KIC The absolute value of KIC (MPa m )
The normalized value of KIC
130.4
1.0
296.1
2.3
334.4
2.5
300M
50
1.0
AerMet100
110
2.2
M54
115
2.3
M-0nm A layer (CI model 1) Simulation results
Experimental results
M-10nm A layer (CI model 3) M-15nm A layer (CI model 4)
PII: DOI: Reference:
S0921-5093(15)30251-3 http://dx.doi.org/10.1016/j.msea.2015.08.003 MSA32637
To appear in: Materials Science & Engineering A Received date: 5 May 2015 Revised date: 30 July 2015 Accepted date: 1 August 2015 Cite this article as: Chenchong Wang, Chi Zhang, Zhigang Yang, Jie Su and Yuqing Weng, Analysis of fracture toughness in High CO-NI secondary hardening steel using FEM, Materials Science & Engineering A, http://dx.doi.org/10.1016/j.msea.2015.08.003 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Analysis of Fracture Toughness in High Co-Ni Secondary Hardening Steel Using FEM
Chenchong Wang1,Chi Zhang1,*, Zhigang Yang1, Jie Su2, Yuqing Weng1,2
1.
Key Laboratory of Advanced Materials of Ministry of Education, School of Materials Science and
Engineering, Tsinghua University, Beijing 100084, China
2.
Institute for Structural Materials,Central, Iron and Steel Research Institute,Beijing 100081, China
Corresponding AuthorE-mail address: [email protected]
Abstract The microstructure and mechanical properties of ultrahigh strength steels (300M, Aermet100 and M54) was analyzed. The experiment results showed that the steels with austenite layers at the boundary of martensite laths had higher KIC than those without austenite layers. Finite element method (FEM) was used to establish models based on the actual microstructure of the steels. Extended finite element method (XFEM) was used to study the crack path and crack growth rate. Contour integral method(CIM) was used to study the best thickness of austenite layer, the effect of crack propagation direction and the value of KIC. According to the simulation results,
10-15nm was the best thickness of austenite layer for the fracture toughness of the steels with martensite as matrix. The simulation results of normalized value of KIC were close to the experimental results.
Keywords: Austenite layer; fracture toughness; finite element method.
1. Introduction Ultrahigh strength steels have been receiving great attention for a long time[1-3]. Before the development of high Co-Ni secondary hardening steels, experimental study on the ultrahigh strength steel was mainly limited to increasing strength and few reports were on the breakthrough of optimizing both strength and toughness[4]. Over the past several decades, the studies on high Co-Ni secondary hardening steels resulted in the successful development of HY-180, AF 1410, AerMet100, and more recently, M54[5, 6]. As commercial steels, AerMet100 and M54 greatly increased the fracture toughness (especially KIC) of the traditional ultrahigh strength steels and partly replaced 300M steel in application[7, 8]. It is generally accepted that fracture toughness of steels strongly depends on the microstructure[9].In 1970’s, Rice and Johnson[10] reported that decreasing the size of precipitates in the matrix of the steel could decrease the crack growth rate effectively and increase the fracture toughness. Recently, several studies about material design suggested that soft phase layer had an important role in crack trapping and inhibiting the crack propagation[11, 12]. Therefore, in order to further enhance fracture toughness and hydrogen embrittlement (HE) resistence of secondary hardening steel,
the austenite layers formed between martensite lath boundaries in AerMet100 and M54 were of great concern[6, 8, 13, 14]. Although TEM observation results of austenite layers were reported in several studies about AerMet100 and M54[6, 8, 13], few discussion was made on the specific function of the austenite layers and the mechanism of fracture toughness improvement in high Co-Ni secondary hardening steels. In this paper, the actual microstructure of AerMet100 and M54 was observed by TEM and the relationship between austenite layers and fracture toughness was analyzed. According to the characteristic of actual microstructure, Extended finite element method (XFEM) and contour integral method (CIM) finite element models were developed to analyze the crack propagation and fracture toughness in high Co-Ni secondary hardening steel.
2. Materials and methods 300M, AerMet100 and M54 steels were chosen for the present study. The main composition of the steels in this study was listed in Table.1. All the steels subjected the optimum heat treatment. Specimens of M54 were austenitized at 1060oC for 1.5h and quenched in oil to room temperature. Then immediately transferred to a cryogenic bath held at -73oC for 2h, and finally aged at 515oC for 8h. The specimens of AerMet100 were austenitized at 890oC for 1h and quenched in oil to room temperature. Then immediately transferred to a cryogenic bath held at -73oC for 2h, and finally aged at 482oC for 8h. Specimens of 300M were austenitized at 870oC for 1h and quenched in oil to room temperature, then aged at 315oC for 2h.
Thin foils for TEM were cut from the specimens and ground to a thickness of about 50μm. The thin foils were electropolished in a perchloric acid-ethanol solution at -30 to -40oC. All the TEM samples were observed by JEOL JEM2011 (Japan Electron Optics Ltd., Tokyo) at 200kV. KIC was measured by precracked (W/B=2, a/W = 0.45 to 0.55) three-point single edge bend specimens (10×10×55mm) and standard compact tension specimens (25.4mm in thickness) using linear elastic fracture mechanics (LEFM) criteria per ASTM 399-90.
3.Microstructure and fracture toughness results As traditional ultra-high strength steel, the microstructure of 300M was reported in detail by many studies[15-17]. The conclusion in previous studies was that the microstructure of 300M included martensite/bainite laths as matrix and carbides as precipitation in matrix[15-17]. No austenite layers were observed in the previous or present studies of 300M. In 1993, Ayer and Machmeier[8] reported the microstructure of AerMet100. In Ayer and Machmeier’s study, besides martensite laths and carbides precipitation (M2C), austenite layers were observed at the boundary of martensite laths in AerMet100 and the thickness of the austenite layers were about 3nm[8]. In present study, austenite layers at the boundary of martensite laths in AerMet100 were also observed (Fig.1), but the thickness was from 3 to 10nm. Recently, M54, as new kind of high Co-Ni secondary hardening steel, was developed and studied. Wang et al.[5] reported the microstructure of M54 in detail. In Wang’s study[5], the austenite layers, which were very similar with those in AerMet100, was also observed in M54.
In present study, the thickness of the austenite layers in M54 was from 5 to 20nm as Fig.2 showed. The electron diffraction of the austenite layers and XRD results were reported by previous work, so it would not be mentioned again in this study. These special austenite layers were reported by many studies[5, 8], but few studies reported the formation mechanism of these austenite layers. More experiments and analysis should be made to explain the formation mechanism of these austenite layers in future studies. Traditional mechanical properties as tensile strength, yield strength and hardness of high Co-Ni secondary hardening steels were reported by many studies[4, 8], so these traditional data would not be reported in this study again. Now, most experts mainly paid attention to the fracture toughness of high Co-Ni secondary hardening steels, which was mainly discussed in this study. Fracture toughness (KIC) of the steels was measured and the results were close to the optimal value reported in the previous studies[4, 8]. Based on the results from both previous and present studies, the microstructure and fracture toughness of 300M, AerMet100 and M54 was summarized in Table.2. As Table.2 shown, the steels with austenite layers at the boundary of martensite laths (AerMet100/M54) had higher KIC than those without austenite layers (300M).
4. Finite element models 4.1 XFEM model Based on TEM observation results, two XFEM models were built: martensite
without austenite layer (XFEM model 1) and martensite with austenite layer (XFEM model 2) as Fig.3. The thickness of martensite laths in all the models was set to 150nm according to the TEM observation results. The property of martensite was elasticity with EM= 200GPa and v=0.3[18-20]. As the austenite layer in AerMet100 and M54 was very different with traditional austenite. It has great lattice distortion which make its lattice constant instable. Also, the residual stress in this layer may cause the deformation of the layer before loading[5]. Therefore, austenite layers in the models were considered to be an elastic-plastic solid with EA= EM/10GPa,v = 0.3,
s 380 MPa and b 580 MPa[21-24]. Because the crack propagation formed across the martensite as quasi-cleavage crack[6, 7], the interface between martensite and austenite layer was set as ‘fixed’. A 4-node bilinear plane strain elements (CPE4R) were used in these 2D XFEM models. The uniform increasing displacement loading was applied on the top and bottom of the models in the y direction. In actual material, the thickness of austenite layers was only 3-20nm. However, for simulation, this thickness was too small for us to see the effect of austenite layers on crack propagation. In order to make the simulation results of crack propagation direction clear, the thickness of the austenite layer in XFEM model 2 was set to 50nm, instead of 3-20nm. Also, in these XFEM models, the initial crack propagation direction was perpendicular to the austenite layer and no crystal orientation was considered in the models. In these situations, these XFEM models still had big differences with actual materials, so it could only qualitatively explain the effect of austenite layers on crack propagation. The simulation results could not show the real crack propagation in
actual materials. 4.2 CIM model Based on TEM observation results, five CIM models were built: martensite without austenite layer (CIM model 1), martensite with 5nm austenite layer (CIM model 2), 10nm austenite layer (CIM model 3), 15nm austenite layer (CIM model 4) and 20nm austenite layer (CIM model 5). Other parameters, as the thickness of martensite laths and the property of phases, were the same with XFEM models. A 4-node bilinear plane stress elements (CPS4R) were used in these 2D CIM models. In CIM models, we simulated the critical state when crack propagation just began, in order to calculate the KIC value. So, the loading value used in CIM models was a constant value. According to the simulation results of crack propagation by XFEM models, we could determine the loading value, which could make the material in the critical state when crack propagation just began. The uniaxial tensile loading was applied on the top of the models in the y direction and the bottom of the models was encastred. As Fig.4 shown, 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 CIM models, the initial crack propagation direction was not only perpendicular to the austenite layer. The models in which the initial crack propagation direction was 30o (CIM model 6) and 45o (CIM model 7) to the austenite layers were built as Fig.5. Their simulation results were compared with the models in which the initial crack propagation direction was just perpendicular to the austenite layer (CIM model 4). In CIM models, the sizes of the materials built in the models were much smaller than the
sizes of actual specimens which were used for the KIC testing in experiments. Therefore, without considering the size effect and crystal orientation, the absolute values of KIC calculated by these contour integral models were meaningless. However, the normalized value could be used to prove the accuracy of these models.
5. Simulation results and discussion 5.1 Crack propagation XFEM method was widely used to simulate the crack propagation in steels, especially dual-phase steels[9, 25, 26]. Based on previous study, when the longitudinal tensile loading was applied on an isotropic material with a transverse micro-crack, the direction of crack propagation tended to be transverse as a straight line[27]. However, for the dual-phase steels, the different properties between two phases (martensite/bainite or martensite/ferrite) in the steels could change the direction of crack propagation[9, 25, 26]. Fig.6 showed the simulation results of XFEM models in present study. For XFEM model 1 (martensite without austenite layer), crack propagation was along the X axis as a straight line and the spending time for the crack propagation process was about 0.2 (Fig.6 (a)). For XFEM model 2 (martensite with austenite layer), the direction of crack propagation was changed by austenite layer and the spending time for the crack to path through austenite layer was about 0.6 (Fig.6 (b)). Although these models were only qualitative models which couldn’t show the real crack propagation in actual materials as mentioned in Part 4.1, but we can draw the basic conclusion from the simulation results that austenite layer
could change the direction of crack propagation and decreased the crack growth rate. That meant, compared with the steels without austenite layers, energy consumption of crack propagation increased and fracture toughness was improved for the steels with austenite layers. Therefore, the simulation results of XFEM models qualitatively explained that austenite layers could improve the fracture toughness of high Co-Ni secondary hardening steel
5.2 Effect of crack propagation direction As the results of XFEM simulation, the austenite layer could change the crack propagation direction. Therefore, not all the crack propagation direction was just perpendicular to the austenite layer and the effect of crack propagation direction on the calculation of KIC should be analyzed. Fig.7 showed the results of stress field at the crack tip in CIM model 4, CIM model 6 and CIM model 7. All these models had 15nm austenite layer, but their crack propagation direction was different. As Fig.7, the stress field at the crack tip in all these models was similar. The value of KIC for CIM model 4, CIM model 6 and CIM model 7 was respectively 334.4, 320.5 and 307.0 MPa m . It meant the angles between the initial crack propagation direction and the austenite layer had little effect on the simulation results of K IC. Therefore, during the calculation of KIC, the models can be simplified, without considering the difference of initial crack propagation direction.
5.3 Stress field and KIC
Fig.8 showed the simulation results of stress field at the crack tip in CIM model 1 to CIM model 5. As the results in Fig.8 (a), significant stress concentration formed at the crack tip of CIM model 1(martensite without austenite layer). This stress concentration was greatly reduced by adding austenite layer at the boundary of matensite laths (Fig.8 (b)-(e)). However, when the thickness of the austenite layer was only 5nm, stress concentration formed behind the austenite layer (Fig.8 (b)). Fig.9 showed the relations between stress and distance from the crack tip for CIM models. It could be seen that stress concentration formed behind the layer when the layer’s thickness was less than 10nm. And when the thickness of austenite layer was larger than 15nm, the results were similar with the CIM model 4, whose thickness of austenite layer was just 15nm. All the simulation results in CIM models were similar with the well known solutions for crack propagation in layered materials with alternating hard and soft layers[11]. Based on the simulation results in CIM models, if the thickness of austenite layer was less than 10nm, the stress concentration still formed behind the austenite layer. That meant the austenite layer was too thin to reduce the stress concentration in this case. Also, if the thickness of austenite layer was larger than 15nm, its function is the same with the layers which was just 15nm in thickness. In addition, for the actual materials, an austenite in large size would become less homogeneous than an austenite in small size. Therefore, for austenite layer, the increase of its size would probably lead to the decrease of its property. In summary, although the simulation results showed no difference between the materials with 15nm and 20nm austenite layers, but the materials with 15nm austenite layers
would probably have better mechanical properties than the materials with 20nm austenite layers in actual situation because 15nm austenite layers would probably be more homogeneous and have better properties than 20nm austenite layers. In this case, there is no need to increase the thickness of austenite layer to larger than 15nm. Therefore, 10-15nm is the best thickness of austenite layer for the fracture toughness of the steels with martensite as matrix. The simulation and experimental results of KIC was listed in Table.3. As all the CIM models were 2D shell models without considering size effect and crystal orientation, all the simulation results of KIC belong to plane stress state. But the experimental results of KIC belong to plane strain state. According to theory of elastic mechanics[28], the calculation results of KIC should be larger than the experimental results. Therefore, as Table.3 shown, the absolute value of KIC obtained by simulation was larger than the value obtained by experiments. But the simulation results of normalized value were close to the experimental results.
6. Conclusion (1) As experimental results, the steels with austenite layers at the boundary of martensite laths (AerMet100/M54) had higher KIC than those without austenite layers (300M). (2) As XFEM simulation results, austenite layer changed the direction of crack propagation and decreased the crack growth rate. Therefore, compared with the steels without austenite layers, energy consumption of crack propagation increased and
fracture toughness was improved for the steels with austenite layers. (3) As CIM simulation results. 10-15nm is the best thickness of austenite layer for the fracture toughness of the steels with martensite as matrix. The angles between the initial crack propagation direction and the austenite layer had little effect on the simulation results of KIC. (4) Because the models used in present study were all 2D shell models without considering size effect and crystal orientation, the absolute value of KIC obtained by simulation was larger than the value obtained by experiments. But the simulation results of normalized value were close to the experimental results.
Acknowledgements This work was financially supported by National Basic Research Programs of China (No.2015GB118001 and No.2015CB654802). Greatly acknowledged the financial support provided by the National Natural Science Foundation of China (Grant No. 51471094). The authors acknowledge the assistance of J.M. Zhao and her group in Department of Engineering Mechanics in Tsinghua University with the FEM modeling.
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Figure Captions Fig.1 Austenite layers at the boundary of martensite laths in AerMet100: (a) 5nm in thickness;
(b) 10nm in thickness.
Fig.2 Austenite layers at the boundary of martensite laths in M54: (a) 5nm in thickness;
(b) 10nm in thickness;
(c) bright-field image;
(d) dark-field image.
Fig.3 The structure and mesh of XFEM models. Fig.4 The structure and mesh of CIM models. Fig.5 The CIM models with different crack propagation direction. Fig.6 The simulation results of XFEM models: (a) XFEM model 1; model 2.
(b) XFEM
Fig.7 The simulation results of CIM models with different crack propagation direction: (a) CIM model 4;
(b) CIM model 6;
(c) CIM model 7.
Fig.8 The simulation results of CIM models: (a) CIM model 1; (c) CIM model 3;
(d) CIM model 4;
(b) CIM model 2;
(e) CIM model 5.
Fig.9 The relations between stress and distance from the crack tip for CIM models.
Table.1 Main composition of the steels (wt. %). Table.2 Microstructure and fracture toughness of the steels. Table.3 The simulation and experimental results of KIC.
Table.1 Main composition of the steels (wt. %) Main composition (wt.%) Steel
C
Ni
Co
Mo
W
Cr
V
Si
Mn
M54
0.3
10.07
7.31
2.31
1.3
1.17
0.11
0.13
--
AerMet100
0.25
11.59
13.64
1.40
--
3.26
--
0.14
--
300M
0.4
1.83
--
0.40
--
0.85
0.1
1.56
0.75
Table.2 Microstructure and fracture toughness of the steels Steel
With/Without austenite layer
Thichness of austenite layer (nm)
KIC (MPa m )
300M AerMet100
Without With
-3-10
50 110
M54
With
5-20
115
Table.3The simulation and experimental results of KIC The absolute value of KIC (MPa m )
The normalized value of KIC
130.4
1.0
296.1
2.3
334.4
2.5
300M
50
1.0
AerMet100
110
2.2
M54
115
2.3
M-0nm A layer (CI model 1) Simulation results
Experimental results
M-10nm A layer (CI model 3) M-15nm A layer (CI model 4)