- Email: [email protected]
Numerical investigation on the prefabricated crack propagation of FV520B stainless steel
Accepted Manuscript Numerical investigation on the prefabricated crack propagation of FV520B stainless steel Ming Qin, Juyi Pan, Songying Chen PII: DOI: Reference:
S2211-3797(17)30870-7 http://dx.doi.org/10.1016/j.rinp.2017.09.024 RINP 942
To appear in:
Results in Physics
Received Date: Revised Date: Accepted Date:
21 May 2017 30 August 2017 13 September 2017
Please cite this article as: Qin, M., Pan, J., Chen, S., Numerical investigation on the prefabricated crack propagation of FV520B stainless steel, Results in Physics (2017), doi: http://dx.doi.org/10.1016/j.rinp.2017.09.024
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 proof before it is published in its final 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.
Numerical investigation on the prefabricated crack propagation of FV520B stainless steel Ming Qin, Juyi Pan, Songying Chen* Key Laboratory of High-efficiency and Clean Mechanical Manufacture, School of mechanical engineering, Shandong University, Jinan, 250061, P. R. China
Abstract: FV520B is a common stainless steel for manufacturing centrifugal compressor impeller and shaft. The internal metal flaw destroys the continuity of the material matrix, resulting in the crack propagation fracture of the component, which seriously reduces the service life of the equipment. In this paper, Abaqus software was used to simulate the prefabricated crack propagation of FV520B specimen with unilateral gap. The results of static crack propagation simulation results show that the maximum value of stress - strain located at the tip of the crack and symmetrical distributed like a butterfly along the prefabricated crack direction, the maximum stress is 1990MPa and the maximum strain is 9.489×10-3. The Mises stress and stress intensity factor KI increases with the increase of the expansion step, the critical value of crack initiation is reached at the 6th extension step. The dynamic crack propagation simulation shows that the crack propagation path is perpendicular to the load loading direction. Similarly, the maximum Mises stress located at the crack tip and is symmetrically distributed along the crack propagation direction. The critical stress range of the crack propagation is 23.3 ~ 43.4MPa. The maximum value of stress - strain curve located at the 8th extension step, that is, the crack initiation point, the maximum stress is 55.22MPa, and the maximum strain is 2.26×10-4. On the crack tip, the stress changed as 32.24 ~ 40.16MPa, the strain is at 1.292×10-4 ~ 1.897×10-4. Key words: FV520B; crack propagation; Mises stress; stress-strain; numerical investigation.
1 Introduction FV520B steel is a new type of acid and heat-resistant stainless steel, because of its high strength, plasticity, toughness and corrosion resistance, it is widely used in shafts, rotors and large centrifugal * Corresponding author. E-mail: [email protected]
compressor impeller and other occasions with higher materials requirements [1-4]. In actual industrial production, the ideal mechanical components without defects or without minor cracks are relatively less, especially for large mechanical components. The existence of the crack flaw not only destroys the matrix continuity of the raw material, but also causes the stress concentration on the crack tip, and it will promote the further expansion of the crack under external stress. When the crack length reaches a certain critical value, the crack will quickly expand until the structure fractures, as the saying goes, "thousands of miles of the embankment, collapse in the ants", this proverb vividly shows the dangers of crack source on the structure [5-9]. Therefore, it is very important to study the crack propagation law of FV520B steel. So far, scholars have made some progress in the study of fracture properties of FV520B steel. Qiaoguo Wu [10] found that FV520B steel has a strong sensitivity to strain rate, and the flow stress increases with the increase of strain rate. The fracture mechanism is ductile fracture of microporous coalescence and fracture toughness Jld increases linearly with the increase of the load rate, and the variation range is 0 ~ 6.32 ×106kJm-2 / s. Xiaolan Han [11] Studied the thermal deformation behavior of FV520B steel by isothermal compression test, verified the validity of statistical analysis equation, and confirmed that the improved constitutive equation can accurately predict the flow stress of FV520B steel. Qianqing Zhou [12] found that the FV520B steel, which has been tempered at higher temperature, has excellent low temperature tensile properties. During the deformation of the material at -196℃, part of the Austenite is transformed into Martensite, and its ductility significantly enhanced, consistent with the results of the study at room temperature. Shaopeng Wei [13] studied the laser deposition tensile fracture behavior of FV520B, and found that the fracture occurred at high fluctuation micro-hardness caused by multi-layer laser heating, the competitive destruction of the microporous coalescence in the heat affected zone and the interface of the composite layer/heat affected zone leads to three forms of tensile fracture. Particle refinement and sediment dissolution occur in the heat affected zone, which reduces the strength of the material and increases the toughness. Ming Qin [14] carried out WOL prefabricated crack propagation test on FV520B steel, the results show that the crack propagation rate of FV520B steel is 1.941 ~ 5.748×10-7mm/s, and the critical stress intensity factor KISCC is not more than 36.83MPa
, in the same environment, the
crack growth rate and the critical stress intensity factor are increasing with the increase of the initial loading stress intensity factor. Yunpan Zhong [15] found that the larger the thickness of the corrosion product film, the smaller the crack initiation strength of the FV520B, the easier the nucleation and expansion of the crack, the lower the stress corrosion threshold of the V-type unilateral notch specimen. Under the tensile load, the crack is progressively expanded into the matrix. Up to now, most scholars and engineer focused on the mechanical behavior, surface treatment, heat treatment performance, stress corrosion behavior and fatigue life etc.
[14, 16-21]
, the simulation of
FV520B material crack propagation law is relatively few. In this paper, the numerical investagation of FV520B by Abaqus software was carried out to obtain the Mises stress, stress intensity factor KI and stress-strain distribution of the crack tip, which are of great significance to the damage tolerance, residual life and maintenance evaluation of the components.
2 Prefabricated crack propagation simulation 2.1 Materials and geometric models FV520B Martensitic stainless steel is selected as the simulation material, its chemical composition is shown in Table 1, the parameters of mechanical properties are shown in Table 2, the slow tensile stress-strain curves obtained at room temperature and pressure are shown in Fig.1. In this paper, two different model samples are used to simulate the prefabricated crack propagation. The size of the simulated specimen is as follows: the length is 100mm, static plate width 80mm, dynamic plate width 50mm, thickness 2mm, prefabricated crack length 10mm. The geometric model is designed by Abaqus CAE finite element pretreatment software, as shown in Figure 2. 2.2 Grid partitioning and parameter setting For the static crack propagation model, the tetrahedral planar strain unit is used for free meshing. The crack tip adopts the triangular element to carry out free grid encryption division, and the total number of grids is 2921. For the dynamic crack propagation model, the tetrahedral planar strain unit is used for free meshing, and the total number of meshes is 10000, as shown in Fig.3.
Table 1 Chemical composition of FV520B material (wt%) Element
C
Si
Mn
S
P
Ni
Cr
Cu
Mo
Nb
Mass fraction
0.03
0.30
0.41
≤0.025
≤0.030
5.24
14.51
1.54
1.95
0.65
Table 2 FV520B material mechanical properties parameters
FV520B
/Kg/m3
Young's
Poisson's
Yield
Tensile
modulus
ratio
Strength
strength
E/GPa
v
/MPa
/MPa
210
0.3
7800
1029
1078
Hardness HV
Section shrinkage ψ(%)
300
1200 1000 stress/MPa
Material
Density
800 600 400 200 0 0
0.05
0.1
0.15
strain
Figure 1. FV520B martensitic stainless steel stress-strain curve
(a) Static crack propagation model
(b) Dynamic crack propagation model
Figure 2. Geometry model of the simulation
61.3
(a) Static board model meshing
(b) Dynamic board model meshing
(c) Static plate model crack tip encryption grid Figure 3. Finite element model meshing The boundary conditions of the crack propagation simulation are as follows: the bottom of the model is fixed and the top surface sustains uniform stress load, the maximum tensile load is 80% , which ensures that the model has only the Y direction displacement, there is no bending and torsion, the material keeps isotropic, the failure displacement shown in Fig.4.
3 Simulation results and analysis 3.1 Static crack propagation simulation
is 0.5mm, and the boundary condition is
The change of the Mises stress distribution in the static crack propagation simulation is shown in Fig. 5. It can be seen from the figure that with the application of the external load, the local plastic deformation occurs at the tip of the crack, and the increase of the load leads to the increase of the
(a) Static crack propagation
(b) Dynamic crack propagation
boundary condition
boundary condition
Figure 4. Model boundary condition setting
crack tip opening angle. The Mises stress at the crack tip is symmetrical distributed like a butterfly in the direction of the prefabricated crack, and the maximum is 1930MPa. At this time, the tip has had plastic deformation and crack propagation. The Mises stress decreases from the tip to the surrounding area and the distribution is fan-shaped, the rest is almost zero stress. The stress-strain distribution of the tip is shown in Fig. 6. It can be seen that the change trend of the stress and strain is almost the same, they are symmetrical direction along the X-axis. The maximum stress and strain are located at the tip, fan-shaped diminishing. The maximum stress reaches 1990MPa, however, the actual stress value can’t exceed the tensile strength of the material, and the maximum strain is 9.489×10-3. The tip has begun to crack expansion at this time.
Figure 5. Mises stress distribution of crack tip
Figure 6. Stress-strain distribution of crack tip/MPa
The trend of the stress intensity factor KI of the crack tip with the expansion step is shown in Fig. 7. The stress intensity factor KI increases with the increase of the crack growth step. In the initial loading step, the KI increases slowly. The critical threshold is attained at the 11th extension step, the crack starts to crack and the KI increases rapidly, and the maximum KI is 712.6 MPa
. The Mises
stress of the crack tip varies with the expansion step. As shown in Fig. 8, the Mises stress increases with increasing load. At the 11th expansion step, the Mises stress has exceeded the tensile strength of the material, and the crack tip has come into being a plastic deformation and crack expanded.
800 700
KI/MPa
600 500 400 300 200 100 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 Extension step/n
Figure7. Curve of stress intensity factor KI and extended step
2000 1800 Mises stress/MPa
1600 1400 1200 1000 800 600 400 200 0 1
2
3
4
5
6
7 8 9 10 11 12 13 14 15 16 Extension step/n
Figure 8. Relationship between Mises stress and the extended step at crack tip
3.2 Dynamic crack propagation simulation The entire crack propagation path is shown in Fig. 9. It can be seen that the crack propagation direction is generally perpendicular to the applied load direction. In the initial stage of crack propagation, the stress distribution at the tip is not uniform due to the combined effect of material properties, prefabricated crack and external load etc., and the crack propagation direction is shifted. Then the whole stress field of the model changes, the crack propagation tends to be stable, and extends along the direction of the initial prefabricated crack. The direction of the extension is
perpendicular to the stress loading direction until the specimen is broken. The simulation results are in agreement with the theoretical results and the experimental results.
Figure 9. Dynamic propagation path for cracks
As shown in Fig. 10, there are changes of Mises stress distribution in crack propagation at the first step, the seventh, the eighth ,the ninth, the twentieth and the twenty-first step, respectively. The stress value is small under the initial load, and it has not yet reached the critical threshold of material damage cracking. The Mises stress of the crack tip increases with the increase of the external load, and the tip opening is increasing and the stress concentration at the crack tip is gradually deteriorated. When the maximum principal stress reaches the critical value of the damage criterion, an initiation crack occurs and that completes an extension cycle. The crack propagation leads to the change of the stress field of the crack tip structure unit, so that the Mises stress at the tip becomes smaller. With the additional load increasing, the Mises stress increases again for the propagation accumulation of the next unit, which causes the further expansion of the crack. It repeats this process until the sample fracture. The critical stress range of the crack propagation is 23.3 ~ 43.4MPa. The maximum Mises stress is located at the tip and is symmetrically distributed along the crack propagation direction, decreasing from the tip to the surrounding area. In the dynamic crack propagation process, the variation tendency of the stress-strain of the crack tip changing with the expansion step is as shown in Fig. 11. It can be seen that the variation trend of stress and strain curve is almost the same. At the beginning of the applied load, the stress - strain
(a) the first expansion step
(b) the seventh expansion step
(c) the eighth expansion step
(d) the ninth extension step
(e) the twentieth expansion step
(f) the twenty-first expansion step
Figure 10. Stress distribution of dynamic crack propagation/MPa
increases with the increase of the load, when the load reaches the critical value of the tensile strength of the material, the stress and strain of the crack tip reach the maximum at the same time, the
maximum stress is 55.22 MPa and the maximum strain is 2.26×10-4. At this time, the tip starts to crack. After the 8th step, the stress-strain varies wave-like with the increase of the expansion step, because the crack propagation changes the stress-strain distribution at the tip, which decrease the stress-strain. With the increase of the load, it reaches the next initiation crack point, this process is repeated until the sample fracture. The stress range of the crack tip is 32.24 ~ 40.16 MPa, and the strain range is 1.292 ~ 1.897 ×10-4, which are consistent with the experimental results, not more than 36.83MPa. 25
Stress 应力 应变 Strain
20
stress/MPa
40
15
30
10
20
strain/×10-5
50
5
10 0
0 1
3
5
7
9
11
13
15
17
19
21
23
25
Expansion step/n
Figure 11. The stress-strain of the crack tip changes with the extended step curve
4 Conclusion (1) The static crack propagation simulation shows that the maximum stress-strain located at the tip of the crack, and is symmetrically distributed like the butterfly along the prefabricated crack direction. The maximum stress reaches 1990MPa and the maximum strain is 9.489×10-3. With the load increasing, local plastic deformation led to crack expansion at the tip. The Mises stress and stress intensity factor KI increases linearly with the expansion step, and reaches the critical value of crack initiation at the 6th step. (2) The dynamic crack propagation simulation shows that the propagation path of the crack is perpendicular to the load loading direction. The maximum Mises stress is located at the crack tip, is
symmetrically distributed along the crack propagation direction, and is reduced from the crack tip to the surrounding area. The critical stress range is 23.3 ~ 43.4MPa. (3) The stress and strain trend of the crack tip coincides with each other, the maximum value is both in the 8th expansion step, that is, the crack initiation point, the maximum stress is 55.22 MPa, and the maximum strain is 2.26×10-4. With the crack continues to expand, the stress - strain is wavy changes until the model fracture, the stress of the crack tip range is 32.24 ~ 40.16 MPa, and the strain range is 1.292 ~ 1.897×10-4. Acknowledgement The authors acknowledge the support of Science and Technology Development Planning of Shandong Province, P. R. China (2014GGX108001 and 2016GGX104018).
References [1] Xu BS, Fang JX. Heat-affected zone microstructure evolution and its effects on mechanical properties for laser cladding FV520B stainless steel. Acta Metallurgica Sinica, 2016, 52(1):1-9. [2] Wang Guangcun, Li Jianfeng. Study on erosion behavior and mechanism of impeller's material FV520B in centrifugal compressor. Journal of Mechanical Engineering, 2014, 50(19):182-190. [3] Song YN， Wang HD. Effect of fretting wear on very high cycle bending fatigue behaviors of FV520B steel. Tribology International，2016，103:132-138. [4] Xu Binshi, Fang Jinxiang, et al. Heat-affected zone microstructure evolution and its effects on mechanical properties for laser cladding fv520b stainless steel. Acta Metallurgica Sinica, 2016, 52:1-9. [5] Li Huilu, Feng Jianing, Chu Wuyang. Metallographic microscope track investigation of stress corrosion cracking of the high-strength steels WOL. Rare Metal Materials and Engineering, 2012, 41(S2):247-249. [6] Nguyen T.-T,Bolivar J. A phase field method for modeling stress corrosion crack propagation in a nickel base alloy. International Journal of Solids and Structures, 2017, 112:65-82. [7] Zheng Botong, Dawood Mina. Fatigue crack growth analysis of steel elements reinforced with shape memory alloy (SMA)/fiber reinforced polymer (FRP) composite patches. Composite
Structures, 2017, 164:158-169. [8] Zhang Min, Chu Qiaoling, et al. Failure analysis of a welded impeller in coke oven gas environment. Engineering Failure Analysis, 2014, 38:16-24. [9] Chu Qiaoling, Zhang Min, Li Jihong. Failure analysis of impeller made of FV520B martensitic precipitated hardening stainless steel. Engineering Failure Analysis, 2013, 34:501-510. [10] Wu QG, Chen XD. Engineering fracture assessment of FV520B steel impeller subjected to dynamic loading FV520B. Engineering Fracture Mechanics, 2015, 146:210-223. [11] Han Xiaolan, Zhao Shengdun, et al. Prediction of FV520B Steel Flow Stresses at High Temperature and Strain Rates. High Temperature Materials and Processes, 2015, 34(6):529-538. [12] Zhou Qianqing, Yong Xingping. Study on cryogenic tensile properties of precipitation hardened FV520B steel. Corrosion Science and Protection Technology, 2009, 21(3):299-301. [13] Wei Shaopeng, Wang Gang. Competitive failure analysis on tensile fracture of laser-deposited material for martensitic stainless steel. Materials & Design, 2017, 118:1-10. [14] Qin Ming, Li Jianfeng, Chen Songying. Experimental study on stress corrosion crack propagation rate of FV520B in carbon dioxide and hydrogen sulfide solution. Results in Physics, 2016, 6:365-372. [15] Zhong Yunpan. Research on the stress corrosion cracking of FV520B precipitation-hardening martensitic stainless steel. Shandong University Dissertation, 2016. [16] Zhang Yubo, Xu Binshi, et al. An experimental analysis of fatigue behavior of a welded impeller made by FV520B stainless steel in an over-speed preloading process. Engineering Failure Analysis, 2016, 59:111-121. [17] Fan J, Guo X, Wu C. Influence of heat treatments on mechanical behavior of FV520B steel. Experimental Techniques, 2015, 39(2):55-64. [18] SUN Jiao, CHEN Songying. Stress corrosion behavior of FV520B steel in H2S/CO2 environment. Journal of Northeastern University, 2015, 36(12): 1790-1794. [19] Wang Jinlong, Zhang Yuanliang. Competitive giga-fatigue life analysis owing to surface defect and internal inclusion for FV520B-I. International Journal of Fatigue, 2016, 87:203-209.
[20] Hao Shengzhi, Zhao Limin, et al. Improving corrosion and wear resistance of FV520B steel by high current pulsed electron beam surface treatment. Nuclear Instruments & Methods in Physics Research Section B-beam Interactions with Materials and Atoms, 2015, 356:12-16. [21] Nie Defu, Chen Xuedong, et al. Failure analysis of a slot-welded impeller of recycle hydrogen centrifugal compressor. Engineering Failure Analysis, 2014, 42:1-9.
S2211-3797(17)30870-7 http://dx.doi.org/10.1016/j.rinp.2017.09.024 RINP 942
To appear in:
Results in Physics
Received Date: Revised Date: Accepted Date:
21 May 2017 30 August 2017 13 September 2017
Please cite this article as: Qin, M., Pan, J., Chen, S., Numerical investigation on the prefabricated crack propagation of FV520B stainless steel, Results in Physics (2017), doi: http://dx.doi.org/10.1016/j.rinp.2017.09.024
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 proof before it is published in its final 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.
Numerical investigation on the prefabricated crack propagation of FV520B stainless steel Ming Qin, Juyi Pan, Songying Chen* Key Laboratory of High-efficiency and Clean Mechanical Manufacture, School of mechanical engineering, Shandong University, Jinan, 250061, P. R. China
Abstract: FV520B is a common stainless steel for manufacturing centrifugal compressor impeller and shaft. The internal metal flaw destroys the continuity of the material matrix, resulting in the crack propagation fracture of the component, which seriously reduces the service life of the equipment. In this paper, Abaqus software was used to simulate the prefabricated crack propagation of FV520B specimen with unilateral gap. The results of static crack propagation simulation results show that the maximum value of stress - strain located at the tip of the crack and symmetrical distributed like a butterfly along the prefabricated crack direction, the maximum stress is 1990MPa and the maximum strain is 9.489×10-3. The Mises stress and stress intensity factor KI increases with the increase of the expansion step, the critical value of crack initiation is reached at the 6th extension step. The dynamic crack propagation simulation shows that the crack propagation path is perpendicular to the load loading direction. Similarly, the maximum Mises stress located at the crack tip and is symmetrically distributed along the crack propagation direction. The critical stress range of the crack propagation is 23.3 ~ 43.4MPa. The maximum value of stress - strain curve located at the 8th extension step, that is, the crack initiation point, the maximum stress is 55.22MPa, and the maximum strain is 2.26×10-4. On the crack tip, the stress changed as 32.24 ~ 40.16MPa, the strain is at 1.292×10-4 ~ 1.897×10-4. Key words: FV520B; crack propagation; Mises stress; stress-strain; numerical investigation.
1 Introduction FV520B steel is a new type of acid and heat-resistant stainless steel, because of its high strength, plasticity, toughness and corrosion resistance, it is widely used in shafts, rotors and large centrifugal * Corresponding author. E-mail: [email protected]
compressor impeller and other occasions with higher materials requirements [1-4]. In actual industrial production, the ideal mechanical components without defects or without minor cracks are relatively less, especially for large mechanical components. The existence of the crack flaw not only destroys the matrix continuity of the raw material, but also causes the stress concentration on the crack tip, and it will promote the further expansion of the crack under external stress. When the crack length reaches a certain critical value, the crack will quickly expand until the structure fractures, as the saying goes, "thousands of miles of the embankment, collapse in the ants", this proverb vividly shows the dangers of crack source on the structure [5-9]. Therefore, it is very important to study the crack propagation law of FV520B steel. So far, scholars have made some progress in the study of fracture properties of FV520B steel. Qiaoguo Wu [10] found that FV520B steel has a strong sensitivity to strain rate, and the flow stress increases with the increase of strain rate. The fracture mechanism is ductile fracture of microporous coalescence and fracture toughness Jld increases linearly with the increase of the load rate, and the variation range is 0 ~ 6.32 ×106kJm-2 / s. Xiaolan Han [11] Studied the thermal deformation behavior of FV520B steel by isothermal compression test, verified the validity of statistical analysis equation, and confirmed that the improved constitutive equation can accurately predict the flow stress of FV520B steel. Qianqing Zhou [12] found that the FV520B steel, which has been tempered at higher temperature, has excellent low temperature tensile properties. During the deformation of the material at -196℃, part of the Austenite is transformed into Martensite, and its ductility significantly enhanced, consistent with the results of the study at room temperature. Shaopeng Wei [13] studied the laser deposition tensile fracture behavior of FV520B, and found that the fracture occurred at high fluctuation micro-hardness caused by multi-layer laser heating, the competitive destruction of the microporous coalescence in the heat affected zone and the interface of the composite layer/heat affected zone leads to three forms of tensile fracture. Particle refinement and sediment dissolution occur in the heat affected zone, which reduces the strength of the material and increases the toughness. Ming Qin [14] carried out WOL prefabricated crack propagation test on FV520B steel, the results show that the crack propagation rate of FV520B steel is 1.941 ~ 5.748×10-7mm/s, and the critical stress intensity factor KISCC is not more than 36.83MPa
, in the same environment, the
crack growth rate and the critical stress intensity factor are increasing with the increase of the initial loading stress intensity factor. Yunpan Zhong [15] found that the larger the thickness of the corrosion product film, the smaller the crack initiation strength of the FV520B, the easier the nucleation and expansion of the crack, the lower the stress corrosion threshold of the V-type unilateral notch specimen. Under the tensile load, the crack is progressively expanded into the matrix. Up to now, most scholars and engineer focused on the mechanical behavior, surface treatment, heat treatment performance, stress corrosion behavior and fatigue life etc.
[14, 16-21]
, the simulation of
FV520B material crack propagation law is relatively few. In this paper, the numerical investagation of FV520B by Abaqus software was carried out to obtain the Mises stress, stress intensity factor KI and stress-strain distribution of the crack tip, which are of great significance to the damage tolerance, residual life and maintenance evaluation of the components.
2 Prefabricated crack propagation simulation 2.1 Materials and geometric models FV520B Martensitic stainless steel is selected as the simulation material, its chemical composition is shown in Table 1, the parameters of mechanical properties are shown in Table 2, the slow tensile stress-strain curves obtained at room temperature and pressure are shown in Fig.1. In this paper, two different model samples are used to simulate the prefabricated crack propagation. The size of the simulated specimen is as follows: the length is 100mm, static plate width 80mm, dynamic plate width 50mm, thickness 2mm, prefabricated crack length 10mm. The geometric model is designed by Abaqus CAE finite element pretreatment software, as shown in Figure 2. 2.2 Grid partitioning and parameter setting For the static crack propagation model, the tetrahedral planar strain unit is used for free meshing. The crack tip adopts the triangular element to carry out free grid encryption division, and the total number of grids is 2921. For the dynamic crack propagation model, the tetrahedral planar strain unit is used for free meshing, and the total number of meshes is 10000, as shown in Fig.3.
Table 1 Chemical composition of FV520B material (wt%) Element
C
Si
Mn
S
P
Ni
Cr
Cu
Mo
Nb
Mass fraction
0.03
0.30
0.41
≤0.025
≤0.030
5.24
14.51
1.54
1.95
0.65
Table 2 FV520B material mechanical properties parameters
FV520B
/Kg/m3
Young's
Poisson's
Yield
Tensile
modulus
ratio
Strength
strength
E/GPa
v
/MPa
/MPa
210
0.3
7800
1029
1078
Hardness HV
Section shrinkage ψ(%)
300
1200 1000 stress/MPa
Material
Density
800 600 400 200 0 0
0.05
0.1
0.15
strain
Figure 1. FV520B martensitic stainless steel stress-strain curve
(a) Static crack propagation model
(b) Dynamic crack propagation model
Figure 2. Geometry model of the simulation
61.3
(a) Static board model meshing
(b) Dynamic board model meshing
(c) Static plate model crack tip encryption grid Figure 3. Finite element model meshing The boundary conditions of the crack propagation simulation are as follows: the bottom of the model is fixed and the top surface sustains uniform stress load, the maximum tensile load is 80% , which ensures that the model has only the Y direction displacement, there is no bending and torsion, the material keeps isotropic, the failure displacement shown in Fig.4.
3 Simulation results and analysis 3.1 Static crack propagation simulation
is 0.5mm, and the boundary condition is
The change of the Mises stress distribution in the static crack propagation simulation is shown in Fig. 5. It can be seen from the figure that with the application of the external load, the local plastic deformation occurs at the tip of the crack, and the increase of the load leads to the increase of the
(a) Static crack propagation
(b) Dynamic crack propagation
boundary condition
boundary condition
Figure 4. Model boundary condition setting
crack tip opening angle. The Mises stress at the crack tip is symmetrical distributed like a butterfly in the direction of the prefabricated crack, and the maximum is 1930MPa. At this time, the tip has had plastic deformation and crack propagation. The Mises stress decreases from the tip to the surrounding area and the distribution is fan-shaped, the rest is almost zero stress. The stress-strain distribution of the tip is shown in Fig. 6. It can be seen that the change trend of the stress and strain is almost the same, they are symmetrical direction along the X-axis. The maximum stress and strain are located at the tip, fan-shaped diminishing. The maximum stress reaches 1990MPa, however, the actual stress value can’t exceed the tensile strength of the material, and the maximum strain is 9.489×10-3. The tip has begun to crack expansion at this time.
Figure 5. Mises stress distribution of crack tip
Figure 6. Stress-strain distribution of crack tip/MPa
The trend of the stress intensity factor KI of the crack tip with the expansion step is shown in Fig. 7. The stress intensity factor KI increases with the increase of the crack growth step. In the initial loading step, the KI increases slowly. The critical threshold is attained at the 11th extension step, the crack starts to crack and the KI increases rapidly, and the maximum KI is 712.6 MPa
. The Mises
stress of the crack tip varies with the expansion step. As shown in Fig. 8, the Mises stress increases with increasing load. At the 11th expansion step, the Mises stress has exceeded the tensile strength of the material, and the crack tip has come into being a plastic deformation and crack expanded.
800 700
KI/MPa
600 500 400 300 200 100 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 Extension step/n
Figure7. Curve of stress intensity factor KI and extended step
2000 1800 Mises stress/MPa
1600 1400 1200 1000 800 600 400 200 0 1
2
3
4
5
6
7 8 9 10 11 12 13 14 15 16 Extension step/n
Figure 8. Relationship between Mises stress and the extended step at crack tip
3.2 Dynamic crack propagation simulation The entire crack propagation path is shown in Fig. 9. It can be seen that the crack propagation direction is generally perpendicular to the applied load direction. In the initial stage of crack propagation, the stress distribution at the tip is not uniform due to the combined effect of material properties, prefabricated crack and external load etc., and the crack propagation direction is shifted. Then the whole stress field of the model changes, the crack propagation tends to be stable, and extends along the direction of the initial prefabricated crack. The direction of the extension is
perpendicular to the stress loading direction until the specimen is broken. The simulation results are in agreement with the theoretical results and the experimental results.
Figure 9. Dynamic propagation path for cracks
As shown in Fig. 10, there are changes of Mises stress distribution in crack propagation at the first step, the seventh, the eighth ,the ninth, the twentieth and the twenty-first step, respectively. The stress value is small under the initial load, and it has not yet reached the critical threshold of material damage cracking. The Mises stress of the crack tip increases with the increase of the external load, and the tip opening is increasing and the stress concentration at the crack tip is gradually deteriorated. When the maximum principal stress reaches the critical value of the damage criterion, an initiation crack occurs and that completes an extension cycle. The crack propagation leads to the change of the stress field of the crack tip structure unit, so that the Mises stress at the tip becomes smaller. With the additional load increasing, the Mises stress increases again for the propagation accumulation of the next unit, which causes the further expansion of the crack. It repeats this process until the sample fracture. The critical stress range of the crack propagation is 23.3 ~ 43.4MPa. The maximum Mises stress is located at the tip and is symmetrically distributed along the crack propagation direction, decreasing from the tip to the surrounding area. In the dynamic crack propagation process, the variation tendency of the stress-strain of the crack tip changing with the expansion step is as shown in Fig. 11. It can be seen that the variation trend of stress and strain curve is almost the same. At the beginning of the applied load, the stress - strain
(a) the first expansion step
(b) the seventh expansion step
(c) the eighth expansion step
(d) the ninth extension step
(e) the twentieth expansion step
(f) the twenty-first expansion step
Figure 10. Stress distribution of dynamic crack propagation/MPa
increases with the increase of the load, when the load reaches the critical value of the tensile strength of the material, the stress and strain of the crack tip reach the maximum at the same time, the
maximum stress is 55.22 MPa and the maximum strain is 2.26×10-4. At this time, the tip starts to crack. After the 8th step, the stress-strain varies wave-like with the increase of the expansion step, because the crack propagation changes the stress-strain distribution at the tip, which decrease the stress-strain. With the increase of the load, it reaches the next initiation crack point, this process is repeated until the sample fracture. The stress range of the crack tip is 32.24 ~ 40.16 MPa, and the strain range is 1.292 ~ 1.897 ×10-4, which are consistent with the experimental results, not more than 36.83MPa. 25
Stress 应力 应变 Strain
20
stress/MPa
40
15
30
10
20
strain/×10-5
50
5
10 0
0 1
3
5
7
9
11
13
15
17
19
21
23
25
Expansion step/n
Figure 11. The stress-strain of the crack tip changes with the extended step curve
4 Conclusion (1) The static crack propagation simulation shows that the maximum stress-strain located at the tip of the crack, and is symmetrically distributed like the butterfly along the prefabricated crack direction. The maximum stress reaches 1990MPa and the maximum strain is 9.489×10-3. With the load increasing, local plastic deformation led to crack expansion at the tip. The Mises stress and stress intensity factor KI increases linearly with the expansion step, and reaches the critical value of crack initiation at the 6th step. (2) The dynamic crack propagation simulation shows that the propagation path of the crack is perpendicular to the load loading direction. The maximum Mises stress is located at the crack tip, is
symmetrically distributed along the crack propagation direction, and is reduced from the crack tip to the surrounding area. The critical stress range is 23.3 ~ 43.4MPa. (3) The stress and strain trend of the crack tip coincides with each other, the maximum value is both in the 8th expansion step, that is, the crack initiation point, the maximum stress is 55.22 MPa, and the maximum strain is 2.26×10-4. With the crack continues to expand, the stress - strain is wavy changes until the model fracture, the stress of the crack tip range is 32.24 ~ 40.16 MPa, and the strain range is 1.292 ~ 1.897×10-4. Acknowledgement The authors acknowledge the support of Science and Technology Development Planning of Shandong Province, P. R. China (2014GGX108001 and 2016GGX104018).
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