- Email: [email protected]
Molecular Dynamics Simulation of Porous Layer-enhanced Dislocation Emission and Crack Propagation in Iron Crystal
J. Mater. Sci. Technol., 2011, 27(11), 1025-1028.
Molecular Dynamics Simulation of Porous Layer-enhanced Dislocation Emission and Crack Propagation in Iron Crystal D. Li1) , F.Y. Meng1) , X.Q. Ma1)† , L.J. Qiao2) and W.Y. Chu2) 1) Department of Physics, University of Science and Technology Beijing, Beijing 100083, China 2) Corrosion and Protection Center, Key Lab of Environmental Fracture (Ministry of Education), University of Science and Technology Beijing, Beijing 100083, China [Manuscript received June 22, 2010, in revised form August 31, 2010]
The internal stress induced by a porous layer or passive layer can assist the applied stress to promote dislocation emission and crack propagation, e.g. when the pipeline steel is buried in the soil containing water, resulting in stress corrosion cracking (SCC). Molecular dynamics (MD) simulation is performed to study the process of dislocation emission and crack propagation in a slab of Fe crystal with and without a porous layer on the surface of the crack. The results show that when there is a porous layer on the surface of the crack, the tensile stress induced by the porous layer can superimpose on the external applied stress and then assist the applied stress to initiate crack tip dislocation emission under lowered stress intensity KI , or stress. To respond to the corrosion accelerated dislocation emission and motion, the crack begins to propagate under lowered stress intensity KI, resulting in SCC. KEY WORDS: Molecular dynamics simulation; Dislocation emission; Crack propagation; Porous layer; Stress intensity
1. Introduction A lot of disruptive accidents of buried gas or oil transmission pipelines, which were caused by stress corrosion, happened in many countries[1] . Therefore, great attention has been focused on this topic[1–6] . When the X60 pipeline steel is buried in the soilcontaining water, a passive layer or porous layer is formed on the surface. Then the internal stress induced by the porous layer or passive layer assists the applied stress to promote dislocation emission and crack propagation, resulting in stress corrosion cracking (SCC). The corrosion process can enhance dislocation emission and motion, and crack propagation is related to the internal stress induced by the porous layer or the passive film on the surface of pipeline steel. Experiments show that brass in an ammonia solution[7,8] and α-Ti in a methanol solution[9] with a † Corresponding author. Prof., Ph. D.; Tel.: +86 10 62334074; Fax: +86 10 62327283; E-mail address: [email protected] (X.Q. Ma).
protective layer formed on one side and one end fixed is deflected during corrosion. This corrosion (porous layer or passive film) induced stress also exists during SCC, and then assists the applied stress to enhance crack tip dislocation emission and crack propagation, resulting in SCC[10,11] . Li et al.[12,13] calculated the tensile stress of Cu3 Au alloy with a dealloyed layer on the surface. The tensile stress induced by the dealloyed layer can assist the applied stress to enhance crack tip dislocation emission and motion, and crack propagation. Our previous work[14] showed that Fe single crystal with one end fixed and a porous layer on the surface was deflected toward the porous layer during relaxation, resulting in a macro tensile stress. It was also shown that the maximum tensile stress induced by the porous layer was located at the matrix near the interface between the porous layer and the matrix. The aim of this paper is to investigate the effect of the porous layer in the surface of the crack on the process of dislocation emission and crack propagation
1026
D. Li et al.: J. Mater. Sci. Technol., 2011, 27(11), 1025–1028
Fig. 1 Geometry configuration of Fe crystal with a preexisting crack. An external tensile stress σapplied is applied along y direction
in low carbon steel pipeline; and to show how an additive tensile stress caused by the porous layer influences the stress intensity (stress) for dislocation emission and crack propagation. In order to perform the simulation more conveniently, we study Fe crystal with a porous layer where vacancies or voids are linearly distributed instead of low carbon steel pipeline with an irregular distribution of vacancies or voids of porous layer in the experiments. 2. Simulation Process In order to study the effect of the porous layer on dislocation emission and crack propagation, a single edge crack in Fe crystal with and without a porous layer on the surface of the crack is simulated. The geometry configuration of the simulated crystal without the porous layer is shown in Fig. 1. The dimensional size of Fe crystal is 36.5 nm (W )×36.7 nm (L)×1.2 nm (B), containing 138240 atoms. The Fe crystal for the simulation consists of 180 atomic layers along [10¯1] direction, 256 atomic layers along [010] direction, and 6 atomic layers along [101] direction. A single edge crack is considered pre-existing automatically. The crack surface is the (010) plane, and the crack front is oriented along [101] direction. The length (a) and width (w) of the crack are 10.96 nm and 0.57 nm, respectively. The ratio of the crack length to the Fe crystal length is a/L=0.3. An external tensile stress (σapplied ) is applied along the y ([010]) direction, perpendicular to the crack surface of the (010) plane. a0 =0.287 nm is the lattice constant of the Fe crystal. A slab of Fe crystal with the porous layer introduced on the surface of the crack is shown in Fig. 2, where the porous layer is the cross shaded area. The depth of the porous layer is indicated by d. The ratio of the porous layer depth to the crystal length is
Fig. 2 Schematic representation of Fe crystal with a porous layer on the surface of the crack. The shaded area around the crack indicates porous layer and the shaded area on the top and bottom surfaces stands for the region for loading
d/L=0.05. The maximum vacancy concentration CV on the outside surface is 45% and decreases linearly from CV to zero inwardly. The higher vacancy concentration corresponds to the more severe corrosion degree or the longer corrosion time. Periodic boundary condition is imposed along the z direction to simulate the plane strain conditions, while free boundary conditions are employed along the x and y directions. The crack is loaded by the mode-I isotropic elastic K displacement field[15] . The top and the bottom layers of atoms in the y direction are designated as boundary region (Fig. 2), where the external forces are exerted. The external load is applied increasingly by updating the position of atoms in the boundary region, which is further used as the fixed-displacement boundary condition in the atomistic simulation. Considering the anisotropy of a discrete lattice, KIC can be expressed as the following formula[16] : KIC = (2γ)1/2 {(S11 S22 /2)1/2 [(S22 /S11 )1/2 + (2S12 + S66 )/2S11 ]1/2 }−1/2
(1)
where KIC is the critical stress intensity factor, γ is the free surface energy, and Sij are the compliance coefficients corrected for plane strain conditions. In order to obtain the critical stress intensity factor KIC , the free surface energy of the (010) plane calculated by using the Farkas potential[17,18] is 1.627 J·m−2 , which is very close to the value 1.625 J·m−2 given by previous calculation[19] . The critical stress intensity factor KIC calculated by Eq. (1) is 0.743 MPa·m1/2 . An expression has been developed that relates stress intensity factor KI and stress σI as KI = σI (πa)1/2
(2)
where a is the crack length. In the present paper, the stress intensity factor KI is used to express the corresponding applied tensile stress σI .
D. Li et al.: J. Mater. Sci. Technol., 2011, 27(11), 1025–1028
1027
Fig. 3 Dislocation emission and crack propagation of Fe crystal without a porous layer: (a) the stacking sequence of (¯ 121) plane is ABCDEDEFABCDEF· · ·, the stacking faults are labeled by D and E; (b) the first a/6[1¯ 1¯ 1](12¯ 1) Shockley partial dislocation is emitted at KIe =0.96 MPa·m1/2 ; (c) the first Shockley partial dislocationa/6[11¯ 1](¯ 121) is emitted at KIe =0.92 MPa·m1/2 ; (d) the crack tip moves by one atomic distance at KIp =1.80 MPa·m1/2
The interatomic potential used here is the Farkas potential[17,18] , a well known embedded atom method (EAM) many-body potential. The time integration of atomic motion is performed by applying the Gear algorithm[20] . The mode-I loading rate is dKI /dt= 0.1 (MPa·m1/2 )/ps. The time step for the MD simulation is Δt=0.1 fs. The temperature for the simulation is T =300 K and the Berendsen isothermal method[21] is used to keep the temperature invariant during the loading process. 3. Results and Discussion It is well known that stacking faults (SFs) can not be generated in the general close-packed plane of {110} or {100} in bcc crystals because of their stacking sequence · · ·ABAB· · · However, for the {112} planes, containing six different layers along the <112> direction with the stacking sequence · · ·ABCDEFABCDEF· · · and with the interplanar √ a/ 6, SFs or multilayer twin formations may occur. In the present paper, the crystallographic orientation of the crack makes {112} slip planes available for activation under mode-I loading. When there is no porous layer introduced on the surface of the crack, the stacking sequence is changed from ABCDEFABCDEF· · · to ABCDEDEFABCDEF· · ·. The stacking faults are labeled by D and E, as indicated in Fig. 3(a). The first Shockley partial dislocation with a Burgers vector [11¯1]/6 on the (¯121) plane is emitted from the crack tip, as shown in Fig. 3(b). The stress intensity for the emission of the first dislocation KIe is 0.96 MPa·m1/2 (KIe =1.29KIC ). Figure 3(c) illustrates that the other Shockley partial dislocation with a Burgers vector [1¯ 1¯1]/6 on the (12¯ 1) plane is emitted from the crack tip, and KIe is 0.92 MPa·m1/2 (KIe =1.24KIC ). As KI increases, the crack tip moves by one atomic distance (from A to B), as indicated in Fig. 3(d). The stress intensity for crack propagation KIp is 1.80 MPa·m1/2
(KIp =2.42KIC ). When the porous layer is introduced on the surface of the crack, the process of dislocation emission and crack propagation is accelerated. It is illustrated that the staking sequence changes from ABCDEFABCDEF· · · to ABCDEDEFABCDEF· · ·, where the stacking faults are labeled by D and E, as indicated in Fig. 4(a). It is shown that the dislocation is emitted from the interface between the porous layer and the bulk. The first Shockley partial dislocation with a Burgers vector [1¯1¯1]/6 on the (¯121) plane is emitted from the crack tip, and the stress intensity ∗ is 0.84 for the emission of the first dislocation KIe ∗ =1.13KIC ), as illustrated in Fig. 4(b). MPa·m1/2 (KIe Figure 4(c) reveals that the other Shockley partial dislocation with a Burgers vector [11¯1]/6 on the (12¯1) plane is emitted from the crack tip, and the stress ∗ intensity for the emission of the first dislocation KIe 1/2 ∗ is 0.82 MPa·m (KIe =1.1KIC ). As KI increases, the crack tip moves by one atomic distance (from A to B), as indicated in Fig. 4(d), and the stress in∗ is 1.52 MPa·m1/2 tensity for crack propagation KIp ∗ (KIp =2.05KIC ). When there is a porous layer on the surface during SCC, a tensile stress generates in the matrix near the interface between the porous layer and the matrix[14] . In this paper, MD simulation results reveal that the tensile stress induced by the porous layer on the surface of the crack superimposes on the applied stress and then assists the applied stress to promote dislocation emission and crack propagation. The critical stress intensity for dislocation emission along [11¯1] direction is reduced from KIe =0.96 MPa·m1/2 ∗ to KIe =0.84 MPa·m1/2 . From Eq. (2), the applied stress σI for dislocation emission along [11¯1] direction is decreased approximately by 640 MPa. As KI increases, the critical stress intensity for crack propagation is reduced from KIp =1.80 MPa·m1/2 to
1028
D. Li et al.: J. Mater. Sci. Technol., 2011, 27(11), 1025–1028
Fig. 4 Dislocation emission and crack propagation of Fe crystal with porous layer on the surface of the crack: (a) the stacking sequence of (¯ 121) plane is ABCDEDEFABCDEF· · ·; the stacking fault are labeled by D and ∗ E; (b) the first a/6[11¯ 1](¯ 121) Shockley partial dislocation is emitted at KIe =0.84 MPa·m1/2 ; (c) the first ∗ 1/2 Shockley partial dislocation a/6 [1¯ 1¯ 1](12¯ 1) is emitted at KIe =0.82 MPa·m ; (d) the crack tip moves by ∗ one atomic distance at KIp =1.52 Mpa·m1/2 ∗ KIp =1.52 MPa·m1/2 , and the applied stress σI for crack propagation is decreased approximately by 1500 MPa. The stress intensity or the stress for dislocation emission and crack propagation decreased is related to the internal stress induced by the porous layer on the surface of the crack. The value of the internal stress induced by the porous layer is approved by our previous work[14] , which shows that the maximum tensile stress is generated in the matrix near the interface between the porous layer and the matrix is 480 MPa for the Fe crystal with porous layer of CV =37.5% when d/B=1/3.
4. Conclusion When a porous layer is introduced on the surface of the crack, the tensile stress induced by the porous layer superimposes on the external applied stress and then assists the applied stress to promote dislocation emission and crack propagation. The critical stress intensity for dislocation emission along [11¯1] direction is reduced from KIe =0.96 MPa·m1/2 ∗ to KIe =0.84 MPa·m1/2 and that along [1¯ 1¯ 1] direc1/2 ∗ to KIe =0.82 tion is reduced from KIe =0.92 MPa·m 1/2 MPa·m . As KI increases, the critical stress intensity for crack propagation of one atomic distance ∗ =1.52 is decreased from KIp =1.80 MPa·m1/2 to KIp 1/2 MPa·m .
Acknowledgements This work was supported by the National Natural Science Foundation of China (Grant No. 50731003) and the NSAF Foundation (Grant No. 10776068). Meng acknowledges grants from the National Natural Science foundation of China (Grant No. 50902009). The authors are indebted to Professor J. Rifkin from Center for Materials Simulation of University of Connecticut for providing the XMD code.
REFERENCES [1 ] R.N. Parkins: Proc. of Corrosion 2000, NACE Inter, Houston, Texas, 2000, 00363,. [2 ] I. Cerny and V. Linhart: Eng. Fract. Mech., 2004, 71, 913. [3 ] J.Q. Wang and A. Atrens: Corros. Sci., 2003, 45, 2199. [4 ] Z.Y. Liu, X.G. Li, C.W. Du , G.L. Zhai and Y.F. Cheng: Corros. Sci., 2008, 50, 2251. [5 ] G. Van Boven, W. Chen and R. Rogge: Acta Mater., 2007, 55, 29. [6 ] B.W. Pan, X. Peng, W.Y. Chu, Y.J. Su and L.J. Qiao: Mater. Sci. Eng. A, 2006, 434, 76. [7 ] X.Z. Guo, K.W. Gao, L.J. Qiao and W.Y. Chu: Metall. Mater. Trans. A, 2001, 32, 1309. [8 ] X.J. Guo, K.W. Gao, L.J. Qiao and W.Y. Chu: Corros. Sci., 2002, 44, 2367. [9 ] X.Z. Guo, K.W. Gao, W.Y. Chu and L.J. Qiao: Mater. Sci. Eng. A, 2003, 346, 1. [10] H. Lu, K.W. Gao and W.Y. Chu: Corros. Sci ., 1998, 40, 1663. [11] H. Lu, K.W. Gao, Y.B. Wang and W.Y. Chu: Corrosion, 2000, 56, 1112. [12] Q.K. Li, Y. Zhang and W.Y. Chu: Comput. Mater. Sci., 2002, 25, 510. [13] Q.K. Li, Y. Zhang, S.Q. Shi and W.Y. Chu: Mater. Lett., 2002, 56, 927. [14] D. Li, F.Y. Meng, X.Q. Ma, L.J. Qiao and W.Y. Chu. Comput. Mater. Sci., 2010, 49, 641. [15] J.F. Knott: Foundamentals of Fracture Mechanics, Butterworths, London, 1973, 57. [16] G.C. Sih and H. Liebowitz: Fracture: an Advanced Treatise, Vol. 2, Academic Press, New York and London, 1968, 127. [17] M.S. Daw and M.I. Baskes: Phys. Rev. B, 1984, 29, 6443. [18] V. Shastry and D. Farkas: Mater. Res. Soc. Symp. Proc., 1996, 409, 75. [19] B. Mutasa and D. Farkas: Surf. Sci., 1998, 415, 312. [20] S. Toxvaerd: J. Comput. Phys., 1982, 47, 444. [21] H.J. C. Berendsen, J.P.M. Postma, W.F.V. Gunsteren, A. Dinola and J.R. Haak: J. Chem. Phys., 1984, 81, 3684.
Molecular Dynamics Simulation of Porous Layer-enhanced Dislocation Emission and Crack Propagation in Iron Crystal D. Li1) , F.Y. Meng1) , X.Q. Ma1)† , L.J. Qiao2) and W.Y. Chu2) 1) Department of Physics, University of Science and Technology Beijing, Beijing 100083, China 2) Corrosion and Protection Center, Key Lab of Environmental Fracture (Ministry of Education), University of Science and Technology Beijing, Beijing 100083, China [Manuscript received June 22, 2010, in revised form August 31, 2010]
The internal stress induced by a porous layer or passive layer can assist the applied stress to promote dislocation emission and crack propagation, e.g. when the pipeline steel is buried in the soil containing water, resulting in stress corrosion cracking (SCC). Molecular dynamics (MD) simulation is performed to study the process of dislocation emission and crack propagation in a slab of Fe crystal with and without a porous layer on the surface of the crack. The results show that when there is a porous layer on the surface of the crack, the tensile stress induced by the porous layer can superimpose on the external applied stress and then assist the applied stress to initiate crack tip dislocation emission under lowered stress intensity KI , or stress. To respond to the corrosion accelerated dislocation emission and motion, the crack begins to propagate under lowered stress intensity KI, resulting in SCC. KEY WORDS: Molecular dynamics simulation; Dislocation emission; Crack propagation; Porous layer; Stress intensity
1. Introduction A lot of disruptive accidents of buried gas or oil transmission pipelines, which were caused by stress corrosion, happened in many countries[1] . Therefore, great attention has been focused on this topic[1–6] . When the X60 pipeline steel is buried in the soilcontaining water, a passive layer or porous layer is formed on the surface. Then the internal stress induced by the porous layer or passive layer assists the applied stress to promote dislocation emission and crack propagation, resulting in stress corrosion cracking (SCC). The corrosion process can enhance dislocation emission and motion, and crack propagation is related to the internal stress induced by the porous layer or the passive film on the surface of pipeline steel. Experiments show that brass in an ammonia solution[7,8] and α-Ti in a methanol solution[9] with a † Corresponding author. Prof., Ph. D.; Tel.: +86 10 62334074; Fax: +86 10 62327283; E-mail address: [email protected] (X.Q. Ma).
protective layer formed on one side and one end fixed is deflected during corrosion. This corrosion (porous layer or passive film) induced stress also exists during SCC, and then assists the applied stress to enhance crack tip dislocation emission and crack propagation, resulting in SCC[10,11] . Li et al.[12,13] calculated the tensile stress of Cu3 Au alloy with a dealloyed layer on the surface. The tensile stress induced by the dealloyed layer can assist the applied stress to enhance crack tip dislocation emission and motion, and crack propagation. Our previous work[14] showed that Fe single crystal with one end fixed and a porous layer on the surface was deflected toward the porous layer during relaxation, resulting in a macro tensile stress. It was also shown that the maximum tensile stress induced by the porous layer was located at the matrix near the interface between the porous layer and the matrix. The aim of this paper is to investigate the effect of the porous layer in the surface of the crack on the process of dislocation emission and crack propagation
1026
D. Li et al.: J. Mater. Sci. Technol., 2011, 27(11), 1025–1028
Fig. 1 Geometry configuration of Fe crystal with a preexisting crack. An external tensile stress σapplied is applied along y direction
in low carbon steel pipeline; and to show how an additive tensile stress caused by the porous layer influences the stress intensity (stress) for dislocation emission and crack propagation. In order to perform the simulation more conveniently, we study Fe crystal with a porous layer where vacancies or voids are linearly distributed instead of low carbon steel pipeline with an irregular distribution of vacancies or voids of porous layer in the experiments. 2. Simulation Process In order to study the effect of the porous layer on dislocation emission and crack propagation, a single edge crack in Fe crystal with and without a porous layer on the surface of the crack is simulated. The geometry configuration of the simulated crystal without the porous layer is shown in Fig. 1. The dimensional size of Fe crystal is 36.5 nm (W )×36.7 nm (L)×1.2 nm (B), containing 138240 atoms. The Fe crystal for the simulation consists of 180 atomic layers along [10¯1] direction, 256 atomic layers along [010] direction, and 6 atomic layers along [101] direction. A single edge crack is considered pre-existing automatically. The crack surface is the (010) plane, and the crack front is oriented along [101] direction. The length (a) and width (w) of the crack are 10.96 nm and 0.57 nm, respectively. The ratio of the crack length to the Fe crystal length is a/L=0.3. An external tensile stress (σapplied ) is applied along the y ([010]) direction, perpendicular to the crack surface of the (010) plane. a0 =0.287 nm is the lattice constant of the Fe crystal. A slab of Fe crystal with the porous layer introduced on the surface of the crack is shown in Fig. 2, where the porous layer is the cross shaded area. The depth of the porous layer is indicated by d. The ratio of the porous layer depth to the crystal length is
Fig. 2 Schematic representation of Fe crystal with a porous layer on the surface of the crack. The shaded area around the crack indicates porous layer and the shaded area on the top and bottom surfaces stands for the region for loading
d/L=0.05. The maximum vacancy concentration CV on the outside surface is 45% and decreases linearly from CV to zero inwardly. The higher vacancy concentration corresponds to the more severe corrosion degree or the longer corrosion time. Periodic boundary condition is imposed along the z direction to simulate the plane strain conditions, while free boundary conditions are employed along the x and y directions. The crack is loaded by the mode-I isotropic elastic K displacement field[15] . The top and the bottom layers of atoms in the y direction are designated as boundary region (Fig. 2), where the external forces are exerted. The external load is applied increasingly by updating the position of atoms in the boundary region, which is further used as the fixed-displacement boundary condition in the atomistic simulation. Considering the anisotropy of a discrete lattice, KIC can be expressed as the following formula[16] : KIC = (2γ)1/2 {(S11 S22 /2)1/2 [(S22 /S11 )1/2 + (2S12 + S66 )/2S11 ]1/2 }−1/2
(1)
where KIC is the critical stress intensity factor, γ is the free surface energy, and Sij are the compliance coefficients corrected for plane strain conditions. In order to obtain the critical stress intensity factor KIC , the free surface energy of the (010) plane calculated by using the Farkas potential[17,18] is 1.627 J·m−2 , which is very close to the value 1.625 J·m−2 given by previous calculation[19] . The critical stress intensity factor KIC calculated by Eq. (1) is 0.743 MPa·m1/2 . An expression has been developed that relates stress intensity factor KI and stress σI as KI = σI (πa)1/2
(2)
where a is the crack length. In the present paper, the stress intensity factor KI is used to express the corresponding applied tensile stress σI .
D. Li et al.: J. Mater. Sci. Technol., 2011, 27(11), 1025–1028
1027
Fig. 3 Dislocation emission and crack propagation of Fe crystal without a porous layer: (a) the stacking sequence of (¯ 121) plane is ABCDEDEFABCDEF· · ·, the stacking faults are labeled by D and E; (b) the first a/6[1¯ 1¯ 1](12¯ 1) Shockley partial dislocation is emitted at KIe =0.96 MPa·m1/2 ; (c) the first Shockley partial dislocationa/6[11¯ 1](¯ 121) is emitted at KIe =0.92 MPa·m1/2 ; (d) the crack tip moves by one atomic distance at KIp =1.80 MPa·m1/2
The interatomic potential used here is the Farkas potential[17,18] , a well known embedded atom method (EAM) many-body potential. The time integration of atomic motion is performed by applying the Gear algorithm[20] . The mode-I loading rate is dKI /dt= 0.1 (MPa·m1/2 )/ps. The time step for the MD simulation is Δt=0.1 fs. The temperature for the simulation is T =300 K and the Berendsen isothermal method[21] is used to keep the temperature invariant during the loading process. 3. Results and Discussion It is well known that stacking faults (SFs) can not be generated in the general close-packed plane of {110} or {100} in bcc crystals because of their stacking sequence · · ·ABAB· · · However, for the {112} planes, containing six different layers along the <112> direction with the stacking sequence · · ·ABCDEFABCDEF· · · and with the interplanar √ a/ 6, SFs or multilayer twin formations may occur. In the present paper, the crystallographic orientation of the crack makes {112} slip planes available for activation under mode-I loading. When there is no porous layer introduced on the surface of the crack, the stacking sequence is changed from ABCDEFABCDEF· · · to ABCDEDEFABCDEF· · ·. The stacking faults are labeled by D and E, as indicated in Fig. 3(a). The first Shockley partial dislocation with a Burgers vector [11¯1]/6 on the (¯121) plane is emitted from the crack tip, as shown in Fig. 3(b). The stress intensity for the emission of the first dislocation KIe is 0.96 MPa·m1/2 (KIe =1.29KIC ). Figure 3(c) illustrates that the other Shockley partial dislocation with a Burgers vector [1¯ 1¯1]/6 on the (12¯ 1) plane is emitted from the crack tip, and KIe is 0.92 MPa·m1/2 (KIe =1.24KIC ). As KI increases, the crack tip moves by one atomic distance (from A to B), as indicated in Fig. 3(d). The stress intensity for crack propagation KIp is 1.80 MPa·m1/2
(KIp =2.42KIC ). When the porous layer is introduced on the surface of the crack, the process of dislocation emission and crack propagation is accelerated. It is illustrated that the staking sequence changes from ABCDEFABCDEF· · · to ABCDEDEFABCDEF· · ·, where the stacking faults are labeled by D and E, as indicated in Fig. 4(a). It is shown that the dislocation is emitted from the interface between the porous layer and the bulk. The first Shockley partial dislocation with a Burgers vector [1¯1¯1]/6 on the (¯121) plane is emitted from the crack tip, and the stress intensity ∗ is 0.84 for the emission of the first dislocation KIe ∗ =1.13KIC ), as illustrated in Fig. 4(b). MPa·m1/2 (KIe Figure 4(c) reveals that the other Shockley partial dislocation with a Burgers vector [11¯1]/6 on the (12¯1) plane is emitted from the crack tip, and the stress ∗ intensity for the emission of the first dislocation KIe 1/2 ∗ is 0.82 MPa·m (KIe =1.1KIC ). As KI increases, the crack tip moves by one atomic distance (from A to B), as indicated in Fig. 4(d), and the stress in∗ is 1.52 MPa·m1/2 tensity for crack propagation KIp ∗ (KIp =2.05KIC ). When there is a porous layer on the surface during SCC, a tensile stress generates in the matrix near the interface between the porous layer and the matrix[14] . In this paper, MD simulation results reveal that the tensile stress induced by the porous layer on the surface of the crack superimposes on the applied stress and then assists the applied stress to promote dislocation emission and crack propagation. The critical stress intensity for dislocation emission along [11¯1] direction is reduced from KIe =0.96 MPa·m1/2 ∗ to KIe =0.84 MPa·m1/2 . From Eq. (2), the applied stress σI for dislocation emission along [11¯1] direction is decreased approximately by 640 MPa. As KI increases, the critical stress intensity for crack propagation is reduced from KIp =1.80 MPa·m1/2 to
1028
D. Li et al.: J. Mater. Sci. Technol., 2011, 27(11), 1025–1028
Fig. 4 Dislocation emission and crack propagation of Fe crystal with porous layer on the surface of the crack: (a) the stacking sequence of (¯ 121) plane is ABCDEDEFABCDEF· · ·; the stacking fault are labeled by D and ∗ E; (b) the first a/6[11¯ 1](¯ 121) Shockley partial dislocation is emitted at KIe =0.84 MPa·m1/2 ; (c) the first ∗ 1/2 Shockley partial dislocation a/6 [1¯ 1¯ 1](12¯ 1) is emitted at KIe =0.82 MPa·m ; (d) the crack tip moves by ∗ one atomic distance at KIp =1.52 Mpa·m1/2 ∗ KIp =1.52 MPa·m1/2 , and the applied stress σI for crack propagation is decreased approximately by 1500 MPa. The stress intensity or the stress for dislocation emission and crack propagation decreased is related to the internal stress induced by the porous layer on the surface of the crack. The value of the internal stress induced by the porous layer is approved by our previous work[14] , which shows that the maximum tensile stress is generated in the matrix near the interface between the porous layer and the matrix is 480 MPa for the Fe crystal with porous layer of CV =37.5% when d/B=1/3.
4. Conclusion When a porous layer is introduced on the surface of the crack, the tensile stress induced by the porous layer superimposes on the external applied stress and then assists the applied stress to promote dislocation emission and crack propagation. The critical stress intensity for dislocation emission along [11¯1] direction is reduced from KIe =0.96 MPa·m1/2 ∗ to KIe =0.84 MPa·m1/2 and that along [1¯ 1¯ 1] direc1/2 ∗ to KIe =0.82 tion is reduced from KIe =0.92 MPa·m 1/2 MPa·m . As KI increases, the critical stress intensity for crack propagation of one atomic distance ∗ =1.52 is decreased from KIp =1.80 MPa·m1/2 to KIp 1/2 MPa·m .
Acknowledgements This work was supported by the National Natural Science Foundation of China (Grant No. 50731003) and the NSAF Foundation (Grant No. 10776068). Meng acknowledges grants from the National Natural Science foundation of China (Grant No. 50902009). The authors are indebted to Professor J. Rifkin from Center for Materials Simulation of University of Connecticut for providing the XMD code.
REFERENCES [1 ] R.N. Parkins: Proc. of Corrosion 2000, NACE Inter, Houston, Texas, 2000, 00363,. [2 ] I. Cerny and V. Linhart: Eng. Fract. Mech., 2004, 71, 913. [3 ] J.Q. Wang and A. Atrens: Corros. Sci., 2003, 45, 2199. [4 ] Z.Y. Liu, X.G. Li, C.W. Du , G.L. Zhai and Y.F. Cheng: Corros. Sci., 2008, 50, 2251. [5 ] G. Van Boven, W. Chen and R. Rogge: Acta Mater., 2007, 55, 29. [6 ] B.W. Pan, X. Peng, W.Y. Chu, Y.J. Su and L.J. Qiao: Mater. Sci. Eng. A, 2006, 434, 76. [7 ] X.Z. Guo, K.W. Gao, L.J. Qiao and W.Y. Chu: Metall. Mater. Trans. A, 2001, 32, 1309. [8 ] X.J. Guo, K.W. Gao, L.J. Qiao and W.Y. Chu: Corros. Sci., 2002, 44, 2367. [9 ] X.Z. Guo, K.W. Gao, W.Y. Chu and L.J. Qiao: Mater. Sci. Eng. A, 2003, 346, 1. [10] H. Lu, K.W. Gao and W.Y. Chu: Corros. Sci ., 1998, 40, 1663. [11] H. Lu, K.W. Gao, Y.B. Wang and W.Y. Chu: Corrosion, 2000, 56, 1112. [12] Q.K. Li, Y. Zhang and W.Y. Chu: Comput. Mater. Sci., 2002, 25, 510. [13] Q.K. Li, Y. Zhang, S.Q. Shi and W.Y. Chu: Mater. Lett., 2002, 56, 927. [14] D. Li, F.Y. Meng, X.Q. Ma, L.J. Qiao and W.Y. Chu. Comput. Mater. Sci., 2010, 49, 641. [15] J.F. Knott: Foundamentals of Fracture Mechanics, Butterworths, London, 1973, 57. [16] G.C. Sih and H. Liebowitz: Fracture: an Advanced Treatise, Vol. 2, Academic Press, New York and London, 1968, 127. [17] M.S. Daw and M.I. Baskes: Phys. Rev. B, 1984, 29, 6443. [18] V. Shastry and D. Farkas: Mater. Res. Soc. Symp. Proc., 1996, 409, 75. [19] B. Mutasa and D. Farkas: Surf. Sci., 1998, 415, 312. [20] S. Toxvaerd: J. Comput. Phys., 1982, 47, 444. [21] H.J. C. Berendsen, J.P.M. Postma, W.F.V. Gunsteren, A. Dinola and J.R. Haak: J. Chem. Phys., 1984, 81, 3684.