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Effect of Multiaxial State of Stress on Creep Rupture Behaviour of 2.25Cr-1Mo Steel
Available online at www.sciencedirect.com
Procedia Engineering 55 (2013) 510 – 516
6th International Conference on Cree ep, Fatigue and Creep-Fatigue Interaction [CF-6 6]
Effect of Multiaxial State off Stress on Creep Rupture Behavio our of 2.225Cr-1Mo Steel Sunil Goyal∗, K. Laha, V. D. V Vijayanand, S. Panneer Selvi, M. D. Mathew Mechanical Metallurgy Division, Indira Gaandhi Centre for Atomic Research, Kalpakkam- 603 102, India
Abstract Creep tests on both plain and notched specimens havving ratio of notch throat radius to notch root radius ranging fro om 1 to 20 keeping the specimen diameter to notch throat diiameter ratio fixed at 1.67. The creep rupture life of the materrial was found to increase in presence of notch at all the appllied stresses. The extent of increase in rupture life was more att higher applied stresses. Creep rupture life was found to increease with notch acuity and tend to saturate at larger notch acuity y. SEM fractography investigation revealed the presence of bboth plasticity induced dimpled intragranular ductile failure an nd creep cavitation induced intergranular brittle failure. The relative proportion of plasticity induced ductile failure to o creep e cavitation induced brittle failure decreased with inccrease in notch acuity and decrease in applied stress. Finite element analysis was carried out to study the effect of notch aacuity on the stress distribution across the notch during creep ex xposure and its effect on creep rupture life. The variation of sstresses at the skeletal point with notch acuity was used to charaacterize the state of stress in the notched specimen. The reduuction in von-Mises stress with notch acuity at the skeletal po oint has been considered for the increase in rupture life of the relatively ductile 2.25Cr-1Mo steel. © 2013 Authors. Published by Elsevier Ltd. © 2013The The Authors. Published by Elsevier Ltd. Selection and/or peer-review under responsibility of the Indira Selection Centre and peer-review under responsibility Gandhi for Atomic Research of the Indira Gandhi Centre for Atomic Research.
Keywords: Multiaxial state of stress; finite element analysis;; stress distribution; creep cavitation
1. Introduction Ferritic steels are used extensively as a strructural material in steam generating systems of nucleear and conventional power plants and petrochemical inndustries. The choice of these materials is based on its ad dequate creep resistance in the temperature range 673-8223 K. Structural components operating at high temperatu ures are subjected to creep damage, which results froom the formation, growth and coalescence of cavities. The components may be subjected to multiaxial statte of stress as a result of mode of loading or from sharp change c in geometry which causes local stress concenntration. In order to assess the life of such components, it is important to accurately predict the extent of ccreep damage under multiaxial state of stress and accorrdingly rupture life. It is very difficult to carryout the crreep tests in multiaxial state of stress. Creep testing on notched n specimen can overcome this difficulty and cchange in notch profile can provide different multiax xialities
∗
Corresponding Author: E-mail address: [email protected]
1877-7058 © 2013 The Authors. Published by Elsevier Ltd. Selection and peer-review under responsibility of the Indira Gandhi Centre for Atomic Research. doi:10.1016/j.proeng.2013.03.288
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Sunil Goyal et al. / Procedia Engineering 55 (2013) 510 – 516
depending on the notch radius. Creep experiments were carried out on notched specimen may lead to o notch strengthening or weakening compared to plain specimen depending on the deformation behavior of material m under multiaxial creep conditions. Earlier stuudies carried out on 0.5Cr-0.5Mo-0.25V steel showed notch strengthening for shallow notches and tendencyy towards notch weakening for sharp notches [1]. Otherr study carried out by Eggeler et al. on P91 steel showeed the notch strengthening behavior [2]. As the deformation and damage in the material is associated with the stresses developed around notch, finite element (FE) an nalysis coupled with continuum damage mechanics hass been extensively used for the creep rupture life estimaation in notched specimens [3-6]. Studies have shown that the presence of notch during creep exposure leads to o stress redistribution at the notched region due to the difference d in creep deformation rates across the notch plaane [7]. Hayhurst et al. analysed the damage in notchedd specimens observed a good agreement between experimental observation and numerical analysis [3]. In the present investigation, effect of notch on o creep behaviour of 2.25Cr-1Mo steel has been studieed. The different notch acuities have been introduced to study the multiaxial state of stress. The creep rupture of the material under multiaxial state of stress has beeen explained based on the stress distribution around thee notch estimated using FE analysis. 2. Experimental 9 MPa Creep experiments were carried out on plain specimen of 2.25Cr-1Mo steel at stress levels of 210 to 90 and at 873 K in air. Chemical composition of thee material is given in Table 1. Table 1. Chemicaal composition of the material (wt %). Material 2.25Cr-1Mo steel
C
Si
Mn
P
S
Cr
Mo
Fe
0.06
0.18
0.48
0.008
0.008
2.18
0.93
Bal.
Creep tests were also carried out on circumfeerentially U notched specimens with various notch geometries at net stress of 210 to 110 MPa and 873 K. The geometry g of the notched specimens is illustrated in Fig. 1 along with the major dimensions, Table 2.
Fig. 1. Specimen geometry aloong with different notch radii used for experiments.
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Sunil Goyal et al. / Procedia Engineering 55 (2013) 510 – 516
Table 2. Major dimensions of notched specimens. D
8.35 mm
d
5.0 mm
R
5.0 mm to 0.25 mm
The minimum diameter of the notched specimen was kept same as plain specimen to study the notch strengthening or weakening effects. The notch depth ratio (D/d) was fixed as 1.67 [8] and varied the notch acuity ratios (d/R) ranging from 1 to 20. Double notched specimens were used for experiment so that un-failed notch could be utilized for post test metallography. Tests on notched specimens were carried out in such a way that net stress acting on the notch is equal to the stress on plain specimen. The stresses for the plain specimen were selected to give a rupture life of maximum 1,000 h. The spacing between the notches was kept adequate so that the stresses and strain distribution would not affect each other. In order to understand the creep deformation and damage around the notch, analysis of stress and strain across it during creep exposure was carried out using FE analysis. 2D axisymmetric analysis was carried out using quadrilateral elements. Norton’s creep law relating the steady state creep rate with applied stress (ȑs=Aσn, where ȑs is the strain rate (h-1), σ is the stress (MPa) and A and n are constants) was used as a constitutive equation for the analysis. A mesh convergence analysis was first performed to avoid the effect of mesh size. This was carried out by running different models with varying element size until the difference in results between two consecutive models was negligible. The elastic modulus E was taken as 160 GPa and A was chosen to give a creep rate of 10-5 h-1 at a stress of 150 MPa for a given value of n. A net stress of 150 MPa was applied at the notch throat section of the specimen of various notch acuities and calculations were made for n ranging from 1 to 9. Typical finite element mesh used in FE analysis is shown in Fig. 2. The analysis was continued till the stress redistribution in the notch throat was completed and steady state had been achieved.
Fig. 2. Typical mesh used for the FE analysis.
3. Results and discussions 3.1. Creep rupture life The creep rupture life of the material was found to increase in presence of notch at all the applied stresses, Fig. 3. The extent of increase in rupture life was more at higher applied stresses. Creep rupture life was found to increase with notch acuity ratio and tend to saturate at larger notch acuity.
Sunil Goyal et al. / Procedia Engineering 55 (2013) 510 – 516
Fig. 3. Creep rupture life as a function of notch acuity ratio at different stress levels, 873 K.
SEM fractography investigation revealed the presence of both plasticity induced dimpled intragranular ductile failure and creep cavitation induced intergranular brittle failure, Fig. 4. The relative proportion of plasticity induced ductile failure to creep cavitation induced brittle failure decreased with increase in notch acuity ratio, Fig. 5.
Fig. 4. SEM fractograph revealing the presence of both plasticity induced dimpled intragranular ductile failure and creep cavitation induced intergranular brittle failure for notch radius of 0.25 mm at 130 MPa and 873 K.
Fig. 5.(a) SEM fractograph revealing the intergranular brittle failure near surface for notch radius of 0.25 mm and 130 MPa and (b) the presence of plasticity induced dimpled intragranular ductile failure for notch radius of 5.0 mm and 130 MPa.
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3.2. Finite element analysis Creep deformation and fracture under multiaxial state of stress is associated with the cavity nucleation, their growth and final fracture. Nucleation of creep cavity is associated with the stress concentration around particles which is produced by the inhomogeneous plastic deformation. Since the shear stress is required for the plastic deformation to occur, von-Mises stress plays a major role in creep cavitation [9-10]. The diffusive growth of intergranular cavities is associated with the maximum principal stress acting on those grain boundaries which are perpendicular to the stress. Therefore, growth of creep cavities is strongly dependent on the maximum principal stress. In order to understand the effect of multiaxial state of stress on creep deformation behaviour of the material, FE analysis was carried out. The value of stress exponent ‘n’ was varied to obtain the skeletal point stresses. Figure 6 shows the stress distribution across the notch after elastic deformation. The maximum stress at the root matched with the theoretical stress as calculated from Peterson’s equation [11] indicating the adequacy of mesh size refinement in FE analysis. The analysis carried out for different values of stress exponent and notch acuities showed that stress redistribution was found to be dependent on constraint developed across the notch and the value of stress exponent n of Norton’s creep law. Figure 6 shows the variation of maximum principal stress and von-Mises stress across the notch plane after achieving the stationary state for different n values and notch acuity ratio of 1 and 20.
Fig. 6. Normalized stress distribution after the elastic deformation.
The stress redistribution in the notched region was found to be independent of the stress exponent and intersected at one point, except at very low values of n. This point is called as skeletal point and could be used to characterize the deformation and failure of material under multiaxial creep conditions [12]. For shallow notch, the principal stress was found to be maximum at the centre of notch, Fig. 7(a). The maxima of principal stress shifted from centre to notch root with increase in notch severity, Fig. 7(b). The von-Mises stress was found to be stationary with distance from notch for shallow notch, Fig. 6(c). The stress was found to be maximum near notch throat for sharper notches, Fig. 7(d). High principal stress and von-Mises stress near the notch root would lead to creep cavitation induced brittle fracture near surface, Fig. 5(a). However, central region of the specimen notch plane would be typical dimpled ductile fracture in sharper notches, Fig. 4. Whereas, constant von-Mises stress throughout the notch plane in shallow notch indicates the uniform cavitation, Fig. 5(b). Creep rupture life in case of multiaxial state of stress is generally defined by the representative stress (σrep). The representative stress is the stress when applied to plain specimen, gives the same rupture life as that of notched specimen. The material is found to show notch weakening if σrep is higher than net applied stress, whereas notch strengthening if the σrep is lesser than net applied stress. Many relationships have been developed to predict the creep rupture life under multiaxial state of stress using the skeletal point stresses [12]. Among the existing relationships, the most popular relationship is by Hayhurst [13] which uses skeletal point
Sunil Goyal et al. / Procedia Engineering 55 (2013) 510 – 516
von-Mises and maximum principal stress to define the representative stress. The skeletal point von-Mises stress, maximum principal stress and hydrostatic stresses as a function of notch acuity ratio is shown in Fig. 8. All the stresses were found to saturate after notch acuity ratio of 10 suggesting the rate of strengthening saturates as observed experimentally. In the present investigation steady state analysis was carried out without considering the tertiary stage of creep deformation. Introduction of damage variable in material model could have given more insight to the fracture behavior under multiaxial state of stress.
(a)
(b)
(c)
(d)
Fig. 7. Variation of stress around the notch subjected to creep exposure at 150 MPa and 873 K (a) Principal stress distribution for shallow notch (notch radius = 5.0 mm) and (b) sharp notch (notch radius = 0.25 mm), (c) von-Mises stress distribution for shallow notch (notch radius = 5.0 mm) and (d) sharp notch (notch radius = 0.25 mm).
Fig. 8. Variation of von-Mises stress, maximum principal stress and hydrostatic stress obtained at skeletal point for different notch acuities. The stresses were normalized by net stress.
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Sunil Goyal et al. / Procedia Engineering 55 (2013) 510 – 516
4. Conclusions Based on the creep experiments on notch and plain specimens and finite element analysis, the following conclusions have been drawn. • 2.25Cr-1Mo steel used in this investigation was found to show notch strengthening at all stress levels and notch acuities. • Creep rupture life was found to increase with notch acuity ratio and tend to saturate at larger notch acuity ratios. • For shallow notch, the principal stress was found to be maximum at the centre of notch. The maxima of principal stress shifted from centre to notch throat with increase in notch severity. • The skeletal point von-Mises stress, maximum principal stress and hydrostatic stresses were found to saturate with increase in notch acuity ratio.
Acknowledgements The authors are grateful to Shri S. C. Chetal, Director, IGCAR and Dr. T. Jayakumar, Director, Metallurgy and Materials Group, IGCAR for their constant encouragement and support. The authors are also thankful to Dr. A. K. Bhaduri, AD, MDTG for his keen interest in this work.
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13]
S.E.Ng, G.A.Webster, B.F.Dyson, Notch weakening and strengthening in creep of 0.5Cr-0.5Mo-0.25V steel. In: Francois D. et al, editors. Advances in Fracture Research, Pergamon Press, New York; 1980, p. 1275- 1283. G.Eggeler, W.Tato, P.Jemmely, B.deMestral, Creep rupture of circular notched P91 specimens: influence of heat treatment and notch geometry. Scripta Metal. Mater. 27(1992)1091- 96. D.R.Hayhurst, P.R.Dimmer, M.W.Chernuka, Estimates of the creep rupture life time of structures using the finite element method. J. Mech. Phy. Solids (1975) 23: 335- 55. D.R.Hayhurst, J.Lin, R.J.Hayhurst, Failure in notched tension bars due to high temperature creep: Interaction between nucleation controlled cavity growth and continuum cavity growth. Int. J. Solids Struct. (2008) 45: 2233- 50. T.H.Hyde, L.Xia, A.A.Becker, Prediction of creep failure in aeroengine materials under multiaxial stress states. Int. J. Mech. Sc.i 38(1996)385- 403. Qiang Xu, Simon Barrans, The development of multiaxial creep damage constitutive equations for 0.5Cr-0.5Mo-0.25V ferritic steel at 590° C. JSME Int. J. 46(2003)51- 59. D.R.Hayhurst, J.T.Henderson, Creep stress redistribution in notched bars. Int. J. Mech. Sci. 19(1977)133- 146. D.R.Hayhurst, F.A.Leckie, J.T.Henderson, Design of notched bars for creep-rupture testing under tri-axial stresses. Int. J. Mech. Sci. 19(1977)147- 159. W.D.Nix, Mechanisms and controlling factors in creep fracture. Mater. Sci. Engg. A 103(1988)103- 110. B.J.Cane, Creep damage accumulation and fracture under multiaxial stresses. In: Francois D. et al, editors. Advances in Fracture Research, Pergamon Press, New York; 1981, p. 1285- 1293. W.D.Pilkey, Peterson’s Stress Concentration Factors. 2nd ed. New York: Wiley; 1997. G.A.Webster, S.R.Holdsworth, M.S.Loveday, K.Nikbin, I.J.Perrin, H.Purper, R.P.Skelton, M.W.Spindler, A code of practice for conducting notched bar creep tests and for interpreting the data. Fattigue Frac. Engg. Mater. Struct. 27(2004)319- 342. D.R.Hayhurst, Creep rupture under multiaxial states of stress. J. Mech. Phy Solids 20(1972)381- 390.
Procedia Engineering 55 (2013) 510 – 516
6th International Conference on Cree ep, Fatigue and Creep-Fatigue Interaction [CF-6 6]
Effect of Multiaxial State off Stress on Creep Rupture Behavio our of 2.225Cr-1Mo Steel Sunil Goyal∗, K. Laha, V. D. V Vijayanand, S. Panneer Selvi, M. D. Mathew Mechanical Metallurgy Division, Indira Gaandhi Centre for Atomic Research, Kalpakkam- 603 102, India
Abstract Creep tests on both plain and notched specimens havving ratio of notch throat radius to notch root radius ranging fro om 1 to 20 keeping the specimen diameter to notch throat diiameter ratio fixed at 1.67. The creep rupture life of the materrial was found to increase in presence of notch at all the appllied stresses. The extent of increase in rupture life was more att higher applied stresses. Creep rupture life was found to increease with notch acuity and tend to saturate at larger notch acuity y. SEM fractography investigation revealed the presence of bboth plasticity induced dimpled intragranular ductile failure an nd creep cavitation induced intergranular brittle failure. The relative proportion of plasticity induced ductile failure to o creep e cavitation induced brittle failure decreased with inccrease in notch acuity and decrease in applied stress. Finite element analysis was carried out to study the effect of notch aacuity on the stress distribution across the notch during creep ex xposure and its effect on creep rupture life. The variation of sstresses at the skeletal point with notch acuity was used to charaacterize the state of stress in the notched specimen. The reduuction in von-Mises stress with notch acuity at the skeletal po oint has been considered for the increase in rupture life of the relatively ductile 2.25Cr-1Mo steel. © 2013 Authors. Published by Elsevier Ltd. © 2013The The Authors. Published by Elsevier Ltd. Selection and/or peer-review under responsibility of the Indira Selection Centre and peer-review under responsibility Gandhi for Atomic Research of the Indira Gandhi Centre for Atomic Research.
Keywords: Multiaxial state of stress; finite element analysis;; stress distribution; creep cavitation
1. Introduction Ferritic steels are used extensively as a strructural material in steam generating systems of nucleear and conventional power plants and petrochemical inndustries. The choice of these materials is based on its ad dequate creep resistance in the temperature range 673-8223 K. Structural components operating at high temperatu ures are subjected to creep damage, which results froom the formation, growth and coalescence of cavities. The components may be subjected to multiaxial statte of stress as a result of mode of loading or from sharp change c in geometry which causes local stress concenntration. In order to assess the life of such components, it is important to accurately predict the extent of ccreep damage under multiaxial state of stress and accorrdingly rupture life. It is very difficult to carryout the crreep tests in multiaxial state of stress. Creep testing on notched n specimen can overcome this difficulty and cchange in notch profile can provide different multiax xialities
∗
Corresponding Author: E-mail address: [email protected]
1877-7058 © 2013 The Authors. Published by Elsevier Ltd. Selection and peer-review under responsibility of the Indira Gandhi Centre for Atomic Research. doi:10.1016/j.proeng.2013.03.288
511
Sunil Goyal et al. / Procedia Engineering 55 (2013) 510 – 516
depending on the notch radius. Creep experiments were carried out on notched specimen may lead to o notch strengthening or weakening compared to plain specimen depending on the deformation behavior of material m under multiaxial creep conditions. Earlier stuudies carried out on 0.5Cr-0.5Mo-0.25V steel showed notch strengthening for shallow notches and tendencyy towards notch weakening for sharp notches [1]. Otherr study carried out by Eggeler et al. on P91 steel showeed the notch strengthening behavior [2]. As the deformation and damage in the material is associated with the stresses developed around notch, finite element (FE) an nalysis coupled with continuum damage mechanics hass been extensively used for the creep rupture life estimaation in notched specimens [3-6]. Studies have shown that the presence of notch during creep exposure leads to o stress redistribution at the notched region due to the difference d in creep deformation rates across the notch plaane [7]. Hayhurst et al. analysed the damage in notchedd specimens observed a good agreement between experimental observation and numerical analysis [3]. In the present investigation, effect of notch on o creep behaviour of 2.25Cr-1Mo steel has been studieed. The different notch acuities have been introduced to study the multiaxial state of stress. The creep rupture of the material under multiaxial state of stress has beeen explained based on the stress distribution around thee notch estimated using FE analysis. 2. Experimental 9 MPa Creep experiments were carried out on plain specimen of 2.25Cr-1Mo steel at stress levels of 210 to 90 and at 873 K in air. Chemical composition of thee material is given in Table 1. Table 1. Chemicaal composition of the material (wt %). Material 2.25Cr-1Mo steel
C
Si
Mn
P
S
Cr
Mo
Fe
0.06
0.18
0.48
0.008
0.008
2.18
0.93
Bal.
Creep tests were also carried out on circumfeerentially U notched specimens with various notch geometries at net stress of 210 to 110 MPa and 873 K. The geometry g of the notched specimens is illustrated in Fig. 1 along with the major dimensions, Table 2.
Fig. 1. Specimen geometry aloong with different notch radii used for experiments.
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Sunil Goyal et al. / Procedia Engineering 55 (2013) 510 – 516
Table 2. Major dimensions of notched specimens. D
8.35 mm
d
5.0 mm
R
5.0 mm to 0.25 mm
The minimum diameter of the notched specimen was kept same as plain specimen to study the notch strengthening or weakening effects. The notch depth ratio (D/d) was fixed as 1.67 [8] and varied the notch acuity ratios (d/R) ranging from 1 to 20. Double notched specimens were used for experiment so that un-failed notch could be utilized for post test metallography. Tests on notched specimens were carried out in such a way that net stress acting on the notch is equal to the stress on plain specimen. The stresses for the plain specimen were selected to give a rupture life of maximum 1,000 h. The spacing between the notches was kept adequate so that the stresses and strain distribution would not affect each other. In order to understand the creep deformation and damage around the notch, analysis of stress and strain across it during creep exposure was carried out using FE analysis. 2D axisymmetric analysis was carried out using quadrilateral elements. Norton’s creep law relating the steady state creep rate with applied stress (ȑs=Aσn, where ȑs is the strain rate (h-1), σ is the stress (MPa) and A and n are constants) was used as a constitutive equation for the analysis. A mesh convergence analysis was first performed to avoid the effect of mesh size. This was carried out by running different models with varying element size until the difference in results between two consecutive models was negligible. The elastic modulus E was taken as 160 GPa and A was chosen to give a creep rate of 10-5 h-1 at a stress of 150 MPa for a given value of n. A net stress of 150 MPa was applied at the notch throat section of the specimen of various notch acuities and calculations were made for n ranging from 1 to 9. Typical finite element mesh used in FE analysis is shown in Fig. 2. The analysis was continued till the stress redistribution in the notch throat was completed and steady state had been achieved.
Fig. 2. Typical mesh used for the FE analysis.
3. Results and discussions 3.1. Creep rupture life The creep rupture life of the material was found to increase in presence of notch at all the applied stresses, Fig. 3. The extent of increase in rupture life was more at higher applied stresses. Creep rupture life was found to increase with notch acuity ratio and tend to saturate at larger notch acuity.
Sunil Goyal et al. / Procedia Engineering 55 (2013) 510 – 516
Fig. 3. Creep rupture life as a function of notch acuity ratio at different stress levels, 873 K.
SEM fractography investigation revealed the presence of both plasticity induced dimpled intragranular ductile failure and creep cavitation induced intergranular brittle failure, Fig. 4. The relative proportion of plasticity induced ductile failure to creep cavitation induced brittle failure decreased with increase in notch acuity ratio, Fig. 5.
Fig. 4. SEM fractograph revealing the presence of both plasticity induced dimpled intragranular ductile failure and creep cavitation induced intergranular brittle failure for notch radius of 0.25 mm at 130 MPa and 873 K.
Fig. 5.(a) SEM fractograph revealing the intergranular brittle failure near surface for notch radius of 0.25 mm and 130 MPa and (b) the presence of plasticity induced dimpled intragranular ductile failure for notch radius of 5.0 mm and 130 MPa.
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Sunil Goyal et al. / Procedia Engineering 55 (2013) 510 – 516
3.2. Finite element analysis Creep deformation and fracture under multiaxial state of stress is associated with the cavity nucleation, their growth and final fracture. Nucleation of creep cavity is associated with the stress concentration around particles which is produced by the inhomogeneous plastic deformation. Since the shear stress is required for the plastic deformation to occur, von-Mises stress plays a major role in creep cavitation [9-10]. The diffusive growth of intergranular cavities is associated with the maximum principal stress acting on those grain boundaries which are perpendicular to the stress. Therefore, growth of creep cavities is strongly dependent on the maximum principal stress. In order to understand the effect of multiaxial state of stress on creep deformation behaviour of the material, FE analysis was carried out. The value of stress exponent ‘n’ was varied to obtain the skeletal point stresses. Figure 6 shows the stress distribution across the notch after elastic deformation. The maximum stress at the root matched with the theoretical stress as calculated from Peterson’s equation [11] indicating the adequacy of mesh size refinement in FE analysis. The analysis carried out for different values of stress exponent and notch acuities showed that stress redistribution was found to be dependent on constraint developed across the notch and the value of stress exponent n of Norton’s creep law. Figure 6 shows the variation of maximum principal stress and von-Mises stress across the notch plane after achieving the stationary state for different n values and notch acuity ratio of 1 and 20.
Fig. 6. Normalized stress distribution after the elastic deformation.
The stress redistribution in the notched region was found to be independent of the stress exponent and intersected at one point, except at very low values of n. This point is called as skeletal point and could be used to characterize the deformation and failure of material under multiaxial creep conditions [12]. For shallow notch, the principal stress was found to be maximum at the centre of notch, Fig. 7(a). The maxima of principal stress shifted from centre to notch root with increase in notch severity, Fig. 7(b). The von-Mises stress was found to be stationary with distance from notch for shallow notch, Fig. 6(c). The stress was found to be maximum near notch throat for sharper notches, Fig. 7(d). High principal stress and von-Mises stress near the notch root would lead to creep cavitation induced brittle fracture near surface, Fig. 5(a). However, central region of the specimen notch plane would be typical dimpled ductile fracture in sharper notches, Fig. 4. Whereas, constant von-Mises stress throughout the notch plane in shallow notch indicates the uniform cavitation, Fig. 5(b). Creep rupture life in case of multiaxial state of stress is generally defined by the representative stress (σrep). The representative stress is the stress when applied to plain specimen, gives the same rupture life as that of notched specimen. The material is found to show notch weakening if σrep is higher than net applied stress, whereas notch strengthening if the σrep is lesser than net applied stress. Many relationships have been developed to predict the creep rupture life under multiaxial state of stress using the skeletal point stresses [12]. Among the existing relationships, the most popular relationship is by Hayhurst [13] which uses skeletal point
Sunil Goyal et al. / Procedia Engineering 55 (2013) 510 – 516
von-Mises and maximum principal stress to define the representative stress. The skeletal point von-Mises stress, maximum principal stress and hydrostatic stresses as a function of notch acuity ratio is shown in Fig. 8. All the stresses were found to saturate after notch acuity ratio of 10 suggesting the rate of strengthening saturates as observed experimentally. In the present investigation steady state analysis was carried out without considering the tertiary stage of creep deformation. Introduction of damage variable in material model could have given more insight to the fracture behavior under multiaxial state of stress.
(a)
(b)
(c)
(d)
Fig. 7. Variation of stress around the notch subjected to creep exposure at 150 MPa and 873 K (a) Principal stress distribution for shallow notch (notch radius = 5.0 mm) and (b) sharp notch (notch radius = 0.25 mm), (c) von-Mises stress distribution for shallow notch (notch radius = 5.0 mm) and (d) sharp notch (notch radius = 0.25 mm).
Fig. 8. Variation of von-Mises stress, maximum principal stress and hydrostatic stress obtained at skeletal point for different notch acuities. The stresses were normalized by net stress.
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4. Conclusions Based on the creep experiments on notch and plain specimens and finite element analysis, the following conclusions have been drawn. • 2.25Cr-1Mo steel used in this investigation was found to show notch strengthening at all stress levels and notch acuities. • Creep rupture life was found to increase with notch acuity ratio and tend to saturate at larger notch acuity ratios. • For shallow notch, the principal stress was found to be maximum at the centre of notch. The maxima of principal stress shifted from centre to notch throat with increase in notch severity. • The skeletal point von-Mises stress, maximum principal stress and hydrostatic stresses were found to saturate with increase in notch acuity ratio.
Acknowledgements The authors are grateful to Shri S. C. Chetal, Director, IGCAR and Dr. T. Jayakumar, Director, Metallurgy and Materials Group, IGCAR for their constant encouragement and support. The authors are also thankful to Dr. A. K. Bhaduri, AD, MDTG for his keen interest in this work.
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13]
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