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Effect of Notch on Creep Behavior of 316L(N) SS
Available online at www.sciencedirect.com
Procedia Engineering 55 (2013) 517 – 525
6th International Conference on Cree ep, Fatigue and Creep-Fatigue Interaction [CF-6 6]
Effect of Notch on C Creep Behavior of 316L(N) SS S.R.Chardea, A.R. Ballalb*,, D D.R.Peshweb, M.D.Mathewc, R.K.Paretkarb a Government College oof Engineering, Amravati - 444604, India Visvesvaraya National Innstitute of Technology, Nagpur- 440010, India c Indira Gandhi Centre for Atomic Research, Kalpakkam - 603 102, India
b
Abstract Creep tests on 316 L (N) stainless steel notched specimens with varying notch acuity were carried out and notch efffect was studied. Various multiaxial stress states were generaated by providing circumferential V-notch. The tests were carrried out under load of 300 MPa and at 873 K temperature. The creep life of notched specimens was found to be in the range between 1500-3800 hours. Material exhibited notch sstrengthening effect which was attributed to the multiaxiality reesulting into stress distribution during creep. Mixed mode off fracture was observed. The scanning electron micrographs reevealed that, the location of transition from brittle to ductilee mode was pulled in towards center of cross-section as the deegree of constraint was reduced. Finite element analysis resullts showed that, the stress distribution was a local event in thee highly constrained specimen and a global event for specimenn having lower constraint. © Authors. Published by Elsevier Ltd. © 2013 2013The Published by Elsevier Ltd. Selection and/oor peer-review under responsibility of the Indira Gandhi Cen ntre for Selection and peer-review under responsibility of the Indira Gandhi Centre for Atomic Research. Atomic Research
Keywords: Creep; notch; multiaxiality, 316 L (N) steel
1. Introduction There are many practical applications where materials are required to survive for long periods under load at high temperatures, such as power plants, reeactors, refineries etc. The trend towards higher opeerating temperatures, for efficient and better performannce demands materials with higher temperature capacity y. New materials employed to work under multiaxialitty of stresses and higher temperatures are being contin nuously explored. Efforts are always in the direction of ddeveloping new materials because most of the componentts work under multiaxial stress condition [1]. The design codes for components working unnder multiaxial stress state consider the stress- strain histo ory and while meeting these codes, it is required to perfoorm detailed inelastic analysis and study the time dependent i.e. creep as well as time independent deformation behavior of the material. In this context, loading history is one of the major factors in the design of Prototype F Fast Breeder Reactor (PFBR) [2]. However, modern approaches to repair, rejuvenate, or replace critical componnents require rapid turnaround and seek accurate assessm ment of material performance capability.
*
Corresponding author: E-mail address: [email protected]; ballal.atul@gm mail.com
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.2013.03.289
518
S.R. Charde et al. / Procedia Engineering 55 (2013) 517 – 525
Uniaxial creep rupture properties provide the primary basis for the selection of materials and design of components for high temperature applications. These tests usually last up to 10,000 hours and it is generally believed that, the longer the test time, the more accurate may be the life prediction of the component as indicated by David A.Woodford [3]. There is a need to generate suitable material data such as creep strength and fracture resistance in short time by conducting accelerated creep tests. The complexity of phenomenon is acceptable if the test suitably reflects the operating conditions [4]. Stress concentration developed by notch may be presumed to influence the creep and rupture properties of the alloy. Investigation of notch properties of alloys provides the designer with information regarding the effects of stress concentrations of varying magnitude. Also, it helps to gain a better understanding of how stresses influence fracture in creep loading. Many researchers [5, 6, 7] have used Finite Element (FE) analysis to study the role of specimen geometry, material ductility, and constitutive law on creep behavior of material under various stress states on cylindrical specimen with circular notch. Various parameters deciding the degree of constraint are maximum principal stress, strain at notch tip, mean stress, and triaxiality factor. According to Nao-Aki Noda et al [8], the triaxiality factor is more relevant amongst the above parameters. This paper is an attempt to address issues regarding notch effect on 316L(N) SS under creep conditions. Experimental observations on the creep behavior of 316L(N) SS at 300 MPa and 873K under various multiaxial stress states are critically examined by providing circumferential V-notch. 2. Experimental 2.1. Material Nuclear grade 316 L (N) SS differs from the normal commercial variety in the fact that, it has closely controlled composition, lower residual element concentration, and lower inclusion content. The chemical composition of 316 L (N) SS in wt.% is shown in Table 1. Table 1. - Chemical composition of 316 L (N) SS (wt.%). Material
C
Mn
Ni
Cr
Mo
N
S
P
316 L(N)SS
0.025
1.75
12
17
2.4
0.07
0.002
0.023
2.2. Specimen preparation Specimens were prepared out of 316L(N) SS plate in the direction of rolling. The specimens had 50 mm gauge length and 9.5 mm gross diameter. Circumferential 600 V-notch was prepared exactly in the center of gauge length of the specimen. The geometrical details of creep specimens are shown in Fig.1.
Fig. 1. Notch geometry (L = Gauge length, D = gross diameter, d = net diameter, t = notch depth, ȡ= notch root radius and ș = notch angle in degrees.
Different multiaxial stress states were created in the specimen by changing the notch profile which is given in Table 2. In line with the Peterson’s diagram and available literature on circumferential 600 V-notch, the
S.R. Charde et al. / Procedia Engineering 55 (2013) 517 – 525
519
notch geometries and the stress concentration Kt factor for the present work were decided. Material constants and other related data are those pertaining to similar experimentation conducted on smooth specimens. Table 2. Notch geometry details (Kt = stress concentration factor). Specimen
Notch depth
Net dia.
Notch root radius
nomenclature
(t) mm
(d) mm
(ȡ) mm
BM1
0.60
8.3
0.141
4.168
Kt
BM2
0.80
7.9
0.16
4.17
BM3
1.282
6.936
0.3
3.2
BM4
2.03
5.44
0.3
3.15
BM5
2.303
4.894
0.16
1.58
2.3. Creep rupture test 316 L (N) SS notched specimens with notch profiles as given in Table 2 were creep tested at a constant load of 300 MPa and 873 K. The creep rupture tests have been carried out on single lever creep testing machine as per ASTM E 139 and 292-01. 2.4. Post test investigations Experimentally generated data were used to investigate the influence of stress state on creep behavior of 316 L (N) SS. The graphical interpretation of creep data provides a comparison on life spans for the selected geometry of notches in the specimen. Scanning Electron Microscopy (SEM) was utilized for the characterization of fractured surfaces. Precipitates were identified using Energy Dispersive Spectroscopy (EDS). Also, optical microscopy was carried out on longitudinal section of fractured specimen for studying the changes in microstructure during creep. The quantification of the parameters defining degree of constraint is important to know notch effect. According to fracture mechanics, the geometrical constraint can be quantified by the parameters defining multiaxial stresses, namely; von Mises equivalent stress ıeq , mean stress ım, and the maximum principal stress ı1. It could be realized that, the graphical representation of creep data, fractography, and optical microscopy of longitudinal section of specimens have limitations on quantifying the multiaxial stress parameters and its distribution at notch root. To overcome the limitation for assessing the stress distribution during creep, analytical method is proposed. 2.5. Analytical approach 2.5.1. Degree of constraint Analytical approach was adopted for studying the stress levels at various locations from the notch root to the center of the specimen, as it was beyond the scope of experimental measurements. The consideration of advanced life time assessment and modeling of damage and failure behavior is planned for analytical method and so the inelastic calculations in the present work are based on the Norton’s constitutive model for steady state creep stage. Precisely, the advantage of implementing Norton creep law in the present analysis has allowed a better description of strain hardening. For a given material at a given temperature, the process of stress distribution depends mainly on the degree of constraint [2]. The degree of constraint may arise as a combination of: (i) Specimen geometry:- A notch imposes constraint on the specimen. The influence of specimen geometry on degree of constraint includes the notch depth ratio, (t/d/2) and the notch to net radius ratio (ȡ/d/2). The
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degree of constraint imposed due to various (t/dd/2) ratios according to Table 2 was identified in an ascending order as, BM1 > BM2 > BM3 > BM4 > BM5. (ii) Stress level:- For the notched specimens under tensile steady state creep conditions distribution of o ıeq , ım , and ı1 was studied. (iii) Material property:- It is known that, thhe ductile fracture of metals occurs as a result of nucleation, growth, and coalescence of microscopic voids that t initiate at inclusions and second phase particles. Thee main parameters that influence void nucleation and grrowth, and hence ductile fracture, are the triaxiality facto or (ım / ıeq) and the plastic strain. 2.5.2. FE analysis Finite element analysis was carried out and the results were simulated with ANSYS 10.0. The consttitutive behavior used for FE simulation was obtained frrom the secondary creep rates of 316L(N) SS smooth speccimens under uniaxial loading with various applied loads at 873 K. Norton power law relationship stated as, steady creep rate ε s = Aσ n where, A and n being materiaal constant and stress index, respectively while ı is the applied a stress in MPa, holds good for the present creep conditions. •
3. Results and discussion 3.1. Creep life For studying the effect of specimen geomettry on the creep behavior, a comparison is made between n creep rupture lives of notched specimens with five diffferent notch geometries. It is observed from the Fig. 2 th hat, the creep life of notched specimens was found to bee in the range between 1500-3800 hours. In other words, all the notched specimens exhibited notch strengtheninng effect. In particular, the creep life was found to increasse with increase in notch depth ratio. As the geomettrical constraint was reduced, the creep life of the speecimen increased. Further, to explore the reasons of nootch strengthening effect, the information regarding perccentage reduction in area, fracture modes, and grain boundary b precipitation for the specimens after creep teest was collected and is presented in the following sectioons.
Fig. 2. Increasse in rupture life with notch depth.
3.2. Percentage reduction in area Percentage reduction in area is a measure off creep ductility since it is more sensitive measure of du uctility than elongation at high temperatures. Table 3 shows s the % reduction in area with degree of constraintts. It is observed that, as the notch depth increases the percentage reduction in area increases. In other words, as the constraint reduces percentage reduction in area increases. i
S.R. Charde et al. / Procedia Engineering 55 (2013) 517 – 525
Table 3. Percentage reduction in area for various multiaxialities. Specimen
% Reduction in area
BM1
10.2
BM2
13.1
BM3
18.2
BM4
22.9
BM5
24.3
Smooth specimen
62
3.3. Creep fracture modes Metallographic studies were carried out on fracture surfaces of specimens to explore the modes of fracture. A schematic of the locations showing point nos.1, 2 and 3 at which SEM examination was carried out is shown in Fig. 3. In order to observe more features, SEM was also carried out at locations 1, 2 and 3 by tilting fracture surfaces to 45-55 degrees.
Fig. 3. Locations (1-notch root, 2-critical point, 3-net section center) for scanning electron microscopy study and SE micrographs for (a) overall view, (b) at notch root, (c) at critical location, (d) at net section center, and (e) at fracture surface tilted at 450 for BM1.
The cracks were seen at notch root along the circumference of notch cross section as seen in overall view Fig. 3 (a) and a mixed mode of fracture was seen in the lower magnification SEM micrographs of fracture surface in all the specimens i.e. brittle intergrannular fracture at notch root Fig. 3 (b), and ductile transgrannular fracture in the center of specimen Fig. 3 (d). The fractography observations were in line with the results obtained by Li Bin Niu [9] on austenitic steel with high ductility. It can be stated that, brittle intergrannular fracture was observed near the notch root and with approaching the central area of specimen (away from notch) it behaved like a smooth specimen so the notch effect got reduced and a ductile transgrannular mode was exhibited. It is inferred that, brittle intergrannular fracture occurred due to nucleation and growth of grain
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boundary cavitation near notch root whereby; creep deformation was accelerated and as a result the stress got relieved and the ductile transgrannular fracture occured at the center of specimen. It was observed that, the location of transition in fracture mode (brittle intergrannular Æ ductile transgrannular) changed with the notch geometry. It was also observed that, the location of this transition mode was pulled in towards center of the net section as the constraint was reduced. Also, with increasing the notch depth, brittle intergrannular fracture occurred even at the central areas as well as near the notch root in the notch cross section. In the transition zone, the fracture was found to be intergrannular in nature but with increasing portion of dimple morphology areas towards center of specimen. The region of transition zone was followed by region of ductile fracture with dimpled surface, which ultimately resulted in separation into two surfaces. The process of microvoid coalescence continued to form larger cracks, which had approximately half of each cavity on each side of the fracture surface as a tiny cup or “dimple”. The actual fracture surface of a ductile metal, therefore, was essentially nothing but a mass of dimples, or half-voids. It was observed that, as notch depth increased the average dimple size decreased. Examination of these dimples is exceedingly useful in studying fractures because the dimples are extremely sensitive to the direction of stress that caused them. To know the grain boundary precipitations, EDS was carried out at notch root, center of notch, and critical locations of fractured surfaces. The analysis exhibited Cr- and Mo-rich precipitations on the grain boundary. 3.4. Optical microscopy The optical micrographs at notch root locations for BM1 to BM5 samples are shown in Fig.4. The grain boundary precipitations were seen in the microstructures as shown in Fig. 4. It was also observed that, number of cracks at notch root was more in high constraint specimen, BM1. The number of cracks seemed to be lessened as constraint was reduced. In highly constrained specimen, stresses higher than the yield stress were developed resulting in plastic flow at notch root. Due to high constraint, plastic flow could not relieve the high elastic stress and it limited the peak stress to the yield stress resulting into higher number of cracks. Above discussion on fracture modes and microstructure shows that, the developing intergrannular precipitation and following coarsening of grain boundary particles of M23C6 coupled with triaxiality on account of notch are responsible for the significant changes in creep behavior from creep plasticity point of view. 3.5. Analytical approach 3.5.1. Study of influence of constraints on creep stress distribution under multiaxiality using FE analysis The loading conditions and mesh, for BM5 is illustrated in Fig.5. Uniformly distributed load of 300 MPa was applied at remote end of the specimen. The applied loads to produce 300 MPa stress condition were changed according to the net section area of notch of various specimens. The material constants used in FE analysis were evaluated from creep data for smooth 316 L (N) SS specimen at the stress levels of 100 to 400 MPa and 823 to 923 K by regression method. The Young’s modulus and Poisson’s ratio were 145 GPa and 0.33, respectively. The solution control option was operated with Newton-Raphson convergent criterion and automatic time stepping was made ON. Input sub-steps were varied till the convergence of output to non-linear solution for each geometry was satisfied. The results were acquired in the form of stress distribution and creep strain at notch root with the help of general post- processor.
S.R. Charde et al. / Procedia Engineering 55 (2013) 517 – 525
a
b
c
d
e
Fig. 4. Optical micrographs on longitudinal sectionn of fracture surfaces of (a) BM1 (b) BM2 (c) BM3 (d) BM4 (e) BM5.
Fig. 5. Typical specimen geometry moddel and mesh used in FE, mesh refinement near notch root.
3.5.2. Indicators of degree of constraint (a) Maximum principal stress distribution-T The maximum principal stress ı1 was plotted against diistance from the notch root for BM1-BM5 at creep expoosure for 1000 hours as shown in the Fig. 6. It can be seeen that, the higher the constraint, the higher the value off maximum stress and the nearer this peak value is to thee notch
523
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S.R. Charde et al. / Procedia Engineering 55 (2013) 517 – 525
root as in case of BM1. For the least constraaint case BM5, the peak axial stress moved to the cen nter of specimen. Also, the peak stress values decreasedd with decreasing degree of constraint. (b) Von Mises stress distribution-The von Mises’ stress distribution was found to be similar to that t of maximum principal stress distribution. Maximuum principal stress at notch root was found to be more than von Mises stress in all the cases. Stress concentratiion was found to be more localized in highly constraineed case BM1 and it is non- localized in least constrainedd case BM5.
Fig. 6. Maxim mum principal stress distribution.
(c) Triaxiality factor (TF)- A plot of triaxialiity factor ım /ıeq , for 1000 h of creep against distance from the notch root is shown in Fig. 7. It was observed that, ım /ıeq was independent of applied stress, while ım , ıeq t changed with it. For this reason, at higher stresses intergrannular cavities nucleate due to ıeq and grew due to ım. Since, ım was smaller than ıeq, the rupturre occurred before the cavities grew to coalescence. Theerefore, the rupture surfaces exhibited many dimples showing ductile transgrannular fracture with large creep deformation. At highest notch depth (BM5) triaxiality faactor was found to be highest and uniformly distributed d from notch root towards center of specimen. At loweest notch depth (BM1), triaxiality factor decreased and became b non-uniform from notch root towards center of o specimen. For BM1, BM2 and BM3 (at locations maarked), there was sudden change in the value of triaxiliity factor. The location of change in fracture mode obserrved in SEM pictures as discussed above could be co-reelated with the factor marked on the graph, as shown in Fig.7. 4. Conclusions Creep life of notched specimen of 316L(N) SS was found to be much higher than that of smooth speecimen confirming that, the material exhibited notch strengthening phenomenon. Severity of notch strengthen ning, in turn creep life, increases with reduction in notch n geometrical constraint. The microstructural analy ysis of multiaxiality revealed that, specimens exhibbited mixed mode of failure. The structural changees like precipitation, nucleation and growth of cavities, and grain boundary sliding have contributed to the deform mation mechanism.
Dϯ
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Ϭ͘ϲ Dϱ Ϭ͘ϱϱ Dϰ
Ϭ͘ϱ
Dϯ
Ϭ͘ϰϱ Ϭ͘ϰ
DϮ
Ϭ͘ϯϱ Dϭ Ϭ͘ϯ Ϭ ϭϬ ϮϬ ϯϬ ϰϬ ϱϬ ϲϬ ϳϬ ϴϬ ϵϬ ϭϬϬ
DϮ
ĚŝƐƚĂŶĐĞĨƌŽŵŶŽƚĐŚƌŽŽƚ
Dϭ Fig. 7. Change in triaxiality faactor from notch root towards centre of specimen.
S.R. Charde et al. / Procedia Engineering 55 (2013) 517 – 525
The number of cracks located at notch root was observed to be decreasing with decrease in geometrical constraint. It can be concluded that, the driving force ahead of the crack tip is utilized in overcoming the barriers imposed by grain boundary precipitations. Distribution of multiaxial stress components at notch root was found to be localized in case of highly constraint specimen and globalised in case of least constraint specimen.
References [1] European Creep Collaborative Committee (ECCC), part V, volumes 2, 3, 8 and 9, part 1 vol.2.AC/MC/99/issue 1/15.8.05. [2] RCCMR (2000) French design Code. [3] D.A.Woodford, Accelerated high temperature performance evaluation for alloy optimization, embrittlement and life assessment, Materials Performance Analysis Inc. 1-18. [4] G.A.Webster, A code of practice for conducting notched bar creep tests and for interpreting the data, Fatigue and Fracture of Engineering Materials and Structures, ;27: 319-342. [5] K.D.Faddagh et al, Steady State Stress distribution in circumferential notches bars subjected to creep, Journal of Strain Analysis, 1982, 17 No.3: 123-132. [6] H.M.Tlilan et al, Strain concentration factor of circumferentially V-notched cylindrical bars under static tension, Journal of Mechanics, 2008, 24 No.4: 419-427. [7] G.Eggeler, C.Wiesner, A numerical study of parameters controlling stress redistribution in circular notched specimens during creep, Journal of Strain Analysis, 1993; 28 No.1: 13-22. [8] Nao-Aki Noda and Y. Takase, Stress concentration formula useful for all notch shape in a round bar (comparison between torsion, tension and bending), International Journal of Fatigue, 28(2008)151-163. [9] Li Bin Niu et al, Effects of stress state on creep fracture modes of austenitic steel with high ductility, ISIJ International, 2000; 40 No.5: 511-518.
525
Procedia Engineering 55 (2013) 517 – 525
6th International Conference on Cree ep, Fatigue and Creep-Fatigue Interaction [CF-6 6]
Effect of Notch on C Creep Behavior of 316L(N) SS S.R.Chardea, A.R. Ballalb*,, D D.R.Peshweb, M.D.Mathewc, R.K.Paretkarb a Government College oof Engineering, Amravati - 444604, India Visvesvaraya National Innstitute of Technology, Nagpur- 440010, India c Indira Gandhi Centre for Atomic Research, Kalpakkam - 603 102, India
b
Abstract Creep tests on 316 L (N) stainless steel notched specimens with varying notch acuity were carried out and notch efffect was studied. Various multiaxial stress states were generaated by providing circumferential V-notch. The tests were carrried out under load of 300 MPa and at 873 K temperature. The creep life of notched specimens was found to be in the range between 1500-3800 hours. Material exhibited notch sstrengthening effect which was attributed to the multiaxiality reesulting into stress distribution during creep. Mixed mode off fracture was observed. The scanning electron micrographs reevealed that, the location of transition from brittle to ductilee mode was pulled in towards center of cross-section as the deegree of constraint was reduced. Finite element analysis resullts showed that, the stress distribution was a local event in thee highly constrained specimen and a global event for specimenn having lower constraint. © Authors. Published by Elsevier Ltd. © 2013 2013The Published by Elsevier Ltd. Selection and/oor peer-review under responsibility of the Indira Gandhi Cen ntre for Selection and peer-review under responsibility of the Indira Gandhi Centre for Atomic Research. Atomic Research
Keywords: Creep; notch; multiaxiality, 316 L (N) steel
1. Introduction There are many practical applications where materials are required to survive for long periods under load at high temperatures, such as power plants, reeactors, refineries etc. The trend towards higher opeerating temperatures, for efficient and better performannce demands materials with higher temperature capacity y. New materials employed to work under multiaxialitty of stresses and higher temperatures are being contin nuously explored. Efforts are always in the direction of ddeveloping new materials because most of the componentts work under multiaxial stress condition [1]. The design codes for components working unnder multiaxial stress state consider the stress- strain histo ory and while meeting these codes, it is required to perfoorm detailed inelastic analysis and study the time dependent i.e. creep as well as time independent deformation behavior of the material. In this context, loading history is one of the major factors in the design of Prototype F Fast Breeder Reactor (PFBR) [2]. However, modern approaches to repair, rejuvenate, or replace critical componnents require rapid turnaround and seek accurate assessm ment of material performance capability.
*
Corresponding author: E-mail address: [email protected]; ballal.atul@gm mail.com
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.2013.03.289
518
S.R. Charde et al. / Procedia Engineering 55 (2013) 517 – 525
Uniaxial creep rupture properties provide the primary basis for the selection of materials and design of components for high temperature applications. These tests usually last up to 10,000 hours and it is generally believed that, the longer the test time, the more accurate may be the life prediction of the component as indicated by David A.Woodford [3]. There is a need to generate suitable material data such as creep strength and fracture resistance in short time by conducting accelerated creep tests. The complexity of phenomenon is acceptable if the test suitably reflects the operating conditions [4]. Stress concentration developed by notch may be presumed to influence the creep and rupture properties of the alloy. Investigation of notch properties of alloys provides the designer with information regarding the effects of stress concentrations of varying magnitude. Also, it helps to gain a better understanding of how stresses influence fracture in creep loading. Many researchers [5, 6, 7] have used Finite Element (FE) analysis to study the role of specimen geometry, material ductility, and constitutive law on creep behavior of material under various stress states on cylindrical specimen with circular notch. Various parameters deciding the degree of constraint are maximum principal stress, strain at notch tip, mean stress, and triaxiality factor. According to Nao-Aki Noda et al [8], the triaxiality factor is more relevant amongst the above parameters. This paper is an attempt to address issues regarding notch effect on 316L(N) SS under creep conditions. Experimental observations on the creep behavior of 316L(N) SS at 300 MPa and 873K under various multiaxial stress states are critically examined by providing circumferential V-notch. 2. Experimental 2.1. Material Nuclear grade 316 L (N) SS differs from the normal commercial variety in the fact that, it has closely controlled composition, lower residual element concentration, and lower inclusion content. The chemical composition of 316 L (N) SS in wt.% is shown in Table 1. Table 1. - Chemical composition of 316 L (N) SS (wt.%). Material
C
Mn
Ni
Cr
Mo
N
S
P
316 L(N)SS
0.025
1.75
12
17
2.4
0.07
0.002
0.023
2.2. Specimen preparation Specimens were prepared out of 316L(N) SS plate in the direction of rolling. The specimens had 50 mm gauge length and 9.5 mm gross diameter. Circumferential 600 V-notch was prepared exactly in the center of gauge length of the specimen. The geometrical details of creep specimens are shown in Fig.1.
Fig. 1. Notch geometry (L = Gauge length, D = gross diameter, d = net diameter, t = notch depth, ȡ= notch root radius and ș = notch angle in degrees.
Different multiaxial stress states were created in the specimen by changing the notch profile which is given in Table 2. In line with the Peterson’s diagram and available literature on circumferential 600 V-notch, the
S.R. Charde et al. / Procedia Engineering 55 (2013) 517 – 525
519
notch geometries and the stress concentration Kt factor for the present work were decided. Material constants and other related data are those pertaining to similar experimentation conducted on smooth specimens. Table 2. Notch geometry details (Kt = stress concentration factor). Specimen
Notch depth
Net dia.
Notch root radius
nomenclature
(t) mm
(d) mm
(ȡ) mm
BM1
0.60
8.3
0.141
4.168
Kt
BM2
0.80
7.9
0.16
4.17
BM3
1.282
6.936
0.3
3.2
BM4
2.03
5.44
0.3
3.15
BM5
2.303
4.894
0.16
1.58
2.3. Creep rupture test 316 L (N) SS notched specimens with notch profiles as given in Table 2 were creep tested at a constant load of 300 MPa and 873 K. The creep rupture tests have been carried out on single lever creep testing machine as per ASTM E 139 and 292-01. 2.4. Post test investigations Experimentally generated data were used to investigate the influence of stress state on creep behavior of 316 L (N) SS. The graphical interpretation of creep data provides a comparison on life spans for the selected geometry of notches in the specimen. Scanning Electron Microscopy (SEM) was utilized for the characterization of fractured surfaces. Precipitates were identified using Energy Dispersive Spectroscopy (EDS). Also, optical microscopy was carried out on longitudinal section of fractured specimen for studying the changes in microstructure during creep. The quantification of the parameters defining degree of constraint is important to know notch effect. According to fracture mechanics, the geometrical constraint can be quantified by the parameters defining multiaxial stresses, namely; von Mises equivalent stress ıeq , mean stress ım, and the maximum principal stress ı1. It could be realized that, the graphical representation of creep data, fractography, and optical microscopy of longitudinal section of specimens have limitations on quantifying the multiaxial stress parameters and its distribution at notch root. To overcome the limitation for assessing the stress distribution during creep, analytical method is proposed. 2.5. Analytical approach 2.5.1. Degree of constraint Analytical approach was adopted for studying the stress levels at various locations from the notch root to the center of the specimen, as it was beyond the scope of experimental measurements. The consideration of advanced life time assessment and modeling of damage and failure behavior is planned for analytical method and so the inelastic calculations in the present work are based on the Norton’s constitutive model for steady state creep stage. Precisely, the advantage of implementing Norton creep law in the present analysis has allowed a better description of strain hardening. For a given material at a given temperature, the process of stress distribution depends mainly on the degree of constraint [2]. The degree of constraint may arise as a combination of: (i) Specimen geometry:- A notch imposes constraint on the specimen. The influence of specimen geometry on degree of constraint includes the notch depth ratio, (t/d/2) and the notch to net radius ratio (ȡ/d/2). The
520
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degree of constraint imposed due to various (t/dd/2) ratios according to Table 2 was identified in an ascending order as, BM1 > BM2 > BM3 > BM4 > BM5. (ii) Stress level:- For the notched specimens under tensile steady state creep conditions distribution of o ıeq , ım , and ı1 was studied. (iii) Material property:- It is known that, thhe ductile fracture of metals occurs as a result of nucleation, growth, and coalescence of microscopic voids that t initiate at inclusions and second phase particles. Thee main parameters that influence void nucleation and grrowth, and hence ductile fracture, are the triaxiality facto or (ım / ıeq) and the plastic strain. 2.5.2. FE analysis Finite element analysis was carried out and the results were simulated with ANSYS 10.0. The consttitutive behavior used for FE simulation was obtained frrom the secondary creep rates of 316L(N) SS smooth speccimens under uniaxial loading with various applied loads at 873 K. Norton power law relationship stated as, steady creep rate ε s = Aσ n where, A and n being materiaal constant and stress index, respectively while ı is the applied a stress in MPa, holds good for the present creep conditions. •
3. Results and discussion 3.1. Creep life For studying the effect of specimen geomettry on the creep behavior, a comparison is made between n creep rupture lives of notched specimens with five diffferent notch geometries. It is observed from the Fig. 2 th hat, the creep life of notched specimens was found to bee in the range between 1500-3800 hours. In other words, all the notched specimens exhibited notch strengtheninng effect. In particular, the creep life was found to increasse with increase in notch depth ratio. As the geomettrical constraint was reduced, the creep life of the speecimen increased. Further, to explore the reasons of nootch strengthening effect, the information regarding perccentage reduction in area, fracture modes, and grain boundary b precipitation for the specimens after creep teest was collected and is presented in the following sectioons.
Fig. 2. Increasse in rupture life with notch depth.
3.2. Percentage reduction in area Percentage reduction in area is a measure off creep ductility since it is more sensitive measure of du uctility than elongation at high temperatures. Table 3 shows s the % reduction in area with degree of constraintts. It is observed that, as the notch depth increases the percentage reduction in area increases. In other words, as the constraint reduces percentage reduction in area increases. i
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Table 3. Percentage reduction in area for various multiaxialities. Specimen
% Reduction in area
BM1
10.2
BM2
13.1
BM3
18.2
BM4
22.9
BM5
24.3
Smooth specimen
62
3.3. Creep fracture modes Metallographic studies were carried out on fracture surfaces of specimens to explore the modes of fracture. A schematic of the locations showing point nos.1, 2 and 3 at which SEM examination was carried out is shown in Fig. 3. In order to observe more features, SEM was also carried out at locations 1, 2 and 3 by tilting fracture surfaces to 45-55 degrees.
Fig. 3. Locations (1-notch root, 2-critical point, 3-net section center) for scanning electron microscopy study and SE micrographs for (a) overall view, (b) at notch root, (c) at critical location, (d) at net section center, and (e) at fracture surface tilted at 450 for BM1.
The cracks were seen at notch root along the circumference of notch cross section as seen in overall view Fig. 3 (a) and a mixed mode of fracture was seen in the lower magnification SEM micrographs of fracture surface in all the specimens i.e. brittle intergrannular fracture at notch root Fig. 3 (b), and ductile transgrannular fracture in the center of specimen Fig. 3 (d). The fractography observations were in line with the results obtained by Li Bin Niu [9] on austenitic steel with high ductility. It can be stated that, brittle intergrannular fracture was observed near the notch root and with approaching the central area of specimen (away from notch) it behaved like a smooth specimen so the notch effect got reduced and a ductile transgrannular mode was exhibited. It is inferred that, brittle intergrannular fracture occurred due to nucleation and growth of grain
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boundary cavitation near notch root whereby; creep deformation was accelerated and as a result the stress got relieved and the ductile transgrannular fracture occured at the center of specimen. It was observed that, the location of transition in fracture mode (brittle intergrannular Æ ductile transgrannular) changed with the notch geometry. It was also observed that, the location of this transition mode was pulled in towards center of the net section as the constraint was reduced. Also, with increasing the notch depth, brittle intergrannular fracture occurred even at the central areas as well as near the notch root in the notch cross section. In the transition zone, the fracture was found to be intergrannular in nature but with increasing portion of dimple morphology areas towards center of specimen. The region of transition zone was followed by region of ductile fracture with dimpled surface, which ultimately resulted in separation into two surfaces. The process of microvoid coalescence continued to form larger cracks, which had approximately half of each cavity on each side of the fracture surface as a tiny cup or “dimple”. The actual fracture surface of a ductile metal, therefore, was essentially nothing but a mass of dimples, or half-voids. It was observed that, as notch depth increased the average dimple size decreased. Examination of these dimples is exceedingly useful in studying fractures because the dimples are extremely sensitive to the direction of stress that caused them. To know the grain boundary precipitations, EDS was carried out at notch root, center of notch, and critical locations of fractured surfaces. The analysis exhibited Cr- and Mo-rich precipitations on the grain boundary. 3.4. Optical microscopy The optical micrographs at notch root locations for BM1 to BM5 samples are shown in Fig.4. The grain boundary precipitations were seen in the microstructures as shown in Fig. 4. It was also observed that, number of cracks at notch root was more in high constraint specimen, BM1. The number of cracks seemed to be lessened as constraint was reduced. In highly constrained specimen, stresses higher than the yield stress were developed resulting in plastic flow at notch root. Due to high constraint, plastic flow could not relieve the high elastic stress and it limited the peak stress to the yield stress resulting into higher number of cracks. Above discussion on fracture modes and microstructure shows that, the developing intergrannular precipitation and following coarsening of grain boundary particles of M23C6 coupled with triaxiality on account of notch are responsible for the significant changes in creep behavior from creep plasticity point of view. 3.5. Analytical approach 3.5.1. Study of influence of constraints on creep stress distribution under multiaxiality using FE analysis The loading conditions and mesh, for BM5 is illustrated in Fig.5. Uniformly distributed load of 300 MPa was applied at remote end of the specimen. The applied loads to produce 300 MPa stress condition were changed according to the net section area of notch of various specimens. The material constants used in FE analysis were evaluated from creep data for smooth 316 L (N) SS specimen at the stress levels of 100 to 400 MPa and 823 to 923 K by regression method. The Young’s modulus and Poisson’s ratio were 145 GPa and 0.33, respectively. The solution control option was operated with Newton-Raphson convergent criterion and automatic time stepping was made ON. Input sub-steps were varied till the convergence of output to non-linear solution for each geometry was satisfied. The results were acquired in the form of stress distribution and creep strain at notch root with the help of general post- processor.
S.R. Charde et al. / Procedia Engineering 55 (2013) 517 – 525
a
b
c
d
e
Fig. 4. Optical micrographs on longitudinal sectionn of fracture surfaces of (a) BM1 (b) BM2 (c) BM3 (d) BM4 (e) BM5.
Fig. 5. Typical specimen geometry moddel and mesh used in FE, mesh refinement near notch root.
3.5.2. Indicators of degree of constraint (a) Maximum principal stress distribution-T The maximum principal stress ı1 was plotted against diistance from the notch root for BM1-BM5 at creep expoosure for 1000 hours as shown in the Fig. 6. It can be seeen that, the higher the constraint, the higher the value off maximum stress and the nearer this peak value is to thee notch
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root as in case of BM1. For the least constraaint case BM5, the peak axial stress moved to the cen nter of specimen. Also, the peak stress values decreasedd with decreasing degree of constraint. (b) Von Mises stress distribution-The von Mises’ stress distribution was found to be similar to that t of maximum principal stress distribution. Maximuum principal stress at notch root was found to be more than von Mises stress in all the cases. Stress concentratiion was found to be more localized in highly constraineed case BM1 and it is non- localized in least constrainedd case BM5.
Fig. 6. Maxim mum principal stress distribution.
(c) Triaxiality factor (TF)- A plot of triaxialiity factor ım /ıeq , for 1000 h of creep against distance from the notch root is shown in Fig. 7. It was observed that, ım /ıeq was independent of applied stress, while ım , ıeq t changed with it. For this reason, at higher stresses intergrannular cavities nucleate due to ıeq and grew due to ım. Since, ım was smaller than ıeq, the rupturre occurred before the cavities grew to coalescence. Theerefore, the rupture surfaces exhibited many dimples showing ductile transgrannular fracture with large creep deformation. At highest notch depth (BM5) triaxiality faactor was found to be highest and uniformly distributed d from notch root towards center of specimen. At loweest notch depth (BM1), triaxiality factor decreased and became b non-uniform from notch root towards center of o specimen. For BM1, BM2 and BM3 (at locations maarked), there was sudden change in the value of triaxiliity factor. The location of change in fracture mode obserrved in SEM pictures as discussed above could be co-reelated with the factor marked on the graph, as shown in Fig.7. 4. Conclusions Creep life of notched specimen of 316L(N) SS was found to be much higher than that of smooth speecimen confirming that, the material exhibited notch strengthening phenomenon. Severity of notch strengthen ning, in turn creep life, increases with reduction in notch n geometrical constraint. The microstructural analy ysis of multiaxiality revealed that, specimens exhibbited mixed mode of failure. The structural changees like precipitation, nucleation and growth of cavities, and grain boundary sliding have contributed to the deform mation mechanism.
Dϯ
ƚƌŝĂdžŝĂůůŝƚLJ ĨĂĐƚŽƌʍŵͬʍĞƋ
Ϭ͘ϲ Dϱ Ϭ͘ϱϱ Dϰ
Ϭ͘ϱ
Dϯ
Ϭ͘ϰϱ Ϭ͘ϰ
DϮ
Ϭ͘ϯϱ Dϭ Ϭ͘ϯ Ϭ ϭϬ ϮϬ ϯϬ ϰϬ ϱϬ ϲϬ ϳϬ ϴϬ ϵϬ ϭϬϬ
DϮ
ĚŝƐƚĂŶĐĞĨƌŽŵŶŽƚĐŚƌŽŽƚ
Dϭ Fig. 7. Change in triaxiality faactor from notch root towards centre of specimen.
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The number of cracks located at notch root was observed to be decreasing with decrease in geometrical constraint. It can be concluded that, the driving force ahead of the crack tip is utilized in overcoming the barriers imposed by grain boundary precipitations. Distribution of multiaxial stress components at notch root was found to be localized in case of highly constraint specimen and globalised in case of least constraint specimen.
References [1] European Creep Collaborative Committee (ECCC), part V, volumes 2, 3, 8 and 9, part 1 vol.2.AC/MC/99/issue 1/15.8.05. [2] RCCMR (2000) French design Code. [3] D.A.Woodford, Accelerated high temperature performance evaluation for alloy optimization, embrittlement and life assessment, Materials Performance Analysis Inc. 1-18. [4] G.A.Webster, A code of practice for conducting notched bar creep tests and for interpreting the data, Fatigue and Fracture of Engineering Materials and Structures, ;27: 319-342. [5] K.D.Faddagh et al, Steady State Stress distribution in circumferential notches bars subjected to creep, Journal of Strain Analysis, 1982, 17 No.3: 123-132. [6] H.M.Tlilan et al, Strain concentration factor of circumferentially V-notched cylindrical bars under static tension, Journal of Mechanics, 2008, 24 No.4: 419-427. [7] G.Eggeler, C.Wiesner, A numerical study of parameters controlling stress redistribution in circular notched specimens during creep, Journal of Strain Analysis, 1993; 28 No.1: 13-22. [8] Nao-Aki Noda and Y. Takase, Stress concentration formula useful for all notch shape in a round bar (comparison between torsion, tension and bending), International Journal of Fatigue, 28(2008)151-163. [9] Li Bin Niu et al, Effects of stress state on creep fracture modes of austenitic steel with high ductility, ISIJ International, 2000; 40 No.5: 511-518.
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