Review of creep–fatigue endurance and life prediction of 316 stainless steels

Accepted Manuscript Review of creep-fatigue endurance and life prediction of 316 stainless steels Xiao-Li Yan, Xian-Cheng Zhang, Shan-Tung Tu, Sardari-Lal Mannan, Fu-Zhen Xuan, Yong-Cheng Lin PII:

S0308-0161(14)00124-0

DOI:

10.1016/j.ijpvp.2014.12.002

Reference:

IPVP 3422

To appear in:

International Journal of Pressure Vessels and Piping

Received Date: 3 October 2014 Revised Date:

14 December 2014

Accepted Date: 18 December 2014

Please cite this article as: Yan X-L, Zhang X-C, Tu S-T, Mannan S-L, Xuan F-Z, Lin Y-C, Review of creep-fatigue endurance and life prediction of 316 stainless steels, International Journal of Pressure Vessels and Piping (2015), doi: 10.1016/j.ijpvp.2014.12.002. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

ACCEPTED MANUSCRIPT Review of creep-fatigue endurance and life prediction of 316 stainless steels Xiao-Li Yana, Xian-Cheng Zhanga∗, Shan-Tung Tua, Sardari-Lal Mannanb, Fu-Zhen Xuana, Yong-Cheng Linc a

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Key Laboratory of Pressure Systems and Safety, Ministry of Education, East China

University of Science and Technology, Shanghai 200237, P. R. China b

School of Mechanical and Electrical Engineering, Central South University,

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c

Gas Turbine Research Establishment (GTRE), Bangalore 560093, India

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Changsha 410083, China

Abstract

The effects of different factors on the creep-fatigue endurance of 316 stainless steel

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are reviewed in this paper. The factors include hold period, strain range, stress range at half-life and stress relaxation behavior. The strength and limitation of different creep-fatigue life prediction methods are also summarized from the available data. It

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is found that each method shows some agreement with prediction with a specific set of testing data. Standard deviations of different prediction methods are calculated to

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evaluate the prediction capacity of these methods. It is showed that ductility exhaustion model exhibits highest accuracy at two different temperatures. Keywords: Creep-fatigue, Hold period, Strain range, Stress relaxation, Life prediction

∗

Corresponding author: Key Laboratory of Pressure Systems and Safety, Ministry of Education,

Meilong Road 130, Xuhui District, Shanghai 200237, P. R. China. Tel.: +86 021 64253149. E-mail address: [email protected] Page -1-

ACCEPTED MANUSCRIPT 1. Introduction

Stainless steels are widely used in power plants for components which operate at elevated temperatures. For the high-temperature components, the temperature and

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loading change with time at start up and shut down conditions, leading to the combined creep-fatigue deformation. The start up and shut down operations produce the fatigue damage, leading to fatigue failure by crack. While, the creep damage may

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occur during dwell time and creep failure is generally manifested as creep voids on interior grain boundaries by cavitation damage. However, during creep fatigue

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interaction, the creep cavitation damage is often found within the material while fatigue crack damage is observed at surface. The interaction and linking of these two damage mechanisms result in an accelerated failure [1]. When such interaction occurs, the failure path would become mixed (trans-plus intergranular), as seen in Fig.1. The

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main damage mechanism can change with test condition [2].

Figure 1 Schematic showing the creep-fatigue interaction and the failure modes due to fatigue, creep and creep-fatigue interaction. The combined creep-fatigue deformation is known to be one of the most important problems for design of high-temperature components. It is often simulated in the Page -2-

ACCEPTED MANUSCRIPT laboratory by high-temperature low-cycle fatigue (HTLCF) tests with incorporation of hold period at constant strain or stress. In the past decades, considerable efforts have been devoted to characterize the HTLCF behavior of structural materials. It was found that various factors such as frequency, strain rate, wave form, hold position, hold

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period and strain range had important influences on HTLCF resistance [2]. Hence, it is difficult to accurately predict the HTLCF life due to the complicated damage mechanisms. More than 100 creep-fatigue life prediction models have been proposed

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over the past half-century [3]. More recently, Manson and Halford reviewed the methods now in use, or contemplated for use, for creep-fatigue conditions [4].

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In this paper, the effects of the different factors, such as hold period, strain range, and stress relaxation, on the creep-fatigue lives of different types of 316 stainless steels (SSs), including type 316 SS, 316FR SS, 316L SS and 316 LN SS, are summarized from the available data. The strength and limitation of the different

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creep-fatigue life predictions which usually used for 316 SSs are also reviewed. The basis and current status of development of various approaches to predict the combined creep-fatigue endurance are presented. Then, the accuracy of the existing life

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prediction models is discussed. It should be noted that all the data are collected from

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the tests conducted in air and in strain control condition with hold period at the peak strain in tension or compression on the hysteresis loop.

2. Effect of different factors on creep-fatigue endurance of 316 SS

2.1. Hold period effect Introducing the hold time at the peak tensile strain or peak compressive strain would cause stress relaxation. The effect of hold period, th , on the number of cycles Page -3-

ACCEPTED MANUSCRIPT to failure, N f , of 316 SSs at 550 °C, 593 °C, and 600 °C with respect to different total strain ranges, ∆ε t , is shown in Fig. 2, where, for reference purposes, data plotted at hold period of 0.1 min represent the data obtained in continuous cycling.

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The compressive hold period and tensile hold period are respectively denoted as tc and tt . The testing data at 550 °C, 593 °C, and 600 °C were respectively collected from Refs. [5-13], [14-16] and [2,5,7,17,18]. Figure 3 shows the effect of compressive

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hold period on the on the number of cycles to failure, of 316 SSs at 600 °C [2,10,19,20]. Three features can be reflected in Figs. 2 and 3. Firstly, the number of

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cycles to failure decreases linearly with increasing hold period at a given strain range in double logarithmic coordinate except the cases with extremely long hold period. When the temperature is 593 °C and the total strain range is 2.0%, the value of N f with hold period of 1440 min is higher than that with hold period of 600 min, as seen

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in Fig. 2b. This phenomenon may be due to aging of materials in long-hold testing [16]. By comparing with the continuous cycling, the reduction in fatigue life containing dwell time may be due to the interaction between the steady advancing

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fatigue crack and the creep damage formed during periods of stress relaxation [21].

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Secondly, the slope of N f − th line at lower strain range is higher than that at higher strain range. This result indicates that at a given tt , the lower strain range causes more reduced fatigue life by comparing with continuous cycling than higher strain range. Thirdly, the value N f in the symmetrical hold testing is generally higher than that in the tension hold testing at a given hold period, as seen in Fig. 3, indicating that the tension hold would produce more damage than the compressive hold of 316 SS in creep fatigue testing. The similar results can also be found from creep-fatigue testing of type 316 SS at other temperatures, as seen in Fig. 4 [19]. Page -4-

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Fig. 2 Effect of tensile hold time, tt , on the number of cycles to failure, N f , of 316 SSs with respect to different total strain ranges at (a) 550 °C, (b) 593 °C, and (c) 600°C. The solid symbol, open symbol, upper half-filled symbol, and lower half-filled symbol respectively denote the material of type 316 SS, 316FR SS, 316LN SS and Page -5-

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316L SS.

Fig. 3 Effect of hold time, th , on the number of cycles to failure, N f ,of 316 SSs

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with respect to two different total strain ranges at 600 °C. The solid symbol, open symbol and upper half-filled symbol respectively denote the materials of type 316 SS ,

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316FR SS and 316LN SS.

Fig. 4 The influence of hold time, th , on number of cycles to failure, N f , of type 316 SS at different temperatures.

2.2. Relationship between hold time and time to fracture

The effect of tensile hold time on the time to failure, t f , of type 316 SS tested at 593 °C is shown in Fig. 5, where the strain ranges are 1.0%, 2.0% and 4.0%, and the Page -6-

ACCEPTED MANUSCRIPT strain rate is 4×10-3 s-1 [22]. The time to failure increases linearly with increasing the hold time. This trend appears to be contradicted to Fig. 2, which indicates that the fatigue life decreases as tensile hold time increases. In fact, no contradiction exists and both trends are correct and consistent mutually. Because introducing a hold time

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into the strain cycle, the cyclic time could increase by a factor, that is greater than that corresponding to the reduction in cycles to failure [1,23]. Hence, introducing the tensile hold time would lead to decrement of the number of cycles to failure and

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increment of the time to failure.

Fig. 5 Effect of tensile hold time, tt , on the time to failure, t f ,of type 316 SS at

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593 °C.

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The variations of t f along with N f of different types of 316 SSs tested at 550 °C and 600 °C with respect to various tensile hold periods are summarized in Fig. 6, where the strain rate is kept to be 4×10-3 s-1. The data at 550 °C and 600 °C are respectively collected from Refs. [5-8,10,11,13,24-27] and [2,10,17,18,19,28-30]. The data of time to failure is obtained by experiments or calculated by tf =

Nf f

+ N f th

(1)

where f is the continuous cycling frequency and can be calculated as,

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ACCEPTED MANUSCRIPT f =

ε&

(2)

2∆ε

where ε& is the strain rate. And hence, time to failure can be written as,  2 ∆ε t  tf = N f  + th   ε& 

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(3)

Fig. 6 The time to failure versus cycles to failure tested at (a) 550 °C and (b) 600 °C with respect to different total strain ranges and tensile hold periods. The solid symbol, open symbol, upper half-filled symbol, and lower half-filled symbol respectively denote the material of type 316 SS, 316FR SS, 316LN SS and 316L SS. From Fig. 6, it can be seen that, as increasing the tensile hold period at a given strain range, the time to failure increases and the number of cycles to failure decreases.

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( )

( )

The negative slope of log t f − log N f

line is dependent of total strain range. In

( )

( )

double logarithmic coordinate, the log t f − log N f

line at higher strain range is

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steeper than that at lower strain range.

2.3. Cyclic time effect

Figure 7 shows the relationship between the number of cycles to failure and time

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for one cycle, ct , of type 316 SS at 600 °C [19], where the strain rate is 6.7×10-3 s-1. When ct is very short or long, the value of N f is independent of ct for

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continuous cycling. For instance, the saturation phenomenon of the continuous cycling can be observed when ct is longer than 1 min and 10 min at the total strain range of 1.0% and 2.0%, respectively. A consistent behavior is indicated for tension-hold-only and symmetrical hold testing, namely the value of N f decreases

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linearly with increasing ct in double logarithmic coordinate. At a given cyclic time, the value of N f in the symmetrical hold testing is generally higher than that in the

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tensile hold only testing.

Fig. 7 The relationship between the cyclic time, ct , and cycles to failure, N f , of type Page -9-

ACCEPTED MANUSCRIPT 316 SS at 600 °C.

2.4. Strain range effect

Figure 8 shows the effect of the total strain range, ∆ε t , on N f of different types of

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316 SSs at different temperatures with respect to different tensile hold periods. The data at 550 °C, 593 °C and 600 °C are respectively collected from Refs. [6,7,10,12,13,24,26], [14,15,22] and [2,7,9,17,18,19,28,29,31,32]. It is shown that

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introducing the tensile hold period would lead to the decrement in fatigue life at a given strain range and the effect of tension hold on the value of N f becomes more

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obvious at higher temperature. For instance, as seen in Fig. 8a, introducing the hold period in tension has a small influence on the value of N f when the testing temperature is 550°C. However, when the testing temperature sare 593 °C and 600 °C,

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testing is obvious.

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the gap between N f − ∆ε t lines of continuous cycling testing and creep-fatigue

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Fig. 8 Effect of total strain range, ∆ε t , on number of cycles to failure, N f , with

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respect to different hold periods at (a) 550 °C, (b) 593 °C, and (c) 600 °C. The solid

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symbol, open symbol, upper half-filled symbol, and lower half-filled symbol respectively denote the materials of type 316 SS, 316FR SS, 316LN SS and 316L SS. Figure 9 shows the relationship between the plastic strain range, ∆ε p , and number

of cycles to failure in creep fatigue testing at 593 oC [21] and 600 oC [19,32,33,34] with respect to different tensile hold periods. In these plots, the value of N f decreases with increasing hold period at a given ∆ε p . At a given hold period, the relationship between ∆ε p and N f is identical to the Coffin-Manson plot [14], Page -11-

ACCEPTED MANUSCRIPT namely ∆ε p 2

= A ( 2N f

)

c

(4)

where A and c are the fatigue ductility coefficient and fatigue ductility exponent,

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respectively. The values of A with a positive sign and c with a negative sign increase with increasing the tensile hold period. Hence, the ∆ε p - N f curve becomes steeper at longer hold period. The curves in Fig. 9 provide a method of extrapolating results

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from relatively short hold period tests at high plastic strain range to much low plastic strain ranges. Moreover, more experiments should be carried out to determine the

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∆ε p - N f curves at different temperatures. Then, the values of A and c could be

fitted with respect to hold time and temperature. A phenomenological model, which can be considered as the modification of Coffin-Manson equation, could be developed

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to predict the value of N f at a given ∆ε p .

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ACCEPTED MANUSCRIPT Fig. 9 Relationship between the plastic strain range, ∆ε p , and the number of cycles to failure, N f , with respect to different tensile hold periods at (a) 593 °C, and (b) 600 °C. The solid symbol and lower half-filled symbol respectively denote the

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materials of type 316 SS and 316L SS.

2.5. Stress relaxation behavior

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Considering the creep fatigue interaction which introduced hold period at the peak tensile strain or the peak compression strain, the stress relaxation behavior in the

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cyclic regime near half-life can be schematically defined in Fig. 10. The correlations of stress-amplitude, ∆σ , at N f 2 with time-to-fracture, t f , of type 316 SS obtained from tension-hold-only testing and continuous cycling testing at two different temperatures are shown in Fig. 11 [22,23]. For continuous cycling testing and tension-hold-only testing, the numbers indicate the total strain range in percent

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and hold period in minute, respectively. There is a linear relationship between ∆σ and t f in double logarithmic coordinate and the value of ∆σ decreases with

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increasing t f . For the tension-hold-only testing, the values of ∆σ decrease and t f

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increase with increasing the hold period. The variations of ∆σ along with ∆ε p for continuous cycling fatigue and tension-hold-only creep-fatigue tests of type 316 SS at different temperatures are shown in Fig. 12 [16]. The value of stress amplitude increases gradually with increasing the plastic strain range. At a given value of ∆ε p , the stress amplitude in cycling fatigue test is higher than that in tension-hold-only creep-fatigue test.

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Fig. 10 Definition of various stress values observed in hold-time tests.

Fig. 11 The relationship between stress-amplitude at half-life and time to failure of type 316 SS at (a) 593 °C and (b) 650 °C. The numbers denoted by arrows in Fig. 11b represented the total strain range in percent. Page -14-

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Fig. 12 The relationship between the stress amplitude at half-life and the plastic strain

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range of type 316 SS at (a) 593 °C and (b) 625 °C. The variations of tensile stress relaxation, σ r ,tension , along with the hold period at

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different temperatures and strain ranges of different types of 316 SSs are shown in Fig. 13 [5,21-23,35,36].The definition of σ r ,tension can be seen in Fig. 10. The creep fatigue testing of type 316 SS and 316 LN exhibits cyclic hardening characteristics. The shape of the relaxation curve is strongly influenced by strain range and temperature. The degree of stress relaxation would be higher at higher temperature or higher strain range. However, when the hold period is extremely long, the degree of stress relaxation almost keeps constant, as indicated by the arrow in Fig. 13a. Page -15-

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Fig. 13 Tensile stress relaxation along with the hold periods with respect to (a)

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different total strain ranges at different temperatures, and (b) different plastic strain ranges at 625 °C. The solid symbol, upper half-filled symbol, and lower half-filled

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symbol respectively denote the material of type 316 SS, 316LN SS and 316L SS. The relationship between normalized stress relaxation rate, which is defined as

log (σ r ,tension σ max ) , and the hold period at 625 oC can be seen in Fig. 14. It can be

seen that the negative value of normalized stress relaxation rate decreases with increasing the hold period. In double logarithmic coordinate, the value of -

log(σ r ,tension σ max ) decreases linearly with increasing the tensile hold period, as seen Fig. 15, where the slops of the lines are dependent of strain ranges. Page -16-

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Fig. 14 Effect of tensile hold time on the normalized stress relaxation rate,

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log (σ r ,tension σ max ) at 625 °C with respect to different plastic strain ranges. The solid symbol and lower half-filled symbol respectively denote the material of type 316 SS

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and 316L SS.

Fig. 15 Linear relationship between − log (σ r ,tension σ max ) and tensile hold time at 625°C in double logarithmic coordinate. The solid symbol and lower half-filled symbol respectively denote the material of type 316 SS and 316L SS.

3. Creep-fatigue life prediction for316 SS

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ACCEPTED MANUSCRIPT In the past decades, lots of life prediction approaches have been proposed to evaluate the lives of components under creep-fatigue conditions. For 316 SSs, the following methods have been usually used, namely, linear damage summation (LDS) method, strain range partitioning (SRP) method, ductility exhaustion (DE) method,

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cavitation method by Nam et al. [28] and artificial neural network (ANN) method. Detailed reviews of these models mentioned above are available in the literatures

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[5,7-11,14,20,24,28,37-39].

3.1 LDS method

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The LDS method was developed on the basis of assumption that the creep and fatigue damage mechanisms were independent in nature. This method has been incorporated in Appendix of Code Case N47 of the ASME Code [40]. In this method, creep damage and fatigue damage are evaluated separately, where cycle fractions are

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used as a measure of fatigue damage and time fractions are used as a measure of creep damage. The total failure can be expressed as Nf pf

+∑

t =1 tr

(5)

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∑N

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where N f is the number of cycles to failure at a given strain range, N pf is the pure fatigue cycles at the same strain range, t is the time at a given stress, and tr is the time to rupture under pure monotonic creep loading at the same stress. The ASME design criterion is altered slightly from LDS method through assuming that the allowable creep-fatigue damage is D. Moreover, N pf and tr are replaced by N d and td respectively, q  Nf   t    +∑  ≤ D ∑ j =1  N d  j k =1  t d  k p

(6) Page -18-

ACCEPTED MANUSCRIPT where N f and Nd are respectively the numbers of cycles and design-allowable cycles under loading condition j, t is time duration of load condition k, and td is allowable time at a given stress intensity. The value for allowable damage D is varied

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from different materials. Campbell proposed a failure criterion for 316 SS in all existing design code, where the allowable damage D is fitted by the bilinear criterions through connecting (1, 0), (0.3, 0.3) and (0, 1) [41].

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The creep-fatigue interaction diagram based on LDS method for type 316 SS at 625 o

C obtained by Lloyd [37] is shown in Fig. 16, where the hold periods in hour are

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indicated by the numbers. Figure17 shows the accumulated creep and fatigue damage of 316 FR SS at failure at two temperatures [10]. From Fig. 16 and Fig. 17, it can be noted that no correlation between the creep damage and fatigue damage can be found. The accumulated fatigue damage tends to become smaller at higher total strain range

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or higher hold period in most cases. The accumulated creep damage increases with increasing temperature. When the temperature is 550 oC, all data of the creep damage of 316 FR SS are less than 0.2. The value of total creep and fatigue damage below

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D=1 curve when the temperature are 550 oC and 600 oC.

Fig. 16 Creep-fatigue interaction diagram with respect to different tensile hold periods and total strain ranges of type 316 SS at 625 °C based on LDS method. Page -19-

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Fig. 17 Creep-fatigue interaction diagram of 316FR SS predicted by using LDS at two different temperatures.

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The fatigue life prediction results of 316 LN SS and 316 FR SS at 550 °C and 600 °C obtained by the LDS method was given by Sauzay et al.[5] and Takahashi et al.[10], as seen in Fig. 18. The dashed lines indicate the deviation of the predicted life

from the experimental life by a factor of two. The LDS method generates

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non-conservative results for loading case of tension-hold-only, especially at relatively low temperature, since predicted lives tend to be longer than the test results. For 304 SS, Takahashi et al. [42] compared the experimental creep-fatigue lives and

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predictions through LDS method at different temperatures and found the similar phenomenon. Hence, temperature dependence of creep-fatigue life is not well

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represented by the LDS method, perhaps because of ignorance of the temperature dependence of ductility [43]. Although the LDS method has been extensively employed in design codes due to

its simplicity for life prediction, this method has some limitations. Firstly, there is little support for the inherent assumption of load path independent of each other of the creep and fatigue damage processes in this method. This would become evident from isothermal tests designed to simulate the thermally induced creep fatigue deformation mode commonly encountered in high-temperature plant operation. Here, cyclic strain Page -20-

ACCEPTED MANUSCRIPT is induced by thermal transients while creep strain accumulates during the time (hold period at temperature) between the transients [43]. Secondly, the tensile hold and compressive hold periods are considered equally damaging in LDS method. The "healing" effect of compressive dwells on prior tensile dwells is not taken into

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account. Thirdly, in this model, the strain rate dependent of creep damage accumulation is not considered. Hence, this method cannot be used for waveforms

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without tensile hold periods.

Fig. 18 Creep-fatigue life prediction by using LDS method at 550 °C and 600 °C of (a) 316LN SS and (b) 316 FR SS. The numbers in Figs. 18a and 18b are respectively denote the tensile hold period in minute and the total strain range in percent.

3.2 DE method

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ACCEPTED MANUSCRIPT The DE method mainly developed in the UK [10] and has been incorporated into the R5 procedure [44]. This method has been received much attention in the application to long-life components, including fossil fire power plants and nuclear power plants. In DE method, the fatigue damage and creep damage are evaluated

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separately and creep-fatigue life is estimated by using the so called interaction diagrams. The number of cycles to failure can be simply estimated by

1 Dc + D f

(7)

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Nf =

where the creep damage, Dc , and fatigue damage, D f , can be respectively

Df =

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expressed as

1 Nf0

DC = ∫

th

δ ( ε&in , Tabs )

dt

(8b)

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0

ε&in

(8a)

where N f 0 is the number of pure fatigue cycles by using the best fit fatigue curve at a given strain range, ε&in is the inelastic strain rate and δ is the strain limit which is

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defined as creep ductility, and Tabs is the absolute temperature.

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The creep-fatigue interaction diagram predicted by using DE method for 316FR SS at two different temperatures is shown in Fig. 19 [10]. It can be seen that the total damage value is close to D=1 curve at both temperatures. The DE method can give reasonable predictions for different wave shapes with different hold periods, as seen in Fig. 20 [24], where the number denote the tensile hold period in minute. Moreover, creep damage term of DE approach can easily be incorporated in the modification of ASME code case N47 due to its ability to predict lives under hold-period conditions. However, DE approach predicts a relatively larger creep damage at low strain rates Page -22-

ACCEPTED MANUSCRIPT due to decreased elongation to rupture. This can be reflected in Fig. 21[2], which gives the relationship between creep damage and total strain range at 570 oC. It is clear that exhausted creep damage decreases gradually with increasing the total strain

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range.

Fig. 19 Creep-fatigue interaction diagram of 316FR SS obtained by DE method at two

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temperatures.

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Fig. 20 Creep-fatigue life prediction of 316 FR SS by using DE method at 550 °C.

Fig. 21 The relationship between fractional creep damage at failure predicted by DE method and total strain range of 316 SS at 570 °C. Page -23-

ACCEPTED MANUSCRIPT 3.3 SRP method

The SRP method was introduced by Manson et al. at the NASA-Lewis Research Center as an attempt to overcome many limitations of other high temperature creep-fatigue life prediction methods in 1970s [45]. SRP recognition is made on the

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basis of assumption that the inelastic strain range can be partitioned into four components depending on the directions of straining (tension or compression) and the type of inelastic strain (time dependent creep or time independent plasticity). The

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inelastic strain range components include tensile plastic strain followed by compressive plastic strain, tensile creep strain followed by compressive plastic strain,

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tensile plastic strain followed by compressive creep strain and tensile creep strain followed by compressive creep strain. The damage fractions resulting from each of the partitioned strain range components are summed up by an interaction damage rule to predict the creep-fatigue lives. The failure is assumed to occur when the summation

seen in Ref. [4].

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of the damage fractions equaled unity. The detailed introduction of this method can be

For type 316 SS, SRP approach is found to predict life satisfactorily, as seen in

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Fig.22 [38], where the total strain range in percent is denoted by the number and the

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testing temperature is 593oC. Most of the predicted data tend to fall inside the factor of 2 scatter band on life, even though the tensile hold period is very long, i.e., 300 min. Lloyd et al. compared the experimental lives and predictions through SRP method for 316 SS at four different temperatures with respect to different hold periods [37], as seen in Fig. 23. It can be seen that SRP method may overestimate the creep-fatigue life when the temperature is 600 oC, while it underestimates the life when the temperature is higher than 700 oC.

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Fig. 22 Creep-fatigue life prediction by using SRP method of 316 SS at 593 °C.

Fig. 23 Creep-fatigue life prediction by using SRP method of 316 SS at four different temperatures.

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Although the SRP approach has been widely used, it still has some inherent

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limitations. For instance, SRP method is useful for large plastic strains and cannot be extrapolated to low inelastic strain range [1]. Accurate knowledge of cyclic history is required when this method is used and complex loops naturally become difficult to partition.

3.4 Cavitation model

Nam et al. developed the model on the basis of the concept of round-type cavity nucleation factor at grain boundaries [28]. The method is called Nam's cavitation (NC) Page -25-

ACCEPTED MANUSCRIPT model in this paper. This model is developed on the basis of the assumption that the mechanically generated vacancies during the tensile ramp of fatigue lead to the formation of cavities. These cavities grow during the tensile hold period by grain boundary diffusion. The number of nucleated cavities formed in every cycle during

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the cyclic loading is dependent on the plastic strain range, cavity nucleation factor and the number of cycles. Creep fatigue failure is assumed to be mainly controlled by the cavitational damage [33]. Fatigue life is defined by the unstable crack advance, which

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happens if the crack tip opening displacement becomes equal to the spacing of the nucleated intergranular cavities. However, the cavity nucleation factor is found to be

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closely related to the density of grain boundary precipitates. Hence when NC model is used, the generalized relationship between the characteristics of grain boundary precipitates of a given material and the value of cavity nucleation factor should be known. For type 316 SS, the method will generate non-conservative results of life

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prediction at high total strain range and conservative results at low total strain range,

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as seen in Fig. 24 [14], where the number denotes the tensile hold period in minute.

. Fig. 24 Creep-fatigue life prediction of type 316 SS by using NC method at 593 °C.

3.5 ANN approach Page -26-

ACCEPTED MANUSCRIPT The concept of ANN is to imitate the structure and workings of the human brain by means of mathematical models [8,46]. Recently, it has been used in creep-fatigue life prediction and becomes a possible and potential alternative technique. The main advantage of ANN approach over other phenomenological models is that it needn't

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know the relationship among the variables during testing. However, in order to carry out the prediction task, the input data and corresponding output data are repeatedly presented to the neural network. For creep-fatigue life prediction, input data generally

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include four variables, namely, temperature, total strain range, strain rate, and hold period. The values of these variables are normalized in the range from 0 to 1 so that

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all variables get same significance during the learning process. Srinivasan et al. [8] used the ANN method to predict the low cycling fatigue and creep-fatigue lives of 316 LN SS with a wide variety of testing conditions. Results show that the ANN approach lead to low cycling fatigue and creep-fatigue life prediction within a factor of 2 and in

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most of the cases within a factor of 1.5, as seen in Fig. 25 [8], where the number denotes the total strain range in percent. However, sufficient care should be taken over selection of input variables, normalization of data and transformation of input

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variables to obtain the optimum values of ANN parameters when this method is used.

Fig. 25 Creep-fatigue life prediction of 316LN SSat different temperatures by using ANN method. Page -27-

ACCEPTED MANUSCRIPT 3.6 Comparison of prediction capacities of different methods

The standard deviation (SD) method is often used to estimate the prediction capacities of different methods. For a given set of data, the life prediction method with the lower value of SD generally exhibits higher accuracy. The value of SD can

∑ (log N n

where

i =1

− log N e )

2

p

(9)

n −1

n is the number of testing data,

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SD =

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be expressed as,

N p is the predicted life, Ne is

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experimental life. The calculated values of SD for LDS, DE and SRP methods at two temperatures can be seen in Fig. 26 [5,7,10,24,37,39], where LDS-a and LDS-b are obtained from two different set of predicted data with different value of allowable damage D i.e., 1 and bilinear line connecting (1, 0), (0.3, 0.3) and (0, 1). It can be

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seen that DE model exhibits lowest SD value and LDS method generates highest value at both temperatures, indicating that DE model exhibits highest accuracy among these models. However, more experiments with the wide range of experimental

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conditions should be carried out to support this result.

Fig. 26 Comparison of prediction capacities of LDS, DE, and SRP methods through SD analyses at two temperatures. Page -28-

ACCEPTED MANUSCRIPT Although the SD method could evaluate the prediction capacities of different models easily, it cannot illustrate whether the prediction method generates conservative or non-conservative results. Hence, the second method is introduced to estimate the prediction capacities, which is based on the evaluation of N e N p [47].

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When value of N e N p is less than 1, the method will generate non-conservative result. While, the method is conservative if the ratio is higher 1. Figure 27 shows the

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calculated values of N e N p for type 316 SS by SRP method with respect to different total strain ranges and tensile hold periods at 593 °C [38]. It can be seen that the

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values of N e N p by SRP method increases and decreases respectively with increasing the total strain range and tensile hold period. This result indicates the SRP method tends to become non-conservative when the total strain range is relatively

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small and (or) tensile hold period is relatively long.

Fig. 27 The calculated values of N e N p for type 316 SS by SRP method with respected to different total strain ranges at 593 °C.

4. Conclusions

The complex nature of creep fatigue phenomenon of 316 SS has been presented in Page -29-

ACCEPTED MANUSCRIPT this review. The effects of different factors, such as strain range, temperature, hold period, and stress relaxation behavior on the creep-fatigue endurance of 316 SS were discussed. Then, the life prediction methods, which have been usually used for 316 SS under creep fatigue conditions, were reviewed. The prediction capacities of these

1.

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methods were discussed. The following conclusions could draw from this work:

The tensile hold period produced more damage than compressive hold period of 316 SS in creep fatigue testing when other experimental conditions were given.

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The number of cycles to failure would decrease and the time to fracture generally increased due to introducing the tensile hold period. However, when the hold

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period was extremely long, the effect of hold period on the creep-fatigue life may be not obvious. 2.

The relationship between number of cycles to failure and the plastic strain range under creep-fatigue conditions tested with different tensile hold periods at

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different temperatures followed the Coffin-Manson equation. As the length of hold time increased, the ∆ε p - N f curve became steeper. More experiments

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should be carried out to determine the ∆ε p - N f curves at different temperatures to develop a phenomenological model. The 316 SS exhibited cyclic-hardening characteristics under creep-fatigue testing

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3.

conditions. The shape of the relaxation curve was strongly dependent on temperature and strain range. A linear relationship between negative value of normalized stress relaxation rate and hold period can be plotted in double logarithmic coordinate.

4.

The basis and current status of the various methods, which have been usually used to predict the creep-fatigue interaction life of 316 SS were reviewed. Each method had some degree of dealing with a specific set of creep fatigue data. Page -30-

ACCEPTED MANUSCRIPT 5.

By using standard deviation, the creep-fatigue life prediction capacities among linear damage summation model, strain range partitioning model, and ductility exhaustion method are compared at two different temperatures. The ductility exhaustion model exhibited highest accuracy. Although the strain range

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partitioning method has been widely used, it tended to generate non-conservative results of life prediction when the total strain range was relatively small and (or)

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tensile hold period was relatively long.

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Acknowledgements

The authors are grateful for the support by National Natural Science Foundations of China (51322510, 51175177, 11172102). X.C. Zhang is also grateful for the support by New Century Excellent Talents in University (NCET-11-0643) and Shanghai

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Pujiang Program and Key Research Program of Shanghai Science and Technology

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List of Figure captions Fig. 1 Schematic showing the creep-fatigue interaction and the failure modes due to

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fatigue, creep and creep-fatigue interaction. Fig. 2 Effect of tensile hold time, tt , on the number of cycles to failure, N f , of 316 SSs with respect to different total strain ranges at (a) 550 °C, (b)593 °C, and (c)

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600 °C. The solid symbol, open symbol, upper half-filled symbol, and lower half-filled symbol respectively denote the material of type 316 SS, 316FR SS, 316LN

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SS and 316L SS.

Fig. 3 Effect of hold time, th , on the number of cycles to failure, N f ,of 316 SSs with respect to two different total strain ranges at 600 °C. The solid symbol, open symbol and upper half-filled symbol respectively denote the materials of type 316 SS ,

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316FR SS and 316LN SS.

Fig. 4 The influence of hold time, th , on number of cycles to failure, N f , of type 316 SS at different temperatures.

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593 °C.

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Fig. 5 Effect of tensile hold time, tt , on the time to failure, t f ,of type 316 SS at

Fig. 6 The time to failure versus cycles to failure tested at (a) 550 °C and (b) 600 °C with respect to different total strain ranges and tensile hold periods. The solid symbol, open symbol, upper half-filled symbol, and lower half-filled symbol respectively denote the material of type 316 SS, 316FR SS, 316LN SS and 316L SS. Fig. 7 The relationship between the cyclic time, ct , and cycles to failure, N f , of type 316 SS at 600 °C. Fig. 8 Effect of total strain range, ∆ε t , on number of cycles to failure, N f , with Page -37-

ACCEPTED MANUSCRIPT respect to different hold periods at (a) 550 °C, (b) 593 °C, and (c) 600 °C. The solid symbol, open symbol, upper half-filled symbol, and lower half-filled symbol respectively denote the materials of type 316 SS, 316FR SS, 316LN SS and 316L SS. Fig. 9 Relationship between the plastic strain range, ∆ε p , and the number of cycles

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to failure, N f , with respect to different tensile hold periods at (a) 593 °C, and (b) 600 °C. The solid symbol and lower half-filled symbol respectively denote the

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materials of type 316 SS and 316L SS.

Fig. 10 Definition of various stress values observed in hold-time tests.

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Fig. 11 The relationship between stress-amplitude at half-life and time to failure of type 316 SS at (a) 59 3°C and (b) 650 °C. The numbers denoted by arrows in Fig. 11b represented the total strain range in percent.

Fig. 12 The relationship between the stress amplitude at half-life and the plastic strain range of type 316 SS at (a) 593 °C and (b) 625 °C.

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Fig. 13 Tensile stress relaxation along with the hold periods with respect to (a) different total strain ranges at different temperatures, and (b) different plastic strain

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ranges at 625 °C. The solid symbol, upper half-filled symbol, and lower half-filled symbol respectively denote the material of type 316 SS, 316LN SS and 316L SS.

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Fig. 14 Effect of tensile hold time on the normalized stress relaxation rate,

log (σ r ,tension σ max ) at 625 °C with respect to different plastic strain ranges. The solid symbol and lower half-filled symbol respectively denote the material of type 316 SS and 316L SS.

Fig. 15 Linear relationship between − log (σ r ,tension σ max ) and tensile hold time at 625°C in double logarithmic coordinate. The solid symbol and lower half-filled symbol respectively denote the material of type 316 SS and 316L SS. Page -38-

ACCEPTED MANUSCRIPT Fig. 16 Creep-fatigue interaction diagram with respect to different tensile hold periods and total strain ranges of type 316 SS at 625 °C based on LDS method. Fig. 17 Creep-fatigue interaction diagram of 316FR SS predicted by using LDS at two different temperatures.

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Fig. 18 Creep-fatigue life prediction by using LDS method at 550 °C and 600 °C of (a) 316LN SS and (b) 316 FR SS. The numbers in Figs. 18a and 18b are respectively denote the tensile hold period in minute and the total strain range in percent.

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Fig. 19 Creep-fatigue interaction diagram of 316FR SS obtained by DE method at two temperatures.

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Fig. 20 Creep-fatigue life prediction of 316 FR SS by using DE method at 550 °C. Fig. 21 The relationship between fractional creep damage at failure predicted by DE method and total strain range of 316 SS at 570 °C.

Fig. 22 Creep-fatigue life prediction by using SRP method of 316 SS at 593 °C.

temperatures.

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Fig. 23 Creep-fatigue life prediction by using SRP method of 316 SS at four different

Fig. 24 Creep-fatigue life prediction of type 316 SS by using NC method at 593 °C.

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ANN method.

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Fig. 25 Creep-fatigue life prediction of 316LN SSat different temperatures by using

Fig. 26 Comparison of prediction capacities of LDS, DE, and SRP methods through SD analyses at two temperatures. Fig. 27 The calculated values of N e N p for type 316 SS by SRP method with respected to different total strain ranges at 593 °C.

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ACCEPTED MANUSCRIPT Highlight


Effects of different factors on the creep-fatigue endurance of 316 SS are reviewed




Tensile hold period produces more damage than compressive hold period of 316




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SS The 316 SS exhibits cyclic-hardening characteristics under creep-fatigue conditions

Different creep-fatigue life prediction methods are summarized




The creep-fatigue life prediction capacities are evaluated

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