# RAFM钢蠕变行为的模拟.pdf

TECHNICAL PAPER Modeling of Creep Deation Behaviour of RAFM Steel V. S. Srinivasan1J. Vanaja1B. K. Choudhary1K. Laha1 Received 5 November 2015/Accepted 7 December 2015/Published online 2 January 2016 The Indian Institute of Metals - IIM 2016 AbstractCreep tests were carried out on reduced acti- vation ferritic–martensitic steel at 773, 823 and 873 K. Creep strain–time trajectory obtained was subsequently modeled by 4-theta projection ology. An optimum cutoff strain was defi ned in tertiary regime for better rep- resentation of creep curves. The theta values were corre- lated with applied stresses and temperatures by artifi cial neural network for robust prediction. Following this, the design related creep properties such as time to reach 1 strain, time to rupture and minimum creep rate were pre- dicted successfully. KeywordsRAFM steel Creep Theta projection Neural network Prediction 1 Introduction In nuclear fusion reactors, blanket module faces thermo- mechanical loads and irradiation damage by high energy neutrons [1, 3]. Reduced activation ferritic–martensitic RAFM steel is chosen as the candidate structural material forblanketmoduleofInternationalThermonuclear Experimental Reactor ITER [1, 2] to withstand the severe environment and loading conditions. It has adequate mechanical properties, excellent void swelling resistance and favorable thermal properties. Recently, Indian RAFM steel was developed successfully for ITER by modifying thechemicalcompositionofGrade91steel[1]. Molybdenum was replaced by tungsten and niobium by tantalum to minimize residual radioactivity [1–3]. In addition, several undesirable elements were limited to ppm levels [1–3]. The operating temperature faced by RAFM steel in ITER is about 773 K and creep deation and damage are important considerations for engineering design of this material [1–4]. In order to minimize the time consuming and costly experimentation, theta projection approach has been used widely to predict the long term creep behavior from short term creep tests on various structural materials [5–9]. Towards this goal, creep deation behaviour of RAFM steel was modeled by 4-theta projection. For the fi rst time, the potential role of artifi cial neural network in achieving accurate prediction of creep properties through prediction of variation in theta values as a function of temperature and stress has been brought out. 2 Experimental Details The RAFM steel was produced indigenously by M/s. Mishra Dhatu Nigam Limited MIDHANI, Hyderabad, India. Chemical composition of the steel in wt is given in Table 1. The material was subjected to normalizing at 1253 K for 30 min followed by air cooling. Tempering treatment involved soaking at 1033 K for 1 h followed by air cooling. The microstructural details of normalized and tempered RAFM steel are given elsewhere [4]. Cylindrical creep specimens with 50 mm gauge length and 5 mm gauge diameter were machined with gauge length parallel to the rolling direction of the steel plate. Constant load creep tests were carried out at 773, 823 and 873 K in the stress range of 120-320 MPa. Time to rupture values varied from about 30 h to about 14,000 h. 1 where ec is the creep strain. The fi rst term represents the decaying primary creep regime and the second term rep- resents the accelerating tertiary creep. The parameters h1 and h3correspond to limiting strain in primary and tertiary stages and h2and h4are rate parameters characterizing the curvatures of the primary and tertiary stages. In addition, each theta can be described as function of a stress and temperature by various relations [5]. A typical relation often employed is loghi ai bir ciT dirT;2 where r is stress, T is the temperature and i 1, 2, 3, 4. The functions can be defi ned on the basis of short term tests and longtermcreepdatacanbepredicted.However,littleresearch has gone into validating the functional of the theta interpolation/extrapolation function for a given material [5]. The creep rate can be obtained by differentiating the Eq. 1. The time to reach minimum creep rate tmcan be obtained by differentiating creep rate equation with respect to time and setting it equal to zero. Substituting tmin creep rate equation yields minimum creep rate. tm 1 h2 h4 ln h1h22 h3h42 3 There are relations other than theta projection to describe the creep behavior [10]. Equation 1 was fi tted to experimental creep curves by using Levenberg-Marqudt LM iterative, non-linear curve fi tting technique with proper initial solution. However, Eq. 1 could not describe the overall creep curve well and it took large number of iterations. This issue was solved by defi ning a suitable cut-off strain in tertiary region for sat- isfactory representation of all the creep curves. The cut-off strain arrived at was about 5 . It must be pointed out that the difference between time to reach 5 strain and rupture life is negligible in this alloy. After defi ning cut-off strain, L-M algorithm took a few iterations about 3–10 and creep curves at 773, 823 and 873 K were represented accurately by theta projection ology Fig. 1. The theta parameters were obtained by fi tting Eq. 1. Figure 2a, b depict the variation of log h1strain parame- ter and log h4rate parameter at 773, 823 and 873 K. It can be seen from Fig. 2 that there is complex variation in theta values in terms of magnitude and trend as a function stress and temperature. Complex variations have been Table 1 Chemical composition wt of Indian RAFM steel CrCVWTaNNbMoP, S 9.040.080.221.00.060.02260.0010.0010.002 Fig. 1 Representation of creep curves by theta projection with a cut- off strain of about 0.052. Symbols represent experimental data and prediction of creep strain–time data is represented by solid line 568Trans Indian Inst Met 2016 692567–571 123 noted for other thetas also. It can also be seen from Fig. 2 that variation in theta values shows a small break between high stress corresponding to time to rupture below about 300 h and low stress levels. 5 Prediction of Creep Behaviour of RAFM Steel For a given stress and temperature, functional s such as Eq. 2 can be used to predict the four theta parameters, which in turn can be used to predict the creep curves by using Eq. 1. Evans [5] has explored various relations to model the variation in theta values and stressed their importance for reliable extrapolation. However, the varia- tion of thetas with stress and temperature for RAFM steel could not be represented by relations such as Eq. 2, accurately R2value less than 0.6. Hence, multilayer perceptron MLP type artifi cial neural network ANN has been used successfully to establish the complex interrela- tions between theta parameters with applied stress and temperature Fig. 2. ANN is a powerful nonlinear regression tool used for prediction and pattern recognition applications [11]. The architecture and the operating procedure of Multi layer Perceptron MLP type ANN can be found elsewhere [9, 11]. After defi ning a suitable architecture, MLP is fi rst trained with training data set. Following this, the trained MLP model is tested with test data which was not used in training. If the perance is satisfactory during testing, one can go for prediction. Otherwise retraining is necessary after modifying the architecture of MLP. In the present investigation, the parameters used in ANN modeling were applied stress and temperature. The output is theta parameters in Eq. 1. As number of data sets is 13 in the present investigation 13, only one prediction data set corresponding to 773 K/280 MPa test condition was used. In the remaining data, two short-term data sets were used for testing and the remaining sets were used for training. The ANN model developed was used to predict/repro- duce the theta parameters obtained by theta projection ology, at various stresses and temperatures. Fig- ure 3a, b compares the fi tted and predicted theta-1 and theta-4 values respectively. It can be seen from Fig. 3 that the predictions are excellent in spite of complex variation in theta values as a function of applied stress and temper- ature Fig. 2. The predicted theta values in turn were used to estimate the design related creep properties using Eq. 1. The prediction of creep properties has been carried out for all the data sets to assess how accurately the creep behavior can be represented by the combination of these two techniques for subsequent use for long term extrapo- lation in future. 5.1 Time to Reach a Limiting Strain Time to reach a limiting strain is an important criterion from design viewpoint. As an example, for a time-depen- dent analysis, ASME nuclear Code NH requires ina- tion on the time or stress to produce 1 strain. Time to reach a given creep strain can be calculated by solving Eq. 1 iteratively by techniques such as Newton–Raphson . Figure 4 depicts the time to reach 1 creep strain as a function of stress at 773, 823 and 873 K. The pre- dictions at this low strain level are in good agreement with experimental data. It has been observed that time to reach 1 strain decreases with increase in applied stress and its variation with stress is found to be linear in log–log scale Fig. 4. Further, the isothermal lines are not parallel to each other and they tend to diverge at longer durations of creep. Fig. 2 Variations of a h1and b h4with stress and temperature Trans Indian Inst Met 2016 692567–571569 123 5.2 Minimum Creep Rate as a Function of Stress and Temperature Minimum creep rate can be used to predict long-term creep life from short-term data. In order to uate it, time at which creep rate becomes minimum tm was obtained from Eq. 3 which is based on theta ology. The minimum creep rate can then be calculated by substituting tmin creep rate equation obtained by differentiating Eq. 1. The predictions as a function of stress and tem- perature are depicted in Fig. 5, superimposed with exper- imental data. The predictions are closer to experimental data. It is seen that minimum creep rate increases with increase in applied stress and temperature Fig. 5. It must be pointed out that minimum creep rate being a differential quantity is very sensitive to creep behavior of the material and to the error involved in fi tting the creep curve. 5.3 Rupture Life Creep rupture life is one of the important high temperature design criteria. In order to predict the rupture life at various test conditions from Eq. 1, it is necessary to know the variation of rupture strain with applied stress and temper- ature. For example, rupture strain can be expressed as a function of temperature and stress similar to Eq. 2 [12]. However for RAFM steel, the variation of rupture strain with test conditions is not signifi cant and not systematic. Hence an average value of 5 strain to failure is defi ned for all the test conditions. The error of estimating time to fracture by this defi nition is generally small as the fi nal part of the tertiary region of creep rate increases rapidly and only small fraction of creep life is spent above 5 strain. Figure 6 compares the calculated and experimental rupture Fig. 3 Comparison of fi tted and predicted a h1and b h4at various stresses and temperatures Fig. 4 Time to reach 1 strain as a function of applied stress at 773, 823 and 873 K Fig. 5 Minimum creep rate versus applied stresses at different temperatures 570Trans Indian Inst Met 2016 692567–571 123 lives. Predicted lives are in close agreement with experi- mental lives for both the relations. 6 Conclusions 1.Four theta ology satisfactorily represents the creep curves of RAFM steel after incorporating about 5 cut-off strain in the tertiary regime. 2. The theta parameters fi tted as a function of applied stresses and temperatures were represented by ANN model. The prediction of creep properties by this combined approach was excellent. 3.In future, physically based analytical relations can be developed between theta parameters and test conditions for RAFM steel. On the other hand, it is also possible to model the creep curves fully by ANN so as to have an intelligent database for long term predictions. References 1. Vanaja J, Laha K, Mathew M D, Jayakumar T, and Kumar E R, Procedia Eng 55 2013 271. 2. Lindau R et al., Fusion Eng Des, 75–79 2005 989. 3. Mathew M D, Vanaja J, Laha K, Reddy G V, Chandravathi K S, and Rao K B S, J Nucl Mater 417 2011 77. 4. Vanaja J, Laha K, Mythili R, Chandravathi K S, Saroja S and Mathew M D, Mater Sci Eng A 533 2012 17. 5. Evans M, J Mater Sci 37 2002 2871. 6. Kim W-G, Yin S-N, Kim Y-W and Chang J-H, Eng Fract Mech, 75 2008 4985. 7. Evans R W and Scharning P, Mater Sci Technol 17 2001 487. 8. Lin Y C, Xia Y-C, Chen M-S, Jiang Y-Q and Li L-T, Comput Mater Sci 67 2013 243. 9. Ibanez A R, Srinivasan V S and Saxena A, Fatigue Fract Eng Mater Struct 29 2006 1010. 10. Sawada K, Tabuchi M and Kimura K, Mater Sci Eng A 510–511 2009 190. 11. Srinivasan V S, Valsan M, Rao K B S, Mannan S L and Raj B, Int J Fatigue, 25 2003 1327. 12. Wolf H, Mathew M D, Mannan S L and Rodriguez P, Mater Sci Eng A 159 1992 199. Fig. 6 Rupture life versus applied stresses at different temperatures Trans Indian Inst Met 2016 692567–571571 123