Elsevier

Measurement

Volume 97, February 2017, Pages 242-250
Measurement

Thermo-mechanical modeling of metallic alloys for nuclear engineering applications

https://doi.org/10.1016/j.measurement.2016.11.003Get rights and content

Highlights

  • Thermomechanical stress analysis of SS304 alloys using finite element model.

  • High temperature characterization of SS304 crucial for safe nuclear systems design.

  • Developed analytical model conforms to elastic theory satisfactorily.

  • Proposed model useful for determining optimal design parameters of nuclear systems.

Abstract

Austenitic stainless steel 304 (SS304) alloy has been used exclusively in nuclear power systems due to its excellent mechanical properties at elevated temperature environments. Despite its wide popularity, the effect of various factors such as temperature, applied strain, and strain rate on the mechanical strength of the alloy needs to be investigated. In light of this, this research article focuses on development of a finite element based analytical modeling approach for modeling the mechanical strength of SS304 with respect to considered input factors. The proposed analytical approach combines the interface of finite element modeling and the heuristic optimization algorithm of genetic programming. The developed analytical model shows good conformance of the mechanical strength with the experimental observations. Sensitivity and parametric analysis of the derived model was also able to accurately predict the elastic and plastic regime of the alloy and shows that temperature remains the major factor in influencing the mechanical strength of the alloy. The proposed approach is anticipated to be useful for nuclear engineers for optimizing the design criteria for nuclear pressure vessels which can lead to increased material savings and hence lead to more sustainable design of nuclear power generation facilities.

Introduction

The recent demand for the need of clean and cheaper energy technologies has resulted in the spurt of nuclear based power generation systems. Austenitic stainless steel (SS304) alloy with its excellent corrosion resistance properties under deep sea water has proven to be an indispensable material for construction of reactor pressure vessels in nuclear reactors. The reactor pressure vessels play an important role in containing the reactor core at elevated temperatures during which the dislocations in the alloy gets obstructed by interstitial solute atoms. However, application of high stress will eventually make the dislocation overcome the obstruction which again gets obstructed by other solute atoms and the process repeats. This characteristic of SS304 is the dynamic strain ageing (DSA) regime which is more common at the nuclear reactor operating temperatures. Hence understanding the effect of various parameters on the mechanical strength of SS304 at elevated temperatures is vital for designing safer and more efficient nuclear power systems.

The mechanics of SS304 has been well studied in the literature predominantly by experimental methods. Bhonsle and Van Karsen [1] studied the mechanical properties of cold worked SS304 using a series of static and dynamic tests. It was found that the high temperature optimizes the fatigue strength while decreasing the Young’s modulus and other elastic properties of steel. Baldissera [2] investigated the hardness and tensile strength of SS304 through experimental testing. The results showed that deep cryogenic treatment on austenitic stainless steel slightly reduces the elastic modulus of the steel alloy. Zhao et al. [3] deployed a novel thermo-mechanical processing technique with a rapid cooling technique for processing austenitic steel for pipeline applications. The mechanical tests conducted on the processed material showed that the austenitic component along with the acicular ferrite and bainitic ferrite phase imparted excellent combination of strength, toughness and crack arrest property. Li et al. [4] studied the microstructural surface characteristics of austenitic steel with emphasis on the fatigue behavior. It was found that the coatings formed on the surface using surface mechanical attrition treatment improves the fatigue strength by as much as 13.1% for the steel alloy. In addition to these experiments, some simulations studies have also been conducted to study the mechanical properties of SS304. It can be seen that all of the above mentioned studies utilized experiments for characterizing mechanical response of SS304. However, as SS304 exhibits unique characteristics at elevated temperatures, it would be interesting to develop a thermo-mechanical simulation model which would enable a more accurate description of the physics of mechanisms involved in the material deformation process. Furthermore, FEM techniques have been successfully deployed in the past studies for characterizing mechanical strength of materials [5], [6], [7], [8], [9]. FEM simulation works on the principle of describing the mechanisms in the material based on physical equation. Hence, FEM simulation is capable of generating accurate solutions in predicting engineering properties of alloy systems with minimal cost and high rapidity [10], [11], [12], [13]. The FEM model can be used to generate the input data for analytical models based in place of conducting expensive and time-consuming experiments [14], [15], [16], [17]. The analytical model can then be used to generate complex non-linear mathematical models by considering the actual physics of mechanisms involved in mechanical testing of materials [18], [19], [20]. Additionally, among the various available analytical models, genetic programming (GP) offers the advantage of a fast and cost-effective formulation of a functional expression based on the multiple input variables without any incorporation and need of the existing analytical models [21], [22], [23]. It is to the best of author’s knowledge that limited or no work exists on the application of FEM based GP analytical model on evaluating the effect of input factors on mechanical strength of SS304. The potential future applications of SS304 in nuclear power industry require a thorough understanding and investigation of various factors on the mechanical strength characteristics of SS304.

In view of the above research gap which has been highlighted, the main objective of this research article will focus on investigating the effect of various input factors in mechanical strength of SS304 alloy using an integrated FEM based GP model. The procedure adopted by the authors to accomplish the research objective outlined in this work is presented as follows. At first, the experimental setup for measurement of tensile strength of SS304 alloy has been presented. The experiments are conducted to determine the elastic constants of SS304 alloy which are used for modeling the material in FEM simulation. Following this, the description of the FEM model for predicting the tensile stress of SS304 alloy with respect to various input factors is described. The validation of FEM simulation with experiments has also been presented next. Following this, the description of evolutionary algorithm based on GP for formulating the complex non-linear relationship is discussed. Finally, sensitivity and parametric analysis is presented, which shows the measure of sensitivity to which each of the considered input factors affects the mechanical strength of SS304 alloy.

Section snippets

Experimental studies on SS304 alloy

The tensile strength of the SS304 alloy was measured using the Instron tensile testing machine. The dimensions of the work piece used are 0.9 mm thick. The tensile testing machine has a maximum load carrying capacity of 100 kN. Firstly, the quality of the work piece was improved by providing proper finishing to it using the non-conventional EDM technique. After this, the specimens were cut to specific size as specified by ASTM standard. The specimen is then loaded in the tensile testing machine

Finite element modeling of SS304

For the purpose of conducting FEM analysis, we used the commercial ABAQUS/Explicit Version 6.14 software [24] with fully coupled thermal stress analysis for modeling the mechanical characteristics of SS304. This is essential to study the strength characteristics of the steel alloy at elevated temperatures and the thermal-stress analysis enables modeling the loading conditions with temperature and displacement boundary conditions. The SS304 geometry is modeled in the FEM software based on the

Analytical modeling of tensile loading characteristics

The data generated from the FEM simulation is used to model the complex non-linear relationship between various input loading parameters and the tensile stress of the SS304 alloy. The non-linear analytical model is formulated using an evolutionary algorithm based on the principle of GP to formulate the mathematical relation between the input variables (x1,,n) and the output (y). In this case, the input variables are temperature (x1), strain rate (x2) and strain (x3) and output variable is

Conclusions

The present work introduced an integrated finite element based analytical modeling technique for modeling tensile loading characteristics of SS304 with various input factors. Finite element simulation was integrated with analytical modeling based on evolutionary algorithm to account for the complex mechanisms observed in SS304 alloy subjected to tensile loading at elevated temperatures. The data predicted from the analytical model showed good correlation with the experimental data which shows

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