Thermo-mechanical modeling of metallic alloys for nuclear engineering applications
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
References (38)
Deep cryogenic treatment of AISI 302 stainless steel: part I - Hardness and tensile properties
Mater. Des.
(2010)- et al.
Effect of microstructure on the crack propagation behavior of micro alloyed 560 MPa (X80) strip during ultra-fast cooling
Mater. Sci. Eng., A
(2016) - et al.
The effect of nanostructured surface layer on the fatigue behaviors of a carbon steel
Appl. Surf. Sci.
(2009) - et al.
Numerical predictions of cratering and scabbing in concrete slabs subjected to projectile impact using a modified version of HJC material model
Int. J. Impact Eng
(2016) - et al.
On the characterisation of transverse tensile properties of molten unidirectional thermoplastic composite tapes for thermoforming simulations
Compos. A Appl. Sci. Manuf.
(2016) - et al.
A physically-based constitutive model applied to AA6082 aluminium alloy at large strains, high strain rates and elevated temperatures
Mater. Des.
(2016) - et al.
The effect of residual stress due to interference fit on the fatigue behavior of a fastener hole with edge cracks
Eng. Fail. Anal.
(2016) - et al.
Measurement of properties of graphene sheets subjected to drilling operation using computer simulation
Meas.: J. Int. Meas. Confederation
(2014) - et al.
FEM and experimental investigation of the thermal drift in ultra-high precision measuring machines for dimensional metrology
Meas.: J. Int. Meas. Confederation
(2016) - et al.
Experimental modal analysis of masonry arches strengthened with graphene nanoplatelets reinforced prepreg composites
Meas.: J. Int. Meas. Confederation
(2016)
Welding residual stress in roots between deck plate and U-rib in orthotropic steel decks
Meas.: J. Int. Meas. Confederation
Data fusion of acceleration and angular velocity for improved model updating
Meas.: J. Int. Meas. Confederation
Dynamic error compensation for industrial robot based on thermal effect model
Meas.: J. Int. Meas. Confederation
Experimental and numerical study of membrane properties and pore pressure transmission of Ghom shale
Meas.: J. Int. Meas. Confederation
On the design and analysis of an octagonal-ellipse ring based cutting force measuring transducer
Meas.: J. Int. Meas. Confederation
Empirical investigation of environmental characteristic of 3-D additive manufacturing process based on slice thickness and part orientation
Meas.: J. Int. Meas. Confederation
Framework based on number of basis functions complexity measure in investigation of the power characteristics of direct methanol fuel cell
Chemometr. Intell. Lab. Syst.
Mechanical, electrochemical and tribological properties of nano-crystalline surface of 304 stainless steel
Wear
An enhanced Johnson-Cook strength model for splitting strain rate and temperature effects on lower yield stress and plastic flow
Comput. Mater. Sci.
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