Primary Membrane Stress Research Articles

Maximum steady stress of various cross-section beams under combined loadings during creep

In the simplified method based on stress classification for estimating the stress at the steady stage during creep, an empirical correction factor is needed to account for the relaxation of primary bending stress during creep. An analysis of a rectangular beam subjected to tensile loading and bending moment during creep is carried out to demonstrate the applicability of the Kt, which is the correction factor proposed by the ASME code, in this work. In view of the effects of material creep property and the primary membrane stress on the relaxation of the primary bending stress, a method for accessing the parameter Kt is proposed and validated. The results reveal that the parameter Kt will increase with the tensile loading due to the relaxation of the primary bending stress accelerated by the primary membrane stress. Good agreement between the results of inelastic analysis and the modified method is observed for the beams with different material properties, combined loadings, and cross-section shapes.

Investigation about Effect of Thickness in Stress Classification of Nozzle Attached to Cylindrical Vessel by 3D-FE Analyses

In current practices, stress analyses of Class 1 vessels with internal pressure of nuclear power plants have been carried out using the minimum thickness of the component. In this paper, effects of thickness on stresses have been investigated by comparing stress analysis results for two kinds of 3D-FEA models of a typical nozzle attached to a cylindrical vessel with minimum thickness and nominal thickness. Since variations of stresses between minimum and nominal thickness models are small, nominal thickness can be employed in the 3D-FE analysis. However, in case of evaluations for primary stresses, a correction method to multiply primary membrane stress by the thickness ratio and primary bending stress by the thickness ratio squared should be used in order to conduct conservative evaluation.

Optimum Design of Liquified Natural Gas Bi-lobe Tanks using Finite Element, Genetic Algorithm and Neural Network

A comprehensive set of ten artificial neural networks is developed to suggest optimal dimensions of type ‘C’ Bi-lobe tanks used in the shipping of liquefied natural gas. Multi-objective optimization technique considering the maximum capacity and minimum cost of vessels are implemented for determining optimum vessel dimensions. Generated populations from a genetic algorithm are used by Finite Element Analysis to develop new models and find primary membrane and local stresses to compare with their permissible ranges using PYTHON coding. The optimum design space is mathematically modeled by training ten artificial neural networks with design variables generated by the Taguchi method. The results are compared with actual design data and the 93% achieved accuracy shows the precision of the developed design system.

A modification on 3S criterion and simplified elastic-plastic ratcheting analysis in ASME VIII-2

Ratcheting is a common and important failure mode in pressure vessels. ASME VIII-2 2019 edition provides two kinds of ratcheting assessment methods——the elastic stress ratcheting assessment (paragraph 5.5.6) applied to the design by elastic stress analysis and the elastic-plastic ratcheting assessment (paragraph 5.5.7) applied to the design by elastic-plastic stress analysis. This paper focuses on the elastic stress ratcheting assessment, which includes again two methods——the elastic ratcheting analysis (paragraph 5.5.6.1), i.e. the 3S criterion, and the thermal stress ratcheting assessment (paragraph 5.5.6.3). This article reviews the development history of 3S criterion and discusses its applicable scope. The study found that the 3S criterion is not a complete elastic ratcheting assessment criterion, when the primary membrane stress range exceeds two-thirds of the cyclic yield stress, i.e. (2/3)Sy, the ratcheting assessment based on 3S criterion is unsafe for some situations. When the general primary membrane stress Pm and the local primary membrane stress PL, which allowable limit exceeds (2/3)Sy, are applied simultaneously, there is still the possibility of ratcheting failure in the structure even if the 3S criterion is met. As an extension of the 3S criterion, a complete and safe criterion on three-dimensional elastic ratcheting assessment is proposed in this paper. In order to avoid the inconvenience of partition assessment, a simplified thermal stress ratcheting assessment method based on double checking surfaces is proposed. It is a simple and conservative assessment method. Finally, elastic ratcheting analysis, thermal stress ratcheting assessment and simplified elastic-plastic analysis in ASME VIII-2 are integrated, a universal elastic stress ratcheting assessment is proposed.

Design of the European DEMO vacuum vessel inboard wall

The pre-concept design of the DEMO Vacuum Vessel is going on in view of the 2020 gate review; moreover the nuclear heat loads on the vessel inner shell were determined and found to be about one order of magnitude higher compared to ITER. A subsequent thermal-structural analysis of the vessel inner shell revealed high thermal stresses and a large temperature gradient through the inner shell thickness. Given the simultaneous occurrence of primary membrane stresses in the entire vessel inboard wall and, in proximity of the vessel ribs, high bending stresses due to the coolant pressure, a survey of all options within the design rules was required to identify the inter-dependencies of the individual stress limits (primary membrane, primary bending, thermal membrane plus bending). In order to face this kind of issues a detailed assessment on the design of the inboard wall of DEMO Vacuum Vessel has been conducted and is presented here. The current work evaluates both P and S type damages for the inboard wall of DEMO Vacuum Vessel in case of high nuclear heat load, vacuum vessel coolant pressure and toroidal field coil fast discharge. The elastic analysis method has been used to check the rules for prevention of both types of damage. The rules applied to prevent the aforementioned damages are compliant to Level A criteria, in case of negligible creep and negligible irradiation. In order to check the structural integrity of the inboard wall of DEMO VV against high thermal and mechanical loads, optimization structural analyses were performed and checked against the rules provided in the applicable design code (RCC MRx).

The ratchet–shakedown diagram for a thin pressurised pipe subject to additional axial load and cyclic secondary global bending

The ratchet and shakedown boundaries are derived analytically for a thin cylinder composed of elastic-perfectly plastic Tresca material subject to constant internal pressure with capped ends, plus an additional constant axial load, F, and a cycling secondary global bending load. The analytic solution is in good agreement with solutions found using the linear matching method. When F is tensile, ratcheting can occur for sufficiently large cyclic bending loads in which the pipe gets longer and thinner but its diameter remains the same. When F is compressive, ratcheting can occur in which the pipe diameter increases and the pipe gets shorter, but its wall thickness remains the same. When subject to internal pressure and cyclic bending alone (F = 0), no ratcheting is possible, even for arbitrarily large bending loads, despite the presence of the axial pressure load. The reason is that the case with a primary axial membrane stress exactly equal to half the primary hoop membrane stress is equipoised between tensile and compressive axial ratcheting, and hence does not ratchet at all. This remarkable result appears to have escaped previous attention.

Solution of the ratchet-shakedown Bree problem with an extra orthogonal primary load

The complete shakedown and ratcheting solution is derived analytically for a flat plate subject to unequal biaxial primary membrane stresses and a cyclic secondary bending stress in one in-plane direction (x). The Tresca yield condition and elastic-perfectly plastic behaviour are assumed. It is shown that the results can be expressed in the form of a “universal” ratchet diagram applicable for all magnitudes of orthogonal load. For sufficiently large cyclic bending stresses, tensile ratcheting can occur in the x direction if the x direction primary membrane stress exceeds half that in the orthogonal direction. Conversely, for sufficiently large cyclic bending stresses ratcheting in the x direction will be compressive if the x direction primary membrane stress is less than half that in the orthogonal direction. When the x direction primary membrane stress is exactly half that in the orthogonal direction ratcheting cannot occur however large the cyclic secondary bending stress.

Application of RCC-MR for the structural design of tube sheet of intermediate heat exchanger for a sodium cooled fast reactor

The structural mechanics behavior of tube sheets of a sodium to sodium heat exchanger for a fast reactor, with circular tube holes pattern, less addressed subject in the literature, is investigated in detail. The tube sheet design rules recommended in the French design code RCC-MR-2007 and the associated solid mechanics basis are explained. A finite element analysis of tube sheets of intermediate heat exchanger of a typical 500MWe pool type fast reactor is presented to study the effects of some specific parameters viz., (i) small solid rim portion with connecting shell and (ii) grooves on rim area. For the analysis, the distribution of holes on the last row is assumed to be symmetric and axial stiffening of tubes on tube sheet is included toward realistic estimation of stresses in the tube sheets. The effects are studied on the primary and secondary stresses induced along the interface between solid to perforated region. The aspects covered include linearization of radial and circumferential stress components, thereby deriving primary membrane and bending stress intensities along the radial directions with particular focus at the interfaces between solid portions and perforated portions including the effect of filet radius at the junction of tube sheet and shell. These investigations thus help to optimize the design of IHX tube sheets with high confidence. The analysis has been carried out by CAST3M, a structure analysis software granted by CEA, France.

The Bree problem with different yield stresses on-load and off-load and application to creep ratcheting

The ratchet boundaries and ratchet strains are derived for the Bree problem and an elastic-perfectly plastic material with different yield stresses on-load and off-load. The Bree problem consists of a constant uniaxial primary membrane stress and a cycling thermal bending stress. The ratchet problem with differing yield stresses is also solved for a modified loading in which both the primary membrane and thermal bending stresses cycle in-phase. The analytic solutions for the ratchet boundaries are compared with the results of deploying the linear matching method (LMM) and excellent agreement is found. Whilst these results are of potential utility for purely elastic–plastic behaviour, since yield stresses will often differ at the two ends of the cycle, the solution is also proposed as a means of assessing creep ratcheting via a creep ductility exhaustion approach.

The Bree problem with primary load cycling in-phase with the secondary load

Shakedown and ratcheting behaviour is derived for uniaxial primary membrane and thermal bending stresses both cycling strictly in-phase. The complete analytic solution for perfect plasticity is presented, including the shakedown/ratcheting diagram and the ratchet strains or cyclic plastic strains where relevant. This cyclic loading is shown to be considerably more benign than that of the original Bree problem in which the primary membrane stress does not cycle.

Stress-on-a-Surface Method and its Application in Stress Classification of Nozzle-Cylinder Intersection

According to the expansion trend of plastic area, the locations and extension direction of five stress classification surfaces are determined in the danger position of nozzle-cylinder intersection. Through the orthogonal experimental design, the structure dimensions of 32 models of nozzle-cylinder intersection are determined. With the area where 0.2% plastic strain intensity occur being designated as the scope of the stress classification surface, extension length of these computation models can be obtained by FEA, and the empirical equations of extension length and structure dimensions are given by using the multivariate regression analysis method. Then all of the stress components are linearized and classified, based on a method of linearizing stresses on a curved surface( stress-on-a-surface method)suggested in this paper. At last, the limits of kinds of nominal stress intensities are taken as the stress criteria of the nozzle-cylinder intersection. The results show that, in the range of parameters for calculation, stress criteria vary with locations and their minimum is that the primary local membrane stress intensity SII is less than or equal to 1.5 times design stress intensity Sm and the primary membrane plus primary bening stress intensity SIII is not more than 1.5times Sm.

Equivalent Stress Linearization Method Based on Assessment Line of Nozzle-Cylinder Intersection

The limit internal pressures of the nozzle-cylinder intersection with different dimension are calculated by nonliner FEM and are used to determine stresses of this structure in elastic analysis.The elastic nominal stresses linearized by stress-along-a-line method are classified at the danger location and the limits of kinds of nominal stress intensities are taken as the stress assess criteria of the nozzle-cylinder intersection. The results show that, in the range of parameters for calculation, the primary local membrane stress intensity SII is less than or equal to 2.0 times design stress intensity Sm,and the primary membrane plus primary bening stress intensity is not more than 2.1 times Sm.

The Strength Analysis of Tower Vacuum Dryer Structural

Tower vacuum dryer room is the key device for continuous vacuum dryer. In order to lower the cost of manufacture, the wall of dryer should be thinner. But as the pressure container, it must have the well intensity while operating. Because its complex structure, the simple calculation is not enough, the finite element analysis in intensity control was carried out. The model of vacuum dryer was built, the intensity of general primary membrane stress and the intensity of primary bending stress was picked-up on the max stress intensity point through the path of wall thickness. Accord with JB4732-1995, the structural strength was fulfilled the requirement.

A Reliability-Based Approach for the Design of Nuclear Piping for Internal Pressure

Nuclear pipes are designed to withstand primary membrane stresses generated by internal pressure according to the American Society of Mechanical Engineers (ASME) Boiler and Pressure Vessel (B&PV) Code, Section III, Parts NB-3641, NC-3641, and ND-3641, which uses the allowable stress design (ASD) method. This paper presents limit states and equations for the design of nuclear pipes for internal pressure based on the load and resistance factor design (LRFD) method. The LRFD method is shown and explained to be more consistent than the ASD method. The paper presents the procedure for the derivation of the partial safety factors. Moreover, these factors are evaluated, example calculations are provided, and comparisons with the present design are made.

Effects of nuclear island connected buildings on seismic behaviour of reactor internals in a pool type fast breeder reactor

The seismic analysis of reactor assembly housing the primary circuit of a typical 500 MWe capacity pool type fast breeder reactor (PFBR) is reported. The reactor assembly is supported on the reactor vault within the nuclear island connected buildings (NICB). The seismic responses, viz. critical displacements, sloshing heights, stresses and strain energy values in the vessels are determined for the reactor assembly by detailed finite element analysis including the fluid–structure interaction and sloshing effects. Analysis is carried out to quantify the effects of inter-connection of the reactor vault with the adjacent buildings under the assumptions that the reactor vault along with reactor assembly is: (1) an isolated structural system from the adjacent buildings within reactor containment building (RCB) and (2) connected with the adjacent civil structures through floor slabs. Analysis indicates that, by inter-connecting the vault with the NICB, there are overall increases of all the governing parameters which decide the seismic design criteria. The significant effects are increases of: (1) radial and axial displacements of core top and absorber rods and vertical accelerations of core subassemblies which are of concern to reactor safety, (2) primary membrane stress intensities for the inner vessel and (3) strain energies developed at the critical portions which can enhance the buckling risks of main vessel, inner vessel and thermal baffles. Hence, it is preferable to isolate the reactor vault, directly constructing from the base raft without inter-connecting it with the NICB, from the seismic loading considerations.

KSNP+ reactor vessel head drop analysis for a 5.5M free fall

The KSNP+ RV closure head drop analysis was carried out to assess the reactor core coolability in case of the RV closure head drop accident during the refueling operation. The analysis consists of a number of different RV head drop scenarios as the postulated accident events during refueling that include a concentric head drop case and three different cases of laterally offset head drop cases. The analysis was initiated due to the adoption of the IHA (Integrated Head Assembly) in the KSNP+ reactor design, which increases the weight of the RV closure head assembly. Four different analysis models were developed that correspond to the RV head drop analysis scenarios. An in-house dynamic analysis code was used for the RV head drop analysis. The entire reactor internals and fuel assemblies are modeled by using lumped masses and spring elements. Because of the extreme load exerted by RV head drop, most members experience stresses that are beyond the elastic limits. A separate elastic—plastic analysis for some members was carried out and the resulting load-deflection curve was used as the stiffness of the element. The effect of water above the reactor vessel in the refueling pool was ignored for the conservative estimation of the analysis. The analysis shows that the concentric head drop is the most severe case of loading condition. It also reveals that the local deformation of some reactor internals and the fuel assemblies is occurred; however the primary membrane stresses are within the bound of allowable stress limits. Consequently the reactor core remains in coolable state.

Study on short term stress limit in fast reactor fuel pin designs

The rationalization of a short term stress limit for primary membrane stress in fast reactor fuel pin design was investigated for the purpose of the advanced designs of fast reactors, using the idea of the structure reliability. Fuel pins made of 20% cold-worked modified 316 stainless steel (PNC316) were tested in transient over power event conducted in EBR-II and no failure occurred in these pins. The stress due to fission gas pressure at the transient over power event was estimated for these pins and compared with the tensile strength of the irradiated PNC316 cladding. The result demonstrated the excess margin included in a currently used design stress limit value. Then, the reliability evaluation was conducted for the tensile strength of PNC316, where the failure probabilities were calculated in the design stress limit with its safety factors varied. The allowable failure probability was determined to prevent any fuel pin failures for 60 years life time of the prototype fast reactor. The safety factors in the design stress limit were investigated so as to maintain the failure probability to be lower than the allowable probability. The results obtained was that the rationalization made possible 30-40% increasing of the currently used design stress limit in the neutron fluence range 0-about 20 x 10 26 n/m 2 (E>0.1 MeV), which was maximum neutron fluence of the irradiation results of PNC316.

Materials design data for reduced activation martensitic steel type F82H

This paper presents materials data for design of ITER test blanket modules with the reduced activation ferritic martensitic steel type F82H as structural material. From the physical properties databases, variations of modulus of elasticity, density, thermal conductivity, thermal diffusivity, specific heat, mean and instantaneous linear coefficients of thermal expansion versus temperature are derived. Also reported are Poisson's ratio and magnetic properties. From the tension test results, nominal and minimum stress values of S y and S u are derived and used for calculation of allowable primary membrane stress intensity S m. Likewise, uniform and total elongations, as well as reduction of area data, are used for calculation of minimum and true ductility at rupture values. From the instrumented Charpy impact and fracture toughness test data, ductile to brittle transition temperature, toughness and behavior of material in different fracture modes are evaluated. The effect of specimen size and geometry are discussed but preference is given to standard size specimens. From the fatigue data, total strain range versus number of cycles to failure curves are plotted and used to derive fatigue design curves, using a reduction factor of 2 on strain and a reduction factor of 20 on number of cycles to failure. Cyclic hardening curves are also derived and compared with monotonic hardening curves. From the creep data, time dependent allowable stresses S r and S t are calculated. Combination of tension and creep results are used to deduce S mt and isochronus curves. Finally, irradiated and aged materials data are compared to insure that the safety margins incorporated in unirradiated design limits are not exceeded.

Structural design criteria for high heat flux components

The high temperature design rules of the international thermonuclear experimental reactor (ITER) structural design criteria (ISDC) are applied to first wall designs with high heat flux. The maximum coolant pressure and surface heat flux capabilities are shown to be determined not only by the mechanical properties of the first wall material but also by the details of the blanket-design. In a high power density self-cooled lithium blanket, the maximum primary stress in the first wall is controlled by many of the geometrical parameters of the blanket, such as, first wall span, first wall curvature, first wall thickness, side wall thickness, and second wall thickness. Also, the creep-ratcheting lifetime of the first wall is controlled by many of the same geometrical parameters as well as the coolant temperature. According to most high temperature design codes, the time-dependent primary membrane stress allowable are based on the average temperature (ignoring thermal stress). Such a procedure may sometimes be unconservative, particularly for embrittled first walls with large temperature gradients. The effect of secondary (thermal) stresses on the accumulation of creep deformation is illustrated with a vanadium-alloy, flat plate first-wall design.

Effects of simultaneous boron and nitrogen implantation on microhardness and fatigue properties of Fe13Cr15Ni alloys: Rao, G.R., Lee, E.H. and Chin, B.A. Metall. Trans. A (Jan. 1994) 25A (1), 193–202

The ratchet boundaries and ratchet strains are derived for the Bree problem and an elastic-perfectly plastic material with different yield stresses on-load and off-load. The Bree problem consists of a constant uniaxial primary membrane stress and a cycling thermal bending stress. The ratchet problem with differing yield stresses is also solved for a modified loading in which both the primary membrane and thermal bending stresses cycle in-phase. The analytic solutions for the ratchet boundaries are compared with the results of deploying the linear matching method (LMM) and excellent agreement is found. Whilst these results are of potential utility for purely elastic–plastic behaviour, since yield stresses will often differ at the two ends of the cycle, the solution is also proposed as a means of assessing creep ratcheting via a creep ductility exhaustion approach.