Shakedown at Thermal Discontinuities Involving Thermal Membrane and Thermal Bending Stress

2012 ◽  
Author(s):  
Ali Asadkarami ◽  
Wolf Reinhardt
Keyword(s):  
Thermal Stress ◽  
Stress Gradient ◽  
Axial Direction ◽  
Bending Stress ◽  
Primary Stress ◽  
Perfectly Plastic ◽  
Thermal Bending ◽  
Asme Code ◽  
Elastic Perfectly Plastic ◽  
Shakedown Limit

The current ASME Code Section III NB-3200 rules on thermal stress ratchet require that the thermal stress must be less than the ratchet condition that Bree established for a cyclic pure thermal bending stress as a function of the level of primary membrane stress. It has been shown that this method can predict shakedown when elastic-perfectly plastic analysis shows ratcheting. However, there is also conservatism in the Code rules because the highest stresses that dominate the evaluation of a component are typically found at discontinuities, where there is a stress gradient at least in the axial direction. The stress limits, on the other hand, are based on stress distributions that are constant in the axial (and circumferential) direction. This paper investigates the effect of thermal discontinuities on the shakedown limit in the presence of a thermal through-wall gradient and a pressure-induced primary stress. The investigation is based on the simple model of a cylinder with an isolated thermal discontinuity. The effect of proximity to another discontinuity is explored, to obtain the minimum distance between two discontinuities that would allow them to be considered separately. Simple rules are developed and proposed to take potentially advantage of higher stress limits at an isolated discontinuity.

On the Interaction of Thermal Membrane and Thermal Bending Stress in Shakedown Analysis

2008 ◽  
Author(s):  
Wolf Reinhardt
Keyword(s):  
Thermal Stress ◽  
Bending Stress ◽  
Membrane Stress ◽  
Secondary Stress ◽  
Elastic Plastic ◽  
Plastic Analysis ◽  
Thermal Bending ◽  
Asme Code ◽  
The Impact ◽  
Current Code

When the primary plus secondary stress range exceeds 3 Sm, the current ASME Code rules on simplified elastic-plastic analysis impose two separate requirements to evaluate the potential for ratcheting. The range of primary plus secondary stress excluding thermal bending must be less than 3 Sm, and the thermal stress must satisfy the Bree criterion for thermal stress ratchet. It has been shown previously that this method can be unconservative, i.e. predict shakedown when elastic-plastic analysis shows ratcheting. This paper clarifies the interaction between thermal membrane and bending stress in the presence of a primary membrane stress. An analytical model is used to derive the closed-form ratchet boundary for combined uniform loading of this type. The impact of having stress gradients along the wall that are typical for discontinuities is studied numerically. Simple modifications of the current Code methods are suggested that would achieve a clearer and better-justified set of rules.

Validation of Thermal Stress Ratcheting Criteria

2014 ◽  
Author(s):  
Suzanne McKillop ◽  
Wolf Reinhardt ◽  
Vangala Reddy ◽  
William Koski
Keyword(s):  
Thermal Stress ◽  
Cyclic Loading ◽  
Nuclear Power ◽  
Plastic Material ◽  
Elastic Analysis ◽  
Membrane Stress ◽  
Elastic Plastic ◽  
Perfectly Plastic ◽  
Thermal Bending ◽  
Elastic Perfectly Plastic

Design of components against incremental deformation or “ratcheting” under cyclic loading conditions is addressed in Article NB-3200 of Section III of the ASME Boiler and Pressure Vessel Code. The ratcheting rules, based on the Bree diagram, relate primary stress and secondary stress ranges that are calculated elastically and aim to approximate elastic-plastic material behaviors under cyclic loading. The Bree diagram was developed for cases with through-thickness thermal bending and constant primary membrane stress. It does not account for high thermal membrane stress that can occur near gross structural or thermal discontinuities. Cyclic thermal membrane stress combined with sustained stress can lead to ratcheting that is not accounted for in the current design rules. This paper discusses the validation of proposed criteria for evaluating thermal stress ratcheting under high thermal membrane stress using an elastic analysis. These proposed criteria are confirmed by an analysis of a nozzle that is attached by a partial penetration weld to a vessel head and subjected to severe thermal cycling. Linearized stresses from an elastic analysis under pressure and thermal loadings typical for a nuclear power plant are compared to limits in NB-3200 for thermal stress ratcheting. Additionally, an elastic-perfectly plastic analysis is used to evaluate if the component will shakedown. This analysis demonstrates that the proposed rules prevent ratcheting of a typical geometry with typical operating loads in a nuclear plant. The current thermal stress ratcheting rules evaluated on an elastic basis are enhanced to cover cases with high thermal membrane stress while not removing conservatism. Additionally, the evaluation of the simplified elastic-plastic rules for thermal stress ratcheting are simplified.

Strength Limit of Thimble Tube With Material Plasticity Under Bending Moment and Axial Compression Force

2018 ◽  
Author(s):  
Hisashi Koike ◽  
Masaji Mori ◽  
Daisuke Fujiwara ◽  
Takashi Shimomura
Keyword(s):  
Fuel Assembly ◽  
Seismic Event ◽  
Plastic Material ◽  
Bending Moment ◽  
Normal Operation ◽  
Beam Model ◽  
Allowable Limit ◽  
Perfectly Plastic ◽  
Asme Code ◽  
Elastic Perfectly Plastic

The thimble tube, which is made of Zircaly-4, is one of the main components of a PWR fuel assembly. The thimble tube has an important role as a structural member of the skeleton. Another role of the thimble tube is to guide a rod cluster control assembly (RCCA) for insertion during the reactor operation, and the function has to be assured not only in normal operation but in a seismic event. In a horizontal seismic event, the fuel assembly vibrates laterally, which gives bending moment to the thimble tube. In addition, axial compressive force acts on the thimble tube in a vertical seismic event. The integrity of the thimble tube has to be maintained while this force and moment act. Mitsubishi has confirmed by the elastic stress analysis that the stress of the thimble tube is lower than the limit value requested for the seismic event. The stress evaluation method is based on the ASME code. The ASME code also describes the limit analysis which is available when the predicted stress is beyond elastic region of the material. In the analysis, the material is assumed to be elastic-perfectly plastic, and the maximum load that the structure can carry is calculated. For the reason mentioned above, the allowable limit of the thimble tube should be determined as a function between the force and the moment. We are planning to examine the allowable limit experimentally. As a step before testing, an analytical approach for the limit is discussed in this paper. Firstly, the allowable limit is calculated by a beam model assuming elastic-perfectly plastic material, based on the ASME code. Secondly, a 3D model analysis with elastic-plastic material is performed to predict the practical strength. Based on the comparison with the analysis using elastic-perfectly plastic material, ASME based limit is considerably conservative compared with the one with the actual stress-strain curve. Conversely, this means there is enough room to rationalize the allowable limit. As the future work, the experiment will be conducted to obtain the practical limit of the thimble tube and to verify the analysis results.

Shakedown Limits of a 90-Degree Pipe Bend Using Small and Large Displacement Formulations

2006 ◽  
Author(s):  
Hany F. Abdalla ◽  
Mohammad M. Megahed ◽  
Maher Y. A. Younan
Keyword(s):  
Plastic Material ◽  
Limit Load ◽  
Material Model ◽  
Large Displacement ◽  
Small Displacement ◽  
Pipe Bend ◽  
Perfectly Plastic ◽  
Loading Patterns ◽  
Elastic Perfectly Plastic ◽  
Shakedown Limit

In this paper the shakedown limit load is determined for a long radius 90-degree pipe bend using two different techniques. The first technique is a simplified technique which utilizes small displacement formulation and elastic-perfectly-plastic material model. The second technique is an iterative based technique which uses the same elastic-perfectly-plastic material model, but incorporates large displacement effects accounting for geometric non-linearity. Both techniques use the finite element method for analysis. The pipe bend is subjected to constant internal pressure magnitudes and cyclic bending moments. The cyclic bending loading includes three different loading patterns namely; in-plane closing, in-plane opening, and out-of-plane bending. The simplified technique determines the shakedown limit load (moment) without the need to perform full cyclic loading simulations or conventional iterative elastic techniques. Instead, the shakedown limit moment is determined by performing two analyses namely; an elastic analysis and an elastic-plastic analysis. By extracting the results of the two analyses, the shakedown limit moment is determined through the calculation of the residual stresses developed in the pipe bend. The iterative large displacement technique determines the shakedown limit moment in an iterative manner by performing a series of full elastic-plastic cyclic loading simulations. The shakedown limit moment output by the simplified technique (small displacement) is used by the iterative large displacement technique as an initial iterative value. The iterations proceed until an applied moment guarantees a structure developed residual stress, at load removal, equals or slightly less than the material yield strength. The shakedown limit moments output by both techniques are used to generate shakedown diagrams of the pipe bend for a spectrum of constant internal pressure magnitudes for the three loading patterns stated earlier. The maximum moment carrying capacity (limit moment) the pipe bend can withstand and the elastic limit are also determined and imposed on the shakedown diagram of the pipe bend. Comparison between the shakedown diagrams generated by the two techniques, for the three loading patterns, is presented.

Ratchet Boundary for Superimposed Biaxial Membrane Stress States

2018 ◽  
Author(s):  
Wolf Reinhardt
Keyword(s):  
Thermal Expansion ◽  
Thermal Stress ◽  
Analytical Solution ◽  
Pressure Vessels ◽  
Stress Fields ◽  
Design Codes ◽  
Bending Stress ◽  
Membrane Stress ◽  
Asme Code ◽  
Stress States

Thermal membrane and bending stress fields exist where the thermal expansion of pressure vessel components is constrained. When such stress fields interact with pressure stresses in a shell, ratcheting can occur below the ratchet boundary indicated by the Bree diagram that is implemented in the design Codes. The interaction of primary and thermal membrane stress fields with arbitrary biaxiality is not implemented presently in the thermal stress ratchet rules of the ASME Code, and is examined in this paper. An analytical solution for the ratchet boundary is derived based on a non-cyclic method that uses a generalized static shakedown theorem. The solutions for specific applications in pressure vessels are discussed, and a comparison with the interaction diagrams for specific cases that can be found in the literature is performed.

Effect of Yield Strength to Elastic Modulus Ratio on Finite Element Based Plastic Loads for Elbows Under Bending

2008 ◽  
Author(s):  
Kuk-Hee Lee ◽  
Yun-Jae Kim
Keyword(s):  
Elastic Modulus ◽  
Yield Strength ◽  
Modulus Ratio ◽  
Yield Strain ◽  
Perfectly Plastic ◽  
Plastic Materials ◽  
Out Of Plane ◽  
Asme Code ◽  
Elastic Perfectly Plastic ◽  
Experimental Values

This paper quantifies the effect of the yield strength-to-elastic modulus ratio (yield strain) on plastic loads (defined by the twice-elastic-slope according to the ASME code) for 90° elbows under in-plane and out-of-plane bending. Results are based on extensive and systematic FE limit analyses assuming elastic-perfectly plastic materials. Based on FE results, a simple approximation of plastic loads of pipe bends, incorporating the yield strength-to-elastic modulus ratio effect, is proposed. To validate the proposed approximation, predicted plastic moments are compared with published full-scale pipe test data, showing that the proposed approximation gives overall lower than the FE results and close to experimental values.

Ratcheting With No Thermal Bending and Membrane Stress

2016 ◽  
Author(s):  
R. Adibi-Asl ◽  
W. Reinhardt
Keyword(s):  
Thermal Stress ◽  
Thermal Loading ◽  
Mechanical Load ◽  
Failure Mechanisms ◽  
Extreme Case ◽  
Cyclic Stress ◽  
Maximum Temperature ◽  
Bending Stress ◽  
Thermal Bending ◽  
Stress States

The ASME B&PV Code provides design by analysis rules that address failure mechanisms under cyclic loading. One of these potential failure mechanisms is incremental plastic collapse, or ratcheting. Miller presented the technical basis for the present Code requirements in a technical paper in 1959. Miller’s equations for the ratchet boundary address a beam under a cyclic through-thickness thermal gradient acting together with a steady axial mechanical load. This ratchet boundary applies approximately to a pressurized cylinder with through-thickness thermal bending stress. Conditions arise sometimes in practice where cooling or heating is applied simultaneously to the inner and outer surface of pressure boundary. The extreme case of such a scenario arises when both surfaces experience the same thermal condition such that there is a cyclic thermal stress but both zero membrane thermal stress and zero thermal bending stress The question is, could ratcheting occur in this case? This paper derives the ratchet boundary for cases when the maximum temperature occurs mid-way through the thickness. The linearized stress due to thermal loading is zero. The solution is obtained using FE analysis and the Non-Cyclic Method (NCM) that has been proposed previously by the authors. The NCM is a generalization of the static shakedown theorem and allows the ratchet boundary to be calculated for both elastic and elastic-plastic cyclic stress states.

Assessment of Compact Heat Exchanger Design Following Elastic Perfectly Plastic Methodology

2020 ◽  
Author(s):  
Avinash Shaw ◽  
Heramb P. Mahajan ◽  
Tasnim Hassan
Keyword(s):  
Global Analysis ◽  
Local Level ◽  
Primary Objective ◽  
Analysis Method ◽  
Perfectly Plastic ◽  
Heat Exchanger Design ◽  
Creep Fatigue ◽  
Asme Code ◽  
Computationally Intensive ◽  
Elastic Perfectly Plastic

Abstract Compact Heat Exchangers (CHXs) have a large number of miniature channels inside their core, which makes them highly thermal efficient and thus, prime utile for Next Generation Nuclear Plant (NGNP) applications. The fabrication of a CHX involves diffusion, brazed or welded bonding of plates to form CHX block with a channeled core. The elevated temperature and transient conditions of NGNP operation may induce excessive strain and creep-fatigue failure in channel ligaments. The primary objective of this study is to evaluate the design of CHX for application to NGNPs, following the ASME Code Elastic Perfectly Plastic (EPP) Analysis criteria in a draft ASME Code Section III, Division 5 and using the currently available Division 5 Code Cases (N-861 and N-862). As global analysis considering channels in the core is computationally intensive, a new analysis method is evaluated. In this method, the global analysis is performed by representing the channeled core by an elastic orthotropic material core. Subsequently, at the local level, EPP analysis is performed using models that include the channels, with thermal and pressure loading conditions. An ASME Draft Code Case is under development for the construction of CHXs. The analysis results are used to assess proposed stress limits and classification for load controlled stresses. For strain limits, the analysis results are evaluated using Code Cases N-861 and N-862 against the strain limit and creep-fatigue damage using the channel level submodel analysis. The applicability of the new analysis method, and use of the analysis results for evaluation against ASME proposed limits for various regions of the CHX are presented and discussed.

scholarly journals Shakedown Analysis of “Soil-Pile Foundation-Frame” System under Seismic Action

2018 ◽  
Vol 28 (1) ◽  
pp. 100-114
Author(s):  
Piotr Alawdin ◽  
George Bulanov
Keyword(s):  
Fem Analysis ◽  
Deformation Model ◽  
Seismic Action ◽  
Elastic Halfspace ◽  
Brittle Behavior ◽  
Perfectly Plastic ◽  
Frame System ◽  
Elastic Perfectly Plastic ◽  
Pile Deformation ◽  
Shakedown Limit

Abstract In this article, the seismic shakedown FEM analysis of reinforced concrete and composite spatial frame structures on the deformable foundation, taking into account the elasticplastic and brittle behavior of structures elements, is presented. A foundation consists of group of the piles in the soil. The behavior of soil is described here using+ the elastic halfspace theory. The pile deformation model is assumed to be elastic-perfectly plastic, where the bearing capacity is determined by the results of testing the soils or the piles themselves. An example of seismic shakedown limit analysis is presented.

The Incremental Strain Growth of an Elastic-Plastic Body Loaded in Excess of the Shakedown Limit

1984 ◽  
Vol 51 (3) ◽  
pp. 465-469 ◽  
Author(s):  
A. R. S. Ponter ◽  
A. C. F. Cocks
Keyword(s):  
Thermal Loading ◽  
Thermoelastic Stress ◽  
Point Of View ◽  
The Body ◽  
Elastic Displacement ◽  
Perfectly Plastic ◽  
Incremental Growth ◽  
Elastic Perfectly Plastic ◽  
Shakedown Limit ◽  
Incremental Strain

This paper considers the problem of a body composed of an elastic/perfectly plastic solid that is subjected to constant applied load P and a time-varying cyclic temperature distribution, characterized by a maximum thermoelastic stress σt. For sufficiently large P and σt, in excess of the shakedown limit, the body will begin to suffer incremental growth. A linearized theory is used to obtain a relationship between the increase in displacement Δu per cycle and the increase in ΔP and Δσt, above the shakedown limit. From the result, a simple lower bound is derived for Bree-type problems, which for kinematically determinate structures shows that for moderate thermal loading the displacement increment per cycle is four times the elastic displacement of the body if it were subjected only to the increase ΔP. From a practical point of view the analysis indicates that ratchet rates are always high, in the sense that only a small increase of load above shakedown will produce substantial ratcheting within relatively few cycles.

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