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

Bradford, R.

doi:10.1016/j.ijpvp.2012.07.014

Cited by 32 publications

(56 citation statements)

References 12 publications

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“…Bree 132 investigated the elastic-plastic response of thin-walled tubes subjected to internal pressure and intermittent heat fluxes assuming that a constant pressure component remained across the vessel upon reactor shutdown. Bradford 251 developed an analytical solution along with Bree's failure assessment diagram considering a primary membrane stress cycle stay in-phase with a secondary bending stress. To assess failure mechanisms by means of FE method, standard incremental calculations are employed to verify method ability in analysing degradation overloading cycles which are often computationally complex and expensive., while direct methods are readily applicable in the absence of details of loading spectrum.…”

Section: Ratcheting Analysis By Means Of Numerical Methodsmentioning

confidence: 99%

“…The loading threshold is designed to achieve safe structural response as shakedown theorems are employed within safety domain of specified loads. Direct cyclic analysis 251 was structured based on a Fourier series to calculate the structural response for any loading conditions. This numerical approach was accompanied with an automated search algorithm enabling several trial-error iterations to determine the plastic shakedown 253 through a hierarchical FE framework.…”

Section: Ratcheting Analysis By Means Of Numerical Methodsmentioning

confidence: 99%

See 1 more Smart Citation

Ratcheting in pressurized pipes and equipment: A review on affecting parameters, modelling, safety codes, and challenges

Varvani‐Farahani

Nayebi

2018

Fatigue Fract Eng Mat Struct

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The current study has attempted to comprehensively review ratcheting response of materials involving various influential parameters such as loading spectra, thermal cycles, stress levels, stress raisers, strain rate, and visco‐plasticity and material types with a focus on pressurized pipes and equipment. The mechanism of deformation, types, and the rate of progress over stages of ratcheting were discussed. Safety design codes and procedures were highlighted for reliable design of pressurized pipes against progressive ratcheting and to safeguard the system against catastrophic failure at which both mechanical and thermal ratcheting were integrated. Boundaries and demarcation of ratcheting‐shakedown zones developed based on Bree's diagram were employed to assess plastic deformation accumulation over stress cycles. Shakedown and ratcheting boundaries were discussed through methods developed on the basis of Melan's theorem over last few decades. Ratcheting response of materials was reviewed through descriptions of parametric models and kinematic hardening rules involving various variables and parameters. Interaction of ratcheting with creep and low‐cycle fatigue has promoted progressive damage in materials. Pressurized pipes subjected to thermal cycles and external bending cycles were evaluated by numerical solutions along with kinematic hardening rules to assess ratcheting over stress cycles.

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Section: Ratcheting Analysis By Means Of Numerical Methodsmentioning

confidence: 99%

Section: Ratcheting Analysis By Means Of Numerical Methodsmentioning

confidence: 99%

Ratcheting in pressurized pipes and equipment: A review on affecting parameters, modelling, safety codes, and challenges

Varvani‐Farahani

Nayebi

2018

Fatigue Fract Eng Mat Struct

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“…The temperature dependence of yield stress was taken into account and off-load (no thermal load) yield stress was assumed to be greater than the on-load yield stress. Bradford also carried the investigation over the Bree problem with primary load cycling-strictly in-phase with the secondary load and concluded that this case was substantially more resistant to ratcheting [6].…”

Section: Introductionmentioning

confidence: 99%

Shakedown analysis of thick cylinders with multiple radial openings

Singh

Khan

Sharma

et al. 2016

IOP Conf. Ser.: Mater. Sci. Eng.

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Abstract. Shakedown and ratcheting behaviour of thick cylinder with multiple radial crossholes is investigated in this paper by inelastic finite element analysis. Effect of opening radius ( ⁄ ), thickness of the vessel i.e. thickness ratios ( ⁄ ) and availability of ligament between two openings ( ⁄ ) is studied. In order to normalise the applied pressure, limit load for thick cylindrical vessel without any opening was considered and it was found to be highly conservative. Later, interaction diagram normalised with respect to the limit load for thick cylinder taking into account the effects of opening was plotted. In order to distinguish between plastic shakedown and ratcheting, thickness advantage is taken into consideration. A more practical assessment technique is also discussed where the maximum range of thermal stress is computed through finite element analysis and the results were found to be in accordance with the Bree diagram. However the elastic-plastic shakedown boundary was found to be affected significantly with the incorporation of discontinuities and with changes in the parameters.

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“…Mai et al [2012] developed a three-dimensional phenomenological model to describe the fatigue behavior of concrete on the basis of continuum damage mechanics. Bradford [2012] investigated the shakedown and ratcheting behavior for uniaxial membrane and thermal bending stresses. He presented an analytic solution for perfect plasticity.…”

Section: Introductionmentioning

confidence: 99%

Elasto-Plastic Analysis of a Functionally Graded Rotating Disk Under Cyclic Thermo-Mechanical Loadings Considering Continuum Damage Mechanics

Nayebi

Tirmomenin

Damadam

2015

Int. J. Appl. Mechanics

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The goal of this work is to study the influence of continuum damage mechanics on a functionally graded rotating disk subjected to cyclic temperature gradient loading through nonlinear kinematic hardening rule employed to model the back stress. The formulations have been developed on the basis of von Mises' yield criterion. The material properties are assumed to be independent of temperature and vary according to a power law volume fraction relation but Poisson's ratio is assumed to be constant. Return mapping algorithm (RMA), an incremental method, has been used in the numerical procedure. Material behaviors such as elastic shakedown, plastic shakedown and ratcheting were specified in the existence of continuum damage mechanics to obtain the Bree's interaction diagram for different temperatures and angular velocities.

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

Cited by 32 publications

References 12 publications

Ratcheting in pressurized pipes and equipment: A review on affecting parameters, modelling, safety codes, and challenges

Ratcheting in pressurized pipes and equipment: A review on affecting parameters, modelling, safety codes, and challenges

Shakedown analysis of thick cylinders with multiple radial openings

Elasto-Plastic Analysis of a Functionally Graded Rotating Disk Under Cyclic Thermo-Mechanical Loadings Considering Continuum Damage Mechanics

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