Some classical problems in rate-independent plasticity

2020 ◽  
pp. 434-459
Author(s):  
Lallit Anand ◽  
Sanjay Govindjee
Keyword(s):  
Plane Strain ◽  
Analytical Solutions ◽  
Pressure Vessel ◽  
Plastic Response ◽  
Spring Back ◽  
Elastic Plastic ◽  
Initial Yield ◽  
Cylindrical Pressure Vessel ◽  
Round Bar ◽  
Spherical Pressure

This chapter presents analytical solutions to some classical problems in rate-independent plasticity. Solutions are presented for the elastic-plastic torsion of a round bar, including spring back; for the elastic-plastic response of a thick-walled spherical pressure vessel, including initial yield, partial yield, full yield, and unloading; for the incompressible elastic-plastic response of a plane-strain thick-walled cylindrical pressure vessel, including initial yield, partial yield, and full yield.

scholarly journals Assessment of DBA-L Pressure Vessel Design Method by a Cylindrical Vessel with Hemispherical Ends

2019 ◽  
Vol 256 ◽  
pp. 02001
Author(s):  
Ren Xincheng ◽  
Hongjun Li ◽  
Xun Huang
Keyword(s):  
Stress Analysis ◽  
Pressure Vessel ◽  
Design Method ◽  
Design Methods ◽  
Cylindrical Vessel ◽  
Elastic Analysis ◽  
Explicit Method ◽  
Elastic Plastic ◽  
Cylindrical Pressure Vessel ◽  
Plastic Stress

Stress categorization is an essential procedure in Design by Analysis (DBA) pressure vessel design methods based on elastic analysis in ASME and EN code. It was difficult to implement especially around structural discontinuities. A new elastic analysis, DBA-L, was proposed recently to avoid stress categorization. A model of the cylindrical pressure vessel with spherical end is used to check the validity of this method by comparing with other design methods based on stress categorization procedures and elastic-plastic stress analysis from ASME and EN code. The results indicate that the DBA-L is an economic and explicit method, and can be used an alternative method to stress categorization.

Dynamic Stress Analysis of Multilayered Structure With Radial Gaps of Cylindrical Pressure Vessel Under Plane Strain Conditions

2019 ◽  
Vol 141 (4) ◽  
Author(s):  
Huadong Liu ◽  
Weiqiang Wang
Keyword(s):  
Plastic Deformation ◽  
Dynamic Response ◽  
Plane Strain ◽  
Pressure Vessel ◽  
Single Layer ◽  
Multilayered Structure ◽  
Multilayered Structures ◽  
Loading Process ◽  
Cylindrical Pressure Vessel ◽  
Gap Height

Radial gaps were found in multilayered cylindrical vessels which experience inner explosion accidents in chemical plants in the past few years worldwide. It is necessary to investigate the dynamic response of multilayered structures with radial gaps to ensure the vessel safety. This paper presented a numerical modeling of the dynamic response of a multilayered structure with radial gaps of cylindrical pressure vessel under plane strain conditions by using the ANSYS/ls-dyna package. The effects of the dynamic loading profile and the radial gap height are considered in the investigation. The stress spatial distribution, the stress and the plastic deformation variation curves with time are emphatically analyzed. The results show that the stress variation of the entire loading process can be divided into four stages: the oscillation stage, the yield stage, the fast increase stage, and the redistribution stage. The layer stress distributes discontinuously at the gaps between layers and distributes unevenly in any single layer. The inner layer stress is not always larger than the outer layers' during the whole loading process. The effect of loading profile on the dynamic response is not as obvious as the gap height. As the gap height increases, the stress oscillation stage is suppressed and becomes shorter. While the loading recovers to the operation pressure, the stress and the plastic deformation of inner layers increases and vice versa for the outer layers.

scholarly journals Thermo-Mechanical Autofrettage Process of Spherical Vessel

2020 ◽  
Vol 9 (3) ◽  
pp. 1109-1114
Keyword(s):  
Stress Distribution ◽  
Pressure Vessel ◽  
Mechanical Load ◽  
Pressure Vessels ◽  
Stress Distributions ◽  
Spherical Vessel ◽  
Yield Criteria ◽  
Elastic Plastic ◽  
Spherical Pressure ◽  
Plastic Stress

In this analysis results of Elastic-plastic stress distributions in a spherical pressure vessel with ThermoMechanical loads are discussed. Results of study are obtained with Finite element (FE) analysis. A quarter of pressure vessel is considered and modeled with all realistic details. In addition to presenting the stress distribution of the pressure vessel, in this work the effects thermo-Mechanical autofrettage on different limit strength for spherical pressure vessels are investigated. The effect of changing the load and various geometric parameters is investigated. Consequently, it can be observed that to be the significant differences between the present thermo-Mechanical autofrettage and earlier (Mechanical autofrettage and Thermal autofrettage) method of autofrettage for the predictions of Elastic-plastic stress distributions of spherical pressure vessels. Some realistic examples are considered and results are obtained for the whole vessel by applying thermal load and mechanical load. The actual material curve is used for loading, unloading and residual stress behavior of spherical pressure vessel. Kinematic hardening material is considered and effect of Bauschinger effect factors are studied with thermo-mechanical load. Equivalent Von -Mises yield criteria is used for yield criteria. Behavior of elastic-perfectly plastic is also studied and compared. Influence of Thermo-Mechanical autofrettage over stress distribution and load bearing capacity of spherical vessel is examined. The question of whether Thermo-mechanical autofrettage gives more favorable residual compressive stress distribution and therefore extension of pressure vessel life is investigated in this analysis.

scholarly journals Finite Pure Plane Strain Bending of Inhomogeneous Anisotropic Sheets

Symmetry ◽  
2021 ◽  
Vol 13 (1) ◽  
pp. 145
Author(s):  
Sergei Alexandrov ◽  
Elena Lyamina ◽  
Yeong-Maw Hwang
Keyword(s):  
Plane Strain ◽  
Yield Criterion ◽  
Large Strains ◽  
Rigid Plastic ◽  
Plastic Properties ◽  
Elastic Plastic ◽  
Starting Point ◽  
The Difference ◽  
Inside Radius ◽  
Elastic Unloading

The present paper concerns the general solution for finite plane strain pure bending of incompressible, orthotropic sheets. In contrast to available solutions, the new solution is valid for inhomogeneous distributions of plastic properties. The solution is semi-analytic. A numerical treatment is only necessary for solving transcendent equations and evaluating ordinary integrals. The solution’s starting point is a transformation between Eulerian and Lagrangian coordinates that is valid for a wide class of constitutive equations. The symmetric distribution relative to the center line of the sheet is separately treated where it is advantageous. It is shown that this type of symmetry simplifies the solution. Hill’s quadratic yield criterion is adopted. Both elastic/plastic and rigid/plastic solutions are derived. Elastic unloading is also considered, and it is shown that reverse plastic yielding occurs at a relatively large inside radius. An illustrative example uses real experimental data. The distribution of plastic properties is symmetric in this example. It is shown that the difference between the elastic/plastic and rigid/plastic solutions is negligible, except at the very beginning of the process. However, the rigid/plastic solution is much simpler and, therefore, can be recommended for practical use at large strains, including calculating the residual stresses.

Reactor Pressure Vessel Integrity Assessment: French Simplified Analysis Method Applied to Underclad Postulated Defect in Nozzle

2016 ◽  
Author(s):  
Adolfo Arrieta-Ruiz ◽  
Eric Meister ◽  
Stéphane Vidard
Keyword(s):  
Fracture Mechanics ◽  
Fracture Risk ◽  
Pressure Vessel ◽  
Reactor Pressure Vessel ◽  
Core Area ◽  
Integrity Assessment ◽  
Elastic Plastic ◽  
The Core ◽  
Simplified Method ◽  
Reactor Pressure

Structural integrity of the Reactor Pressure Vessel (RPV) is one of the main concerns regarding safety and lifetime of Nuclear Power Plants (NPP) since this component is considered as not reasonably replaceable. Fast fracture risk is the main potential damage considered in the integrity assessment of RPV. In France, deterministic integrity assessment for RPV vis-à-vis the brittle fracture risk is based on the crack initiation stage. As regards the core area in particular, the stability of an under-clad postulated flaw is currently evaluated under a Pressurized Thermal Shock (PTS) through a dedicated fracture mechanics simplified method called “beta method”. However, flaw stability analyses are also carried-out in several other areas of the RPV. Thence-forward performing uniform simplified inservice analyses of flaw stability is a major concern for EDF. In this context, 3D finite element elastic-plastic calculations with flaw modelling in the nozzle have been carried out recently and the corresponding results have been compared to those provided by the beta method, codified in the French RSE-M code for under-clad defects in the core area, in the most severe events. The purpose of this work is to validate the employment of the core area fracture mechanics simplified method as a conservative approach for the under-clad postulated flaw stability assessment in the complex geometry of the nozzle. This paper presents both simplified and 3D modelling flaw stability evaluation methods and the corresponding results obtained by running a PTS event. It shows that the employment of the “beta method” provides conservative results in comparison to those produced by elastic-plastic calculations for the cases here studied.

Structural Integrity Research for Reactor Pressure Vessel Under In-Vessel Retention of a Core Melt

2016 ◽  
Author(s):  
Yongjian Gao ◽  
Yinbiao He ◽  
Ming Cao ◽  
Yuebing Li ◽  
Shiyi Bao ◽  
...  
Keyword(s):  
Pressure Vessel ◽  
Material Properties ◽  
Power Plants ◽  
Structural Integrity ◽  
Plastic Material ◽  
Plastic Region ◽  
Reactor Pressure Vessel ◽  
Elastic Plastic ◽  
Elastic Plastic Material ◽  
Reactor Pressure

In-Vessel Retention (IVR) is one of the most important severe accident mitigation strategies of the third generation passive Nuclear Power Plants (NPP). It is intended to demonstrate that in the case of a core melt, the structural integrity of the Reactor Pressure Vessel (RPV) is assured such that there is no leakage of radioactive debris from the RPV. This paper studied the IVR issue using Finite Element Analyses (FEA). Firstly, the tension and creep testing for the SA-508 Gr.3 Cl.1 material in the temperature range of 25°C to 1000°C were performed. Secondly, a FEA model of the RPV lower head was built. Based on the assumption of ideally elastic-plastic material properties derived from the tension testing data, limit analyses were performed under both the thermal and the thermal plus pressure loading conditions where the load bearing capacity was investigated by tracking the propagation of plastic region as a function of pressure increment. Finally, the ideal elastic-plastic material properties incorporating the creep effect are developed from the 100hr isochronous stress-strain curves, limit analyses are carried out as the second step above. The allowable pressures at 0 hr and 100 hr are obtained. This research provides an alternative approach for the structural integrity evaluation for RPV under IVR condition.

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