Rigid-perfectly-plastic materials. Two extremal principles

2020 ◽  
pp. 460-482
Author(s):  
Lallit Anand ◽  
Sanjay Govindjee
Keyword(s):  
Lower Bound ◽  
Variational Principles ◽  
Structural Collapse ◽  
Perfect Plasticity ◽  
Perfectly Plastic ◽  
Plastic Materials ◽  
Extremal Principles

This chapter introduces the notion of rigid-perfect plasticity, and provides proofs of the extremum principles of applied loads and velocities. The variational principles are applied to generate the upper- and lower-bound theorems for collapse loads in rigid-perfect plasticity models. The method of sliding rigid blocks is presented for the solution of practical problems in forming operations and structural collapse. To facilitate such modelling the hodograph graphical device is also discussed.

Investigation on the Influence of Stiffener Size on the Buckling Pressures of Circular Cylindrical Shells Under Hydrostatic Pressure

1962 ◽  
Vol 6 (03) ◽  
pp. 24-32
Author(s):  
James A. Nott
Keyword(s):  
Cylindrical Shells ◽  
High Strength ◽  
Plastic Buckling ◽  
Theoretical Derivation ◽  
Perfectly Plastic ◽  
Plastic Materials ◽  
Simple Support ◽  
Circular Cylindrical Shells ◽  
Support Conditions ◽  
Elastic Perfectly Plastic

A theoretical derivation is given for elastic and plastic buckling of stiffened, circular cylindrical shells under uniform external hydrostatic pressures. The theory accounts for variable shell stresses, as influenced by the circular stiffeners, and critical buckling pressures are obtained for simple support conditions at the shell-frame junctures. Collapse pressures for both elastic and plastic buckling are determined by iteration and numerical minimization. The theory is applicable to shells made either of strain-hardening or elastic-perfectly plastic materials. Using the developed analysis, it is shown that a variation in stiffener size can change the buckling pressures. Test data from high-strength steel and aluminum cylinders show agreement between the theoretical and experimental collapse pressures to within approximately six percent.

Plastic Limit Loads for Piping Branch Junctions

2007 ◽  
Vol 345-346 ◽  
pp. 1377-1380 ◽  
Author(s):  
Yun Jae Kim ◽  
Kuk Hee Lee ◽  
Chi Yong Park
Keyword(s):  
Three Dimensional ◽  
Limit Load ◽  
Plastic Limit ◽  
Perfectly Plastic ◽  
Plastic Materials ◽  
Wide Range ◽  
Pipe Radius ◽  
Plastic Limit Load ◽  
The Mean ◽  
Elastic Perfectly Plastic

The present work presents plastic limit load solutions for branch junctions under internal pressure and in-plane bending, based on detailed three-dimensional (3-D) FE limit analyses using elastic-perfectly plastic materials. The proposed solutions are valid for a wide range of branch junction geometries; ratios of the branch-to-run pipe radius and thickness from 0.0 to 1.0, and the mean radius-to-thickness ratio of the run pipe from 5.0 to 20.0.

scholarly journals Principal Stress Ratio Effect at Residual Stress Determination Utilizing the Variation of Indentation Hardness

Lubricants ◽  
2019 ◽  
Vol 7 (6) ◽  
pp. 50
Author(s):  
Per-Lennart Larsson
Keyword(s):  
Residual Stress ◽  
Residual Stresses ◽  
Stress Ratio ◽  
Experimental Situation ◽  
Indentation Hardness ◽  
Stress Determination ◽  
Residual Stress Determination ◽  
Perfectly Plastic ◽  
Plastic Materials ◽  
Elastic Perfectly Plastic

The determination of residual stresses is an important issue when it comes to material failure analysis. The variation of global indentation properties, due to the presence of residual stresses, can serve as a guideline for the size and direction of such stresses. One of these global indentation properties, the material hardness, is unfortunately invariant of residual stresses when metals and alloys are at issue. In this situation, one has to rely on the size of the indentation contact area for residual stress determination. For other materials such as ceramics and polymers, where elastic deformations are of greater importance at indentation, such invariance is no longer present. Here, this variation is investigated based on finite element simulations. The aim is then to determine how the indentation hardness is influenced by the principal residual stress ratio and also discuss if such an influence is sufficient in order to determine the size and direction of such stresses in an experimental situation. It should be emphasized that this work does not suggest a new approach to residual stress determination (by indentation testing) but investigates the applicability of previously derived methods to a situation where the surface stress field is not simplified as equi-biaxial or uniaxial. For simplicity, but not out of necessity, only cone indentation of elastic-perfectly plastic materials is considered.

Effects of Torsion on Equivalent Bending Moment for Limit Load and EPFM Circumferential Pipe Flaw Evaluations

2012 ◽  
Vol 134 (6) ◽  
Author(s):  
Phuong H. Hoang ◽  
Kunio Hasegawa ◽  
Bostjan Bezensek ◽  
Yinsheng Li
Keyword(s):  
Finite Element ◽  
Pressure Vessel ◽  
Large Strain ◽  
Bending Moment ◽  
Limit Load ◽  
Elastic Plastic ◽  
Perfectly Plastic ◽  
Plastic Materials ◽  
Weighted Factor ◽  
Elastic Perfectly Plastic

The circumferential flaw evaluation procedures in ASME Boiler and Pressure Vessel Code Section XI nonmandatory Appendix C are currently limited to straight pipes under pressure and bending loads without consideration of torsion loading. The Working Group on Pipe Flaw Evaluation of the ASME Boiler and Pressure Vessel Code is developing guidance for considering the effects of torsion by a mean of an equivalent bending moment, which is a square root of sum square combination of bending moment and torsion load with a weighted factor for torsion moment. A torsion weighted factor, Ce, is established in this paper using large strain finite element limit load analysis with elastic perfectly plastic materials. Planar flaws and nonplanar flaws in a 10.75 in. (273 mm) OD pipe are investigated. Additionally, a finite element J-integral calculation is performed for a planar through wall circumferential flaw with elastic plastic materials subjected to bending and torsion load combinations. The proposed Ce factor for planar flaws is intended for use with the ASME B&PV Code Section XI, Appendix C for limit load and Elastic Plastic Fracture Mechanics (EPFM) circumferential planar flaw evaluations.

Buckle Propagation Analysis of Deep-Water Petroleum Transmission Pipelines with Axial Tension

2014 ◽  
Vol 1008-1009 ◽  
pp. 1134-1143 ◽  
Author(s):  
Sun Ting Yan ◽  
Yin Fa Zhu ◽  
Zhi Jiang Jin ◽  
Hao Ye
Keyword(s):  
Plastic Hinge ◽  
External Pressure ◽  
Isotropic Hardening ◽  
Rigid Plastic ◽  
Perfectly Plastic ◽  
Fitting Procedure ◽  
Plastic Materials ◽  
Buckle Propagation ◽  
Elastic Perfectly Plastic ◽  
Hinge Model

Quasi-static finite element simulation is carried out on buckle propagation phenomenon of offshore pipelines under external pressure. Arc-length method and volume-controlled static analysis by employing hydrostatic fluid element F3D4 are employed to calculate the steady buckle propagation pressure. After verifying the validity of numerical model, emphasis is on the influence of tension on propagation pressure considering isotropic hardening elastoplastic and elastic-perfectly plastic materials. Parametric study is conducted to include the effect of diameter-thickness ratio, after which two empirical equations are derived by curve fitting procedure. Finally, some comments on the results obtained through rigid-plastic hinge model are presented and a modified plastic hinge model including effect of material anisotropy is derived. The results can serve as a reference for more reasonable design of buckle arrestors.

Incorporation of Strain Hardening Effect Into Simplified Limit Analysis

2010 ◽  
Vol 132 (6) ◽  
Author(s):  
P. S. Reddy Gudimetla ◽  
R. Adibi-Asl ◽  
R. Seshadri
Keyword(s):  
Lower Bound ◽  
Strain Hardening ◽  
Limit Load ◽  
Element Analysis ◽  
Active Volume ◽  
Limit Loads ◽  
Reference Volume ◽  
Perfectly Plastic ◽  
Tangent Method ◽  
Elastic Perfectly Plastic

In this paper, a method for determining limit loads in the components or structures by incorporating strain hardening effects is presented. This has been done by including a certain amount of the strain hardening into limit load analysis, which normally idealizes the material to be elastic perfectly plastic. Typical strain hardening curves such as bilinear hardening and Ramberg–Osgood material models are investigated. This paper also focuses on the plastic reference volume correction concept to determine the active volume participating in plastic collapse. The reference volume concept in combination with mα-tangent method is used to estimate lower-bound limit loads of different components. Lower-bound limit loads obtained compare well with the nonlinear finite element analysis results for several typical configurations with/without crack.

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