Dynamic Spherical Cavity Expansion in an Elastoplastic Compressible Mises Solid

2004 ◽  
Vol 72 (6) ◽  
pp. 887-898 ◽  
Author(s):  
Rami Masri ◽  
David Durban
Keyword(s):  
Strain Hardening ◽  
Spherical Cavity ◽  
Numerical Data ◽  
Approximate Solutions ◽  
Cavity Expansion ◽  
Expansion Velocity ◽  
Perfectly Plastic ◽  
Plastic Materials ◽  
Radial Profiles ◽  
Elastic Perfectly Plastic

The elastoplastic field induced by a self-similar dynamic expansion of a pressurized spherical cavity is investigated for the compressible Mises solid. The governing system consists of two ordinary differential equations for two stress components where radial velocity and density are known functions of these stresses. Numerical illustrations of radial profiles of field variables are presented for several metals. We introduce a new solution based on expansion in powers of the nondimensionalized cavity expansion velocity, for both elastic/perfectly plastic response and strain-hardening behavior. A Bernoulli-type solution for the dynamic cavitation pressure is obtained from the second-order expansion along with a more accurate third-order solution. These solutions are mathematically closed and do not need any best fit procedure to numerical data, like previous solutions widely used in the literature. The simple solution for elastic/perfectly plastic materials reveals the effects of elastic-compressibility and yield stress on dynamic response. Also, an elegant procedure is suggested to include strain-hardening in the simple elastic/perfectly plastic solution. Numerical examples are presented to demonstrate the validity of the approximate solutions. Applying the present cavitation model to penetration problems reveals good agreement between analytical predictions and penetration depth tests.

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.

A General Autofrettage Model of a Thick-Walled Cylinder Based on Tensile-Compressive Stress-Strain Curve of a Material

2005 ◽  
Vol 40 (6) ◽  
pp. 599-607 ◽  
Author(s):  
X. P Huang
Keyword(s):  
Strain Hardening ◽  
Compressive Stress ◽  
Bauschinger Effect ◽  
Strain Curve ◽  
Accurate Prediction ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Perfectly Plastic ◽  
Hardening Models ◽  
Elastic Perfectly Plastic

The basic autofrettage theory assumes elastic-perfectly plastic behaviour. Because of the Bauschinger effect and strain-hardening, most materials do not display elastic-perfectly plastic properties and consequently various autofrettage models are based on different simplified material strain-hardening models, which assume linear strain-hardening or power strain-hardening or a combination of these strain-hardening models. This approach gives a more accurate prediction than the elastic-perfectly plastic model and is suitable for different strain-hardening materials. In this paper, a general autofrettage model that incorporates the material strain-hardening relationship and the Bauschinger effect, based upon the actual tensile-compressive stress-strain curve of a material is proposed. The model incorporates the von Mises yield criterion, an incompressible material, and the plane strain condition. Analytic expressions for the residual stress distribution have been derived. Experimental results show that the present model has a stronger curve-fitting ability and gives a more accurate prediction. Several other models are shown to be special cases of the general model presented in this paper. The parameters needed in the model are determined by fitting the actual tensile-compressive curve of the material, and the maximum strain of this curve should closely represent the maximum equivalent strain at the inner surface of the cylinder under maximum autofrettage pressure.

The Collapse or Ballooning Pressure of Thick-Walled Pressure Vessels

1983 ◽  
Vol 22 ◽  
Author(s):  
B. Crossland
Keyword(s):  
Mild Steel ◽  
Strain Hardening ◽  
Pressure Vessel ◽  
Factor Of Safety ◽  
Plastic Material ◽  
Pressure Vessels ◽  
Bursting Pressure ◽  
Collapse Pressure ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic

ABSTRACTDiscussion of the proposed extension of the ASME pressure vessel code to cover operating pressures up to 1.4 GPa (200000 lbf/in2 ) has generated the proposal that two criteria should be used, of which one would be the collapse or ballooning pressure not the bursting pressure. The present paper examines this proposal in relation to extensive data on the collapse and bursting of thick-walled vessels available to the author.It is concluded that the collapse pressure is only readily calculable for materials which approach the behaviour of an elastic/perfectly plastic material. It also appears for materials with significant strain hardening characteristics, such as mild steel, that the collapse pressure considerably underestimates the bursting pressure, whereas for a material which behaves as an elastic/perfectly plastic material the collapse pressure is nearly coincident with the bursting pressure. Consequently if the collapse pressure was adopted and if the factor of safety against collapse was adequate for one material it might be more or less than adequate for another material, which would appear to be unacceptable.

Penetration of Strain-Hardening Targets With Rigid Spherical-Nose Rods

1991 ◽  
Vol 58 (1) ◽  
pp. 7-10 ◽  
Author(s):  
M. J. Forrestal ◽  
N. S. Brar ◽  
V. K. Luk
Keyword(s):  
Closed Form ◽  
Strain Hardening ◽  
Spherical Cavity ◽  
Cavity Expansion ◽  
Rigid Rods ◽  
Engineering Models ◽  
Spherical Nose ◽  
Spherical Cavity Expansion ◽  
Penetration Depths ◽  
Good Agreement

We developed engineering models that predict forces and penetration depth for long, rigid rods with spherical noses and rate-independent, strain-hardening targets. The spherical cavity expansion approximation simplified the target analysis, so we obtained closed-form penetration equations that showed the geometric and material scales. To verify our models, we conducted terminal-ballistic experiments with three projectile geometries made of maraging steel and 6061-T651 aluminum targets. The models predicted penetration depths that were in good agreement with the data for impact velocities between 0.3 and 1.0 km/s.

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