Plastic Instability of Cylindrical Shells With Rigid End Closures

1963 ◽  
Vol 30 (3) ◽  
pp. 401-409 ◽  
Author(s):  
Martin A. Salmon
Keyword(s):  
Yield Criterion ◽  
Spherical Shape ◽  
Plastic Instability ◽  
Maximum Pressure ◽  
Flow Rule ◽  
Hardening Material ◽  
Hardening Modulus ◽  
Pressure Maximum ◽  
Three Stages ◽  
Associated Flow Rule

Solutions are obtained for the large plastic deformations of a cylindrical membrane with rigid end closures subjected to an internal pressure loading. A plastic linearly hardening material obeying Tresca’s yield criterion and the associated flow rule is considered. It is found that, in general, a shell passes through three stages of deformation, finally assuming a spherical shape. The instability pressure (maximum pressure) may be reached in any of the stages depending on the length/diameter ratio of the shell and the hardening modulus of the material. Although numerical integration is required to obtain solutions for shells in the first stages of deformation, the solution in the final stage is given in closed form.

Descriptions of Reversed Yielding in Internally Pressurized Tubes

2015 ◽  
Vol 138 (1) ◽  
Author(s):  
Sergei Alexandrov ◽  
Woncheol Jeong ◽  
Kwansoo Chung
Keyword(s):  
Yield Criterion ◽  
Numerical Technique ◽  
Kinematic Hardening ◽  
Material Model ◽  
Flow Rule ◽  
Hardening Material ◽  
Hardening Law ◽  
Solving Equations ◽  
Associated Flow Rule ◽  
Reversed Deformation

Using Tresca's yield criterion and its associated flow rule, solutions are obtained for the stresses and strains when a thick-walled tube is subject to internal pressure and subsequent unloading. A bilinear hardening material model in which allowances are made for a Bauschinger effect is adopted. A variable elastic range and different rates under forward and reversed deformation are assumed. Prager's translation law is obtained as a particular case. The solutions are practically analytic. However, a numerical technique is necessary to solve transcendental equations. Conditions are expressed for which the release is purely elastic and elastic–plastic. The importance of verifying conditions under which the Tresca theory is valid is emphasized. Possible numerical difficulties with solving equations that express these conditions are highlighted. The effect of kinematic hardening law on the validity of the solutions found is demonstrated.

Elastic-Plastic Stress Distribution in a Plastically Anisotropic Rotating Disk

2004 ◽  
Vol 71 (3) ◽  
pp. 427-429 ◽  
Author(s):  
N. Alexandrova ◽  
S. Alexandrov
Keyword(s):  
Stress Distribution ◽  
Yield Criterion ◽  
Plastic Anisotropy ◽  
Rotating Disk ◽  
Flow Rule ◽  
Plane State ◽  
Annular Disk ◽  
Elastic Plastic ◽  
State Of Stress ◽  
Associated Flow Rule

The plane state of stress in an elastic-plastic rotating anisotropic annular disk is studied. To incorporate the effect of anisotropy on the plastic flow, Hill’s quadratic orthotropic yield criterion and its associated flow rule are adopted. A semi-analytical solution is obtained. The solution is illustrated by numerical calculations showing various aspects of the influence of plastic anisotropy on the stress distribution in the rotating disk.

A Semi-Analytical 3-D Solution for Bending Under Tension

2012 ◽  
Vol 586 ◽  
pp. 302-305
Author(s):  
Sergei Alexandrov ◽  
Elena Lyamina ◽  
Li Hui Lang
Keyword(s):  
Yield Criterion ◽  
Equivalent Stress ◽  
Three Dimensional ◽  
Equivalent Strain ◽  
Large Strains ◽  
Flow Rule ◽  
Viscoplastic Material ◽  
Equivalent Strain Rate ◽  
Bending Under Tension ◽  
Associated Flow Rule

The paper concerns with three-dimensional analysis of the process of bending under tension for incompressible, rigid viscoplastic material at large strains. The constitutive equations consist of the Mises-type yield criterion and its associated flow rule. No restriction is imposed on the dependence of the equivalent stress on the equivalent strain rate. The problem is reduced to evaluating ordinary integrals and solving transcendental equations.

scholarly journals Influence of Material Compressibility on Displacement Solution for Structural Steel Plate Applications

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Nelli Aleksandrova
Keyword(s):  
Structural Steel ◽  
Yield Criterion ◽  
Flow Rule ◽  
Perfectly Plastic ◽  
Open Hole ◽  
Practical Engineering ◽  
Elastic Perfectly Plastic ◽  
Von Mises ◽  
Associated Flow Rule ◽  
Material Compressibility

Displacement field calculations are necessary for many structural steel engineering problems such as cold expansion of holes, embedment of bolts and rivets, and installation and maintenance of external devices. To this end, rigorous closed form analytical displacement solution is obtained for structural steel open-hole plates with in-plane loading. The material of the model is considered to be elastic perfectly plastic obeying the von Mises yield criterion with its associated flow rule. On the basis of this solution, two simplified engineering formulae are proposed and carefully discussed for practical engineering purposes. Graphical representations of results show validity of each formula as compared with rigorous solution and other studies.

scholarly journals A Method for Determining the Workability Diagram by Varying Friction Conditions in the Upsetting of a Cylinder between Flat Dies

Crystals ◽  
2021 ◽  
Vol 11 (11) ◽  
pp. 1411
Author(s):  
Dejan Movrin ◽  
Mladomir Milutinovic ◽  
Marko Vilotic ◽  
Sergei Alexandrov ◽  
Lihui Lang
Keyword(s):  
Ductile Fracture ◽  
Yield Criterion ◽  
Stress Triaxiality ◽  
Fracture Initiation ◽  
Medium Carbon Steel ◽  
New Method ◽  
Flow Rule ◽  
Rigid Plastic ◽  
Hardening Material ◽  
Workability Diagram

This paper aims to develop a method for determining the workability diagram by varying frictional conditions in the cylinder upsetting test. The method is based on a known theoretical relationship between the average stress triaxiality ratio and in-surface strains if the initiation of fracture occurs at a traction-free surface. This relationship is valid for any rigid/plastic strain hardening material obeying the Mises-type yield criterion and its associated flow rule, which shows the wide applicability of the method. The experimental input to the method is the strain path at the site of fracture initiation. Neither experimental nor numerical determination of stress components is required at this site, though the general ductile fracture criterion involves the linear and quadratic invariants of the stress tensor. The friction law’s formulation is neither required, though the friction stress is the agent for varying the state of stress and strain at the site of ductile fracture initiation. The upsetting tests are carried out on normalized medium-carbon steel C45E, for which the workability diagram is available from the literature. Comparison of the latter and the diagram found using the new method shows that the new method is reliable for determining a certain portion of the workability diagram.

Estimation of the Stresses in Rotational Autofrettage of Thick-Walled Pressure Vessels Using von Mises Yield Criterion

2021 ◽  
Author(s):  
S. M. Kamal ◽  
Faruque Aziz
Keyword(s):  
Plane Strain ◽  
Yield Criterion ◽  
Pressure Vessels ◽  
Flow Rule ◽  
Stress Distributions ◽  
Von Mises Yield Criterion ◽  
Potential Methods ◽  
Von Mises ◽  
Associated Flow Rule ◽  
Theoretical Analyses

Abstract Rotational autofrettage is one of the recently proposed potential methods for eliminating the in-service yielding of thick-walled cylindrical pressure vessels. A few researchers have studied the feasibility of the process theoretically, and asserted certain advantages over the practicing hydraulic and swage autofrettage processes. In the literature, all theoretical analyses on the rotational autofrettage are based on the Tresca yield criterion and its associated flow rule, along with the assumption of different plane end conditions (plane strain and generalized plane strain). In this paper, an analysis of the rotational autofrettage of cylindrical vessel is attempted incorporating von Mises yield criterion. The plane strain condition is used for the analysis. A numerical shooting method is used to solve the governing differential equations providing the elastic-plastic stress distributions in the cylinder during loading. The present procedure is numerically experimented for a typical AH36 pressure vessel. It is found that the achievable level of the maximum stress pressure of the rotationally autofrettaged vessel is 74.46% higher than that of its non-autofrettaged counterpart for an overstrain level of 46.7%.

Hydrostatic bulging of circular diaphragms

1970 ◽  
Vol 5 (3) ◽  
pp. 155-161 ◽  
Author(s):  
J Chakrabarty ◽  
J M Alexander
Keyword(s):  
Numerical Method ◽  
Explicit Form ◽  
Strain Distribution ◽  
Yield Criterion ◽  
Fluid Pressure ◽  
Bulge Test ◽  
Flow Rule ◽  
New Formula ◽  
Associated Flow Rule ◽  
Good Agreement

Tresca's yield criterion and the associated flow rule have been used to develop a solution for the plastic bulging of circular diaphragms by lateral fluid pressure. The strain distribution in the neighbourhood of the pole is derived in explicit form and a new formula is given for the polar strain at instability. The theory is found to be in good agreement with experimental results for the bulge test. A numerical method of solving the problem for Mises materials is also proposed.

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