The Shrink Fit with Nonlinearly Hardening Elastic-Plastic Hub

1987 ◽  
Vol 54 (2) ◽  
pp. 474-476 ◽  
Author(s):  
Udo Gamer
Keyword(s):  
Yield Criterion ◽  
Elastic Region ◽  
Flow Rule ◽  
Elastic Plastic ◽  
Hardening Law ◽  
Elastic Disk ◽  
Shrink Fit ◽  
Associated Flow Rule ◽  
Nonlinear Hardening

Based on Tresca’s yield criterion and the associated flow rule, stresses and displacement in a rotating shrink fit consisting of an elastic disk and a partially plasticized annulus are calculated for an arbitrary nonlinear hardening law. It is shown that the elastic-plastic border radius and the stresses in the elastic region of the hub do not depend on the hardening law.

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.

Transversely isotropic constitutive model of the polypropylene separator based on Rich-Hill elastoplastic constitutive theory

2020 ◽  
pp. 1-26
Author(s):  
Guicheng Zhao ◽  
Huifeng Xi ◽  
Jinbiao Yang
Keyword(s):  
Constitutive Model ◽  
Lithium Ion Batteries ◽  
Large Deformation ◽  
Yield Criterion ◽  
Lithium Ion ◽  
Transversely Isotropic ◽  
Porous Polymer ◽  
Constitutive Theory ◽  
Elastic Plastic ◽  
Hardening Law

Abstract The polypropylene (PP) separator is a kind of transversely isotropic porous polymer film, and it is a key component of lithium-ion batteries. The mechanical properties of the separator affect the strength and security of lithium-ion batteries directly. However, the anisotropy behaviors of the separator remain unclear, which has led to inaccuracy of failure behaviors in lithium-ion battery. A large deformation elastic-plastic constitutive model of the PP separator was developed with the Rich-Hill large deformation elastoplastic constitutive theory. Besides, the hardening law of the PP separator was established according to the Hill yield criterion. The constitutive model accurately captured the anisotropy behaviors and the elastic-plastic process considering the large deformation of the separator. Numerical examples for model validation were presented and in good agreement with stress-strain data of tests up to the hardening stage.

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.

Elastic-plastic stress distributions and limit angular velocities in rotating hyperbolic annular discs

2007 ◽  
Vol 221 (2) ◽  
pp. 137-142 ◽  
Author(s):  
N N Alexandrova ◽  
P M M Vila Real
Keyword(s):  
Rotational Speed ◽  
Yield Criterion ◽  
Circumferential Stress ◽  
Radial Pressure ◽  
Thickness Variation ◽  
Flow Rule ◽  
Stress Distributions ◽  
Elastic Plastic ◽  
Angular Velocities ◽  
Hyperbolic Form

Plastic analytical stress analysis of a rotating annular disc with its contours being free from the radial pressure and with specifically variable thickness is presented in terms of the Mises-yield criterion and its associated flow rule. The hyperbolic form of thickness variation is considered and optimized towards the maximum rotational speed and favourable stress combinations. Radial and circumferential stress distributions in the disc both in the intermediate elastic-plastic and in the limit plastic states are obtained. As a particular case, limit elastic angular velocity parameter is derived. The influences of rotational speed as well as the disc's thickness profile on the plastic solution and size of elastic-plastic zone are demonstrated and discussed. The results obtained may be used for the correct implementation of numerical codes and preliminary engineering design.

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.

A Simple Constitutive Model for Overconsolidated Clays

2011 ◽  
Vol 243-249 ◽  
pp. 2283-2286
Author(s):  
Yang Liu ◽  
Xian De Zhu ◽  
Zhi Gong
Keyword(s):  
Constitutive Model ◽  
Soil Mechanics ◽  
Flow Rule ◽  
Hardening Law ◽  
Proposed Model ◽  
Overconsolidated Clays ◽  
Strain Relationship ◽  
As Stress ◽  
Associated Flow Rule ◽  
Cam Clay

In the framework of critical state soil mechanics, a simple constitutive model for overconsolidated clays is proposed based on subloading surface and normal consolidation yield surface. A more rational hardening law is used to describe the change between subloading surface and the normal consolidation surface with plastic deformation and an associated flow rule is adopted. The model can describe many characteristics of overcaonsolidated clays, such as stress-strain relationship, strain hardening and softening, and stress dilatancy. Compared with the Cam-clay model, two more parameters are required which represents specific physical meanings. Numerical simulation is compared with data from triaxial drained compression test, indicating that the proposed model can rationally describe overconsolidated properties.

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