scholarly journals An Exact Axisymmetric Solution in Anisotropic Plasticity

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 825
Author(s):  
Yaroslav Erisov ◽  
Sergei Surudin ◽  
Fedor Grechnikov ◽  
Elena Lyamina
Keyword(s):  
Yield Criterion ◽  
Numerical Technique ◽  
Plastic Anisotropy ◽  
Incompressible Material ◽  
Flow Rule ◽  
Singular Behavior ◽  
Anisotropic Plasticity ◽  
Axisymmetric Solution ◽  
Approach Infinity ◽  
Associated Flow Rule

A hollow cylinder of incompressible material obeying Hill’s orthotropic quadratic yield criterion and its associated flow rule is contracted on a rigid cylinder inserted in its hole. Friction occurs at the contact surface between the hollow and solid cylinders. An axisymmetric boundary value problem for the flow of the material is formulated and solved, and the solution is in closed form. A numerical technique is only necessary for evaluating ordinary integrals. The solution may exhibit singular behavior in the vicinity of the friction surface. The exact asymptotic representation of the solution shows that some strain rate components and the plastic work rate approach infinity in the friction surface’s vicinity. The effect of plastic anisotropy on the solution’s behavior is discussed.

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.

scholarly journals A Theory of Autofrettage for Open-Ended, Polar Orthotropic Cylinders

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 280 ◽  
Author(s):  
Marina Rynkovskaya ◽  
Sergei Alexandrov ◽  
Lihui Lang
Keyword(s):  
Analytic Solution ◽  
Yield Criterion ◽  
Plastic Anisotropy ◽  
Flow Rule ◽  
Compatibility Equation ◽  
Plastic Properties ◽  
Linear Differential ◽  
Associated Flow Rule ◽  
Polar Orthotropic ◽  
Flow Theory Of Plasticity

Autofrettage is a widely used process to enhance the fatigue life of holes. In the theoretical investigation presented in this article, a semi-analytic solution is derived for a polar, orthotropic, open-ended cylinder subjected to internal pressure, followed by unloading. Numerical techniques are only necessary to solve a linear differential equation and evaluate ordinary integrals. The generalized Hooke’s law connects the elastic portion of strain and stress. The flow theory of plasticity is employed. Plastic yielding is controlled by the Tsai–Hill yield criterion and its associated flow rule. It is shown that using the strain rate compatibility equation facilitates the solution. The general solution takes into account that elastic and plastic properties can be anisotropic. An illustrative example demonstrates the effect of plastic anisotropy on the distribution of stresses and strains, including residual stresses and strain, for elastically isotropic materials.

An Upper Bound Solution for Upsetting of Anisotropic Hollow Cylinders

2009 ◽  
Vol 623 ◽  
pp. 71-78 ◽  
Author(s):  
Elena Lyamina ◽  
Gow Yi Tzou ◽  
Shao Yi Hsia
Keyword(s):  
Velocity Field ◽  
Yield Criterion ◽  
Plastic Anisotropy ◽  
Friction Stress ◽  
Limit Load ◽  
Flow Rule ◽  
Friction Law ◽  
Maximum Friction ◽  
Hollow Cylinders ◽  
Associated Flow Rule

The paper concerns with an effect of plastic anisotropy on the load required to deform hollow cylinders between two parallel, rough dies. It is assumed that the material obeys Hill’s quadratic yield criterion and its associated flow rule. The friction stress is supposed to be proportional to the corresponding shear yield stress, including the maximum friction law as a special case. The kinematically admissible velocity field is chosen such that the stress field following from the associated flow rule satisfies the boundary condition at the plane of symmetry. Moreover, this velocity field is singular in the vicinity of the friction surface. Therefore, in the case of the maximum friction law the friction law is satisfied, again if the associated flow rule is combined with the velocity field. A significant effect of plastic anisotropy on the limit load is illustrated.

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.

scholarly journals Solution Behavior near Envelopes of Characteristics for Certain Constitutive Equations Used in the Mechanics of Polymers

Materials ◽  
2019 ◽  
Vol 12 (17) ◽  
pp. 2725 ◽  
Author(s):  
Sergei Alexandrov ◽  
Lihui Lang ◽  
Elena Lyamina ◽  
Prashant P. Date
Keyword(s):  
Friction Surface ◽  
Yield Criterion ◽  
System Of Equations ◽  
Singular Behavior ◽  
Material Models ◽  
Metal Plasticity ◽  
Plane Strain Deformation ◽  
Stress Components ◽  
Approach Infinity ◽  
Derivatives Of

The present paper deals with plane strain deformation of incompressible polymers that obey quite a general pressure-dependent yield criterion. In general, the system of equations can be hyperbolic, parabolic, or elliptic. However, attention is concentrated on the hyperbolic regime and on the behavior of solutions near frictional interfaces, assuming that the regime of sliding occurs only if the friction surface coincides with an envelope of stress characteristics. The main reason for studying the behavior of solutions in the vicinity of envelopes of characteristics is that the solution cannot be extended beyond the envelope. This research is also motivated by available results in metal plasticity that the velocity field is singular near envelopes of characteristics (some space derivatives of velocity components approach infinity). In contrast to metal plasticity, it is shown that in the case of the material models adopted, all derivatives of velocity components are bounded but some derivatives of stress components approach infinity near the envelopes of stress characteristics. The exact asymptotic expansion of stress components is found. It is believed that this result is useful for developing numerical codes that should account for the singular behavior of the stress field.

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