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 An Analytic Solution for an Expanding/Contracting Strain-Hardening Viscoplastic Hollow Cylinder at Large Strains and Its Application to Tube Hydroforming Design

Processes ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 2161
Author(s):  
Lihui Lang ◽  
Sergei Alexandrov ◽  
Marina Rynkovskaya
Keyword(s):  
Strain Rate ◽  
Hollow Cylinder ◽  
Yield Criterion ◽  
Tube Hydroforming ◽  
Equivalent Strain ◽  
Large Strains ◽  
Flow Rule ◽  
Rigid Plastic ◽  
Equivalent Strain Rate ◽  
Pressure Independent

This paper presents a semi-analytic rigid/plastic solution for the expansion/contraction of a hollow cylinder at large strains. The constitutive equations comprise the yield criterion and its associated flow rule. The yield criterion is pressure-independent. The yield stress depends on the equivalent strain rate and the equivalent strain. No restriction is imposed on this dependence. The solution is facilitated using the equivalent strain rate as an independent variable instead of the polar radius. As a result, it reduces to ordinary integrals. In the course of deriving the solution above, the transformation between Eulerian and Lagrangian coordinates is used. A numerical example illustrates the solution for a material model available in the literature. A practical aspect of the solution is that it readily applies to the preliminary design of tube hydroforming processes.

Analyzing of Stainless Elliptical Cup Drawing Process

2010 ◽  
Vol 443 ◽  
pp. 116-121
Author(s):  
You Min Huang ◽  
Yi Wei Tsai
Keyword(s):  
Yield Criterion ◽  
Equivalent Stress ◽  
Three Dimensional ◽  
Element Model ◽  
Forming Limit ◽  
Flow Rule ◽  
Drawing Ratio ◽  
Drawing Process ◽  
Simple Tension ◽  
Cup Drawing

A methodology of formulating an incremental elasto-plastic three-dimensional finite element model, which is based on Prandtl-Reuss flow rule and von Mises’s yield criterion respectively, associated with an updated Lagrangian formulation, is developed to simulate elliptical cup drawing process. An extended algorithm is proposed to formulate the boundary conditions, such as the yield of element, maximum allowable strain increment, maximum allowable rotation increment, maximum allowable equivalent stress increment, and tolerance for nodes getting out of contact with tool. In order to verify the reliability and accuracy of the FEM code, the fractured thickness of a specimen in the simple tension test is adopted as the fracture criterion of forming limit in simulation. A set of tools was designed to perform the elliptical cup drawing experiment on the hydraulic forming machine. According to the simulation and experimental results, the limit drawing ratio (LDR) amounts to about 2.136 for penetration in the elliptical cup drawing process of this study. This paper also found a comparison of the LDR of different tool radii. According to the definition of LDR, when the die radius is increased from R3.0mm to R9.0mm, the LDR would increase from 2.11 to 2.157. When the punch radius is increased from r3.0mm to r9.0mm, the LDR would increase from 2.07 to 2.181. This paper has provided a better understanding of the elliptical cup drawing process for improving the manufacturing processes and the design of tools.

The strain hardening behaviour of particulate media

1976 ◽  
Vol 13 (3) ◽  
pp. 311-323 ◽  
Author(s):  
S. Frydman
Keyword(s):  
Strain Hardening ◽  
Three Dimensional ◽  
Flow Rule ◽  
Finite Element Program ◽  
Particulate Media ◽  
Stress Strain Relation ◽  
Element Program ◽  
Plastic Components ◽  
Associated Flow Rule ◽  
Particulate Medium

The strain increment resulting from an increment of stress applied to a particulate medium has been expressed in terms of its elastic and plastic components. The concepts of strain-hardening plasticity have been employed to develop an incremental stress–strain relation, based on a non-associated flow rule. The parameters appearing in the relation have been found using results of three-dimensional shear tests on sands and glass-microspheres. It is suggested that relations of the type developed in the paper could be beneficially incorporated into a finite-element program.

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.

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.

Study on Precision Forging Schemes of Hypoid Driving Gear

2012 ◽  
Vol 472-475 ◽  
pp. 692-695
Author(s):  
Jian Hua Wang ◽  
Fu Xiao Chen
Keyword(s):  
Equivalent Stress ◽  
Three Dimensional ◽  
Equivalent Strain ◽  
Precision Forging ◽  
Forming Technology ◽  
Blank Shape ◽  
Simulation Results ◽  
Three Dimensional Models ◽  
3D Software ◽  
Deform 3D

By analyzing the characteristics and forming technology of hypoid driving gear, it was suitable for adopting fully enclosed die forging principle to form the gear. Based on different forging methods, three kinds of blank shape and corresponding forming schemes were designed. The three dimensional models of blank and die were created by the UG software. The three forming schemes were simulated by the Deform-3D software. The simulation results of distribution of equivalent stress, distribution of equivalent strain and load-stroke curve were comparatively analyzed. Then the most reasonable scheme was chosen. At last, the rationality of numerical simulation can be further verified by the optimized scheme was proved by experiment.

Analysis of Residual Stress in the Rotational Autofrettage of Thick-Walled Disks

2018 ◽  
Vol 140 (6) ◽  
Author(s):  
S. M. Kamal
Keyword(s):  
Plastic Deformation ◽  
Residual Stresses ◽  
Yield Criterion ◽  
Three Dimensional ◽  
Circular Disk ◽  
Flow Rule ◽  
Plane Stress Condition ◽  
Radial Temperature ◽  
Fem Validation ◽  
Compressive Residual Stresses

Autofrettage is a means of generating compressive residual stresses at the inner side of a thick-walled cylinder or hollow disk by causing nonhomogeneous plastic deformation of the material at the inner side. The presence of residual compressive stresses at the inner region of the cylinder/disk enhance the pressure withstanding capacity, fatigue life and the resistance to stress corrosion cracking of the component. Despite the hydraulic and swage autofrettage are the widely practiced processes in industries, there are certain disadvantages associated with these processes. In view of this, in the recent years, researchers have proposed new methods of achieving autofrettage. Rotational autofrettage is such a recently proposed autofrettage method for achieving the beneficial compressive residual stresses in the cylinders. In the present work, the rotational autofrettage is studied for a thick-walled hollow circular disk. A theoretical analysis of the residual stresses produced in the disk after unloading are obtained assuming plane stress condition, Tresca yield criterion and its associated flow rule. The analysis takes into account the effect of strain hardening during plastic deformation. Further, the effect of residual stresses in the typical SS304 and aluminum disk is studied by subjecting them into three different types of loads viz., internal pressure, radial temperature difference, and rotational speed individually. A three-dimensional (3D) finite element method (FEM) validation of the theoretical stresses during rotational autofrettage of a disk is also presented.

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