Ideal Flow in Plasticity

2007 ◽  
Vol 60 (6) ◽  
pp. 316-335 ◽  
Author(s):  
Kwansoo Chung ◽  
Sergei Alexandrov
Keyword(s):  
Yield Criterion ◽  
Three Dimensional ◽  
Flow Theory ◽  
Design Guidelines ◽  
Optimum Process ◽  
Computational Aspect ◽  
Flow Rule ◽  
Ideal Flow ◽  
Ideal Plastic ◽  
The Ideal

Ideal plastic flows constitute a class of solutions in the classical theory of plasticity based on, especially for bulk forming cases, Tresca’s yield criterion without hardening and its associated flow rule. They are defined by the condition that all material elements follow the minimum plastic work path, a condition which is believed to be advantageous for forming processes. Thus, the ideal flow theory has been proposed as the basis of procedures for the direct preliminary design of forming processes, which mainly involve plastic deformation. The aim of the present review is to provide a summary of both the theory of ideal flows and its applications. The theory includes steady and nonsteady flows, which are divided into three sections, respectively: plane-strain flows, axisymmetric flows, and three-dimensional flows. The role of the method of characteristics, including the computational aspect, is emphasized. The theory of ideal membrane flows is also included but separately because of its advanced applications based on finite element numerical codes. For membrane flows, restrictions on the constitutive behavior of materials are significantly relaxed so that more sophisticated anisotropic constitutive laws with hardening are accounted for. In applications, the ideal plastic flow theory provides not only process design guidelines for current forming processes under realistic tool constraints, but also proposes new ultimate optimum process information for futuristic processes.

Design of stationary plane strain drawing based on the ideal flow theory and a fracture criterion

2007 ◽  
Vol 196 (3-4) ◽  
pp. 127-137 ◽  
Author(s):  
K.-H. Chung ◽  
K. Chung ◽  
Sergei Alexandrov
Keyword(s):  
Plane Strain ◽  
Fracture Criterion ◽  
Flow Theory ◽  
Ideal Flow ◽  
The Ideal

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.

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.

Ideal Flow Theory of Pressure-Dependent Materials for Design of Metal Forming Processes

2018 ◽  
Vol 920 ◽  
pp. 193-198
Author(s):  
Sergei Alexandrov ◽  
Viacheslav Mokryakov ◽  
Prashant Date
Keyword(s):  
Internal Friction ◽  
Plane Strain ◽  
Contact Pressure ◽  
Metal Forming ◽  
Flow Theory ◽  
Angle Of Internal Friction ◽  
Flow Solution ◽  
Ideal Flow ◽  
Pressure Independent ◽  
The Ideal

The ideal flow theory for pressure-dependent materials is used to calculate an ideal die for plane strain extrusion/drawing. In particular, the double slip and rotation and double shearing model are adopted. Comparison with the available ideal flow solution for pressure – independent material is made. It is shown that the die for pressure-dependent material is shorter than that for pressure-independent material. Moreover, the angle of internal friction has an effect of the distribution of contact pressure.

Incorporation of a Fracture Criterion in Ideal Flow Design

2016 ◽  
Vol 713 ◽  
pp. 143-146 ◽  
Author(s):  
Elena Lyamina ◽  
Sergei Alexandrov
Keyword(s):  
Ductile Fracture ◽  
Metal Forming ◽  
Fracture Criterion ◽  
Design Method ◽  
Stress And Strain ◽  
Preliminary Design ◽  
Ductile Fracture Criterion ◽  
Ideal Flow ◽  
Ideal Plastic ◽  
The Ideal

The theory of sheet and bulk ideal plastic flows is used for the preliminary design of metal forming processes. The present paper develops an approach to incorporate the Cockroft and Latham ductile fracture criterion in this design method for stationary bulk flows. In particular, it is demonstrated that the initiation of ductile fracture can be predicted without having the ideal flow solution for stress and strain in the plastic zone (it is only necessary to know that the solution exists). Using the approach proposed the initiation of ductile fracture in axisymmetric drawing is predicted.

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.

Criteria and Methods for Reliable Three-Dimensional Image Reconstruction

1974 ◽  
Vol 32 ◽  
pp. 330-331
Author(s):  
R. A. Crowther
Keyword(s):  
Image Reconstruction ◽  
Finite Number ◽  
Density Distribution ◽  
Electron Micrographs ◽  
Mathematical Problem ◽  
Three Dimensional ◽  
Ideal Case ◽  
Dimensional Image ◽  
General Object ◽  
The Ideal

The reconstruction of a three-dimensional image of a specimen from a set of electron micrographs reduces, under certain assumptions about the imaging process in the microscope, to the mathematical problem of reconstructing a density distribution from a set of its plane projections.In the absence of noise we can formulate a purely geometrical criterion, which, for a general object, fixes the resolution attainable from a given finite number of views in terms of the size of the object. For simplicity we take the ideal case of projections collected by a series of m equally spaced tilts about a single axis.

scholarly journals Fermi gas approach to general rank theories and quantum curves

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Naotaka Kubo
Keyword(s):  
Matrix Models ◽  
Critical Role ◽  
Three Dimensional ◽  
Fermi Gas ◽  
Fermi Gases ◽  
Partition Functions ◽  
Density Matrices ◽  
General Rank ◽  
Chern Simons ◽  
The Ideal

Abstract It is known that matrix models computing the partition functions of three-dimensional $$ \mathcal{N} $$ N = 4 superconformal Chern-Simons theories described by circular quiver diagrams can be written as the partition functions of ideal Fermi gases when all the nodes have equal ranks. We extend this approach to rank deformed theories. The resulting matrix models factorize into factors depending only on the relative ranks in addition to the Fermi gas factors. We find that this factorization plays a critical role in showing the equality of the partition functions of dual theories related by the Hanany-Witten transition. Furthermore, we show that the inverses of the density matrices of the ideal Fermi gases can be simplified and regarded as quantum curves as in the case without rank deformations. We also comment on four nodes theories using our results.

Numerical solutions for strain-softening surrounding rock under three-dimensional principal stress condition

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Sheng Yu-ming ◽  
Li Chao ◽  
Xia Ming-yao ◽  
Zou Jin-feng
Keyword(s):  
Finite Element ◽  
Principal Stress ◽  
Stress Condition ◽  
Strain Softening ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Strength Criterion ◽  
Surrounding Rock ◽  
Flow Rule ◽  
Finite Element Software

Abstract In this study, elastoplastic model for the surrounding rock of axisymmetric circular tunnel is investigated under three-dimensional (3D) principal stress states. Novel numerical solutions for strain-softening surrounding rock were first proposed based on the modified 3D Hoek–Brown criterion and the associated flow rule. Under a 3D axisymmetric coordinate system, the distributions for stresses and displacement can be effectively determined on the basis of the redeveloped stress increment approach. The modified 3D Hoek–Brown strength criterion is also embedded into finite element software to characterize the yielding state of surrounding rock based on the modified yield surface and stress renewal algorithm. The Euler implicit constitutive integral algorithm and the consistent tangent stiffness matrix are reconstructed in terms of the 3D Hoek–Brown strength criterion. Therefore, the numerical solutions and finite element method (FEM) models for the deep buried tunnel under 3D principal stress condition are presented, so that the stability analysis of surrounding rock can be conducted in a direct and convenient way. The reliability of the proposed solutions was verified by comparison of the principal stresses obtained by the developed numerical approach and FEM model. From a practical point of view, the proposed approach can also be applied for the determination of ground response curve of the tunnel, which shows a satisfying accuracy compared with the measuring data.

scholarly journals Composite hollow truss with multiple vierendeel panels

2013 ◽  
Vol 66 (4) ◽  
pp. 431-438
Author(s):  
Augusto Ottoni Bueno da Silva ◽  
Newton de Oliveira Pinto Júnior ◽  
João Alberto Venegas Requena
Keyword(s):  
Bearing Capacity ◽  
Failure Modes ◽  
Three Dimensional ◽  
Analytical Calculation ◽  
Two Dimensional ◽  
Shear Forces ◽  
Vertical Displacements ◽  
New System ◽  
The Ideal

The aim of this study was to evaluate through analytical calculation, two-dimensional elastic modeling, and three-dimensional plastic modeling, the bearing capacity and failure modes of composite hollow trusses bi-supported with a 15 meter span, varying the number of central Vierendeel panels. The study found the proportion span/3 - span/3 - span/3, as the ideal relationship for the truss - Vierendeel - truss lengths, because by increasing the proportion of the length occupied by the central Vierendeel panels, the new system loses stiffness and no longer supports the load stipulated in the project. Furthermore, they can start presenting excessive vertical displacements and insufficient resistance to external shear forces acting on the panels.

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